Corridors and Elk Migration: A Comparative Analysis of Landscape Connectivity Models and GPS Data in the Greater Yellowstone Ecosystem

Transcription

1 Corridors and Elk Migration: A Comparative Analysis of Landscape Connectivity Models and GPS Data in the Greater Yellowstone Ecosystem Item Type text; Electronic Dissertation Authors Chambers, Samuel Norton Publisher The University of Arizona. Rights Copyright is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Download date 06/06/ :15:06 Link to Item

2 CORRIDORS AND ELK MIGRATION: A COMPARITIVE ANALYSIS OF LANDSCAPE CONNECTIVITY MODELS AND GPS DATA IN THE GREATER YELLOWSTONE ECOSYSTEM by Samuel Norton Chambers Copyright Samuel Norton Chambers 2015 A Dissertation Submitted to the Faculty of the GRADUATE INTERDISCIPLINARY PROGRAM IN ARID LANDS RESOURCE SCIENCES In Partial Fulfillment of the Requirements For the Degree of DOCTOR OF PHILOSOPHY In the Graduate College THE UNIVERSITY OF ARIZONA 2015

3 2 THE UNIVERSITY OF ARIZONA GRADUATE COLLEGE As members of the Dissertation Committee, we certify that we have read the dissertation prepared by Samuel Chambers, titled Corridors and Elk Migration: A Comparative Analysis of Landscape Connectivity Models and GPS Data in the Greater Yellowstone Ecosystem and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of Doctor of Philosophy. Date: 05/13/15 Howard R. Gimblett Date: 05/13/15 Daoqin Tong Date: 05/13/15 David A. Christianson Final approval and acceptance of this dissertation is contingent upon the candidate s submission of the final copies of the dissertation to the Graduate College. I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement. Date: 05/13/15 Dissertation Director: Howard R. Gimblett

4 3 STATEMENT BY AUTHOR This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgement of source is made. Requests for permission for extended quotations from or reproduction of this manuscript in whole or in part may be granted by the copyright holder. SIGNED: Samuel Norton Chambers

5 4 ACKNOWLEDGEMENTS I would first like to thank my committee members for their extensive advice and support. Dave Christianson was especially helpful in the formulation of my analysis process and acquiring data. Daoqin Tong made sure that I include accurate and proper statistical analysis. I am very appreciative of Randy Gimblett for being the advisor I needed and helping form and improve research ideas. I would like to thank all of them for their interest in working with me on such a project. I want to thank the Arid Lands Resource Science (ALRS) Ph.D. Program chair, Istvan Molnar; the Program Coordinator, Marylou Myers; and the former program chair Stuart Marsh in their frequent support and well-appreciated advice. I would also like to thank Iris Patten and Nathan Casler of the School of Geography and Development for their pointers in analysis and scripting. I would also like to thank those that supplied the GPS-collar data: Andrea Ellen Barbknecht of Iowa State University, Eric Cole from the U.S. Fish and Wildlife Service National Elk Refuge, Brandon Scurlock from Wyoming Game and Fish Department, Sarah Dewey from Grand Teton National Park, and John Winnie of Montana State University. Without their hard work and devotion, this study would not have been possible.

6 5 DEDICATION This work is dedicated in memory of Jimbo

7 6 TABLE OF CONTENTS LIST OF FIGURES... 9 LIST OF TABLES ABSTRACT CHAPTER 1: INTRODUCTION Landscape Connectivity Connectivity Strategies Tools Corridor Designer Linkage Mapper FunConn HabMod Conefor Sensinode Connectivity Analysis Toolkit PATH Limitations of Connectivity Models Autocorrelation Advantages and Disadvantages Field Data and Autocorrelation Previous Analysis CHAPTER 2: RESEARCH AND ANALYSIS Goals Methods Results Autocorrelation Circuitscape PATH Linkage Mapper Comparative Analysis Post hoc Analysis Conclusions Implications of the Research... 51

8 7 2.9 Future Research References APPENDIX A: COMPARING A CIRCUIT THEORY BASED LANDSCAPE CONNECTIVITY MODEL TO THE MIGRATORY PATTERNS OF ELK SAMPLED IN THE GREATER YELLOWSTONE ECOSYSTEM ABSTRACT Introduction Data and Method Data Collection Resistance Surface Patch Delineation Current Mapping Migratory Network Delineation Testing for Autocorrelation Results Current and Network Correlation Autocorrelation Conclusions References APPENDIX B: COMPARING AN AGENT BASED LANDSCAPE CONNECTIVITY MODEL TO THE MIGRATORY PATTERNS OF ELK SAMPLED IN THE GREATER YELLOWSTONE ECOSYSTEM ABSTRACT Introduction Data and Method Data Collection Resistance Surface Delineation Patch Delineation Agent based Modeling Migratory Network Delineation Testing for Autocorrelation Results Correlation Autocorrelation and Least Cost Paths Post hoc Analysis Conclusions

9 8 References APPENDIX C: COMPARING A LEAST COST CORRIDOR CONNECTIVITY MODEL TO THE MIGRATORY PATTERNS OF ELK SAMPLED IN THE GREATER YELLOWSTONE ECOSYSTEM ABSTRACT Introduction Data and Method Data Collection Cost Surface Delineation Patch Delineation Building Corridors Migratory Network Delineation Testing for Autocorrelation Results Correlation Autocorrelation and Least Cost Paths Conclusions Acknowledgments References APPENDIX D: FINDING PINCH POINTS IN THE MIGRATORY PATTERNS OF ELK IN THE GREATER YELLOWSTONE ECOSYSTEM ABSTRACT Data and Method Data Collection Resistance Surface Patch Delineation Circuitscape Pinch Points Migratory Pinch Point Delineation Analysis Results Pinch Point Location Conclusions References

10 9 LIST OF FIGURES Figure 1: Process of building resistance surface showing roads (a) and landcover (b) reclassified and added to calculate landscape resistance Figure 2: Location of sampled populations used in connectivity models Figure 3: Migratory Networks of sampled elk in the Greater Yellowstone Ecosystem Figure 4: Comparison of Migratory Network Density and Circuitscape Current in relation to Wetland and Agricultural landcover types for Population Figure 2: Location of sampled populations used in Circuitscape connectivity models Figure 1: Circuitscape resistance surface delineated using landcover and road data Figure 3: Example of least cost paths using the migratory networks and the landscape resistance surface Figure 4: Population 1 kernel density of migratory networks (left) and current map (right) Figure 5: Population 2 kernel density of migratory networks (left) and current map (right) Figure 6: Population 4 kernel density of migratory networks (left) and current map (right) Figure 7 Population 5 kernel density of migratory networks (left) and current map (right) Figure 8: Population 7 kernel density of migratory networks (left) and current map (right) Figure 9: Population 8 kernel density of migratory networks (left) and current map (right) Figure 10: Population 10 kernel density of migratory networks (left) and current map (right) Figure 11: Population 11 kernel density of migratory networks (left) and current map (right) Figure 12: Population 12 kernel density of migratory networks (left) and current map (right) Figure 13: Population 13 kernel density of migratory networks (left) and current map (right) Figure 15: Current map of population 13 reclassified to remove high quality habitat from checkered landscape of low quality habitat wetlands Figure 1: Energy Cost resistance surface Figure 2: Lethality resistance surface Figure 3: Location of sampled populations used in PATH connectivity models Figure 4: Example of least cost paths using the migratory networks and the landscape resistance surfaces Figure 5: Population 1 kernel density of migratory networks (left) and PATH map (right) Figure 6: Population 2 kernel density of migratory networks (left) and PATH map (right) Figure 7: Population 4 kernel density of migratory networks (left) and PATH map (right) Figure 8: Population 5 kernel density of migratory networks (left) and PATH map (right) Figure 9: Population 6 kernel density of migratory networks (left) and PATH map (right) Figure 10: Population 7 kernel density of migratory networks (left) and PATH map (right)

11 10 Figure 11: Population 8 kernel density of migratory networks (left) and PATH map (right) Figure 12: Population 10 kernel density of migratory networks (left) and PATH map (right) Figure 13: Population 11 kernel density of migratory networks (left) and PATH map (right) Figure 14: Population 12 kernel density of migratory networks (left) and PATH map (right) Figure 15: Population 13 kernel density of migratory networks (left) and PATH map (right) Figure 1: Linkage Mapper resistance surface delineated using landcover and road data Figure 2: Location of sampled populations used in Linkage Mapper connectivity models Figure 3: Distribution of values and deviation from normal distribution for (a) LCP L and (b) LCP N Figure 4: Example of least cost paths using the migratory networks and the landscape resistance surface Figure 5: Population 1 kernel density of migratory networks (left) and corridor map (right) Figure 6: Population 2 kernel density of migratory networks (left) and corridor map (right) Figure 7: Population 4 kernel density of migratory networks (left) and corridor map (right) Figure 8: Population 5 kernel density of migratory networks (left) and corridor map (right) Figure 9: Population 6 kernel density of migratory networks (left) and corridor map (right) Figure 10: Population 7 kernel density of migratory networks (left) and corridor map (right). 137 Figure 11: Population 8 kernel density of migratory networks (left) and corridor map (right). 138 Figure 12: Population 10 kernel density of migratory networks (left) and corridor map (right) 139 Figure 13: Population 11 kernel density of migratory networks (left) and corridor map (right) 140 Figure 14: Population 12 kernel density of migratory networks (left) and corridor map (right) 141 Figure 15: Population 13 kernel density of migratory networks (left) and corridor map (right) 142 Figure 6: Corridor map of population 13 reclassified to remove high quality habitat from checkered landscape of low quality habitat wetlands Figure 7: Population 5 kernel density of migratory networks (left) and current map (right)

12 11 LIST OF TABLES Table 2: Reclassification values by landcover Table 3: Pearson s correlation coefficients for each connectivity model and Density of Migratory Networks. All results with Pearson r-values showed a P-value of Table 1: Pearson s r and Moran s I values by population Table 1: Correlation coefficients by population Table 1: Pearsons correlation coefficient and Moran s I values by population Table 1: Percentage of landcover type in MPP and CSPP

13 12 ABSTRACT Landscape connectivity models aim to map the links or corridors that wildlife would or do use between patches of habitat. Migratory species such as elk traverse between such patches which serve as seasonal ranges. The goal of this study was to compare and contrast the suitability of several landscape connectivity models for describing and predicting migration in a long-distance migrant. We measured the suitability of connectivity models for covering and predicting the migratory movements of elk in the Greater Yellowstone Ecosystem. GPS point data was converted to sequential networks for multiple populations of elk.gps data was also used to delineate the summer and winter ranges of each population. The kernel density of routes in the networks was measured for comparison to connectivity models. The ranges served as the patches to be connected by such models. A resistance surface was produced using reclassified landcover data for mapping habitat suitability and linear road data for human presence or obstruction to movement. Landscape connectivity was measured for eleven migratory elk populations using three distinct models. The first measured connectivity using circuit theory; the second, agent based modeling; the third, least cost corridors. The model results were compared to the migratory network density by measuring correlation. This was followed by a new method of measuring the influence of autocorrelation between the models and networks. Some of the models were then altered to test for suspected influences. This study shows that least cost corridors and circuit theory can are limited in their ability to predict the migratory movements between summer and winter ranges but only so much. They lack the ability to predict exploratory movements that do not link

14 13 conspicuous ranges to each other. They also lack the ability to account for all avoidance behaviors in the landscape. Our results suggest that connectivity models need improvement by accounting for exploration outside of prime habitat. It also suggests connectivity models are not adequate predictors of migratory movements and not suited to conservation planning of migratory networks. This supports Sawyer s (et al. 2009) ungulate conservation planning of considering connectivity but basing priority on migratory landscape usage. It is assumed that fragmentation or loss in connectivity impedes seasonal migration, cutting off wildlife from resources (Rudnick et al. 2012). This study shows that migratory elk are actually using less than prime and supposedly fragmented habitat in migration and that there is more than connectivity at play.

15 Landscape Connectivity CHAPTER 1: INTRODUCTION Numerous approaches have been developed for modeling connectivity based on two concepts, reserve design and corridor design. Reserve design strategizes to achieve maximum representation of species reserves and species persistence given restraints. These restraints are typically derived from the theories of Island Biogeography and Metapopulation (Alagador et al. 2012). Corridor design, on the other hand, seeks to optimally link habitats where species of interest occur using at least a permeability or resistance raster surface (Taylor et al. 1993; Alagador et al. 2012). This can be tuned to individual species, multiple species, or general populations (Chetkiewicz and Boyce 2009; Alagador et al. 2012). These concepts have been expanded upon and connectivity planning now includes: climate (Alagador et al. 2012; McRae et al. 2012), landscape integrity (Perkl 2013), behavioral ecology (Belisle 2005), and urban design (Cook 2002; Kilbane 2013). There is also the integration of specific barriers to connectivity models (McRae et al. 2012). There are two components of landscape connectivity: first, the spatial arrangement of different types of habitat in the landscape; and second, the behavior of individuals, species, and/or ecological processes in response to the structure of the landscape and other environmental cues (e.g., predation risk) (Taylor et al. 1993; Tischendorf and Fahrig 2000; Crooks and Sanjayan 2006). The first, or structural connectivity, is typically measured by analyzing landscape structure without reference to wildlife movement or processes (Crooks and Sanjayan 2006). The second, or functional connectivity, requires both the spatial information about habitats and information about the movement of

16 15 wildlife across the landscape (Crooks and Sanjayan 2006). A species focused connectivity model would fall under the functional connectivity type while a naturalness connectivity model would be classified under the structural connectivity type. Several challenges exist for better understanding landscape connectivity including: the behavioral ecology of focal species, the spatial extent of a model, the temporal extent of a model, using caution in extrapolating data, considering non-linear relationships in ecological data, planning for human-induced change to the landscape, and communicating to the public the importance of connectivity (Rudnick et al 2012). 1.2 Connectivity Strategies With the evolution of the concept of landscape connectivity has come an evolution of strategies to conserve landscape connectivity. Using GIS, there are two methods of modeling landscape connectivity: diffusion and dispersal (Wiens 2006). In a diffusion model, structural connectivity is paramount. Dispersal models depend on the behavioral attributes of wildlife and therefore relate to functional connectivity (Wiens 2006). There are also differences in strategy of whether to plan for distinct linkages or corridors or to plan for broader areas of connectivity. A corridor is defined as a swath of land intended to allow passage by a particular wildlife species between 2 or more wildland areas and a linkage as connective land intended to promote movement of multiple focal species or propagation of ecosystem processes (Wiens 2006). The methodology used most often in connectivity models, particularly in such linkage or corridor models, is least cost path. Least cost paths calculate effective distances which delineate an optimal pathway given the resistance values in a permeability surface

17 16 (Baldwin et al. 2010). These measures of resistance can be based on functional or structural connectivity and can be based on discrete or gradient barriers (Perkl 2013). An integration of graph theory with least cost paths allows for the landscape to be modeled as a network of nodes connected by multiple least cost paths (Urban and Keitt 2001; Urban et al. 2009). There are also the methods producing continuous surfaces measuring connectivity rather than discrete areas of connectivity. Circuit theory has also been used to model landscape connectivity by predicting the probability of movement between two nodes or end points. This also identifies constraints or pinch-points within the landscape where movement and resistance are predicted to be high (McRae and Beier 2007; McRae et al 2008). Another method using dispersal, resistance kernels, calculates expected relative densities of dispersers around each cell of a potential source (Compton et al. 2007). 1.3 Tools Corridor Designer Specific GIS tools have been developed to measure and plan landscape connectivity. Corridor Designer (Majka et al. 2007), an ArcGIS toolbox created using Python scripting performs four tasks: models habitat suitability, identifies habitat patches, models corridors between pairs of patches, and the creation of topographic slope position raster surfaces. To do this, at a minimum, corridor designer needs at least one raster layer identifying habitat quality and/or resistance (Majka et al. 2007; Perkl 2013). Corridor Designer models the corridors using a least cost path methodology that is expanded to

18 17 include contiguous cells which exhibit the lowest cumulative cost as the path crosses the landscape (Rudnick et al. 2012). Linkage Mapper Linkage Mapper, another ArcGIS toolbox, similarly uses resistance surfaces to map linkages between core habitat areas (McRae and Kavanagh 2011). It does this by using ArcGIS utilities and numerical Python functions which identify neighboring areas of the least cost path as cost distances which are then normalized, combined, and converted to generate the resulting corridor (McRae and Kavanagh 2011). FunConn FunConn was a now defunct ArcGIS toolbox that calculated minimum spanning trees using graph theory, applied weights, calculated node and edge interaction, and found the shortest paths from each node to all others (Saura and Torne 2009). It used land cover raster data, a cost or resistance raster, and shapefiles to depict habitat quality, patches, and a landscape network which are used to model linkages, edges, and corridors between all patches (Theobald et al. 2006). HabMod HabMod is an ArcGIS tool that produces multivariate habitat prediction rasters by implementing classification and regression, linear, and general additive models. ConnMod ConnMod, an additional tool, uses such output for connectivity modeling on a regional scale (Ryman 2010).

19 18 Conefor Sensinode Using graph theory, Conefor Sensinode identifies and prioritizes critical sites for connectivity, taking habitat and distance into account based on the behavior of species (Saura and Torne 2007). Connectivity Analysis Toolkit Connectivity Analysis Toolkit (CAT), a stand-alone GIS tool, develops and compares three centrality metrics based on suitability and permeability (Carroll et al. 2012). CAT models the best linkages from source to target, in multitude or singularity (Perkl 2013). It is well suited to large scale modeling and uses three metrics: shortest path, current flow, and minimum-cost maximum-flow as measures of centrality (Carroll et al. 2011). Circuitscape Circuitscape is a Python program that uses algorithms from circuit theory to predict the wildlife population movements and landscape connectivity using an ASCII resistance raster (Shah and McRae 2008). It calculates resistance distances though nodal analysis, a circuit analysis algorithm that applies Kirchhoff s current laws in the form of a matrix (Dorf and Svoboda 2010). In such a model, landscapes are represented as conductive surfaces with high resistance and low resistance representing high and low permeability (Theobald et al. 2006). PATH The Pathway Analysis Through Habitat (PATH) tool predicts the location of potential corridors through an algorithm launching random walkers from habitat patches using specified habitat preferences to resemble species behavior (Hargrove et al. 2005).

20 19 Originally designed for simulations on a supercomputer (Hargrove et al. 2005), PATH was altered for PCs using the agent based software NetLogo (Hargrove and Westervelt 2012). 1.4 Limitations of Connectivity Models Shortcomings and opportunities for connectivity conservation exist. To improve connectivity models and reduce uncertainty there is a need for increased research on species persistence, behavioral ecology, and community structure (Rudnick 2012). Species persistence, behavioral ecology, community structure, and climatic conditions are all influenced by human and landscape interactions. 1.4 Autocorrelation Maehr and Fei (2008) describe their issue of dealing with the issue of large data sources like GPS tracking devices. They analyze the data using kernel pathway analysis and suggest that it will improve the power of analyses for, and effectiveness of, conservation programs with wide-ranging species by using intensively collected GPS coordinates (Maehr and Fei 2008). Boyce et al. (2010) illustrates the use of temporal autocorrelation functions (ACF) for analyzing step-length data from GPS telemetry of wildlife. They note that ACFs differ by season, showing changes in foraging behavior. They do demonstrate that there is a decay in step-length ACFs to random patterns in some species, particularly predators (Boyce et al. 2010). Dray et al. (2010) discusses the various issues related to analyzing autocorrelated data, showing how the exploratory analysis can reveal important biological insights and

21 20 improve the accuracy of movement models. They then suggest graphical tools to measure, test, and adjust for temporal autocorrelation. These tools include the most often used random walk (RW) and correlated random walk (CRW) (Marsh and Jones 1988; Dray et al. 2010). RW corresponds to the succession of random steps while CRW assumes that the movement of animals shows directional persistence (Dray et al. 2010). CRW differs from RW mathematically due to the assumption of a unimodal and symmetric distribution of the turning angles. RW assumes a uniform distribution. Both RW and CRW require the independence of successive turning angles and step lengths (Dray et al. 2010). Fieberg et al. (2010) compares the advantages and disadvantages of correlated data regression modelling approaches to studying habitat selection. They start by reviewing methods for first estimating models under the assumption of independence between locations, but then inflating variances using robust standard errors to account for correlation (Nielsen et al. 2002; Clark & Strevens 2008; Craiu et al. 2008; Fieberg et al. 2010). They then review extensions based on generalized estimating quations (GEEs) that allow the use of other correlation structures during the estimation process in conjunction with robust standard errors for inference (Zeger et al. 1988; Fieberg et al. 2009; Koper & Manseau 2009; Fieberg et al. 2010). They also review two methods to model amonganimal variability in habitat selection patterns: 1) a two-stage approach that fits models separately to individual animals and averages regression parameters across individuals to estimate population-level selection patterns; and 2) generalized linear mixed-effects models (GLMMs) that include random effects for individuals and social grouping structures (Glenn et al. 2004; Gillies et al. 2006; Sawyer et al. 2006; Aarts et al. 2008;

22 21 Hebblewhite & Merrill 2008; Fieberg et al. 2010). GEEs are simple to apply but treat correlation as a nuisance and are not informative when dealing with animal-specific response patterns. GEEs with other working structures can be used to increase precision but lead to biased estimators when used with case-control or use-availability sampling designs. Two-stage sampling allows for subject-specific inferences and variance decomposition between and within groups but requires enough data from each individual for separate model fits. GLMMs allow subject-specific inferences and variance decomposition between and within groups with a single model fit but are computationally demanding. Movement-based models may account for autocorrelation and are biologically based but may not fully account for all correlation (Fieberg et al. 2010). 1.5 Advantages and Disadvantages Habitat selection analyses typically infer selection of resources or habitats by comparing landscape characteristics of used points or areas to those of random points or areas that represent available habitat (Johnson et al. 2006; Lele & Keim 2006; Aarts et al. 2008; Lele 2009; Fieberg et al. 2010). Landscape heterogeneity, size, and type are important factors to consider in analysis and results (Johnson et al. 2002; Wittemyer et al. 2008; Fieberg et al. 2010). The spatial data collected for temporal autocorrelation functions such as topography, geology, soils, hydrology, and vegetation has to be accounted for in analysis because the scale of sampling can determine whether you actually capture the extent of variation (Boyce et al. 2003; Boyce et al. 2010; Fieberg et al. 2010). To account for this one can estimate spatial models that include landscape features as predictor covariates and then examine residuals for spatial autocorrelation (Radeloff et al. 2000; Boyce 2006; Boyce et

23 22 al. 2010). Boyce et al. (2010) suggest that modeling the underlying landscape covariates will often account for the primary autocorrelation signal in the data. Adehabitat software uses landscape characteristic, including elevation, aspect, slope, presence of water, usage, and cover, in raster form to examine the habitat traversed by the animal (Calenge 2007; 2011). A shortcoming of this is the available resolution of the raster for spatial analysis. A cell size too large may ignore the local differences and give a false result in predicting movement but a cell size too small may be accurate but take longer in data processing. A value in this is the lack of need for field data. Adehabitat has also been used in the software package Ismetrics to provide landscape connectivity indices (Calenge 2007). Missing values are a frequent problem in the data collected by GPS due to landscape and habitat structure, especially when dealing with elevation and aspect (Frair et al. 2004; Calenge et al. 2009). For instance, the results of ACFs would have inaccuracies related to location, step length, and direction all due to incorrect or missing points when the animal was in a place with poor signal such as a canyon or steep slope. GPS and ACFs do avoid the problems associated with methods like RW, CRW, and adehabitat in that they rely on field data with less assumptions on the location of the animals and more real time events. Maehr and Fei (2008) suggest a method using GPS data and landcover to better predict animal movements for the purpose of planning road crossings. The conservation efforts for wide-ranging species demand refined and large datasets that enable high confidence in describing spatial attributes and fractured landscapes. The path-based kernel density method they describe and intensively collected data help explain how and when the

24 23 animals cross roads and give exact locations to consider for wildlife crossings. It does this more accurately than most approaches (2008). 1.6 Field Data and Autocorrelation Autocorrelation is typically viewed as a problem in telemetry studies because sequential observations are not independent in time or space, violating assumptions for statistical inference but nearly all ecological and behavioral data are autocorrelated in both space and time (Boyce et al. 2010). It is a very general property of ecological varaibles but also an obstacle in studies because it violated the basic assumptions of standard statistical hypothesis testing (Dray et al. 2010). It is usually viewed as a form of bias and is typically eliminated before analysis by subsampling (Turchin 1998; Dray et al. 2010). Autocorrelation is often the consequence of ecological processes, especially long-time processes that show an animal s switching behavior in movements (Dray et al. 2010). Dealing with autocorrelation creates problems of its own. Eliminating autocorrelation from a dataset not only reduces the sample size, but also limits the biological significance of the analysis (de Sola et al. 199). In telemetry studies, field logistics and competing research aims can result in autocorrelation on a temporal scale. The degree of dependence is affected by the animal s movement and behavior and the frequency of observation. When test show dependence, a subsample is usually taken or less frequent samples are taken. This is typical when data are plentiful and goals are limited to large scales such as home range. When the opposite is true and data are few and goals are refined, as in the case of animal movement studies, standard methods lead to loss of data (Nations and Anderson-Sprecher 2006). It is also important to remember that ACFs are not designed to

25 24 handle missing data and tools, such as correlogram, should be used and modified to accept missing values (Legendre and Legendre 1998; Dray et al. 2010). Swihart and Slade (1986) demonstrated that autocorrelation was important in testing for independence in the movement of animals. Boyce et al. (2010) illustrates the utility of temporal ACFs for analyzing step-length data from GPS telemetry of large predators. Calenge et al. (2009) show that if there is a positive aurocorrelation of the relative angles in steps, it indicates that some parts of the trajectories characterized by linear movements and others by sinuous movements. It was also shown that when several trajectories of an animal show autocorrelation of a given parameter, where others do not, it might be from biological constraints differing between the trajectories. They suggest this be dealt with in a case-by-case manner according to the data and biological aims (Calenge et al. 2009). Time is an important issue in dealing with autocorrelation. In analysis of elk and deer paths Brillinger et al. (2004) found autocorrelation after a certain period of time, complicating the interpretation of estimates. Nations and Anderson-Sprecher (2006) found that telemetery has two important consequences for estimation: 1) uncertainty in animal location results from bearing error and 2) observations may be autocorrelated. Dray et al. (2010) showed the importance of ecologists accounting for temporal autocorrelation despite it rarely being accounted for. For instance, if no tests of independence are performed, the probability that a model such as RW or CRW, will be rejected when it is false is lower than expected. This has resulted in subsequent choice of the wrong independence tests and biased results from classical tests. De Sola et al. (1999) used a four-step process to deal with aurocorrelation: 1) they generated locational observations within an area and changed the degree of

26 25 autocorrelation between consecutive observation to determine the effect of autocorrelation on home range size; 2) they compared space use within the home range; 3) they examined the total distance travelled within the home range; and finally 4) they determined if reducing autocorrelation affected the accuracy of the home range size estimate. Maehr and Fei (2008) used the following method to maximize sample size and minimize autocorrelation in samples of black bear coordinates: 1) they checked the GPS consecutively against the first point to see if any points met a specified time interval; 2) if a point met the interval, the first point and this point were placed into the subset, and the process continued; 3) a shapefile was created using the GPS pints in each subset, and straight-line paths were created for pairs with a specified time interval. Calenge (2011) developed an analysis to deal with autocorrelation. It first tested for autocorrelation of the linear parameters; then analyzed the autocorrelation of the parameters; and finally tested the autocorrelation of the angles by analyzing the autocorrelation of the angular parameters. Fieberg et al. (2010) found that movement-based models of availability may account for autocorrelation by modelling independent transition probabilities between locations. 1.7 Previous Analysis A previous study comparing elk migration in the Madison valley of the Greater Yellowstone Ecosystem to connectivity models was recorded in 2012 (Rainey). This study compared GPS collar data to least cost corridors and circuit theory models. It based its connectivity models on a resistance surface using a training set portion of the GPS collar data samples while the other portion served as the validation set (Rainey 2012). The connectivity models were compared to the validation set using a 95 th percentile of

27 26 the corridors to measure overlap, a random path comparison, and a null corridor produced using an equal cost resistance surface. It was concluded that the least cost corridor models generally performed better that circuit theory models (Rainey 2012). 2.1 Goals CHAPTER 2: RESEARCH AND ANALYSIS This thesis will compare three models: Circuitscape to represent a random walker demonstration of connectivity, Linkage Mapper to represent corridor models, and the agent based model PATH that uses random walkers to build a corridor model (Hargrove et al. 2005). To compare, this study seeks to test whether connectivity models could predict the migratory patterns of elk in the Greater Yellowstone Ecosystem by effectively covering the actual movements of elk between summer and winter ranges. It compares geospatial tools using least cost corridors, circuit theory, and agent based modeling. The first question asks whether circuit theory can predict movements of elk between summer and winter ranges. The second if, a PATH agent based model can predict the movements of elk between ranges. Finally, do least cost corridors efficiently cover the actual movements of elk between summer and winter ranges? Conservation planning for migratory ungulates have been based on both migration networks and landscape connectivity (Sawyer et al. 2009) but each has never been extensively compared. Connectivity models are typically chosen because of the simplification even though a multitude of factors could be chosen for such a model (Moilanen and Nieminen 2002). Connectivity models are also based on the corridor

28 27 assumption that organisms do not venture into non-habitat (Tischendorf and Fahrig 2000), or are at least less likely to do so. Migratory elk are well suited to a comparative study because of these assumptions and the assumption that a less connected landscape impedes seasonal migration by cutting species off from needed resources (Rudnick et al. 2012). Circuitscape is a Java software package and ArcGIS tool that uses raster habitat data to produce a matrix of resistance distances among population pairs by representing range maps as graphs, replacing habitat cells with nodes and connecting adjacent nodes with resistors (McRae and Beier 2007). The program calculates resistance distances though nodal analysis, a circuit analysis algorithm that applies Kirchhoff s current law in the form of a matrix (Dorf and Svoboda 2010). Circuitscape has been particularly useful in modeling gene flow in relation to the landscape. It was used for evaluating the effect of habitat and landscape characteristics on population genetic structure in white-footed mice (Marrotte et al. 2014). The model also revealed regionally variable gene flow patterns across the Cope s giant salamander range (Trumbo et al. 2013). Circuitscape was used to show the difference in gene flow and effects of habitat fragmentation separate species of honeyeater birds (Harrisson et al. 2014). This suggests Circuitscape does not work well for all species. In an analysis of the effects of forest management on American martens, it was concluded Euclidean distance better described gene flow than effective distance modeled by circuit theory (Koen et al. 2011). Although it is most desirable to model connectivity across a single surface representing an entire landscape, Circuitscape has been shown as useful in mosaics of overlapping

29 28 high resolution tiles representing portions of the landscape (Pelletier et al. 2014). This was especially useful in identifying pinch points which are narrow corridors individuals may be required to traverse (Pelletier et al. 2014). Cross-validation showed the general validity of Circuitscape models in identifying connectivity of an urban landscape for European hedgehogs with pinch points and other habitat connections (Braaker et al. 2014). There is the question of the effect of the extent of resistance surfaces or the map boundary on the output of Circuitscape. Koen (et al. 2010) concluded that artificial map boundaries using randomized values as a solution for using Circuitscape to model connectivity and genetic flow studies. The Pathway Analysis Through Habitat (PATH) tool was first developed as a supercomputer model to predict the location of corridors between habitat patches using an algorithm of random walkers from said patches (Hargrove et al. 2004). It was simplified for use on PCs using the Agent Based Modeling software NetLogo (Hargrove and Westervelt 2012; Wilensky 1999). Each walker is given preferences of behavior based on 3 grid file inputs representing habitat location, the energy cost outside habitat, and the lethality outside habitat (Hargrove and Westervelt 2012). PATH produces a map of the most heavily traverses migration pathways outside patches (Hargrove and Westervelt 2012). Hargrove and Westervelt (2012) tested PATH in identifying corridors for gopher tortoises between remaining habitat fragments within Fort Benning, GA (Hargrove and Westervelt 2012). Linkage Mapper, a Python script and ArcGIS tool, represents cost of movement, identifying optimal path between multiple habitat patches as a continuous surface corridor (McRae and Kavanagh 2011; Carroll et al. 2013). Like PATH, the raster surfaces

30 29 are to represent cost, difficulty, or mortality risk but unlike PATH mortality cannot be modeled in a least cost corridor. Linkage Mapper was developed for the 2010 Washington Wildlife Habitat Connectivity Working Group statewide connectivity analysis (McRae and Kavanagh 2011). It can be used as a stand-alone tool or in combination with other available tools such as Circuitscape or extensions such as Barrier Mapper software and Climate Linkage Mapper (McRae et al. 2008; McRae 2012; McRae et al. 2012; Carroll et al. 2013; Nunez et al. 2013). It has been used to model for single or multi-species corridors for mammals of various sizes and habitat types (Carroll et al. 2013; Brodie et al. 2014). It has also been used for modeling corridors based on landscape condition (Kilbane 2013). 2.2 Methods A resistance surface was built using Gap analysis landcover data and USGS road data. Landcover was used to delineate potential to less-potential habitat. Roads represented additional cost to movement. The sum of these cost individual surfaces was normalized to a 1 to 100 scale with 1 representing least cost to movement and 100, maximum cost. Landcover accounted for 75% of the cost; distance from roads, 25% (Maika et al. 2010). The reclassification of road values were based on the system designed for CorridorDesigner s Arizona elk tutorial dataset (Majka et al 2010). Although the landcover rating scale and percentage of total remained the same for the resistance as it did for the Arizona elk tutorial, the values were based on percentage of total within sampled migratory elk s summer and winter ranges. This resistance surface served as input for the Linkage Mapper and Circuitscape connectivity models. PATH needed two

31 30 separate resistance surfaces, one using the roads to represent potential lethality and the other using landcover to represent energy cost, both based on values suggested by Hargrove and Westervelt (2012).

32 31 a. b. c. Figure 1: Process of building resistance surface showing roads (a) and landcover (b) reclassified and added to calculate landscape resistance

33 32 Table 1: Reclassification values for distance from roads Distance from roads (m) Resistance Value Table 2: Reclassification values by landcover Resistance Landcover Class Value Colorado Plateau Pinyon-Juniper Woodland 75 Columbia Plateau Ash and Tuff Badland Columbia Plateau Vernal Pool Developed, High Intensity Developed, Medium Intensity Geysers and Hot Springs Great Basin Foothill and Lower Montane Riparian Woodland and Shrub land Great Basin Pinyon-Juniper Woodland Great Basin Xeric Mixed Sagebrush Shrub land Great Plains Prairie Pothole Inter-Mountain Basins Alkaline Closed Depression Inter-Mountain Basins Aspen-Mixed Conifer Forest and Woodland Inter-Mountain Basins Cliff and Canyon Inter-Mountain Basins Interdunal Swale Wetland Inter-Mountain Basins Juniper Savanna Inter-Mountain Basins Playa Inter-Mountain Basins Semi-Desert Grassland Inter-Mountain Basins Semi-Desert Shrub Steppe Inter-Mountain Basins Shale Badland Introduced Riparian and Wetland Vegetation Introduced Upland Vegetation - Shrub Introduced Upland Vegetation - Treed North American Alpine Ice Field North American Arid West Emergent Marsh Northern Rocky Mountain Conifer Swamp Northern Rocky Mountain Foothill Conifer Wooded Steppe Northern Rocky Mountain Wooded Vernal Pool Northwestern Great Plains Floodplain Northwestern Great Plains Shrub land Quarries, Mines, Gravel Pits and Oil Wells Recently Burned Recently burned shrub land

34 Rocky Mountain Alpine Bedrock and Scree Rocky Mountain Alpine Dwarf-Shrub land Rocky Mountain Alpine Fell-Field Rocky Mountain Bigtooth Maple Ravine Woodland Rocky Mountain Cliff, Canyon and Massive Bedrock Rocky Mountain Gambel Oak-Mixed Montane Shrub land Rocky Mountain Lower Montane-Foothill Shrub land Rocky Mountain Poor-Site Lodgepole Pine Forest Rocky Mountain Subalpine-Montane Fen Rocky Mountain Subalpine-Montane Limber-Bristlecone Pine Woodland Rocky Mountain Subalpine-Montane Riparian Shrub land Rocky Mountain Subalpine-Montane Riparian Woodland Southern Rocky Mountain Dry-Mesic Montane Mixed Conifer Forest and Woodland Southern Rocky Mountain Mesic Montane Mixed Conifer Forest and Woodland Southern Rocky Mountain Montane-Subalpine Grassland Southern Rocky Mountain Ponderosa Pine Woodland Western Great Plains Cliff and Outcrop Western Great Plains Closed Depression Wetland Western Great Plains Dry Bur Oak Forest and Woodland Western Great Plains Floodplain Western Great Plains Open Freshwater Depression Wetland Western Great Plains Riparian Woodland and Shrub land Western Great Plains Saline Depression Wetland Western Great Plains Shortgrass Prairie Western Great Plains Wooded Draw and Ravine Harvested Forest - Grass/Forb Regeneration 58.5 Inter-Mountain Basins Active and Stabilized Dune Inter-Mountain Basins Curl-leaf Mountain Mahogany Woodland and Shrub land Inter-Mountain Basins Volcanic Rock and Cinder Land Northern Rocky Mountain Lower Montane Riparian Woodland and Shrub land Northern Rocky Mountain Subalpine Deciduous Shrub land Northern Rocky Mountain Subalpine Woodland and Parkland Recently burned grassland Rocky Mountain Alpine-Montane Wet Meadow Rocky Mountain Foothill Limber Pine-Juniper Woodland Rocky Mountain Lower Montane Riparian Woodland and Shrub land Developed, Low Intensity Harvested Forest-Shrub Regeneration Inter-Mountain Basins Greasewood Flat Northern Rocky Mountain Montane-Foothill Deciduous Shrub land Northern Rocky Mountain Subalpine-Upper Montane Grassland Northwestern Great Plains Riparian Recently burned forest Rocky Mountain Alpine Turf Rocky Mountain Aspen Forest and Woodland Rocky Mountain Subalpine-Montane Mesic Meadow Western Great Plains Sand Prairie Columbia Plateau Low Sagebrush Steppe 42 33

35 34 Columbia Plateau Western Juniper Woodland and Savanna Developed, Open Space Inter-Mountain Basins Mat Saltbush Shrub land Inter-Mountain Basins Mixed Salt Desert Scrub Introduced Upland Vegetation - Perennial Grassland and Forbland Open Water (Fresh) Western Great Plains Badland Wyoming Basins Dwarf Sagebrush Shrub land and Steppe Columbia Basin Foothill and Canyon Dry Grassland Introduced Upland Vegetation - Annual Grassland Middle Rocky Mountain Montane Douglas-fir Forest and Woodland Northern Rocky Mountain Mesic Montane Mixed Conifer Forest Northwestern Great Plains - Black Hills Ponderosa Pine Woodland and Savanna Harvested Forest - Northwestern Conifer Regeneration 25.5 Northern Rocky Mountain Lower Montane, Foothill and Valley Grassland Northern Rocky Mountain Ponderosa Pine Woodland and Savanna Pasture/Hay Rocky Mountain Subalpine Dry-Mesic Spruce-Fir Forest and Woodland Rocky Mountain Subalpine Mesic Spruce-Fir Forest and Woodland Inter-Mountain Basins Big Sagebrush Shrub land Inter-Mountain Basins Montane Sagebrush Steppe Rocky Mountain Lodgepole Pine Forest Northern Rocky Mountain Dry-Mesic Montane Mixed Conifer Forest 9 Northwestern Great Plains Mixedgrass Prairie Cultivated Cropland 0.75 Inter-Mountain Basins Big Sagebrush Steppe Female elk were fitted with Global Positioning System (GPS) radio-collars during in various locations across the eastern Greater Yellowstone Ecosystem. These elk were captured in Grand Teton National Park, National Elk Refuge Buffalo Valley (Barbknecht et al. 2011), Yellowstone National Park, and Gallatin National Forest (Creel et al. 2005). Capture activities were approved by Wyoming Game and Fish Department and Iowa State University Animal Care and Use Committee (Protocol # ). Locational data were collected at a rate of 3-48 points a day, providing a minimum of an 8 hour fix interval.

36 35 GPS collar data was classified by month to determine which elk sampled had separate winter (January-March) and summer (June-August) ranges. Overlapping ranges of separate individuals were merged into population ranges. Thirteen populations of migratory elk were identified from the GPS data. The 85 remaining elk were either non migratory or could not be distinguished from non-migratory elk due to the resolution of the data. The thirteen population ranges served as the patches to connect in each connectivity model. GPS-collar data were used to delineate not only the movements of elk overtime across the landscape but also the probably density of these movements. This was modeled using the data to calculate kernel density, or the probably density of the elk movements through the landscape. This kernel density of the migratory networks would serve as a comparative dataset for each of eleven populations versus the landscape connectivity models developed using a resistance raster. The GPS-collar points outside these ranges were delineated into line shape files based on individual elk, location, and time. Kernel density of these lines or networks were calculated for the full extent of all sampled points in a population. Two populations were removed from analysis due to discrepancies in the point data not allowing for generation of the networks and density properly. A total of eleven final migratory populations were delineated for analysis. Number of individuals in population samples ranged from two to six.

37 Figure 2: Location of sampled populations used in connectivity models Correlation values were calculated between every connectivity model output for each population and every kernel density of migratory networks for each population by each corresponding pair of pixels.

38 37 Additional analysis was run to test for autocorrelation. This was done using a t-test for comparing mean values and a K-S test for comparing the distribution of values for portions of each connectivity model. To run these tests for autocorrelation, portions of the results needed to be extracted for comparison. A least cost path for the landscape (LCPL) from range to range for each population was calculated using the resistance surface. Another set of least cost paths was calculated for each migratory network in a population (LCPN) using a single value in a rasterized version of the networks. These were used to extract values from each resulting connectivity model for each population. Each of the 11 sets of LCPN and LCPL was compared pairwise with a t-test for means and a K-S test for distribution.

39 Figure 3: Migratory Networks sampled in the Greater Yellowstone Ecosystem Figure 3: Migratory Networks of sampled elk in the Greater Yellowstone Ecosystem 38

40 Results We found that current maps showed significant correlation with kernel density of migratory networks with the exception of population 2 which showed consistently negative correlations between modelled corridors and the elk migration network from GPS collar data (Table 1). This particular population showed migratory movement to the north, off the primary axis lying between the summer and winter ranges. The migratory movements were also slightly to the southeast of the predictions of the current map. Correlation did not decrease with distance between ranges. Although the population 6 current maps show a correlation of 0.203, the migratory networks avoided a reservoir while the current maps did not. The lowest correlation of significance was of population 13 where the migratory networks took a further northern route than the current maps. Only three of the populations (1, 7, and 8) showed a significant positive correlation between PATH models and density of networks. Five of the populations (4, 5, 11, 12, and 13) did not produce a corridor. Population 2 had a significantly negative correlation. Population 2 s network had supplementary movement to the north that was not predicted by the corridor. The corridor also predicted a route separate from the major network movements. Overall, correlations decreased with distance between ranges. Population 6 s major corridor avoided a lake in the same manner as the migratory network. Population 1 s corridors predicted movement similar to the networks in two routes but dominance was switched from north to south. Population 8 overestimated the corridor. Population 7 had the highest correlation predicting two routes. All populations showed a significant positive correlation between corridor values and network density. Population 2 s corridor model did not cover supplementary movement

41 40 in the north. It also predicted a slightly more northerly corridor than the dominant network. Population 7 had the highest correlation predicting two routes like the migratory networks. Population 6 s corridors avoided a lake in the same manner as the migratory networks. Correlation stayed relatively constant with increasing distance between summer and winter ranges although the highest correlation values involved the nearest ranges. Table 3: Pearson s correlation coefficients for each connectivity model and Density of Migratory Networks. All results with Pearson r-values showed a P-value of Population Circuitscape to Density of Migratory Networks PATH to Density of Migratory Networks Linkage Mapper to Density of Migratory Networks Autocorrelation Circuitscape The t-test of LCPN and LCPL values returned a p-value of < This concludes that there is a statistically significant difference between LCPN and LCPL. It suggests that the

42 41 current values correlation with migratory networks is not simply a result of autocorrelation. The K-S test showed that distributions of LCPN and LCPL values were independent of each other with a p-value of < Neither were normally distributed but were rather skewed to lower current values but still did not correlate with each other. This suggest that although there were correlations between current maps and network density, it was not necessarily only a result of autocorrelation. PATH The t-test of LCPN and LCPL values returned a p-value of < This concludes that there is a statistically significant difference between LCPN and LCPL. It suggests that the PATH corridor values correlation with migratory networks is not simply a result of autocorrelation. The paired K-S test showed that distributions of LCPN and LCPL values were independent of each other with a p-value of < Distribution of values was abnormal. The values of LCPN and LCPL were skewed to the right because of the values of no use in the PATH model. Excluding this, extracted values were bimodal with relatively similar amounts of dominant and less dominant values from the PATH models. This suggests where there was correlation it was not simply from autocorrelation and that both dominant and less dominant routes in the corridors were observed. The high frequency of empty values plus the decreasing correlations suggests PATH performed poorly in covering migration between summer and winter ranges. Linkage Mapper

43 42 The t-test of LCPN and LCPL values returned a p-value of < This concludes that there is a statistically significant difference between LCPN and LCPL. It suggests that the corridor values correlation with migratory networks is not simply a result of autocorrelation. The paired sample K-S test gave a p-value of < 0.001showing no correlation of distribution between LCPN and LCPL values. Distribution of values in LCPN and LCPL were both bimodal but skewed to the left with corridor values of importance. This is especially true with LCPL which follows the central least cost path of the corridor. The wider distribution of the LCPN values shows the coverage missed or underestimated by the corridors. 2.5 Comparative Analysis Circuitscape predicts connectivity in heterogeneous landscapes for conservation planning for which current densities can be related to individual movement (McRae and Shah 2009). Current densities or values indicate the probability of a random walker passing through each cell between each patch, in this case representing an elk moving across the landscape between summer and winter ranges (Shah and McRae 2008). Pinch points, the narrow corridors individuals may be required to traverse (Pelletier et al. 2014), show high current values which correlate significantly with kernel density of migratory networks in all populations but one. This population had supplemental migration not predicted by Circuitscape. This suggests that pinch points can show corridors individuals are likely to traverse. Movement outside of major migratory movement between ranges can be missed though. The avoidance of bodies of water by the migratory networks and not by the current maps suggests a need for a lower classification or perhaps a total barrier of certain

44 43 water bodies in the resistance surface. Local observation and inclusion of wildlife behavior could improve such a resistance model. Although the migratory network of population 13 crosses South Rim into a separate watershed called the Noble Basin, the current map predicts a following of Beaver Creek tributaries with differing routes and entry and exit points. An inspection of aerial imagery, the gap analysis layer, and landownership shows more federal lands (Bridger- Teton National Forest), fewer wetlands, and less agriculture in the migratory networks compared to the current map. Overlaying additional GPS collar data points from nonmigratory elk reveals that the agricultural lands do in fact support elk populations. An inspection of the pinch points shows they generally follow the pattern of low resistance surface values surrounded by high resistance surface values. These values are the result of a preferred grasslands intermixed with lesser valued wetland landcover. Both migratory elk and the non-migratory elk sampled had avoided this marbled landscape. Circuitscape did not avoid this landscape but funneled current though the lower resistance cells of the grasslands, creating pinch points.

45 44 Figure 4: Comparison of Migratory Network Density and Circuitscape Current in relation to Wetland and Agricultural landcover types for Population 13 The results in population 13 suggested a possibility that the unclustered or checkered pattern in the resistance surface decreased Circuitscape s performance. To test this, a Moran s I value of spatial autocorrelation was calculated for all populations. This value was compared to the correlation or performance of each population s current map to density of migratory networks using linear regression. This was also performed excluding the outlier, population 2. The first regression analysis gave an R Square value of 0.195, showing no recognizable linear relationship between the model performance and the level of clustering. If the two were related, there would be a positive linear pattern of increasing Moran s I with increasing performance. Without population 2, the R Square was 0.037, a lower value. This suggests that the low correlation in population 13 or any

46 45 decrease in correlation in other populations is not a result of the checkered pattern or heterogeneity of the landscape or resistance surface. An examination of population 1 which had a significant correlation of 0.154, shows that although elk migratory networks were observed in the areas of highest current values, this was not the main route but supplementary movement. The primary route was further to the northeast following the Gallatin River, rather than running perpendicular to its tributaries like the pinch points. Points of entry and exit are closer to the Gallatin River also. This suggests a possible influence of slope which was not included in the resistance surface. The migratory networks of population 4 with an Pearson s r-value of show movement following the west side of a lake while Circuitscape shows a pinch point running along the east side, both flats in Grand Teton National Park. There are smaller pinch points on the west side but with lower current values and more dispersed. There are more tributaries along the east side of the lake. The migratory networks of population 5 with a Pearson s r-value of took the eastern route. Population 5 produced pinch points along peninsulas and inlets of multiple lakes, including Jackson Lake, while the migratory networks followed Pacific Creek. This suggests a need for making large bodies of water non-traversable in the model. The different routes taken by populations 4 and 5 show patterns of movement not identified of readily distinguished by Circuitscape which produced the same current patterns where the populations landscapes overlapped. The shape of population 7 s ranges gives rise to two primary routes allowing for correlation that closely matches the paths taken by the elk in the migratory networks. The current radiates from the two peninsula-shaped pieces of the summer range and funnel or

47 46 constrict at the smaller winter range. The pinch points in the current map of population 8 take the shortest path where ranges are nearest each other. The networks on the other hand are further north. Population 10 shows a similar pattern in the opposite direction. Population 11 was predicted well but there are islands of pinch points in the north surrounded by much lower values. Population 12 also has extra pinch points in the west but predicts the general pattern well. Although the migratory network of population 13 crosses South Rim into a separate watershed called the Noble Basin, the corridor predicts a following of Beaver Creek tributaries with differing routes and entry and exit points. An inspection of aerial imagery, the gap analysis layer, and landownership shows more federal lands (Bridger- Teton National Forest), fewer wetlands, and less agriculture in the migratory networks compared to the corridor. Overlaying additional GPS collar data points from nonmigratory elk reveals that the agricultural lands do in fact support elk populations. An inspection of the corridor shows it generally follows the pattern of low resistance surface values surrounded by high resistance surface values. These values are the result of preferred grasslands intermixed with lesser valued wetland landcover. Both migratory elk and the non-migratory elk sampled had avoided this checkered landscape. Linkage Mapper did not avoid this landscape but funneled through the lower resistance cells of the grasslands. The results in population 13 suggested a possibility that the unclustered or checkered pattern in the resistance surface decreased Linkage Mapper s performance. To test this, a Moran s I value was calculated for all populations. This value was compared to the correlation or performance of each population s corridor to density of migratory networks

48 47 using linear regression. This was also performed excluding the outlier, population 2. The first regression analysis gave an R Square value of 0.022, showing no recognizable linear relationship between the model performance and the level of clustering. If the two were related, there would be a positive linear pattern of increasing Moran s I with increasing performance. Without population 2, the R Square was 0.273, a higher value but still not fitted. This suggests that the low correlation in population 13 or any decrease in correlation in other populations is not a result of the checkered pattern or heterogeneity of the landscape or resistance surface. 2.6 Post hoc Analysis To test whether the current map could be improved with reclassification, the checkered area of high and low values was reclassified to a single value corresponding to the wetlands rather than the grasslands. The resulting current map took a route of pinch points south of the wetland area rather than the more northerly route taken by the elk migratory networks. There is the question of whether the elk are basing migratory movements on knowledge of the landscape and decisions that weren t taken into account. Animals may respond to coarser-grained cues in the landscape when migrating (Hargrove and Westervelt 2012). A resampling to larger cell sizes was used to test this. The resistance surface was resampled to 100, 500, and 1000 meters. The general path of the pinch points did not change. A resampling of the raster with a reclassified wetland area did not produce any major change either.

49 48 To determine whether the results were possibly due to a flaw in one set of data, each model was run with zero lethality, followed by zero energy-cost. Each run produced similar results of a large corridor encompassing most of the landscape. To determine if results could improve with a different resolution (Hargrove and Westervelt 2012), all surfaces were resampled to a 1000 m size. Each model produced the same general pattern except for population 6, producing one path following the main route shown in the kernel density of elk migration networks. Settings were then adjusted on the original resolution to determine the influence on results. Corridors took the same routes in a more restricted space when Initial energy-level was reduced. The same was true when maximum turning angle was increased. To test whether the corridor could be improved with reclassification, the checkered area of high and low values was reclassified to a single value corresponding to the wetlands rather than the grasslands. The resulting corridor took a route south of the wetland area rather than the more northerly route taken by the elk migratory networks. There is the question of whether the elk are basing migratory movements on knowledge of the landscape and decisions that weren t taken into account. Animals may respond to coarser-grained cues in the landscape when migrating (Hargrove and Westervelt 2012). An examination of population 1 which had a significant correlation of 0.308, shows that although elk migratory networks were observed in the areas of highest corridor values, this was not the primary route of the corridor. The primary route was further to the northeast following the Gallatin River, rather than running perpendicular to its tributaries. Points of entry and exit are closer to the Gallatin River also. This suggests a possible influence of slope which was not included in the resistance surface. The migratory

50 49 networks of population 4 with a correlation show movement following the west side of a lake while Linkage Mapper shows a corridor running along the east side, both flats in Grand Teton National Park. Population 5 produced corridors on both sides of the same river. There are more tributaries along the east side of the lake. Elk may take both routes but this is an area for closer in the field observation to explain differences outside readily available landcover data. Population 5 produced corridors running through multiple lakes, including Jackson Lake, while the migratory networks followed Pacific Creek. The highest value corridor runs even further to the west. This suggests a need for making large bodies of water non-traversable in the model and the need for other factors. 2.7 Conclusions This study sough to test whether connectivity models could predict the migratory patterns of elk in the Greater Yellowstone Ecosystem by effectively covering the actual movements of elk between summer and winter ranges. It compares geospatial tools using least cost corridors, circuit theory, and agent based modeling. We posed the following research questions and a summary of the results is as follows. Does circuit theory predict movements of elk between summer and winter ranges? Yes circuitscape, dependent on conservation of energy, showed that circuit theory can partially predict the movements of elk between ranges but does not fully account for all movements. Exploratory movements, unlike connectivity models, do not link to or more areas but return to the original area of origin. Areas of high current did not always correspond to migratory paths and did not account for exploratory behavior. Does PATH agent based model predict the movements of elk between ranges?

51 50 No, PATH poorly predicted elk movements between ranges. In most populations, it was unable to connect ranges. Adjustments to the resolution did not change these results. It did allow for exploration by the random walkers but did not record exploration that wasn t connecting the 2 ranges. Do least cost corridors efficiently cover the actual movements of elk between summer and winter ranges. Linkage Mapper revealed that least cost corridors best explained the movements between ranges but still did not efficiently cover all or most of the movements. Migratory networks diverged from the primary path of the corridor and avoided routes that corridors took. They also did not account for exploration. All migratory networks showed exploratory movement outside of the primary routes between summer and winter ranges. Some exploration was more extensive and resulted in lower significant correlation. All three models are designed to connect two or more patches but do not allow for movement that does not link the patches but instead allows for exploration and returning to the original patch. This is true for migration between ranges and suggests a need for a model that allows for not only basic connectivity but also exploration, a kind of connectivity of each range, itself, and the greater landscape. Correlation values, although significant, were not highly significant and showed room for improvement. It was evident that there were needs not only for changing the models but also in the resistance surface. There were factors in play that landcover and roads/human presence did not account for. At first it appeared resolution could be such a factor but a decrease in resolution did not improve performance. The discrepancies involving

52 51 wetlands, rivers, tributaries, and wetlands suggest a need for a greater emphasis on riparian areas not only as landcover. Overall, Linkage Mapper, performed best in predicting elk movement with an average correlation coefficient of using a traditional least cost corridor; versus Circuitscape with an average of using circuit theory. Linkage Mapper performed better than Circuitscape on seven out of eleven populations. Neither Circuitscape, Linkage Mapper, nor PATH effectively covered the migratory movements of elk in the Greater Yellowstone Ecosystem. Discrepancies in the resistance surface plus exploratory behavior were shown to contribute to this. This adds to Tischendorf and Fahrig s (2000) suggestions that proper measure of connectivity requires measurement of actual immigration rates and the assumption that organisms do not venture into nonhabitat but rather stay in corridors is false. Our results suggest that connectivity models need improvement by accounting for exploration outside of prime habitat. It also suggests connectivity models are not adequate predictors of migratory movements and not suited to conservation planning of migratory networks. This supports Sawyer s (et al. 2009) ungulate conservation planning of considering connectivity but basing priority on migratory landscape usage. It is assumed that fragmentation or loss in connectivity impedes seasonal migration, cutting off wildlife from resources (Rudnick et al. 2012). This study shows that migratory elk are actually using less than prime and supposedly fragmented habitat in migration and that there is more than connectivity at play. 2.8 Implications of the Research The research shows that least cost corridors and circuit theory can predict migratory paths but cannot predict all such movements. There are discrepancies, especially involving

53 52 exploratory movements and avoidance behaviors not considered by the connectivity models. Corridors and pinch points should not be assumed as required in the sense they are now as wildlife can use less than suitable paths. The PATH agent based model is not suited to predicting migration and only performs well when dependent on the effects of autocorrelation. Changes in resolution had little effect for any connectivity model despite assumptions it would do so (McRae and Beier 2007, Majka et al. 2010, Carroll et al. 2012, Hargrove and Westervelt 2012). Unlike a previous study (Rainey 2012), this study used a wider sample of the landscape in the Greater Yellowstone Ecosystem. It also used a resistance surface based on the two factors of roads and landcover (Majka et al. 2010) and the local landcover, excluding that in GPS-collar migratory data, but excluding topographical and land ownership factors (Rainey 2012). Both the Rainey (2012) and this study showed correlation but this study validated this on a larger scale. It also shows the importance of local variables and the potential lack of predictability of behavior in relation to certain features in the landscape. These differences ultimately show the importance of the resistances surface and how it is built. Least cost corridors performed better in each study as compared to circuit theory. 2.9 Future Research This all implies a need for inclusion of exploration and avoidance in the modeling of connectivity for migratory species. Such models could allow links not only from patch to patch or range to range but also from a range to the landscape and itself. This could be done by measuring each range s connectivity to its surroundings.

54 53 The observation that the elk did use the less than suitable routes suggests a need for a different classification of the landscape not rating the high quality habitat as prime for movement. Further analysis of the GPS data and landscape structure could contribute to a migration based rather than habitat quality based resistance surface. The presence of non-migratory elk in the areas identified in connectivity models suggests an analysis of the influence of these populations. Field studies and spatial analysis could determine if these populations serve as barriers to the migratory elk. A detailed analysis of the influence of the forms and patterns of riparian areas on migration could also improve the models in a similar manner. This and previous studies suggest a need for a comparative analysis of the influence of resistance surfaces on connectivity models as they compare to migratory data. Shape or arrangement of ranges, patches, and or nodes could also be analyzed for influence on connectivity models. References Aarts, G., MacKenzie, M., McConnell, B., Fedak, M. & Matthiopoulos, J. (2008). Estimating space-use and habitat preference from wildlife telemetry data. Ecography 31, Alagador, D., Trivino, M., Cerdeira, J. O., Brás, R., Cabeza, M., & Araújo, M. B. (2012). Linking like with like: optimising connectivity between environmentally-similar habitats. Landscape ecology, 27(2), Baldwin, R. F., Perkl, R. M., Trombulak, S. C., & Burwell III, W. B. (2010). Modeling ecoregional connectivity. In Landscape-scale Conservation Planning (pp ). Springer Netherlands. Barbknecht, A. E., Fairbanks, W. S., Rogerson, J. D., Maichak, E. J., Scurlock, B. M., & Meadows, L. L. (2011). Elk parturition site selection at local and landscape scales. The Journal of Wildlife Management, 75(3), Creel, S., Winnie Jr, J., Maxwell, B., Hamlin, K., & Creel, M. (2005). Elk alter habitat selection as an antipredator response to wolves. Ecology, 86(12),

55 54 Bélisle, M. (2005). Measuring landscape connectivity: the challenge of behavioral landscape ecology. Ecology, 86(8), Boyce, M. S., Mao, J. S., Merrill, E. H., Fortin, D., Turner, M. G., Fryxell, J. & Turchin, P. (2003). Scale and heterogeneity in habitat selection by elk in Yellowstone National Park. Ecoscience 10, Boyce, M. S. (2006). Scale and resource selection functions. Diver. Distr. 12, Boyce, M. S., J. Pitt, et al. (2010). "Temporal autocorrelation functions for movement rates from global positioning system radiotelemetry data." Royal Society Philosophical Transactions Biological Sciences 365(1550): Braaker, S., Moretti, M., Boesch, R., Ghazoul, J., Obrist, M. K., & Bontadina, F. (2014). Assessing habitat connectivity for ground-dwelling animals in an urban environment. Ecological Applications. Brillinger, D. R., H. K. Preisler, et al. (2004). "An exploratory data analysis (EDA) of the paths of moving animals." Journal of Statistical Planning and Inference 122(1-2): Brodie, J. F., Giordano, A. J., Dickson, B., Hebblewhite, M., Bernard, H., MOHD AZLAN, J. A. Y. A. S. I. L. A. N.,... & Ambu, L. (2014). Evaluating multispecies landscape connectivity in a threatened tropical mammal community. Conservation Biology. Calenge, C. (2007). "Exploring habitat selection by wildlife with adehabitat." Journal of Statistical Software 22(6): Calenge, C., S. Dray, et al. (2009). "The concept of animals' trajectories from a data analysis perspective." Ecological Informatics 4(1): Calenge, C. (2011). "Analysis of Animal Movements in R: the adehabitatlt Package." Carroll, C., McRAE, B. R. A. D., & Brookes, A. (2012). Use of linkage mapping and centrality analysis across habitat gradients to conserve connectivity of gray wolf populations in western North America. Conservation Biology, 26(1), Carroll, C., Fredrickson, R. J., & Lacy, R. C. (2014). Developing metapopulation connectivity criteria from genetic and habitat data to recover the endangered Mexican wolf. Conservation Biology, 28(1), Chetkiewicz, C. L. B., & Boyce, M. S. (2009). Use of resource selection functions to identify conservation corridors. Journal of Applied Ecology, 46(5), Clark, R. G. & Strevens, T. C. (2008). Design and analysis of clustered, unmatched resource selection studies. J. R. Stat. Soc. Ser. C 57, Compton, B. W., McGARIGAL, K. E. V. I. N., Cushman, S. A., & Gamble, L. R. (2007). A Resistant Kernel Model of Connectivity for Amphibians that Breed in Vernal Pools. Conservation Biology, 21(3),

56 55 Cook, E. A. (2002). Landscape structure indices for assessing urban ecological networks. Landscape and urban planning, 58(2), Craiu, R. V., Duchesne, T. & Fortin, D. (2008). Inference methods for the conditional logistic regression model with longitudinal data. Biometr. J. 50, Crooks, K. R., & Sanjayan, M. (2006). Connectivity conservation: maintaining connections for nature. CONSERVATION BIOLOGY SERIES-CAMBRIDGE-, 14, 1. de Solla, S. R., Bonduriansky, R., and Brooks, R. J. (1999), Eliminating Autocorrelation Reduces Biological Relevance of Home Range Estimates, Journal of Animal Ecology, 68, Dorf, R. C., & Svoboda, J. A. (2010). Introduction to electric circuits. John Wiley & Sons. Dray, S., M. Royer-Carenzi, et al. (2010). "The exploratory analysis of autocorrelation in animal-movement studies." Ecological Research 25(3): Fieberg, J., Rieger, R. H., Zicus, M. C. & Schildcrout, J. S. (2009). Regression modelling of correlated data in ecology: subject-specific and population averaged response patterns. J. Appl. Ecol. 46, Fieberg, J., J. Matthiopoulos, et al. (2010). "Correlation and studies of habitat selection: problem, red herring or opportunity?" Royal Society Philosophical Transactions Biological Sciences 365(1550): Filz, K. J., Engler, J. O., Stoffels, J., Weitzel, M., & Schmitt, T. (2013). Missing the target? A critical view on butterfly conservation efforts on calcareous grasslands in southwestern Germany. Biodiversity and conservation, 22(10), Frair, J. L., Nielsen, S. E., Merrill, E. H., Lele, S. R., Boyce, M. S., Munro, R. H.,... & Beyer, H. L. (2004). Removing GPS collar bias in habitat selection studies. Journal of Applied Ecology, 41(2), Glenn, E. M., Hansen, M. C. & Anthony, R. G. (2004). Spotted owl home range and habitat use in young forests of western Oregon. J. Wildl. Manage. 68, Gillies, C. S., Hebblewhite, M., Nielsen, S. E., Krawchuk, M. A., Aldridge, C. L., Frair, J. L., Saher, J., Stevens, C. E. & Jerde, C. L. (2006). Application of random effects to the study of resource selection by animals. J. Anim. Ecol. 75, Hargrove, W. W., Hoffman, F. M., & Efroymson, R. A. (2005). A practical map-analysis tool for detecting potential dispersal corridors. Landscape Ecology, 20(4), Hargrove, W. W., & Westervelt, J. D. (2012). An Implementation of the Pathway Analysis Through Habitat (PATH) Algorithm Using NetLogo. In Ecologist-Developed Spatially-Explicit Dynamic Landscape Models (pp ). Springer US.

57 56 Harrisson, K. A., Pavlova, A., Amos, J. N., Radford, J. Q., & Sunnucks, P. (2014). Does reduced mobility through fragmented landscapes explain patch extinction patterns for three honeyeaters? Journal of Animal Ecology, 83(3), Hebblewhite, M. & Merrill, E. H. (2008). Modelling wildlife-human relationships for social species with mixed-effects resource selection models. J. Appl. Ecol. 45, Johnson, C. J., Parker, K. L., Heard, D. C. & Gillingham, M. P Movement parameters of ungulates and scale-specific responses to the environment. J. Anim. Ecol. 71, Johnson, C. J., Nielsen, S. E., Merrill, E. H.,McDonald, T. L. & Boyce, M. S. (2006). Resource selection functions based on use-availability data: theoretical motivation and evaluation methods. J. Wildl. Manage. 70, Kilbane, S. (2013). Green infrastructure: planning a national green network for Australia. Journal of Landscape Architecture, 8(1), Koen, E. L., Garroway, C. J., Wilson, P. J., & Bowman, J. (2010). The effect of map boundary on estimates of landscape resistance to animal movement. PloS one, 5(7), e Koen, E. L., Bowman, J., Garroway, C. J., Mills, S. C., & Wilson, P. J. (2012). Landscape resistance and American marten gene flow. Landscape Ecology, 27(1), Koper, N. & Manseau, M. L. (2009). Generalized estimating equations and generalized linear mixed-effects models for modeling resource selection. J. Appl. Ecol. 46, Legendre P, Legendre L (1998). Numerical ecology, 2nd edn. Elsevier, Amsterdam Lele, S. R. & Keim, J. L. (2006). Weighted distributions and estimation of resource selection probability functions. Ecology 87, Lele, S. R. (2009). A new method for estimation of resource selection probability function. J. Wildl. Manage. 73, Maehr, D. S. and S. Fei "GPS SAMPLING INTENSITY AND LARGE MAMMAL BEHAVIOR." In Proceedings of the 6th Southern Forestry and Natural Resources GIS Conference (2008), P. Bettinger, K. Merry, S. Fei, J. Drake, N. Nibbelink, and J. Hepinstall, eds. Warnell School of Forestry and Natural Resources, University of Georgia, Athens, GA. Majka, D., Beier, P., & Jenness, J. (2010). Corridor designer ArcGIS toolbox tutorial. Marrotte, R. R., Gonzalez, A., & Millien, V. (2014). Landscape resistance and habitat combine to provide an optimal model of genetic structure and connectivity at the range margin of a small mammal. Molecular ecology, 23(16), Marsh L, Jones R (1988).The form and consequences of random walk movement models. J Theor Biol 133:

58 57 McRae, B. H., & Beier, P. (2007). Circuit theory predicts gene flow in plant and animal populations. Proceedings of the National Academy of Sciences, 104(50), McRae, B. H., Dickson, B. G., Keitt, T. H., & Shah, V. B. (2008). Using circuit theory to model connectivity in ecology, evolution, and conservation. Ecology, 89(10), McRae, B. H., & Kavanagh, D. M. (2011). Linkage Mapper Connectivity Analysis Software. Seattle, WA: The Nature Conservancy. McRae, B. H., & Kavanagh, D. M. (2012). Barrier Mapper Connectivity Analysis Software. Seattle, WA: The Nature Conservancy. McRae, B. H., Hall, S. A., Beier, P., & Theobald, D. M. (2012). Where to restore ecological connectivity? Detecting barriers and quantifying restoration benefits. PloS one, 7(12), e Moilanen, A., & Nieminen, M. (2002). Simple connectivity measures in spatial ecology. Ecology, 83(4), Nations, C. S. and R. C. Anderson-Sprecher (2006). "Estimation of animal location from radio telemetry data with temporal dependencies." Journal of Agricultural Biological and Environmental Statistics 11(1): Nielsen, S. E., Boyce, M. S., Stenhouse, G. B. & Munro, R. H. M Modeling grizzly bear habitats in the Yellowhead ecosystem of Alberta: taking autocorrelation seriously. Ursus 13, Nuñez, T. A., Lawler, J. J., Mcrae, B. H., PIERCE, D., Krosby, M. B., Kavanagh, D. M.,... & Tewksbury, J. J. (2013). Connectivity planning to address climate change. Conservation Biology, 27(2), Pelletier, D., Clark, M., Anderson, M. G., Rayfield, B., Wulder, M. A., & Cardille, J. A. (2014). Applying circuit theory for corridor expansion and management at regional scales: tiling, pinch points, and omnidirectional connectivity. PloS one, 9(1), e Perkl, Ryan M. (2013). Arizona Landscape Integrity and Wildlife Connectivity Assessment. The University of Arizona and the Arizona Game and Fish Department. Tucson, AZ. Radeloff, V. C., Mladenoff, D. J. & Boyce, M. S. (2000). The changing relation of landscape pattern to jack pine budworm populations during an outbreak. Oikos 90, Rainey, M. M. (2012). Validating alternative methods of modeling wildlife corridors using relocation data from migrating elk and dispersing wolverines. MONTANA STATE UNIVERSITY. Rudnick, D., Ryan, S. J., Beier, P., Cushman, S. A., Dieffenbach, F., Epps, C.,... & Trombulack, S. C. (2012). The role of landscape connectivity in planning and implementing conservation and restoration priorities. Issues in Ecology.

59 58 Ryman, G. L. (2010). More than bucks and acres: assessing the value of conserving land. School of the Environment. Duke University, Durham, NC Sawyer, H., Nielsen, R. M., Lindzey, F. & McDonald, L. L. (2006). Winter habitat selection of mule deer before and during development of a natural gas field. J. Wildl. Manage. 70, Sawyer, H., Kauffman, M. J., Nielson, R. M., & Horne, J. S. (2009). Identifying and prioritizing ungulate migration routes for landscape-level conservation. Ecological Applications, 19(8), Saura, S., and J. Torné. (2009). Conefor Sensinode 2.2: a software package for quantifying the importance of habitat patches for landscape connectivity. Environmental Modelling & Software 24: Shah, V. B., & McRae, B. H. (2008, August). Circuitscape: a tool for landscape ecology. In Proceedings of the 7th Python in Science Conference (Vol. 7, pp ). Swihart, R. K. and N. A. Slade (1986). "THE IMPORTANCE OF STATISTICAL POWER WHEN TESTING FOR INDEPENDENCE IN ANIMAL MOVEMENTS." Ecology 67(1): Taylor, P. D., Fahrig, L., Henein, K., & Merriam, G. (1993). Connectivity is a vital element of landscape structure. Oikos, Theobald, D. M., J. B. Norman, and M. R. Sherburne. (2006). FunConn version 1 user s manual: ArcGIS tools for functional connectivity modeling. Natural Resources Ecology Lab, Colorado State University, Fort Collins, Colorado. Tischendorf, L., & Fahrig, L. (2000). On the usage and measurement of landscape connectivity. Oikos, 90(1), Turchin P (1998). Quantitative analysis of movement: measuringand modeling population redistribution in plants and animals. Sinauer Associates, Sunderland Trumbo, D. R., Spear, S. F., Baumsteiger, J., & Storfer, A. (2013). Rangewide landscape genetics of an endemic Pacific northwestern salamander. Molecular ecology, 22(5), Urban, D. and T. Keitt. (2001). Landscape connectivity: a graph-theoretic perspective. Ecology 82: Urban, D. L., E. S. Minor, E. A. Treml, and R. S. Schick. (2009). Graph models of habitat mosaics. Ecology Letters 12: Wiens, J. A. (2006). Introduction: Connectivity research-what are the issues?. CONSERVATION BIOLOGY SERIES-CAMBRIDGE-, 14, 23. Wilensky, U. (2010). Netlogo, Center for Connected Learning and Computer- Based Modeling, Northwestern University. Evanston, IL.

60 59 Wittemyer, G., Polansky, L., Douglas-Hamilton, I. & Getz, W. M. (2008). Disentangling the effects of forage, social rank, and risk on movement autocorrelation of elephants using Fourier and wavelet analyses. Proc. Natl Acad. Sci. USA 105, Zeger, S. L., Liang, K.-Y. & Albert, P. S. (1988). Models for longitudinal data: a generalized estimating equation approach. Biometrics 44, (doi: / ) APPENDIX A: COMPARING A CIRCUIT THEORY BASED LANDSCAPE CONNECTIVITY MODEL TO THE MIGRATORY PATTERNS OF ELK SAMPLED IN THE GREATER YELLOWSTONE ECOSYSTEM Samuel N. Chambers 1, Howard R. Gimblett 2, David A. Christianson 2, Daoqin Tong 1 1 School of Geography and Development, 2 School of Natural Resources and the Environment. The University of Arizona, Tucson AZ, USA Author for correspondence: Samuel Norton Chambers Phone: schambers@ .arizona.edu ABSTRACT

61 60 The Circuitscape tool is used to map the places in the landscape that wildlife would or do use linking patches of habitat. It does this by modeling the landscape as a circuit with flows of current from random walkers serving as the wildlife. Migratory species such as elk traverse between such patches which serve as seasonal ranges. This study sought to use field collected data for the purpose of comparing migratory patterns and the Circuitscape model. With this, we hoped to measure the suitability of circuitscape for covering and predicting the migratory movements of elk in the Greater Yellowstone Ecosystem. To conduct this analysis, GPS point data was converted to sequential networks for multiple populations of elk. The GPS data was also used to delineate the summer and winter ranges of each population. The kernel density of routes in the networks was measured for comparison to the current maps. The ranges served as the patches to be connected in the current maps. A resistance surface was produced using reclassified landcover data for mapping habitat suitability and linear road data for human presence or obstruction to movement. Current maps were produced for eleven migratory elk populations. These maps were compared to the migratory network density by measuring correlation. This was followed by a new method of measuring the influence of autocorrelation between the models and networks. Some of the models were then altered to test for suspected influences. This study shows that circuit theory can predict the migratory movements between summer and winter ranges but only so much. It lacks the ability to predict exploratory movements that do not link ranges to each other. It also lacks the ability to account for all avoidance behaviors in the landscape, particularly in riparian areas. Key Words: Circuitscape, elk, Yellowstone, migration, landscape connectivity

62 61 Introduction Circuitscape is a Java software package and ArcGIS tool that uses raster habitat data to produce a matrix of resistance distances among population pairs by representing range maps as graphs, replacing habitat cells with nodes and connecting adjacent nodes with resistors (McRae and Beier 2007). The program calculates resistance distances though nodal analysis, a circuit analysis algorithm that applies Kirchhoff s current law in the form of a matrix (Dorf and Svoboda 2010). Circuitscape has been particularly useful in modeling gene flow in relation to the landscape. It was used for evaluating the effect of habitat and landscape characteristics on population genetic structure in white-footed mice (Marrotte et al. 2014). The model also revealed regionally variable gene flow patterns across the Cope s giant salamander range (Trumbo et al. 2013). Circuitscape was used to show the difference in gene flow and effects of habitat fragmentation separate species of honeyeater birds (Harrisson et al. 2014). This suggests Circuitscape does not work well for all species. In an analysis of the effects of forest management on American martens, it was concluded Euclidean distance better described gene flow than effective distance modeled by circuit theory (Koen et al. 2012). Although it is most desirable to model connectivity across a single surface representing an entire landscape, Circuitscape has been shown as useful in mosaics of overlapping high resolution tiles representing portions of the landscape (Pelletier et al. 2014). This was especially useful in identifying pinch points which are narrow corridors individuals may be required to traverse (Pelletier et al. 2014). Cross-validation showed the general validity of Circuitscape models in identifying connectivity of an urban

63 62 landscape for European hedgehogs with pinch points and other habitat connections (Braaker et al. 2014). There is the question of the effect of the extent of resistance surfaces or the map boundary on the output of Circuitscape. Koen (et al. 2010) concluded that artificial map boundaries using randomized values as a solution for using Circuitscape to model connectivity and genetic flow studies. While there have been comparative analysis of gene flow and Circuitscape there has yet to a comparative study of Circuitscape and the actual movements of animals. This study seeks to find if there is a positive correlation between the connections mapped by Circuitscape and the migratory movements of Elk in the greater Yellowstone ecosystem. The null hypothesis is that there is either zero or a negative correlation between current maps and migratory networks. The alternative hypothesis predicts a positive correlation. Data and Method 2.1 Data Collection Female elk were fitted with Global Positioning System (GPS) radio-collars during in various locations across the eastern Greater Yellowstone Ecosystem. These elk were captured in Grand Teton National Park, National Elk Refuge, Buffalo Valley (Barbknecht et al. 2011), Yellowstone National Park, and Gallatin National Forest (Creel et al. 2005). Capture activities were approved by Wyoming Game and Fish Department and Iowa State University Animal Care and Use Committee (Protocol # ). Locational data were collected at a rate of 3-48 points a day, providing a minimum of an 8 hour fix interval.

64 63 GPS collar data was classified by month to determine which elk sampled had separate winter (January-March) and summer (June-August) ranges. Overlapping ranges of separate individuals were merged into population ranges. These served as the habitat patches in each connectivity model. The points outside these ranges were delineated into line shape files based on individual elk, location, and time. Kernel density of these lines or networks were calculated for the full extent of all sampled points in a population. Two populations were removed from analysis due to discrepancies in the point data not allowing for generation of the networks and density properly. A total of eleven final populations were delineated for analysis. Number of individuals in population samples ranged from two to six.

65 Figure 2: Location of sampled populations used in Circuitscape connectivity models

66 Resistance Surface A cost raster surface was developed using spatial data for landcover and human infrastructure. The reclassification values were based on the system designed for CorridorDesigner s elk tutorial dataset (Majka et al 2010). This resistance surface as input for the connectivity models. Landcover was used to delineate potential habitat and unsuitable habitat. Human structures included roads representing cost to movement. The sum of these cost individual surfaces was normalized as a 1 to 100 scale with 1 representing least cost to movement and 100, maximum cost.

67 Figure 1: Circuitscape resistance surface delineated using landcover and road data 66

68 Patch Delineation Habitat patches were mapped by identifying areas of distinct summer and winter ranges for distinct populations. Using GPS collar data, a total of thirteen populations were delineated by distinguishing distinct groups based on overlapping ranges. Summer and winter ranges were identified by separating GPS data based on Month. Months of distinct winter range were determined as January, February, and March. The distinct summer months were June, July, and August. The remaining dates were considered migratory months. Number of elk used in mapping these populations and size of summer and winter ranges varied from two to six. 2.3 Current Mapping Each pair of ranges for a population and the cost surface were used as input for the Circuitscape tool to delineate current maps, as a continuous surface raster for each population. 2.4 Migratory Network Delineation The migratory data was used to delineate networks of elk movement outside of the summer and winter ranges. Kernel density was calculated for the linear networks of all elk monitored with distinct summer/winter ranges in each population. All data for kernel densities and the current maps were compiled as a csv table using R. This table consisted of location related values for each surface. Using SPSS, I ran a correlations test between each current map and each kernel density surface.

69 Testing for Autocorrelation To check for autocorrelation of the migratory networks and the current maps based on the summer and winter ranges, I extracted values from the each current map based on the networks and the least cost path between the ranges. To do this I had to extract values from the current maps for each population based on the network of movement and the least cost path between the ranges for each elk. Each elk s network was masked by the ranges, leaving only the migratory network. This was converted to a single value raster. A least cost path model was run to identify the shortest path(s) through each network. These served as Network Least Cost Paths (LCPN). The intersection of each of these with summer and winter ranges was also identified and extracted to serve as nodes for a simple least cost path model. Least cost paths were found for each pair of summer and winter crossing points for each elk. These served as a Landscape Least Cost Paths (LCPL). I then ran a t-test for significant difference between the extracted values. The correlation values were also represented on a scatterplot to determine if there was a relationship between distance between ranges and correlation.

70 Figure 3: Example of least cost paths using the migratory networks and the landscape resistance surface. 69

71 70 To assure that the t-test results were not merely a result of the means, distribution was analyzed using a Kolmogorov Smirnov (K-S) test. The extracted values were analyzed for differentiation from normal distribution. Histograms of LCPN and LCPL could then be compared for similarity based on their distribution. Results 3.1 Current and Network Correlation Current maps showed significant correlation with kernel density of migratory networks except in population 2 with a negative correlation of This population had additional migratory movement to the north, outside of the general movement between the summer and winter ranges. The migratory movements were also slightly to the southeast of the predictions of the current map. Correlation did not decrease with distance between ranges. Although the population 6 current maps show a correlation of 0.203, the migratory networks avoided a reservoir while the current maps did not. The lowest correlation of significance was of population 13 where the migratory networks took a further northern route than the current maps.

72 Figure 4: Population 1 kernel density of migratory networks (left) and current map (right) 71

73 Figure 5: Population 2 kernel density of migratory networks (left) and current map (right) 72

74 Figure 6: Population 4 kernel density of migratory networks (left) and current map (right) 73

75 Figure 7 Population 5 kernel density of migratory networks (left) and current map (right) 74

76 Figure 8: Population 7 kernel density of migratory networks (left) and current map (right) 75

77 Figure 9: Population 8 kernel density of migratory networks (left) and current map (right) 76

78 77 Figure 10: Population 10 kernel density of migratory networks (left) and current map (right)

79 Figure 11: Population 11 kernel density of migratory networks (left) and current map (right) 78

80 Figure 12: Population 12 kernel density of migratory networks (left) and current map (right) 79

81 Figure 13: Population 13 kernel density of migratory networks (left) and current map (right) 80

82 Autocorrelation The t-test of LCPN and LCPL values returned a p-value of This concludes that there is a statistically significant difference between LCPN and LCPL. It suggests that the current values correlation with migratory networks is not simply a result of autocorrelation. The K-S test showed that distributions of LCPN and LCPL values were independent of each other with a p-value of Neither were normally distributed but were rather skewed to lower current values but still did not correlate with each other. This suggest that although there were correlations between current maps and network density, it was not necessarily only a result of autocorrelation.

83 82 (a) (b) Figure 14: Distribution of values and deviation from normal distribution for (a) LCP L and (b) LCP N

84 83 Conclusions Circuitscape predicts connectivity in heterogeneous landscapes for conservation planning for which current densities can be related to individual movement (McRae and Shah 2009). Current densities or values indicate the probability of a random walker passing through each cell between each patch, in this case representing an elk moving across the landscape between summer and winter ranges (Shah and McRae 2008). Pinch points, the narrow corridors individuals may be required to traverse (Pelletier et al. 2014), show high current values which correlate significantly with kernel density of migratory networks in all populations but one. This population had additional migration not predicted by Circuitscape. This suggests that pinch points can show corridors individuals are likely to traverse. Movement outside of major migratory movement between ranges can be missed though. The avoidance of bodies of water by the migratory networks and not by the current maps suggests a need for a lower classification or perhaps a total barrier of certain water bodies in the resistance surface. Local observation and inclusion of wildlife behavior could improve such a resistance model. Although the migratory network of population 13 crosses South Rim into a separate watershed called the Noble Basin, the current map predicts a following of Beaver Creek tributaries with differing routes and entry and exit points. An inspection of aerial imagery, the gap analysis layer, and landownership shows more federal lands (Bridger- Teton National Forest), fewer wetlands, and less agriculture in the migratory networks compared to the current map. Overlaying additional GPS collar data points from nonmigratory elk reveals that the agricultural lands do in fact support elk populations. An

85 84 inspection of the pinch points shows they generally follow the pattern of low resistance surface values surrounded by high resistance surface values. These values are the result of a preferred grasslands intermixed with lesser valued wetland landcover. Bothe migratory elk and the non-migratory elk sampled had avoided this marbled landscape. Circuitscape did not avoid this landscape but funneled current though the lower resistance cells of the grasslands, creating pinch points. The results in population 13 suggested a possibility that the unclustered or checkered pattern in the resistance surface decreased circuitscape s performance. To test this, a Moran s I value was calculated for all populations. This value was compared to the correlation or performance of each population s current map to density of migratory networks using linear regression. This was also performed excluding the outlier, population 2. The first regression analysis gave an R Square value of 0.195, showing no recognizable linear relationship between the model performance and the level of clustering. If the two were related, there would be a positive linear pattern of increasing Moran s I with increasing performance. Without population 2, the R Square was 0.037, a lower value. This suggests that the low correlation in population 13 or any decrease in correlation in other populations is not a result of the checkered pattern or heterogeneity of the landscape or resistance surface.

86 85 Table 1: Pearson s r and Moran s I values by population Population Pearson s r Moran's I An examination of population 1 which had a significant correlation of 0.154, shows that although elk migratory networks were observed in the areas of highest current values, this was not the main route but supplementary movement. The primary route was further to the northeast following the Gallatin River, rather than running perpendicular to its tributaries like the pinch points. Points of entry and exit are closer to the Gallatin River also. This suggests a possible influence of slope which was not included in the resistance surface. The migratory networks of population 4 with a correlation coefficient show movement following the west side of a lake while Circuitscape shows a pinch point running along the east side, both flats in Grand Teton National Park. There are smaller pinch points on the west side but with lower current values and more dispersed. There are more tributaries along the east side of the lake. The migratory networks of population 5 with a correlation coeeficient of took the eastern route. Population 5 produced

87 86 pinch points along peninsulas and inlets of multiple lakes, including Jackson Lake, while the migratory networks followed Pacific Creek. This suggests a need for making large bodies of water non-traversable in the model. The different routes taken by populations 4 and 5 show patterns of movement not identified of readily distinguished by Circuitscape which produced the same current patterns where the populations landscapes overlapped. To test whether the current map could be improved with reclassification, the checkered area of high and low values was reclassified to a single value corresponding to the wetlands rather than the grasslands. The resulting current map took a route of pinch points south of the wetland area rather than the more northerly route taken by the elk migratory networks.

88 87 Figure 15: Current map of population 13 reclassified to remove high quality habitat from checkered landscape of low quality habitat wetlands There is the question of whether the elk are basing migratory movements on knowledge of the landscape and decisions that weren t taken into account. Animals may respond to coarser-grained cues in the landscape when migrating (Hargrove and Westervelt 2012). A resampling to larger cell sizes was used to test this. The resistance surface was resampled to 100, 500, and 1000 meters. The general path of the pinch points did not change. A resampling of the raster with a reclassified wetland area did not produce any major change either.

89 88 References Braaker, S., Moretti, M., Boesch, R., Ghazoul, J., Obrist, M. K., & Bontadina, F. (2014). Assessing habitat connectivity for ground-dwelling animals in an urban environment. Ecological Applications. Barbknecht, A. E., Fairbanks, W. S., Rogerson, J. D., Maichak, E. J., Scurlock, B. M., & Meadows, L. L. (2011). Elk parturition site selection at local and landscape scales. The Journal of Wildlife Management, 75(3), Creel, S., Winnie Jr, J., Maxwell, B., Hamlin, K., & Creel, M. (2005). Elk alter habitat selection as an antipredator response to wolves. Ecology, 86(12), Dorf, R. C., & Svoboda, J. A. (2010). Introduction to electric circuits. John Wiley & Sons. Hargrove, W. W., & Westervelt, J. D. (2012). An Implementation of the Pathway Analysis Through Habitat (PATH) Algorithm Using NetLogo. In Ecologist-Developed Spatially-Explicit Dynamic Landscape Models (pp ). Springer US. Harrisson, K. A., Pavlova, A., Amos, J. N., Radford, J. Q., & Sunnucks, P. (2014). Does reduced mobility through fragmented landscapes explain patch extinction patterns for three honeyeaters?. Journal of Animal Ecology, 83(3), Koen, E. L., Bowman, J., Garroway, C. J., Mills, S. C., & Wilson, P. J. (2012). Landscape resistance and American marten gene flow. Landscape Ecology, 27(1), Majka, D., Beier, P., & Jenness, J. (2010). Corridor designer ArcGIS toolbox tutorial. McRae, B. H., & Beier, P. (2007). Circuit theory predicts gene flow in plant and animal populations. Proceedings of the National Academy of Sciences, 104(50), McRae, B. H., & Shah, V. B. (2009). Circuitscape user guide. ONLINE. The University of California, Santa Barbara. Available at: circuitscape. org. Marrotte, R. R., Gonzalez, A., & Millien, V. (2014). Landscape resistance and habitat combine to provide an optimal model of genetic structure and connectivity at the range margin of a small mammal. Molecular ecology, 23(16), Pelletier, D., Clark, M., Anderson, M. G., Rayfield, B., Wulder, M. A., & Cardille, J. A. (2014). Applying circuit theory for corridor expansion and management at regional scales: tiling, pinch points, and omnidirectional connectivity. PloS one, 9(1), e Shah, V. B., & McRae, B. H. (2008, August). Circuitscape: a tool for landscape ecology. In Proceedings of the 7th Python in Science Conference (Vol. 7, pp ). Trumbo, D. R., Spear, S. F., Baumsteiger, J., & Storfer, A. (2013). Rangewide landscape genetics of an endemic Pacific northwestern salamander. Molecular ecology, 22(5),

90 89

91 90 APPENDIX B: COMPARING AN AGENT BASED LANDSCAPE CONNECTIVITY MODEL TO THE MIGRATORY PATTERNS OF ELK SAMPLED IN THE GREATER YELLOWSTONE ECOSYSTEM Samuel N. Chambers 1, Howard R. Gimblett 2, David A. Christianson 2, Daoqin Tong 1 1 School of Geography and Development, 2 School of Natural Resources and the Environment. The University of Arizona, Tucson AZ, USA Author for correspondence: Samuel Norton Chambers Phone: schambers@ .arizona.edu ABSTRACT

92 91 PATH is an agent based model used to map corridors on the landscape that wildlife would or do use linking patches of habitat. Migratory species such as elk traverse between such patches which serve as seasonal ranges. This study sought to use field collected data for the purpose of comparing migratory patterns and the PATH model. With this, we hoped to measure the suitability of PATH for covering and predicting the migratory movements of elk in the Greater Yellowstone Ecosystem. To conduct this analysis, GPS point data was converted to sequential networks for multiple populations of elk. The GPS data was also used to delineate the summer and winter ranges of each population. The kernel density of routes in the networks was measured for comparison to the corridors. The ranges served as the patches to be connected by corridors. Two resistance surfaces were produced using reclassified landcover data for mapping energy cost and linear road data for potential lethality. Corridor maps were produced for eleven migratory elk populations. Almost half of the maps did not provide corridors. These corridors were compared to the migratory network density by measuring correlation. This was followed by a new method of measuring the influence of autocorrelation between the corridors and networks. Only three showed correlation and all correlation was a result of autocorrelation. This was not improved on even if resolution, model components, and settings were adjusted. This study shows that least cost corridors can predict the migratory movements between summer and winter ranges but only so much. It lacks the ability to predict exploratory movements that do not link ranges to each other. Key Words: PATH, elk, Yellowstone, migration, landscape connectivity, agent based modeling, NetLogo

93 92 Introduction The Pathway Analysis Through Habitat (PATH) tool was first developed as a supercomputer model to predict the location of corridors between habitat patches using an algorithm of random walkers from said patches (Hargrove et al. 2004). It was simplified for use on PCs using the Agent Based Modeling software NetLogo (Hargrove and Westervelt 2012; Wilensky 1999). Each walker is given preferences of behavior based on 3 grid file inputs representing habitat location, the energy cost outside habitat, and the lethality outside habitat (Hargrove and Westervelt 2012). PATH produces a map of the most heavily traverses migration pathways outside patches (Hargrove and Westervelt 2012). Hargrove and Westervelt (2012) tested PATH in identifying corridors for gopher tortoises between remaining habitat fragments within Fort Benning, GA (Hargrove and Westervelt 2012). This study seeks to find if there is a positive correlation between the corridors mapped by PATH and the migratory movements of Elk in the greater Yellowstone ecosystem. The null hypothesis is that there is either zero or a negative correlation between the corridors and migratory networks. The alternative hypothesis predicts a positive correlation. Data and Method 2.1 Data Collection Female elk were fitted with Global Positioning System (GPS) radio-collars during in various locations across the eastern Greater Yellowstone Ecosystem. These elk were captured in Grand Teton National Park, National Elk Refuge, Buffalo Valley (Barbknecht et al. 2011), Yellowstone National Park, and Gallatin National Forest (Creel

94 93 et al. 2005). Capture activities were approved by Wyoming Game and Fish Department and Iowa State University Animal Care and Use Committee (Protocol # ). Locational data were collected at a rate of 3-48 points a day, providing a minimum of an 8 hour fix interval. GPS collar data was classified by month to determine which elk sampled had separate winter (January-March) and summer (June-August) ranges. Overlapping ranges of separate individuals were merged into population ranges. These served as the habitat patches in each connectivity model. The points outside these ranges were delineated into line shape files based on individual elk, location, and time. Kernel density of these lines or networks were calculated for the full extent of all sampled points in a population. Two populations were removed from analysis due to discrepancies in the point data not allowing for generation of the networks and density properly. A total of eleven final populations were delineated for analysis. Number of individuals in population samples ranged from two to six. 2.2 Resistance Surface Delineation Two cost raster surface was developed using spatial data for landcover and human infrastructure. The reclassification values were based on the system designed for CorridorDesigner s elk tutorial dataset (Majka et al 2010). Landcover was used to delineate potential habitat and unsuitable habitat as an energy cost to movement. Human structures included roads representing cost to movement as potential lethality. The energy cost was normalized as an ASCII raster on a 0 to 100 scale with o representing the lowest cost and 100 the most. The potential lethality surface was normalized as an ASCII raster

95 94 on a 0 to 50 scale representing and increasing chance of lethality the nearer to human activity.

96 Figure 1: Energy Cost resistance surface 95

97 Figure 2: Lethality resistance surface 96

98 Patch Delineation Habitat patches were mapped by identifying areas of distinct summer and winter ranges for distinct populations. Using GPS collar data, a total of thirteen populations were delineated by distinguishing distinct groups based on overlapping ranges. Summer and winter ranges were identified by separating GPS data based on Month. Months of distinct winter range were determined as January, February, and March. The distinct summer months were June, July, and August. The remaining dates were considered migratory months. Number of elk used in mapping these populations and size of summer and winter ranges varied from two to six

99 Figure 3: Location of sampled populations used in PATH connectivity models

100 Agent based Modeling Each pair of ranges for a population and the cost surface were used as input for the PATH agent based model in NetLogo used to delineate the corridor maps, as a raster for each population. 2.5 Migratory Network Delineation The migratory data was used to delineate networks of elk movement outside of the summer and winter ranges. Kernel density was calculated for the linear networks of all elk monitored with distinct summer/winter ranges in each population. All data for kernel densities and the PATH corridors were compiled as a csv table using R. This table consisted of location related values for each surface. Using SPSS, I ran a correlations test between each PATH corridor and each kernel density surface. 2.6 Testing for Autocorrelation To check for autocorrelation of the migratory networks and the PATH corridor models based on the summer and winter ranges, I extracted values from the each PATH corridor based on the networks and the least cost path between the ranges. To do this I had to extract values from the PATH corridor maps for each population based on the network of movement and the least cost path between the ranges for each elk. Each elk s network was masked by the ranges, leaving only the migratory network. This was converted to a single value raster. A least cost path model was run to identify the shortest path(s) through each network. These served as Network Least Cost Paths (LCPN). The intersection of each of these with summer and winter ranges was also identified and extracted to serve as nodes for a simple least cost path model. Least cost paths were

101 100 found for each pair of summer and winter crossing points for each elk. These served as a Landscape Least Cost Paths (LCPL). I then ran a t-test for significant difference between the extracted values. The correlation values were also represented on a scatterplot to determine if there was a relationship between distance between ranges and correlation.

102 Figure 4: Example of least cost paths using the migratory networks and the landscape resistance surfaces. 101

103 102 To assure that the t-test results were not merely a result of the means, distribution was analyzed using a paired sample Kolmogorov Smirnov (K-S) test. The extracted values were analyzed for differentiation from normal distribution. Histograms of LCPN and LCPL could then be compared for similarity based on their distribution. Results 3.1 Correlation Only three of the populations (1, 7, and 8) showed a significant positive correlation between PATH models and density of networks. Five of the populations did not produce a corridor. Populations 2, 4, 12, and 13 had significantly negative correlations. Populations 12 and 13 had relatively near summer and winter ranges without corridors. Population 2 s network had supplementary movement to the north that was not predicted by the corridor. The corridor also predicted a route separate from the major network movements. Overall, correlations decreased with distance between ranges. Population 6 s major corridor avoided a reservoir like the network. Population 1 s corridors predicted movement similar to the networks in two routes but dominance was switched from north to south. Population 8 overestimated the corridor. Population 7 had the highest correlation predicting two routes.

104 Figure 5: Population 1 kernel density of migratory networks (left) and PATH map (right) 103

105 Figure 6: Population 2 kernel density of migratory networks (left) and PATH map (right) 104

106 Figure 7: Population 4 kernel density of migratory networks (left) and PATH map (right) 105

107 Figure 8: Population 5 kernel density of migratory networks (left) and PATH map (right) 106

108 Figure 9: Population 6 kernel density of migratory networks (left) and PATH map (right) 107

109 Figure 10: Population 7 kernel density of migratory networks (left) and PATH map (right) 108

110 Figure 11: Population 8 kernel density of migratory networks (left) and PATH map (right) 109

111 Figure 12: Population 10 kernel density of migratory networks (left) and PATH map (right) 110

112 Figure 13: Population 11 kernel density of migratory networks (left) and PATH map (right) 111

113 Figure 14: Population 12 kernel density of migratory networks (left) and PATH map (right) 112

114 Figure 15: Population 13 kernel density of migratory networks (left) and PATH map (right) 113

115 114 Table 1: Correlation coefficients by population Pearson s Population r Autocorrelation and Least Cost Paths The t-test of LCPN and LCPL values returned a p-value of This concludes that there is a statistically significant difference between LCPN and LCPL. It suggests that the PATH corridor values correlation with migratory networks is not simply a result of autocorrelation. The paired K-S test showed that distributions of LCPN and LCPL values were independent of each other with a p-value of Distribution of values was abnormal. The values of LCPN and LCPL were skewed to the right because of the values of no use in the PATH model. Excluding this, extracted values were bimodal with relatively similar amounts of dominant and less dominant values from the PATH models. This suggests where there was correlation it was not simply from autocorrelation and that both dominant and less dominant routes in the corridors were observed. The high frequency of empty values plus the decreasing correlations suggests PATH performed poorly in covering migration between summer and winter ranges.

116 115 (a) (b) Figure 6: Distribution of values and deviation from normal distribution for (a) LCP L and (b) LCP N

117 Post hoc Analysis To determine whether the results were possibly due to a flaw in one set of data, each model was run with zero lethality, followed by zero energy-cost. Each run produced similar results of a large corridor encompassing most of the landscape. To determine if results could improve with a different resolution (Hargrove and Westervelt 2012), all surfaces were resampled to a 1000 m size. Each model produced the same general pattern except for population 6, producing one path following the main route shown in the kernel density of elk migration networks. Settings were then adjusted on the original resolution to determine the influence on results. Corridors took the same routes in a more restricted space when Initial energy-level was reduced. The same was true when maximum turning angle was increased. 4.2 Conclusions PATH performed poorly and was dependent on autocorrelation for any similarity to the migratory networks. Neither changing the resolution or the relative cost improved results. The available adjustments changed the restrictions but not the relative spatial distribution of corridors. It is not well suited to predicting or covering the migration of elk in the Greater Yellowstone Ecosystem. This does not exclude agent based models from connectivity modeling but shows need for improvement and better attention to species behavior. Due to the exploratory nature of the elk migrations, there may be a need to adjust a model such as PATH to record such movements.

118 117 References Barbknecht, A. E., Fairbanks, W. S., Rogerson, J. D., Maichak, E. J., Scurlock, B. M., & Meadows, L. L. (2011). Elk parturition site selection at local and landscape scales. The Journal of Wildlife Management, 75(3), Creel, S., Winnie Jr, J., Maxwell, B., Hamlin, K., & Creel, M. (2005). Elk alter habitat selection as an antipredator response to wolves. Ecology, 86(12), Hargrove, W. W., Hoffman, F. M., & Efroymson, R. A. (2005). A practical map-analysis tool for detecting potential dispersal corridors. Landscape Ecology, 20(4), Hargrove, W. W., & Westervelt, J. D. (2012). An Implementation of the Pathway Analysis Through Habitat (PATH) Algorithm Using NetLogo. In Ecologist-Developed Spatially-Explicit Dynamic Landscape Models (pp ). Springer US. Majka, D., Beier, P., & Jenness, J. (2010). Corridor designer ArcGIS toolbox tutorial.

119 118 APPENDIX C: COMPARING A LEAST COST CORRIDOR CONNECTIVITY MODEL TO THE MIGRATORY PATTERNS OF ELK SAMPLED IN THE GREATER YELLOWSTONE ECOSYSTEM Samuel N. Chambers 1, Howard R. Gimblett 2, David A. Christianson 2, Daoqin Tong 1 1 School of Geography and Development, 2 School of Natural Resources and the Environment. The University of Arizona, Tucson AZ, USA Author for correspondence: Samuel Norton Chambers Phone: schambers@ .arizona.edu

120 119 ABSTRACT Linkage Mapper is a tool used to map the least cost corridors on the landscape that wildlife would or do use linking patches of habitat. Migratory species such as elk traverse between such patches which serve as seasonal ranges. This study sought to use field collected data for the purpose of comparing migratory patterns and the Linkage Mapper model. With this, we hoped to measure the suitability of Linkage Mapper for covering and predicting the migratory movements of elk in the Greater Yellowstone Ecosystem. To conduct this analysis, GPS point data was converted to sequential networks for multiple populations of elk. The GPS data was also used to delineate the summer and winter ranges of each population. The kernel density of routes in the networks was measured for comparison to the corridors. The ranges served as the patches to be connected by corridors. A resistance surface was produced using reclassified landcover data for mapping habitat suitability and linear road data for human presence or obstruction to movement. Corridors were produced for eleven migratory elk populations. These corridors were compared to the migratory network density by measuring correlation. This was followed by a new method of measuring the influence of autocorrelation between the corridors and networks. Some of the models were then altered to test for suspected influences. This study shows that least cost corridors can predict the migratory movements between summer and winter ranges but only so much. It lacks the ability to predict exploratory movements that do not link ranges to each other. It also lacks the ability to account for all avoidance behaviors in the landscape, particularly in riparian areas.

121 120 Key Words: Linkage Mapper, elk, Yellowstone, migration, landscape connectivity, corridors Introduction Linkage Mapper, a Python script and ArcGIS tool, represents cost of movement, identifying optimal path between multiple habitat patches as a continuous surface corridor (McRae and Kavanagh 2011; Carroll et al. 2012). Like PATH, the raster surfaces are to represent cost, difficulty, or mortality risk but unlike PATH mortality cannot be modeled in a least cost corridor. Linkage Mapper was developed for the 2010 Washington Wildlife Habitat Connectivity Working Group statewide connectivity analysis (McRae and Kavanagh 2011). It can be used as a stand-alone tool or in combination with other available tools such as Circuitscape or extensions such as Barrier Mapper software and Climate Linkage Mapper (McRae et al. 2008; McRae 2012; McRae et al. 2012; Carroll et al. 2012; Nunez et al. 2013). It has been used to model for single or multi-species corridors for mammals of various sizes and habitat types (Carroll et al. 2012; Brodie et al. 2014). It has also been used for modeling corridors based on landscape condition (Kilbane 2013). This study seeks to find if there is a positive correlation between the corridors mapped by Linkage Mapper and the migratory movements of Elk in the greater Yellowstone ecosystem. The null hypothesis is that there is either zero or a negative correlation between the corridors and migratory networks. The alternative hypothesis predicts a positive correlation.

122 121 Data and Method 2.1 Data Collection Female elk were fitted with Global Positioning System (GPS) radio-collars during in various locations across the eastern Greater Yellowstone Ecosystem. These elk were captured in Grand Teton National Park, National Elk Refuge, Buffalo Valley (Barbknecht et al. 2011), Yellowstone National Park, and Gallatin National Forest (Creel et al. 2005). Capture activities were approved by Wyoming Game and Fish Department and Iowa State University Animal Care and Use Committee (Protocol # ). Locational data were collected at a rate of 3-48 points a day, providing a minimum of an 8 hour fix interval. GPS collar data was classified by month to determine which elk sampled had separate winter (January-March) and summer (June-August) ranges. Overlapping ranges of separate individuals were merged into population ranges. These served as the habitat patches in each connectivity model. The points outside these ranges were delineated into line shape files based on individual elk, location, and time. Kernel density of these lines or networks were calculated for the full extent of all sampled points in a population. Two populations were removed from analysis due to discrepancies in the point data not allowing for generation of the networks and density properly. A total of eleven final populations were delineated for analysis. Number of individuals in population samples ranged from two to six. 2.2 Cost Surface Delineation

123 122 A cost raster surface was developed using spatial data for landcover and human infrastructure. The reclassification values were based on the system designed for CorridorDesigner s elk tutorial dataset (Majka et al 2010). Landcover was used to delineate potential habitat and unsuitable habitat. Human structures included roads representing cost to movement. The sum of these cost individual surfaces was normalized as a 1 to 100 scale with 1 representing least cost to movement and 100, maximum cost.

124 Figure 1: Linkage Mapper resistance surface delineated using landcover and road data 123

125 Patch Delineation Habitat patches were mapped by identifying areas of distinct summer and winter ranges for distinct populations. Using GPS collar data, a total of thirteen populations were delineated by distinguishing distinct groups based on overlapping ranges. Summer and winter ranges were identified by separating GPS data based on Month. Months of distinct winter range were determined as January, February, and March. The distinct summer months were June, July, and August. The remaining dates were considered migratory months. Number of elk used in mapping these populations and size of summer and winter ranges varied from two to six.

126 Figure 2: Location of sampled populations used in Linkage Mapper connectivity models

127 Building Corridors Each pair of ranges for a population and the cost surface were used as input for the Linkage Mapper tool used to delineate the least cost corridors, as a continuous surface raster for each population. 2.5 Migratory Network Delineation The migratory data was used to delineate networks of elk movement outside of the summer and winter ranges. Kernel density was calculated for the linear networks of all elk monitored with distinct summer/winter ranges in each population. All data for kernel densities and the corridors were compiled as a table using R. This table consisted of location related values for each surface. Using SPSS, I ran a correlations test between each corridor surface and each kernel density surface. 2.6 Testing for Autocorrelation To check for autocorrelation of the migratory networks and the corridors based on the summer and winter ranges, I extracted values from the each corridor map based on the networks and the least cost path between the ranges. To do this I had to extract values from the corridor maps for each population based on the network of movement and the least cost path between the ranges for each elk. Each elk s network was masked by the ranges, leaving only the migratory network. This was converted to a single value raster. A least cost path model was run to identify the shortest path(s) through each network. These served as Network Least Cost Paths (LCPN). The intersection of each of these with summer and winter ranges was also identified and extracted to serve as nodes for a simple least cost path model. Least cost paths were found for each pair of summer and

128 127 winter crossing points for each elk. These served as a Landscape Least Cost Paths (LCPL). I then ran a t-test for significant difference between the extracted values. The correlation values were also represented on a scatterplot to determine if there was a relationship between distance between ranges and correlation. To assure that the t-test results were not merely a result of the means, distribution was analyzed using a paired sample Kolmogorov Smirnov (K-S) test. The extracted values were analyzed for differentiation from normal distribution. Histograms of LCPN and LCPL could then be compared for similarity based on their distribution. Results 3.1 Correlation All populations showed a significant positive correlation between corridor values and network density. Population 2 s corridor model did not cover supplementary movement in the north. It also predicted a slightly more northerly corridor than the dominant network. Population 7 had the highest correlation predicting two routes like the migratory networks. Population 6 s corridors avoided a reservoir like the networks. Correlation stayed relatively constant with increasing distance between summer and winter ranges although the highest correlation values involved the nearest ranges. 3.2 Autocorrelation and Least Cost Paths The t-test of LCPN and LCPL values returned a p-value of This concludes that there is a statistically significant difference between LCPN and LCPL. It suggests that the corridor values correlation with migratory networks is not simply a result of autocorrelation.

129 128 (a) (b) Figure 3: Distribution of values and deviation from normal distribution for (a) LCP L and (b) LCP N

130 129 The paired sample K-S test gave a p-value of showing no correlation of distribution between LCPN and LCPL values. Distribution of values in LCPN and LCPL were both bimodal but skewed to the left with corridor values of importance. This is especially true with LCPL which follows the central least cost path of the corridor. The wider distribution of the LCPN values shows the coverage missed or underestimated by the corridors.

131 Figure 4: Example of least cost paths using the migratory networks and the landscape resistance surface. 130

132 131 Conclusions Although the migratory network of population 13 crosses South Rim into a separate watershed called the Noble Basin, the corridor predicts a following of Beaver Creek tributaries with differing routes and entry and exit points. An inspection of aerial imagery, the gap analysis layer, and landownership shows more federal lands (Bridger- Teton National Forest), fewer wetlands, and less agriculture in the migratory networks compared to the corridor. Overlaying additional GPS collar data points from nonmigratory elk reveals that the agricultural lands do in fact support elk populations. An inspection of the corridor shows it generally follows the pattern of low resistance surface values surrounded by high resistance surface values. These values are the result of preferred grasslands intermixed with lesser valued wetland landcover. Both migratory elk and the non-migratory elk sampled had avoided this checkered landscape. Linkage Mapper did not avoid this landscape but funneled through the lower resistance cells of the grasslands.

133 Figure 5: Population 1 kernel density of migratory networks (left) and corridor map (right) 132

134 Figure 6: Population 2 kernel density of migratory networks (left) and corridor map (right) 133

135 Figure 7: Population 4 kernel density of migratory networks (left) and corridor map (right) 134

136 Figure 8: Population 5 kernel density of migratory networks (left) and corridor map (right) 135

137 Figure 9: Population 6 kernel density of migratory networks (left) and corridor map (right) 136

138 Figure 10: Population 7 kernel density of migratory networks (left) and corridor map (right) 137

139 Figure 11: Population 8 kernel density of migratory networks (left) and corridor map (right) 138

140 Figure 12: Population 10 kernel density of migratory networks (left) and corridor map (right) 139

141 Figure 13: Population 11 kernel density of migratory networks (left) and corridor map (right) 140

142 Figure 14: Population 12 kernel density of migratory networks (left) and corridor map (right) 141

143 Figure 15: Population 13 kernel density of migratory networks (left) and corridor map (right) 142

144 143 The results in population 13 suggested a possibility that the unclustered or checkered pattern in the resistance surface decreased Linkage Mapper s performance. To test this, a Moran s I value was calculated for all populations. This value was compared to the correlation or performance of each population s corridor to density of migratory networks using linear regression. This was also performed excluding the outlier, population 2. The first regression analysis gave an R Square value of 0.022, showing no recognizable linear relationship between the model performance and the level of clustering. If the two were related, there would be a positive linear pattern of increasing Moran s I with increasing performance. Without population 2, the R Square was 0.273, a higher value but still not fitted. This suggests that the low correlation in population 13 or any decrease in correlation in other populations is not a result of the checkered pattern or heterogeneity of the landscape or resistance surface. Table 1: Pearsons correlation coefficient and Moran s I values by population Population Pearson s r Moran's I

145 144 To test whether the corridor could be improved with reclassification, the checkered area of high and low values was reclassified to a single value corresponding to the wetlands rather than the grasslands. The resulting corridor took a route south of the wetland area rather than the more northerly route taken by the elk migratory networks. Figure 6: Corridor map of population 13 reclassified to remove high quality habitat from checkered landscape of low quality habitat wetlands There is the question of whether the elk are basing migratory movements on knowledge of the landscape and decisions that weren t taken into account. Animals may respond to coarser-grained cues in the landscape when migrating (Hargrove and Westervelt 2012).

146 145 An examination of population 1 which had a significant correlation of 0.308, shows that although elk migratory networks were observed in the areas of highest corridor values, this was not the primary route of the corridor. The primary route was further to the northeast following the Gallatin River, rather than running perpendicular to its tributaries. Points of entry and exit are closer to the Gallatin River also. This suggests a possible influence of slope which was not included in the resistance surface. The migratory networks of population 4 with a correlation show movement following the west side of a lake while Linkage Mapper shows a corridor running along the east side, both flats in Grand Teton National Park. Population 5 produced corridors on both sides of the same river. There are more tributaries along the east side of the lake. Elk may take both routes but this is an area for closer in the field observation to explain differences outside readily available landcover data. Population 5 produced corridors running through multiple lakes, including Jackson Lake, while the migratory networks followed Pacific Creek. The highest value corridor runs even further to the west. This suggests a need for making large bodies of water non-traversable in the model and the need for additonal factors.

147 Figure 7: Population 5 kernel density of migratory networks (left) and current map (right) 146

148 147 Acknowledgments References Barbknecht, A. E., Fairbanks, W. S., Rogerson, J. D., Maichak, E. J., Scurlock, B. M., & Meadows, L. L. (2011). Elk parturition site selection at local and landscape scales. The Journal of Wildlife Management, 75(3), Brodie, J. F., Giordano, A. J., Dickson, B., Hebblewhite, M., Bernard, H., MOHD AZLAN, J. A. Y. A. S. I. L. A. N.,... & Ambu, L. (2014). Evaluating multispecies landscape connectivity in a threatened tropical mammal community. Conservation Biology. Carroll, C., McRAE, B. R. A. D., & Brookes, A. (2012). Use of linkage mapping and centrality analysis across habitat gradients to conserve connectivity of gray wolf populations in western North America. Conservation Biology, 26(1), Creel, S., Winnie Jr, J., Maxwell, B., Hamlin, K., & Creel, M. (2005). Elk alter habitat selection as an antipredator response to wolves. Ecology, 86(12), Hargrove, W. W., & Westervelt, J. D. (2012). An Implementation of the Pathway Analysis Through Habitat (PATH) Algorithm Using NetLogo. In Ecologist-Developed Spatially-Explicit Dynamic Landscape Models (pp ). Springer US. Kilbane, S. (2013). Green infrastructure: planning a national green network for Australia. Journal of Landscape Architecture, 8(1), Majka, D., Beier, P., & Jenness, J. (2010). Corridor designer ArcGIS toolbox tutorial. McRae, B. H., Dickson, B. G., Keitt, T. H., & Shah, V. B. (2008). Using circuit theory to model connectivity in ecology, evolution, and conservation. Ecology, 89(10), McRae, B. H., & Kavanagh, D. M. (2011). Linkage Mapper Connectivity Analysis Software. Seattle, WA: The Nature Conservancy. McRae, B. H., & Kavanagh, D. M. (2012). Barrier Mapper Connectivity Analysis Software. Seattle, WA: The Nature Conservancy. McRae, B. H., Hall, S. A., Beier, P., & Theobald, D. M. (2012). Where to restore ecological connectivity? Detecting barriers and quantifying restoration benefits. PloS one, 7(12), e Nuñez, T. A., Lawler, J. J., Mcrae, B. H., PIERCE, D., Krosby, M. B., Kavanagh, D. M.,... & Tewksbury, J. J. (2013). Connectivity planning to address climate change. Conservation Biology, 27(2),

149 148 APPENDIX D: FINDING PINCH POINTS IN THE MIGRATORY PATTERNS OF ELK IN THE GREATER YELLOWSTONE ECOSYSTEM Samuel N. Chambers 1, Howard R. Gimblett 2, David A. Christianson 2, Daoqin Tong 1 1 School of Geography and Development, 2 School of Natural Resources and the Environment. The University of Arizona, Tucson AZ, USA Author for correspondence: Samuel Norton Chambers Phone: schambers@ .arizona.edu ABSTRACT

150 149 The Circuitscape tool is used to map the places in the landscape that wildlife would or do use linking patches of habitat. It does this by modeling the landscape as a circuit with flows of current from random walkers serving as the wildlife. Migratory species such as elk traverse between such patches which serve as seasonal ranges. Circuitscape produces pinch points or narrow corridors individuals may be required to traverse. This study sought to use field collected data for the purpose of finding actual pinch points in the migratory patterns and compare this to the Circuitscape model. With this, the study seeks to determine if there are likely places elk are funneled into or out of in the Greater Yellowstone Ecosystem and how they compare to the predictions of circuitscape. To conduct this analysis, GPS point data was converted to sequential networks for multiple populations of elk. The GPS data was also used to delineate the summer and winter ranges of each population. The sum of intersections determined these pinch points. The ranges served as the patches to be connected in the current maps. A resistance surface was produced using reclassified landcover data for mapping habitat suitability and linear road data for human presence or obstruction to movement. Current maps were produced for seven migratory elk populations. Circuitscape s pinch points were extracted from a reclassified current map. This study shows that although the pinch points are similar in composition, the Circuitscape model does not correctly identify the locations of the actual pinch points of elk. Key Words: Pinch points, Circuitscape, elk, Yellowstone, migration, landscape connectivity

151 150 Introduction The concept of pinch points is a major factor in the use of Circuitscape in mapping landscape connectivity. Circuitscape is a Java software package and ArcGIS tool that uses raster habitat data to produce a matrix of resistance distances among population pairs by representing range maps as graphs, replacing habitat cells with nodes and connecting adjacent nodes with resistors (McRae and Beier 2007). The program calculates resistance distances though nodal analysis, a circuit analysis algorithm that applies Kirchhoff s current law in the form of a matrix (Dorf and Svoboda 2010). Circuitscape has been particularly useful in modeling gene flow in relation to the landscape. It was used for evaluating the effect of habitat and landscape characteristics on population genetic structure in white-footed mice (Marrotte et al. 2014). The model also revealed regionally variable gene flow patterns across the Cope s giant salamander range (Trumbo et al. 2013). Circuitscape was used to show the difference in gene flow and effects of habitat fragmentation separate species of honeyeater birds (Harrisson et al. 2014). This suggests Circuitscape does not work well for all species. In an analysis of the effects of forest management on American martens, it was concluded Euclidean distance better described gene flow than effective distance modeled by circuit theory (Koen et al. 2012). Although it is most desirable to model connectivity across a single surface representing an entire landscape, Circuitscape has been shown as useful in mosaics of overlapping

152 151 high resolution tiles representing portions of the landscape (Pelletier et al. 2014). This was especially useful in identifying pinch points which are narrow corridors individuals may be required to traverse (Pelletier et al. 2014) or constrictions in corridors that could sever connectivity entirely, if lost (Cushman et al. 2013) or areas where alternative pathways are not available (Dickson et al. 2013) or features through which dispersing individuals have a high likelihood (or necessity) of passing (McRae et al. 2008). Pinchpoints can be the result of both natural features and human-altered landscape and their loss can disproportionately disrupt connectivity (Dickson et al. 2013). Crossvalidation has shown the general validity of Circuitscape models in identifying connectivity of an urban landscape for European hedgehogs with pinch points and other habitat connections (Braaker et al. 2014). McRae (et al. 2008) suggested that metrics combining predictions of efficient travel paths, pinch points, and mortality risks could plan for connectivity while minimizing mortality. While there have been comparative analysis of gene flow and Circuitscape there is little comparative analysis of Circuitscape and the actual movements of animals. There is also little research into the pinch points or constrictions of movement. This study seeks to find whether pinch points exist in the migratory patterns of elk and if Circuitscape correctly identifies them. Data and Method 2.1 Data Collection Female elk were fitted with Global Positioning System (GPS) radio-collars during in various locations across the eastern Greater Yellowstone Ecosystem. These elk

153 152 were captured in Grand Teton National Park, National Elk Refuge, Buffalo Valley (Barbknecht et al. 2011), Yellowstone National Park, and Gallatin National Forest (Creel et al. 2005). Capture activities were approved by Wyoming Game and Fish Department and Iowa State University Animal Care and Use Committee (Protocol # ). Locational data were collected at a rate of 3-48 points a day, providing a minimum of an 8 hour fix interval. GPS collar data was classified by month to determine which elk sampled had separate winter (January-March) and summer (June-August) ranges. Overlapping ranges of separate individuals were merged into population ranges. These served as the habitat patches in each connectivity model. The points outside these ranges were delineated into line shape files based on individual elk, location, and time. Six populations were removed from analysis due to similarity in migratory patterns not allowing for generation actual pinch points. A total of seven final populations were delineated for analysis. Number of individuals in population samples ranged from two to ten. 2.1 Resistance Surface A cost raster surface was developed using spatial data for landcover and human infrastructure. The reclassification values were based on the system designed for CorridorDesigner s elk tutorial dataset (Majka et al 2010). This resistance surface as input for the connectivity models. Landcover was used to delineate potential habitat and unsuitable habitat. Human structures included roads representing cost to movement. The sum of these cost individual surfaces was normalized as a 1 to 100 scale with 1 representing least cost to movement and 100, maximum cost.

154 Patch Delineation Habitat patches were mapped by identifying areas of distinct summer and winter ranges for distinct populations. Using GPS collar data, a total of thirteen populations were delineated by distinguishing distinct groups based on overlapping ranges. Summer and winter ranges were identified by separating GPS data based on Month. Months of distinct winter range were determined as January, February, and March. The distinct summer months were June, July, and August. The remaining dates were considered migratory months. Number of elk used in mapping these populations and size of summer and winter ranges varied from two to six. 2.3 Circuitscape Pinch Points Each pair of ranges for a population and the cost surface were used as input for the Circuitscape tool to delineate current maps, as a continuous surface raster for each population. These current maps were reclassified by Natural Jenks (DeSmith et al. 2007). The top tenth jenk of raster cells identified the circuitscape pinch points (CSPP). This uses Pelletier s (et al. 2013) suggestion for comparison by using a brightness-based assessment using the highest current values from histograms. Such pinch points take a similar shape and size to that of the Migratory pinch points (MPP). 2.4 Migratory Pinch Point Delineation The migratory data was used to delineate networks of elk movement outside of the summer and winter ranges. Points were converted to lines for individual elk based on the date and time of each point. These linear networks were converted from line to raster form and classified by individual with each elk s raster cells equaling a value of one. The

155 154 sum total by population was used to identify MPP. If 50% or greater of the individuals crossed a location, the raster cells identified a pinch point. 2.5 Analysis CSPP and MPP were compared based on similarity of locations and landcover. The immediate surroundings of pinch points were also compared by the use of 30 meter or one cell buffers. MPP were further analyzed using 15m imagery to identify specific landscape features not evident in landcover data. Results 3.1 Pinch Point Location MPP and CSPP overlapped by 0.87%. Distance between each varied by a range of zero to 6,024.7 km with a mean of 1,157.3 km and a standard deviation of 1,820.6 km. The landcover values for MPP and CSPP were similar in composition but MPP had a greater variety in cover types. The cover types not found in CSPP but in MPP only accounted for 1.81% of the total cover types in MPP. The immediate surroundings of pinch points had a similar distribution of values to the pinch points themselves. Table 1: Percentage of landcover type in MPP and CSPP Landcover MPP Surroundings CSPP Surroundings Agricultural Vegetation 4.91% 4.36% 1.19% 2.58% Developed & Other Human Use 1.23% 1.47% Forest & Woodland 37.79% 38.89% 35.89% 26.57% Introduced & Semi Natural Vegetation 0.05% 0.10% Nonvascular & Sparse Vascular Rock Vegetation 0.01% 0.01% Open Water 0.06% 0.07% Polar & High Montane Vegetation 0.12% 0.21% Recently Disturbed or Modified 0.35% 0.33% Semi-Desert 50.14% 47.55% 59.54% 63.79%

156 155 Shrubland & Grassland 5.35% 7.02% 3.38% 7.07% Population 2 MPP showed elk weaving between forests and grasslands adjacent to a large creek while the CSPP was atop a forest ridge adjacent to a smaller tributary. The use of Developed and Other Human Use landcover was most prevalent in population 3 where elk converged in and around a golf course and housing development while Circuitscape predicted pinch points within Grand Teton National Park. The elk sampled in population 3 especially converge on the lawns of houses and other buildings. MPP are not as frequent on most of the golf course as the elk are more dispersed compared to the area near buildings. MPP were found north of the Gros Ventre River while the CSPP predicted areas south of the river.

157 156 Figure 1: Comparison of CSPP and MPP locations in population 3 Population 7 MPP were relatively near some of the CSPP in the arid landscape but overall didn t predict the majority of them in forest and grassland areas within Bridger National Forest. MPP were found between and adjacent to lakes in population 8 while the CSPP showed a less linear pattern further from the lakes. Population 10 showed a similar pattern with more elk following the tributaries. Population 11 showed general similarity in location and cover but little overlap. There are fewer roads evident near the MPP suggesting less influence than what the model accounts for in Circuitscape. The CSPP of population 13 are found mostly within semi-desert and shrublands intermixed with