MODELING THE SPATIAL AUTOCORRELATION OF PELAGIC FISH CATCH RATES Kristin Kleisner David Die John F. Walter, III
Spatial Geostatistics and Fisheries Typically use geostatistics for sessile species habitat modeling Can we use these techniques for pelagic species? These fish are very mobile and migratory Some exhibit schooling behavior Not closely associated with permanent structures such as reefs Makes pelagic fish difficult to study and understand
Goals of Work To quantify spatial autocorrelation in pelagic fish catch rates To explore whether observed patterns of spatial autocorrelation reflect physical or oceanographic processes related to habitat preference
Extent of the Pelagic Longline in the western Atlantic Logbook and Pelagic Observer Data for all years
Spatial Autocorrelation What is it? Correlation of a variable with itself through space. Positive spatial autocorrelation: nearby areas more alike No spatial autocorrelation: random Most ecological data exhibit spatial autocorrelation
Methods to estimate spatial Geostatistical Approach autocorrelation Model-based: variogram model Allows spatial prediction via kriging Reduces bias in clustered observations To account for spatial autocorrelation or predict abundance, need some way to fill in areas without observations
Variogram Explains degree of spatial dependence in a random field Sill: Sample variance Semiv variance Range: Distance beyond which samples are independent Nugget Effect: Represents smallscale data variability or sampling errors Distance
Focused on range parameter: Measure of spatial predictability of abundance in a given location May be related to the specific habitat preference of individual species 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Short range = Less predictable Z 25 30 Long range = More predictable 10 15 20 Z 0 5 0 5 10 15 20 25 30
Variogram Calculation Programmed using GeoR library in R (open source programming language) Spherical models Robust variogram estimator Max distance of 400 and a lag of 30 Vessel captains record data from different sets in same location Treated duplicate observations by selecting first observation Species: Bigeye Tuna, Swordfish, Yellowfin Tuna, Dolphinfish, and Wahoo Variograms calculated for Sea Surface Temperature (SST)
Ecological og ca abundance Product of two processes: Yellowfin tuna CPUE by year and season 1. Frequency of occurrence 2. Abundance given occurrence
More appropriate to model each process separately Variogram of two processes: 1. Frequency of occurrence (presence / absence) 2. Abundance given occurrence (positive observations).22 0.20 0. variance semiv 0.18 0.16 0.70 0.60 0.65 riance semivar 0.50 0.55
A Priori Standardization Various factors (bait type, attractants, rigging) affect catch rates. Variograms calculated from GLM residuals Analogous to removing trend or to incorporating known predictors
1987 range= 200 1988 range= 81 1989 range= 141 1990 range= 79 semivariance 5 0.35 semivariance 0.20 0.26 0.32 semivariance 0.10 0.20 semivariance 0.15 0.30 1991 1992 1993 1994 0.20 0.30 0.40 0 0.25 semivariance 0.10 0.25 0.40 semivariance 0.15 0.30 0.45 range= 77 range= 200 range= 131 semivariance 0.20 0.30 0.40 semivariance 1995 1996 1997 range= 107 1998 semiva ariance 0.10 0.25 0.40 semiva ariance 0.10 0..25 0.40 semiva ariance 0.10 0.25 0.40 semiva ariance 0.15 0.30 range= 110 range= 200 range= 161 1999 2000 2001 2002 range= 68 range= 84 range= 53 range= 127 range= 218 semivariance 0.25 0.35 semivariance 0.20 0.30 0.40 0 semivariance.25 0.35 semivariance 0.10 0.25 2003 0 50 150 250 2004 0 50 150 250 2005 0 50 150 250 semivarian nce semivarian nce 0.25 0.35 semivarian nce 0.20 0.30 range= 82 range= 200 range= 200 0 50 150 250 0.20 0.30
Distribution of Ranges By Species ANOVA showed significant differences between ranges by species (p<0.001, α=0.01) Posthoc test showed two groupings g Deep vs. Shallow Dolphinfish Wahoo Yellowfin Tuna SST Bigeye Swordfish 0 50 100 150 200 250 Range (Km)
Swordfish Depth Distribution m) Depth (m Dolphinfish Depth Distribution http://www.soest.hawaii.edu/pfrp/dec03mtg/brill_swordfish.pdf Time of Day (H) De epth (m) http://dolphintagging.homestead.com/dolphinsattagstdycompltnrpt_6-06.pdf
50 DE PTH (m) 0 10 20 30 40 50 Dolphinfish http://dolphintagging.homestead.com/dolphinsattagstdycompltnrpt_6-06.pdf Yellowfin Tuna 150 Brill, R., B. Block, C. Boggs, K. Bigelow, E. Freund, and D. Marcinek. 1999. Bigeye Tuna 600 Musyl, M.K., R.W. Brill, C.H. Boggs, D.S. Curran, T.K. Kazama, and M.P. Seki. 2003.
Processes Affecting Distribution Frontal regions Two water masses of different density converging Concentrates tiny organisms and flotsam Trophic bloom Larger organisms attracted to prey and shelter at convergent zone Everything is patchy in the ocean at some scale
Processes Affecting Distribution Structure of Fronts Defined by Rossby Radius of Deformation Defines the length scale at which there is heterogeneity of water masses A smaller Rossby radius = more variability 25-30 in the Gulf of Mexico, 40 in the mid-atlantic gyre At surface Depth or Height Gravity*Difference in density across thermocline e R d = d ( g' H f 0 ) Coriolis Parameter
Rossby Radius at Depth Because Rd is proportional to depth, it is intuitive that at a deeper depth, the Rossby radius will be greater Species that dwells in the surface layers of the water will be subject to greater heterogeneity of the water masses than a species at depth.
TEMPERATURE RANGE OF AUTOCORRELATION Dolphinfish 50 DE PTH (m) 150 Radius Increas sing Ro ossby Wahoo Yellowfin Tuna SST Bigeye Swordfish 600 4 8 12 16 20 24 C 0 50 50 100 100 150 150 200 200 250 250 KM
Relevant Scales Ecological Scale: Average range of shallow species = 55 Average range of deep species = 135 Sampling Scale: Average range of longline = 30 Oceanographic Scale: Rossby Radius of Deformation = 25-30
Why explore spatial autocorrelation? Can use kriging to map the spatial abundance of species in the study location Provides a means to predict abundance in locations where no observations occur Walters, 2006 Spatial abundance allows for visual and geostatistical analysis of environmental correlations
What is the benefit of a spatial index? Can account for spatial variability in a system that is due to dynamics of the fish or the fishery Not straightforward to delineate the cause MULTIFAN assessments require spatially and seasonally-structured indices Used heavily in Pacific fisheries i Parameterization is typically problematic
1998 Range=65 Range=52 Scattered Fishing Effort/ Shorter Autocorrelation Ranges Range=60 Range=65
2004 Range=126 Range=141 Clustered Fishing Effort/ Longer Autocorrelation Ranges Range=144 Range=166
Conclusions The degree of spatial autocorrelation has impact on indices of abundance Clustered observations of catch Spatial autocorrelation in a system should be addressed when attempting to derive robust indices of abundance. Accounting for spatial variability may prevent bias in the CPUE index if there is a longer range of autocorrelation and clustered catches in an area.
Conclusions There is a need for EMB and analyses that incorporate spatial structure Failing to account for spatial structure can lead to different results Results may be biased or incorrect! Geostatistics provides a means of visually interpreting abundance patterns and filling in areas with no observations
Acknowledgements FUNDING: Fisheries and the Environment (FATE) National Marine Fisheries Service National Science Foundation (NSF) Biocomplexity (Olson et al.) and Florida Straits Billfish Project (Cowen et al.) David Die Beth Babcock Andy Bakun Arthur Mariano Don Olson Josh Sladek Nowlis Jiangang Luo Edward Ryan Geoff Samuels Steve Smith Liz Brooks Craig Brown Guillermo Diaz John Lamkin Mauricio Ortiz Clay Porch Steve Turner
Questions?