Stat 534 Philip Dixon Fall References: Estimating Population Parameters: Closed and Open populations

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1 Stat 534 Philip Dixon Fall 2017 References: Estimating Population Parameters: Closed and Open populations Population Biology: Vandermeer, J.H. and Goldberg, D.E Population Ecology: First Principles. Princeton University Press, Princeton, NJ. Silvertown, Jonathan W. and Deborah Charlesworth Introduction to plant population biology, 4th ed. Blackwell Scientific Publications, Cambridge, MA. two introductory biological texts, cover much more biology than what we look at. Thompson, W. L., White, G. C. and Gowan, C Monitoring vertebrate populations. Academic Press, San Diego. General introduction to the biology and statistics of monitoring. Gitzen, R.A., Millspaugh, J.J., Cooper, A.B., and Licht, D.S Design and Analysis of Long-term Ecological Monitoring Studies. Cambridge Univ. Press, Cambridge UK. If you do monitoring, this is the book to have. Covers from the basics to the detailed. Statistical Theory (introductions for biologists): Hilborn, R. and Mangel, M The ecological detective: confronting models with data. Princeton Univ. Press, Princeton NJ. Still my favorite non-technical summary of different philosophical approaches. Chapter 7 is a simple? introduction to maximum likelihood White, G. C., D. R. Anderson, K. P. Burnham, D. L. Otis Capture-recapture and removal methods for sampling closed populations. Los Alamos National Lab, LA-8787-NERP. Chapter 2 is an introductory discussion of statistical concepts, including ml estimation. Borchers, D.L., Buckland, S.T. and Zucchini, W Closed Populations. Springer, New York. Estimating Animal Abundance: Chapter 2 is a review of ml estimation (one of the assigned readings). Chapter 6 is an introduction to mark-recapture. Texts / Monographs: Amstrup, S.C., McDonald, T.L, and Manly, B.F.J Handbook of Capture-Recapture Analysis. Princeton Univ. Press, Princeton NJ Edited volume. source of many of this year s readings. Includes detailed presentation of using program MARK to fit models. 1

2 Buckland, S.T. and Morgan, B.J.T year anniversary of papers by Cormack, Jolly and Seber. Special issue of Statistical Science 31(2) Collection of papers celebrating the 50 th anniversary of the Cormack, Jolly and Seber open population model papers. Includes conversations with Cormack and Seber. McCrea, R.S. and Morgan, B.J.T Analysis of Capture-Recapture Data. CRC Press, Boca Raton Fl. Concise intermediate-level treatment of classical and modern approaches. Summarizes a huge amount of literature. Otis, David, K. Burnham, G. White, and D. Anderson, Statistical inference from capture data on closed animal populations. Wildlife Monographs # 62. Classic reference on estimation for Mt, Mh, Mb models and their generalizations. Includes complete examples; mathematical details are in the appendices. Pollock, K. H., Nichols, J. D., Brownie, C. and Hines, J. E Statistical inference for capture-recapture experiments. Wildlife Monographs # 107. Comprehensive overview of Jolly-Seber and related techniques for open populations, including robust design. Includes short summary of methods for closed populations. Royle, J.A., Chandler, R.B., Solliman, R., and Gardner, B Spatial Capture-Recapture. Academic Press, Waltham MA. Textbook covering spatially explicit CR from simple to advanced (landscape connectivity, resource selection) and super-advanced (spatial mark-resight, telemetry) Seber, G. A. F The estimation of animal abundance and related parameters, 2nd ed. Oxford Univ. Press. Pulls together the early literature for both closed and open populations. Thompson, D.L., Cooch, E.G., and Conroy, M.J Modeling Demographic Processes in Marked Populations. Springer. Combining population models with mark-recapture (etc.) data. Williams, B.K., Nichols, J.D., Conroy, M.J Analysis and Management of Animal Populations: Modeling, Estimating, and Decision Making. Academic Press Compendium of lots of different approaches for quantitative wildlife management, ranging from mark-recapture to linear programming and decision making. Huge book, but treatment of individual topics is very lean just-the-facts style. Closed population models: Chapman, D. G Some properties of the hypergeometric distribution with applications to zoological censuses. Univ. California Publications in Statistics 1: Derives the approximately unbiased version of the hypergeometric model estimator and its variance. 2

3 Hammond, E.L. and Anthony, R.G Mark-recapture estimates of population parameters for selected species of small mammals. Journal of Mammology 87: Analyzes 1535 data sets from 33 spp of mammals using the standard models to look for general patterns across species (e.g. find heterogeneity in capture probabilities in larger data sets for any species). Huggins, R. M Some practical aspects of a conditional likelihood approach to capture experiments. Biometrics 47: The second, more accessible, of two papers on how to use individual covariates to model heterogeneity. Probably the best solution to heterogeneity if you can choose the right covariates. Jensen, A. L Confidence intervals for nearly unbiased estimators in single-mark and single-recapture experiments. Biometrics 45: ci s based on distribution of 1/ ˆN under binomial and hypergeometric models. Easy to compute. Pledger, S Unified maximum likelihood estimates for closed captuer-recapture models for mixtures. Biometrics 56: Central paper in a sequence by Pledger on mixtures to model between individual heterogeneity in capture probability Open population models: Abadi, F., A. Botha, R. Altwegg, Revisiting the Effect of Capture Heterogeneity on Survival Estimates in Capture-Mark-Recapture Studies: Does It Matter? PLOS One 8(4) Online: /journal.pone Uses simulation and case studies to assess the bias in survival arising from heterogeneity in capture probabilities. Finds a small negative bias that may greatly impact management decisions. Brooks, S.P., Catchpole, E. A. and Morgan, B. J. T Bayesian animal survival estimation. Statistical Science. 15: Review and summary of Bayesian approaches to estimation for open populations. Cubaynes, S. et al Importance of accounting for detection heterogeneity when estimating abundance: the case of French wolves. Conservation Biology 24: Develops a model that on quick inspection seems very similar to Pledger s (2011) open population heterogeneity model. Jolly, G. M Explicit estimates from capture-recapture data with both death and immigration stochastic model. Biometrika 52: Seber, G. A. F A note on the multiple recapture census. Biometrika 52: The two original papers on the Jolly-Seber model 3

4 Kendall, W. L., K. H. Pollock, and C. Brownie A likelihood-based approach to capture-recapture estimation of demographic parameters under the robust design. Biometrics 51: A full likelihood analysis of data from a robust design 4

5 Pledger, S., Pollock, K., and Norris, J Open capture-recapture models with heterogeneity. II. Jolly-Seber model. Biometrics 66: Applies Pledger s mixture model for heterogeneity to open populations. Considers heterogeneity in capture probability and heterogeneity in survival. Also considers the bias introduced by conditioning on first capture (the Cormack trick) when survival probability is not constant. Pollock, K.H A capture-recapture design robust to unequal probability of capture. J. Wildlife Management 46: The robust design is a way of combining open and closed population models to get the best of both. This is the most accessible early paper. Estimation is a combination of ml and ad-hoc. White, G.C., Kendall, W.L., and Barker, R.J Multistate survival models and the extensions in program MARK. J. Wildlife Management 70: Multistate models add another dimension to an individual. The state could be breeder/nonbreeder, or spatial area, or something else. This is a nice review of multistate models. Model Selection and Model Averaging: Barker, R.J. and Link, W.A Bayesian multimodel inference by RJMCMC: a Gibbs sampling approach. American Statistician 67: Introductory paper on Reversible Jump MCMC, probably the most appropriate way to switch between multiple models. Buckland, S.T., Burnham, K.P. and Augustin, N.H Model selection: an integral part of inference. Biometrics 53: Source of the non-bayesian model averaging presented in lecture. Can be used with AIC-derived weights, BIC-derived weights, or true Bayesian posterior model probabilities. Burnham, K. P. and D. R. Anderson, Model selection and inference: a practical information-theoretic approach. Springer-Verlag, New York. Section presents the AIC approach to model averaging. Section 2.2 and 2.4 discuss AIC and refinements. There is now a second edition, but I don t have a copy of it. Burnham, K. P. and D. R. Anderson, Multimodel inference - understanding AIC and BIC in model selection. Sociological Methods and Research 33: Lengthy comparison of AIC and BIC approachs. Partly theory, partly philosophy, partly practical. B&A argue that AIC and BIC are no more than different choices of prior probability of models. Cubaynes, S. C. Lavergne, E. Marboutin, O. Gimenez, Assessing individual heterogeneity using model selection criteria: how many mixture components in capture-recapture models? Method in Ecology and Evolution 3: Compares AIC, BIC and a more recent criterion, ICL, to choose the number of components in a mixture. AIC works slightly better than BIC. When it errs, it tends to choose more components than needed. ICL is biased. 5

6 McCrea, R. S. and B. J. T. Morgan, Multistate Mark-Recapture Model Selection Using Score Tests. Biometrics 67: Multistate models are mark-recapture models where individuals can change state, i.e. what region of the country they are in. Capture and survival parameters can vary among regions. This paper develops a simple model-selection procedure that does not require fitting a model, because it is based on a score test conducted at the null hypothesis. Stanley T. and Burnham K Estimator selection for closed-population capture-recapture. Journal of Agricultural Biological and Environmental Statistics. 3: Stanley T. and Burnham K Information-theoretic model selection and model averaging for closed-population capture-recapture studies Biometrical Journal. 40: Spatial Capture-recapture: Borchers, D.L. and Efford, M.G Spatially explicit maximum likelihood methods for capture-recapture studies. Biometrics 64: If traps are in known locations, you can estimate density (#/area), not just population size. Borchers, D.L A non-technical overview of spatially explicit capture-recapture models. Journal of Ornithology 152:S435-S444 A review of various CR models that incorporate spatial information Chandler, R. and Clark, J Spatially explicit integrated population models. Methods in Ecology and Evolution 5: Two data sources expensive spatial CR data and cheap occupancy data informing a spatial population dynamics model. Specialized Computer Programs: Program Mark: see its web page: and Gary White s page: gwhite/mark/mark.htm R-capture: An R library implementing log-linear models, a different probability model for capture-recapture data. Historically these models are associated with Cormack. A description is at: Baillargeon, S. and Rivest, L.-P. (2012). Rcapture: Loglinear Models for Capture-Recapture Experiments. R package version E-SURGE: French software for multievent SURvival Generalized Estimation Reference given is CHOQUET, R., ROUAN, L., PRADEL, R. (2009). Program E-SURGE: a software application for fitting Multievent models Series: Environmental and Ecological Statistics, Vol. 3 Thomson, David L.; Cooch, Evan G.; Conroy, Michael J. (Eds.) p , or see the web page: 6

7 Appendix G in Williams et al. is a tabulation of software and download sites. Other approaches: Alexander, H.M., A.W. Reed, W.D. Kettle, N.A. Slade, S.A.B. Roels, C.D. Collins, V. Salisbury, Detection and Plant Monitoring Programs: Lessons from an Intensive Survey of Asclepias meadii with Five Observers PLOS One 7(12). Online /journal.pone Five observers surveyed for patches of a rare plant in a burned and an unburned prairie. Detection probabilities varied by observer, whether patch was flowering, and patch size. 3-4 observers found 90-99% of plants; 1 or 2 observers had high error rates. Burnham, K. P. and Overton, W. S Estimation of the size of a closed population when capture probabilities vary among animals. Biometrika 65: Burnham, K. P. and Overton, W. S Robust estimation of population size when capture probabilities vary among animals. Ecology 60: Two papers describing the very first approach to heterogeneity, the jacknife estimator for the Mh model. Current sense is that more recent methods are better. Chao, A., Tsay, P., Lin, S., Shan, W., and Chao, D Tutorial in Biostatistics: The applications of capture-recapture models to epidemiological data. Statistics in Medicine 20: Using multiple lists to estimate sizes of human populations (e.g., infected with a particular disease). Conn, P.B., Kendall, W.L. and Samuel, M.D A General Model for the Analysis of Mark-Resight, Mark-Recapture, and Band-Recovery Data under Tag Loss Biometrics 60: One entry into a current research topic: how to account for tag loss. Ford, J. H., M.V. Bravington, J. Robbins, Incorporating individual variability into mark-recapture models Methods in Ecology and Evolution. 3: Develop a multi-state mark recapture model with individual random effects to account for heterogeneity in sighting rate or site preference. Requires special software, admb-re, an extension of AD Model Builder to approximate the integrated lielihood. Gazey, W. J. and Staley, M. J Population estimation from mark-recapture experiments using a sequential Bayes algorithm. Ecology 67: Develops a Bayesian approach to combine information from many sampling periods, each with a small number of recaptures. Haven t checked all the details, but I believe the sequential Bayes algorithm is similar to what is now known as the Gibbs sampler. 7

8 Gilroy, J.J., T. Virzi, R.L. Boulton, and J.L. Lockwood, 2012 A new approach to the apparent survival problem: estimating true survival rates from mark-recapture studies Ecology 93: The appararent survival issue is that permanent emigration can not be separated from death. Develops a hierarchical Bayesian multistate model to account for predicted rates of permanent emigration. Gwinn, D., Brown, P., Tetzlaff, K. and Allen M Evaluating mark-recapture sampling designs for fish in an open riverine system. Marine and Freshwater Research. 62: Evaluates sampling designs (e.g. size of sampling area, number of sampling occasions) by simulating fish using an individual-based population model. Ivan, J. S., G.C. White, and T.M. Shenk, Using simulation to compare methods for estimating density from capture-recapture data Ecology 94: Compares three methods for estimating density (not just N): Mean maximum distance moved, Spatially explicit capture-recapture, and Telemetry. Telemetry is best SECR may be preferable to Telemetry at low capture probabilities. MMDM is biased. Kendall, W.L., G.C. White, J.E. Hines, C.A. Langtimm, and J. Yoshizaki, Estimating parameters of hidden Markov models based on marked individuals: use of robust design data Ecology 93: Traditional multistate models require no uncertainty in the state at each observation. Hidden Markov Models account for uncertainty in the state. Develops a flexible framework to account for state uncertainty. Laake, J. L., B.A. Collier, M.L. Morrison, R.N. Wilkins, Point-Based Mark-Recapture Distance Sampling Journal of Agricultural Biological and Environmental Statistics 16: Combines traditional point sampling for birds with mark-recapture. Choice of assumptions about independence matters. Lahoz-Monfort, J., Morgan, B., Harris, M., Wanless, S., and Freeman, S A capturerecapture model for exploring multi-species synchrony in survival. Methods in Ecology and Evolution. 2: Considers data from from several related species in the same area. models survival for each species as a sum of a random effect for year (synchronous component) and a species-specific asynchronous component. Lebreton, J.-D., K. P. Burnham, J. Clobert, and D. R. Anderson Modeling survival and testing biological hypotheses using marked animals: case studies and recent advances. Ecological Monographs 62: Uses linear models to relate covariates (e.g. time or experimental treatments) to model parameters (e.g. survival probability or capture probability). Lebreton, J.-D., R. Choquet, O. Gimenez, Simple Estimation and Test Procedures in Capture-Mark-Recapture Mixed Models. Biometrics 68: Develops a simple method to incorporate random effects to model unexplained environmental variation. 8

9 Lee, S. and Chao, A Estimating population size via sample coverage for closed capturerecapture models. Biometrics 50: Various papers by Chao describe the coverage approach. This one is a relatively accessible treatment of all closed models; a 1992 paper by Chao gives more details on a subset of models. McClintock, B.T., White, G.C., Antolin, M.F, and Tripp, D.W Estimating abundance using mark-resight when sampling is with replacement or the number of marked individuals is unknown. Biometrics 65: Mark-resight data are where individuals are captured to be marked, but the marks are sufficiently visible that individuals just need to be resighted to be identified. This sort of data requires more complicated models. Petit, E. and Valiere, N Estimating Population Size with Noninvasive Capture-Mark- Recapture Data. Conservation Biology 20: Evaluation of non-invasive methods. Pradel, R Utilization of capture-mark-recapture for the study of recruitment and population growth rate. Biometrics 52: Pradel, R., Johnson, A.R., Viallefont, A., Hager, R.G., and Cezilly, F Local recruitment in the Greater Flamingo: a new approach using capture-recapture data. Ecology 78: Theory and an example of Pradel s temporal symmetry model to estimate recruitment and population growth rate directly from capture-recapture data. Sollmann, R. B. Gardner, A.W. Parsons, J.J. Stocking, B.T. McClintock, T.R. Simons, K.H. Pollock, and A.F. O Connell, A spatial mark-resight model augmented with telemetry data. Ecology 94: Estimates density using a combination of mark-resight data and telemetry data, which informs parameters related to movement and individual location. Novel tagging methods: Genetic marks, camera traps, and mark-resight Harmsen, B.J., Foster, R., and Doncaster, C Heterogeneous capture rates in low density populations and consequences for capture-recapture analysis of camera-trap data. Population Ecology 53: Camera trapping is non-invasive and low effect, but capture probabilities are often low and heterogeneous. Simulation evaluation of heterogeneity in capture probability, using Burnham s jacknife estimator. Link, W. Yoshizake, J., Bailey, L., and Pollock, K Uncovering a latent multinomial: analysis of mark-recapture data with misidentification. Biometrics 66: One of the key assumptions in mark-recapture is that marks are identified without error. This is a serious concern for genetic marks because genotyping errors do occur. The consequence (almost always) is that two records of the same individual appear to be from different individuals. This is a Bayesian latent variable model that accounts for misidentification. 9

10 Lukacs, P. and Burnham, K.P Review of capture-recapture methods applicable to noninvasive genetic sampling. Molecular Ecology 14: Introduction to another current research area - using genetic markers (e.g. RFLP s from dung) to identify individuals. Madon, B., Gimenez, O., McArdle, B., Baker, C, and Garrigue, C A new method for estimating animal abudance with two sources of data in capture-recapture studies. Methods in Ecology and Evolution 2: Using both photo-identification and DNA markers. New issue considered here is that the two surveys are done separately, so some individuals are in both, some are in only one, and others are completely missed. This method estimates the overlap between the two lists by computing a constant that serves as an adjustment factor. Bonner, S. Response to: a new method for estimating animal abundance with two sources of data in capture-recapture studies. Methods in Ecology and Evolution 4: Argues that Madon et al. s approach is bad. Need something more complicated than a constant adjustment factor. Need to model the observation process. McClintock, B. and Hoeting, J Bayesian analysis of abundance for binomial sighting data with unknown number of marked individuals. Environmental and Ecological Statistics. 17: Mark-resight methods handle individuals once to mark them, but then don t require capturing them again, only resighting them. Traditional models assume the number of marked individuals is known precisely, which is a problem if survival not perfect. This is a Bayesian approach deal with that uncertainty. McClintock, B. T., P.B. Conn, R.S. Alonso, and K.R. Crooks Integrated modeling of bilateral photo-identification data in mark-recapture analyses. Ecology 94: The ideas in Madon et al applied to double camera traps. The issue is that any particular animal may be photoed by the left, the right, or both cameras. Rew, M, Robbins, J., Mattila, D., Palsboll, P. and ABerube, M How many genetic markers to tag an individual? An empirical assessment of false matching rates among close relatives. Ecological Applications 21: Closely related individuals are likely to have similar genotypes, so are more likely to be mis-identified as the same individual. This paper suggests strategies to reduce the frequency of mismatches without requiring lots of extra lab effort. 10