Stat 534
Philip Dixon
Fall 2015
References: Estimating Population Parameters: Closed and Open populations
Population Biology:
Vandermeer, J.H. and Goldberg, D.E. 2013. Population Ecology: First Principles. Princeton
University Press, Princeton, NJ.
Silvertown, Jonathan W. and Deborah Charlesworth. 2001. 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. 1998. 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. 2012. 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. 1997. 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. 1982. 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. 2002. Estimating Animal Abundance:
Closed Populations. Springer, New York.
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. 2005. 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.
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McCrea, R.S. and Morgan, B.J.T. 2015. 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, 1978. 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. 1990. 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 . 2013. 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. 1982. 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. 2009 Modeling Demographic Processes in
Marked Populations. Springer.
Combining population models with mark-recapture (etc.) data.
Williams, B.K., Nichols, J.D., Conroy, M.J. 2002. 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. 1951. Some properties of the hypergeometric distribution with applications
to zoological censuses. Univ. California Publications in Statistics 1:131-160.
Derives the approximately unbiased version of the hypergeometric model estimator and
its variance.
Hammond, E.L. and Anthony, R.G. 2006. Mark-recapture estimates of population parameters
for selected species of small mammals. Journal of Mammology 87:618-627
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).
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Huggins, R. M. 1991. Some practical aspects of a conditional likelihood approach to capture
experiments. Biometrics 47:725-732.
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. 1989. Confidence intervals for nearly unbiased estimators in single-mark and
single-recapture experiments. Biometrics 45:1233-1237.
ci’s based on distribution of 1/N̂ under binomial and hypergeometric models. Easy to
compute.
Pledger, S. 2000. Unified maximum likelihood estimates for closed captuer-recapture models
for mixtures. Biometrics 56:434-442.
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, 2013. Revisiting the Effect of Capture Heterogeneity on
Survival Estimates in Capture-Mark-Recapture Studies: Does It Matter? PLOS One 8(4)
Online: 10.1371/journal.pone.0062636
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. 2000. Bayesian animal survival estimation. Statistical Science. 15:357-376.
Review and summary of Bayesian approaches to estimation for open populations.
Cubaynes, S. et al. 2010. Importance of accounting for detection heterogeneity when estimating abundance: the case of French wolves. Conservation Biology 24:621-626.
Develops a model that on quick inspection seems very similar to Pledger’s (2011) open
population heterogeneity model.
Jolly, G. M. 1965. Explicit estimates from capture-recapture data with both death and
immigration stochastic model. Biometrika 52:225-247.
Seber, G. A. F. 1965. A note on the multiple recapture census. Biometrika 52:249-259.
The two original papers on the Jolly-Seber model
Kendall, W. L., K. H. Pollock, and C. Brownie. 1995. A likelihood-based approach to
capture-recapture estimation of demographic parameters under the robust design. Biometrics
51:293-308.
A full likelihood analysis of data from a robust design
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Pledger, S., Pollock, K., and Norris, J. 2010. Open capture-recapture models with heterogeneity. II. Jolly-Seber model. Biometrics 66:883-890.
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. 1982. A capture-recapture design robust to unequal probability of capture. J.
Wildlife Management 46:757-760.
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. 2006. Multistate survival models and the
extensions in program MARK. J. Wildlife Management 70:1521-1529
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. 2013. Bayesian multimodel inference by RJMCMC: a Gibbs
sampling approach. American Statistician 67:150-156
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. 1997. Model selection: an integral part
of inference. Biometrics 53:603-618.
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, 1998. Model selection and inference: a practical
information-theoretic approach. Springer-Verlag, New York.
Section 4.2.6 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, 2004. Multimodel inference - understanding AIC and
BIC in model selection. Sociological Methods and Research 33:261-304.
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, 2012. Assessing individual heterogeneity using model selection criteria: how many mixture components in capture-recapture
models? Method in Ecology and Evolution 3:564-573.
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.
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McCrea, R. S. and B. J. T. Morgan, 2011. Multistate Mark-Recapture Model Selection Using
Score Tests. Biometrics 67:234-241.
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. 1998. Estimator selection for closed-population capture-recapture.
Journal of Agricultural Biological and Environmental Statistics. 3:131-150
Stanley T. and Burnham K. 1998. Information-theoretic model selection and model averaging
for closed-population capture-recapture studies Biometrical Journal. 40:475-494.
Spatial Capture-recapture:
Borchers, D.L. and Efford, M.G. 2008. Spatially explicit maximum likelihood methods for
capture-recapture studies. Biometrics 64:377-385.
If traps are in known locations, you can estimate density (#/area), not just population
size.
Borchers, D.L. 2012. 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. 2014. Spatially explicit integrated population models. Methods
in Ecology and Evolution 5:1351-1360.
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: http://www.phidot.org/software/mark/
and Gary White’s page: http://warnercnr.colostate.edu/∼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 1.3-1. http://CRAN.R-project.org/package=Rcapture
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 845-865,
or see the web page:
http://www.cefe.cnrs.fr/biostatistiques-et-biologie-des-populations/logiciels
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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, 2012. Detection and Plant Monitoring Programs: Lessons from an Intensive Survey of
Asclepias meadii with Five Observers PLOS One 7(12). Online 10.1371/journal.pone.0052762
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. 1978. Estimation of the size of a closed population when
capture probabilities vary among animals. Biometrika 65:625-633.
Burnham, K. P. and Overton, W. S. 1979. Robust estimation of population size when capture
probabilities vary among animals. Ecology 60:927-936.
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. 2001. Tutorial in Biostatistics: The applications of capture-recapture models to epidemiological data. Statistics in Medicine 20:31233157
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. 2004. A General Model for the Analysis of
Mark-Resight, Mark-Recapture, and Band-Recovery Data under Tag Loss Biometrics 60:900909.
One entry into a current research topic: how to account for tag loss.
Ford, J. H., M.V. Bravington, J. Robbins, 2012. Incorporating individual variability into
mark-recapture models Methods in Ecology and Evolution. 3:1047-1054.
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. 1986. Population estimation from mark-recapture experiments
using a sequential Bayes algorithm. Ecology 67:941-951.
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.
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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: 1509-1516.
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. 2011. Evaluating mark-recapture sampling
designs for fish in an open riverine system. Marine and Freshwater Research. 62:835-840.
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, 2013. Using simulation to compare methods for
estimating density from capture-recapture data Ecology 94:817-826.
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, 2012. Estimating
parameters of hidden Markov models based on marked individuals: use of robust design data
Ecology 93:913-920.
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, 2011. Point-Based Mark-Recapture
Distance Sampling Journal of Agricultural Biological and Environmental Statistics 16:389-408
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. 2011. A capturerecapture model for exploring multi-species synchrony in survival. Methods in Ecology and
Evolution. 2:116-124.
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. 1992. Modeling survival
and testing biological hypotheses using marked animals: case studies and recent advances.
Ecological Monographs 62:6-118.
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, 2012. Simple Estimation and Test Procedures in
Capture-Mark-Recapture Mixed Models. Biometrics 68: 494-503.
Develops a simple method to incorporate random effects to model unexplained environmental variation.
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Lee, S. and Chao, A. 1994. Estimating population size via sample coverage for closed capturerecapture models. Biometrics 50:88-97.
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. 2008. Estimating abundance
using mark-resight when sampling is with replacement or the number of marked individuals
is unknown. Biometrics 65:237-246.
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. 2006. Estimating Population Size with Noninvasive Capture-MarkRecapture Data. Conservation Biology 20:1062-1073.
Evaluation of non-invasive methods.
Pradel, R. 1996. Utilization of capture-mark-recapture for the study of recruitment and
population growth rate. Biometrics 52:703-709.
Pradel, R., Johnson, A.R., Viallefont, A., Hager, R.G., and Cezilly, F. 1997. Local recruitment in the Greater Flamingo: a new approach using capture-recapture data. Ecology
78:1431-1445.
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, 2013. A spatial mark-resight model augmented with telemetry
data. Ecology 94:553-559.
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. 2011. Heterogeneous capture rates in low
density populations and consequences for capture-recapture analysis of camera-trap data.
Population Ecology 53:253-259.
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. 2010. Uncovering a latent multinomial:
analysis of mark-recapture data with misidentification. Biometrics 66:178-185.
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.
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Lukacs, P. and Burnham, K.P. 2005. Review of capture-recapture methods applicable to
noninvasive genetic sampling. Molecular Ecology 14:3909-3919
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. 2011. A new method for
estimating animal abudance with two sources of data in capture-recapture studies. Methods
in Ecology and Evolution 2:390-400.
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 4:585-588.
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. 2010. Bayesian analysis of abundance for binomial sighting
data with unknown number of marked individuals. Environmental and Ecological Statistics.
17:317-332.
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. 2013. Integrated modeling of
bilateral photo-identification data in mark-recapture analyses. Ecology 94:1464-1471.
The ideas in Madon et al. 2011 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. 2011. How many genetic
markers to tag an individual? An empirical assessment of false matching rates among close
relatives. Ecological Applications 21:877-887.
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.
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