Continuous‐time spatially explicit capture–recapture models, with an application to a jaguar camera‐trap survey

Summary Many capture–recapture surveys of wildlife populations operate in continuous time, but detections are typically aggregated into occasions for analysis, even when exact detection times are available. This discards information and introduces subjectivity, in the form of decisions about occasion definition. We develop a spatiotemporal Poisson process model for spatially explicit capture–recapture (SECR) surveys that operate continuously and record exact detection times. We show that, except in some special cases (including the case in which detection probability does not change within occasion), temporally aggregated data do not provide sufficient statistics for density and related parameters, and that when detection probability is constant over time, our continuous-time (CT) model is equivalent to an existing model based on detection frequencies. We use the model to estimate jaguar density from a camera-trap survey and conduct a simulation study to investigate the properties of a CT estimator and discrete-occasion estimators with various levels of temporal aggregation. This includes investigation of the effect on the estimators of spatiotemporal correlation induced by animal movement. The CT estimator is found to be unbiased and more precise than discrete-occasion estimators based on binary capture data (rather than detection frequencies) when there is no spatiotemporal correlation. It is also found to be only slightly biased when there is correlation induced by animal movement, and to be more robust to inadequate detector spacing, while discrete-occasion estimators with binary data can be sensitive to occasion length, particularly in the presence of inadequate detector spacing. Our model includes as a special case a discrete-occasion estimator based on detection frequencies, and at the same time lays a foundation for the development of more sophisticated CT models and estimators. It allows modelling within-occasion changes in detectability, readily accommodates variation in detector effort, removes subjectivity associated with user-defined occasions and fully utilizes CT data. We identify a need for developing CT methods that incorporate spatiotemporal dependence in detections and see potential for CT models being combined with telemetry-based animal movement models to provide a richer inference framework.

[1]  Anne Chao,et al.  Continuous-time capture-recapture models with covariates , 2002 .

[2]  Edward A. Codling,et al.  Random walk models in biology , 2008, Journal of The Royal Society Interface.

[3]  Ben C. Stevenson,et al.  A Unifying Model for Capture–Recapture and Distance Sampling Surveys of Wildlife Populations , 2015, Journal of the American Statistical Association.

[4]  David L. Borchers,et al.  Density Estimation by Spatially Explicit Capture–Recapture: Likelihood-Based Methods , 2009 .

[5]  Paul R Moorcroft,et al.  Stochastic modelling of animal movement , 2010, Philosophical Transactions of the Royal Society B: Biological Sciences.

[6]  N. Becker,et al.  ESTIMATING POPULATION SIZE FROM CAPTURE‐RECAPTURE EXPERIMENTS IN CONTINUOUS TIME , 1984 .

[7]  Rebecca J. Foster,et al.  A critique of density estimation from camera-trap data† , 2012 .

[8]  D. Lin,et al.  Inference for capture-recapture experiments in continuous time with variable capture rates , 1996 .

[9]  D L Borchers,et al.  Spatially Explicit Maximum Likelihood Methods for Capture–Recapture Studies , 2008, Biometrics.

[10]  Yan Wang,et al.  A Unified Parametric Regression Model for Recapture Studies with Random Removals in Continuous Time , 2002, Biometrics.

[11]  Paul S. F. Yip,et al.  Parametric regression models for continuous time removal and recapture studies , 1999 .

[12]  Wen-Han Hwang,et al.  Theory & Methods: Continuous‐time capture‐recapture models with time variation and behavioural response , 2002 .

[13]  Andrew J. Noss,et al.  The use of camera traps for estimating jaguar Panthera onca abundance and density using capture/recapture analysis , 2004, Oryx.

[14]  C. C. Craig,et al.  ON THE UTILIZATION OF MARKED SPECIMENS IN ESTIMATING POPULATIONS OF FLYING INSECTS , 1953 .

[15]  C. C. Heyde,et al.  Estimating population size from multiple recapture experiments , 1990 .

[16]  David R. Anderson,et al.  Continuous-time capture-recapture population estimation when capture probabilities vary over time , 1995, Environmental and Ecological Statistics.

[17]  Paul S. F. Yip,et al.  An Inference Procedure for a Capture and Recapture Experiment with Time-Dependent Capture Probabilities , 1989 .

[18]  Kai Lorenzen,et al.  Apparent survival estimation from continuous mark–recapture/resighting data , 2013 .

[19]  David L. Borchers,et al.  Varying effort in capture–recapture studies , 2013 .

[20]  Murray G. Efford,et al.  Bird population density estimated from acoustic signals , 2009 .

[21]  Murray G Efford,et al.  Population density estimated from locations of individuals on a passive detector array. , 2009, Ecology.

[22]  Juan M. Morales,et al.  EXTRACTING MORE OUT OF RELOCATION DATA: BUILDING MOVEMENT MODELS AS MIXTURES OF RANDOM WALKS , 2004 .

[23]  Rebecca J. Foster,et al.  Habitat Use by Sympatric Jaguars and Pumas Across a Gradient of Human Disturbance in Belize , 2010 .

[24]  Bryan F. J. Manly,et al.  Negative binomial models for abundance estimation of multiple closed populations , 2001 .

[25]  Tapan K. Nayak,et al.  Estimating population size by recapture sampling , 1988 .

[26]  B. Efron.  Better Bootstrap Confidence Intervals , 1987 .

[27]  M. Efford.  Density estimation in live‐trapping studies , 2004 .

[28]  H. Berg.  Random Walks in Biology , 2018 .

[29]  Mathias W. Tobler,et al.  Estimating jaguar densities with camera traps: Problems with current designs and recommendations for future studies , 2013 .

[30]  Anne Chao,et al.  Estimating population size for continuous-time capture-recapture models via sample coverage , 1993 .

[31]  Rebecca J. Foster,et al.  Differential Use of Trails by Forest Mammals and the Implications for Camera‐Trap Studies: A Case Study from Belize , 2010 .

[32]  Marianne K. Soisalo,et al.  Estimating the density of a jaguar population in the Brazilian Pantanal using camera-traps and capture–recapture sampling in combination with GPS radio-telemetry , 2006 .

[33]  J Andrew Royle,et al.  Bayesian inference in camera trapping studies for a class of spatial capture-recapture models. , 2009, Ecology.

[34]  D Y Lin,et al.  Estimation of Population Size Based on Additive Hazards Models for Continuous‐Time Recapture Experiments , 1999, Biometrics.

[35]  Roland Langrock,et al.  Flexible and practical modeling of animal telemetry data: hidden Markov models and extensions. , 2012, Ecology.