Spatial Mark-Resight for Categorically Marked Populations with an Application to Genetic Capture-Recapture

Abstract

The estimation of animal population density is a fundamental goal in wildlife ecology and management, commonly met using mark recapture or spatial mark recapture (SCR) study designs and statistical methods. Mark-recapture methods require the identification of individuals; however, for many species and sampling methods, particularly noninvasive methods, no individuals or only a subset of individuals are individually identifiable. The unmarked SCR model, theoretically, can estimate the density of unmarked populations; however, it produces biased and imprecise density estimates in many sampling scenarios typically encountered. Spatial mark-resight (SMR) models extend the unmarked SCR model in three ways: 1) by introducing a subset of individuals that are marked and individually identifiable, 2) introducing the possibility of individual-linked telemetry data, and 3) introducing the possibility that the capture-recapture data from the survey used to deploy the marks can be used in a joint model, all improving the reliability of density estimates. The categorical spatial partial identity model (SPIM) improves the reliability of density estimates over unmarked SCR along another dimension, by adding categorical identity covariates that improve the probabilistic association of the latent identity samples. Here, we combine these two models into a "categorical SMR" model to exploit the benefits of both models simultaneously. We demonstrate using simulations that SMR alone can produce biased and imprecise density estimates with sparse data and/or when few individuals are marked. Then, using a fisher (Pekania pennanti) genetic capture-recapture data set, we show how categorical identity covariates, marked individuals, telemetry data, and jointly modeling the capture survey used to deploy marks with the resighting survey all combine to improve inference over the unmarked SCR model. As previously seen in an application of the categorical SPIM to a real-world data set, the fisher data set demonstrates that individual heterogeneity in detection function parameters, especially the spatial scale parameter σ, introduces positive bias into latent identity SCR models (e.g., unmarked SCR, SMR), but the categorical SMR model provides more tools to reduce this positive bias than SMR or the categorical SPIM alone. We 2 introduce the possibility of detection functions that vary by identity category level, which will remove individual heterogeneity in detection function parameters than is explained by categorical covariates, such as individual sex. Finally, we provide efficient SMR algorithms that accommodate all SMR sample types, interspersed marking and sighting periods, and any number of identity covariates using the 2-dimensional individual by trap data in conjunction with precomputed constraint matrices, rather than the 3-dimensional individual by trap by occasion data used in SMR algorithms to date.

Generalized spatial mark–resight models with incomplete identification: An application to red fox density estimates

“…This model can be extended to other formulations of SMR, such as temporal or behavioral variation in baseline detection rate, and spatial variation in density, or using categorical covariates (Augustine et al, ). We can recognize in camera‐trap pictures some categorical identities like “male, subadult” or “female, adult” allowing increased precision when data are sparse and/or there are few marked individuals.…”

“…McClintock et al (2014) used a method that accounts for uncertainty in marked individual detection histories when incomplete identifications occur for the two approaches commonly used in nonspatial mark-resight models of abundance, the Poisson log-normal estimator and the logit-normal estimator. MCMC approaches to deal with this issue could be found in Whittington et al (2017) and Augustine, Royle, Stewart, Fisher, and Kelly (2018), and using MLE in Efford and Hunter (2018).…”

“…Sarmento et al (2009) estimated densities of 0.61 (0.54-0.69) individuals/km 2 in Serra de Malcata (Portugal) using nonspatial capture-recapture methods and identifying all individuals by natural marks. Jiménez, Nuñez-Arjona et al (2017) estimated 0.41 (0.21-0.72) individuals/km 2 using SMR in southern Spain.This model can be extended to other formulations of SMR, such as temporal or behavioral variation in baseline detection rate, and spatial variation in density, or using categorical covariates(Augustine et al, 2018). We can recognize in camera-trap pictures some categorical identities like "male, subadult" or "female, adult" allowing increased precision when data are sparse and/or there are few marked individuals.…”

Camera trapping as a method for estimating abundance of Mexican wolves

“…Finally, we classified wolves as uncertain when we could not clearly see their neck, typically due to angle, blur, or distance from the camera. We discarded uncertain records because they do not contribute to the model likelihood when fitting spatial mark‐resight models (Efford and Hunter 2017, Augustine et al 2018). Our sampling process yielded 4 datasets of classified photos: winter and summer datasets developed without the aid of GPS information (hereafter, winter no telemetry and summer no telemetry), and winter and summer datasets developed with the aid of GPS information (hereafter, winter telemetry and summer telemetry).…”