Optimal sampling design for spatial capture-recapture

Abstract

10Spatial capture-recapture (SCR) has emerged as the industry standard for 11 analyzing observational data to estimate population size by leveraging information from 12 spatial locations of repeat encounters of individuals. The resulting precision of density 13 estimates depends fundamentally on the number and spatial configuration of traps.14 Despite this knowledge, existing sampling design recommendations are heuristic and 15 their performance remains untested for most practical applications -i.e., 16spatially-structured and logistically challenging landscapes. To address this issue, we 17 propose a genetic algorithm that minimizes any sensible, criteria-based objective 18 function to produce near-optimal sampling designs. To motivate the idea of optimality, 19 we compare the performance of designs optimized using two model-based criteria 20 related to the probability of capture. We use simulation to show that these designs 21 out-perform those based on existing recommendations in terms of bias, precision, and 22 accuracy in the estimation of population size. Our approach allows conservation 23 practitioners and researchers to generate customized sampling designs that can improve 24 monitoring of wildlife populations. 25Keywords-SCR, spatial capture-recapture, spatially-explicit capture-recapture, 26 camera traps, density, optimal design, sampling design, spatial sampling, trap spacing 27 29 (Williams et al., 2002) which has driven the development of data collection and estimation 30 methods, especially those that can account for imperfect detection. Capture-recapture (CR), 31 and more recently, spatial capture-recapture (SCR: Royle et al., 2014) methods were 32 developed specifically for this purpose and are now routinely applied in ecological research. 33 Concurrently, SCR methods estimate detection, space use, and density by analyzing 34 2 individual encounter histories while explicitly incorporating auxiliary information from the 35 spatial organization of encounters (Efford, 2004; Royle et al., 2014). Despite widespread 36 adoption and rapid method development, recommendations about spatial sampling design 37 have received relatively little attention and are arguably heuristic. 38 The effects of sampling design have been investigated for both CR (Dillon and Kelly 39 2007; Bondrup-Nielsen 1983; Gardner et al. 2010) and SCR methods (discussed in the next 40 paragraph). While CR methods aim to balance the number of captures and the number of 41 recaptures, SCR requires a third consideration, the number of spatial recaptures, i.e., the 42 number of times individuals are observed at multiple locations. The ability to reliably 43 estimate these quantities is directly related to the quality of the data collected: the number of 44 captured individuals n is the sample size; the number of recaptures is directly related to the 45 baseline detection probability, g 0 ; and the number and spatial distribution of recaptures are 46 directly related to the spatial scale parameter, σ. Therefore, improving sampling design...

Fast, flexible alternatives to regular grid designs for spatial capture–recapture

“…The approach essentially combines the optimization framework used by Dupont et al. (2020), which employs a genetic algorithm to iteratively improve candidate designs, with a new objective function using Efford and Boulanger (2019)’s approximation of the (standardized) precision of density, . Our approach can in principle be extended to any variant of SCR for which and can be rapidly evaluated.…”

“…(2014) considered four design objectives—minimizing the trace of the variance–covariance matrix of the MLEs of detection model parameters; minimizing , the variance of the MLE of the mean detection probability (the probability that an animal in A is detected by the survey); maximizing the mean detection probability; and minimizing , where is a conditional estimator of N and n is the number of animals detected—while Dupont et al. (2020) maximized , the mean probability that an animal is detected on two or more detectors. All except the fourth criterion in Royle et al.…”

“…We then used a standard genetic algorithm implemented in the r package kofnGA (Wolters, 2015), following Dupont et al. (2020), that is much less susceptible to this problem (Figure 1e). The algorithm begins by generating a population of random designs, typically several hundred.…”

“…(2014) and Dupont et al. (2020), who considered designs optimizing a suite of objective functions, are exceptions, although the functions they used are either related only indirectly to the main objective of estimating animal density precisely by focusing on detection parameters or relied on simplifying assumptions that are untested and available only for certain types of detection models.…”

“…The motivation for using these designs is that they can be expected to return unbiased density estimates with relatively good precision under a wide range of conditions (Efford & Fewster, 2013). However, placing detectors at regular intervals may be impossible in some survey areas, and better designs may be achievable without the constraint of regular spacing even if that spacing is feasible (Dupont et al., 2020).…”