A Monte Carlo resampling framework for implementing goodness‐of‐fit tests in spatial capture‐recapture models

Abstract

Abstract Spatial capture‐recapture (SCR) models provide estimates of animal density from spatially referenced encounter data and has become the most widely adopted approach for estimating density. Despite the rapid growth in the development and application of spatial capture‐recapture methods, approaches for assessing model fit have received very little attention when compared to other classes of hierarchical models in ecology. Here, we develop an approach for testing goodness‐of‐fit (GoF) for frequentist SCR models using Monte Carlo simulations. We derive probability distributions of activity centres from the fitted model. From these, we calculate the expected encounters in the capture history based on the SCR parameter estimates, propagating the uncertainty of the estimates and the activity centre locations via Monte Carlo simulations. Aggregating these test statistics result in count data, allowing us to test fit with Freeman‐Tukey tests. These tests are based on summary statistics of the total encounters of each individual at each trap (FT‐ind‐trap), total encounters of each individual (FT‐individuals) and total encounters at each trap (FT‐traps). We assess the ability of these GoF tests to diagnose lack of fit under a range of assumption violating scenarios. FT‐traps had the strongest response to unmodelled spatial and trap heterogeneity in detection probability (power = 0.53–0.56), while FT‐ind‐traps had the strongest responses to random individual variation in detectability (power = 0.88) and non‐spatial discrete variation in g0 (power = 0.35). The tests, designed to diagnose poor fit in the detection parameters, were insensitive to unmodelled heterogeneity in density (power = <0.001). They also demonstrated low false positive rates (<0.001) when the correct models were fitted; therefore, it is very unlikely that they will provide false indications of poor model fit. We demonstrate that these GoF tests are capable of detecting lack‐of‐fit when unmodelled heterogeneity is present in the detection sub‐model. When used jointly, the combinations of test results are also able to infer the type of lack‐of‐fit in certain cases. Our Monte Carlo sampling methods may be extended to a wider range of GoF tests, thereby providing a platform for developing more GoF methods for SCR.

Keywords

• density estimation
• goodness‐of‐fit
• Monte Carlo resampling
• spatial capture‐recapture