Does the punishment fit the crime? Consequences and diagnosis of misspecified detection functions in Bayesian spatial capture–recapture modeling

Spatial capture–recapture (SCR) analysis is now used routinely to inform wildlife management and conservation decisions. It is therefore imperative that we understand the implications of and can diagnose common SCR model misspecifications, as flawed inferences could propagate to policy and interventions. The detection function of an SCR model describes how an individual's detections are distributed in space. Despite the detection function's central role in SCR, little is known about the robustness of SCR‐derived abundance estimates and home range size estimates to misspecifications. Here, we set out to (a) determine whether abundance estimates are robust to a wider range of misspecifications of the detection function than previously explored, (b) quantify the sensitivity of home range size estimates to the choice of detection function, and (c) evaluate commonly used Bayesian p‐values for detecting misspecifications thereof. We simulated SCR data using different circular detection functions to emulate a wide range of space use patterns. We then fit Bayesian SCR models with three detection functions (half‐normal, exponential, and half‐normal plateau) to each simulated data set. While abundance estimates were very robust, estimates of home range size were sensitive to misspecifications of the detection function. When misspecified, SCR models with the half‐normal plateau and exponential detection functions produced the most and least reliable home range size, respectively. Misspecifications with the strongest impact on parameter estimates were easily detected by Bayesian p‐values. Practitioners using SCR exclusively for density estimation are unlikely to be impacted by misspecifications of the detection function. However, the choice of detection function can have substantial consequences for the reliability of inferences about space use. Although Bayesian p‐values can aid the diagnosis of detection function misspecification under certain conditions, we urge the development of additional custom goodness‐of‐fit diagnostics for Bayesian SCR models to identify a wider range of model misspecifications.