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

Abstract

AbstractSpatial capture-recapture (SCR) is now used widely to estimate wildlife densities. At the core of SCR models lies the detection function, linking individual detection probability to the distance from its latent activity center. The most common function (half-normal) assumes a bivariate normal space use and consequently detection pattern. This is likely an oversimplification and misrepresentation of real-life animal space use patterns, but studies have reported that density estimates are relatively robust to misspecified detection functions. However, information about consequences of such misspecification on space use parameters (e.g. home range area), as well as diagnostic tools to reveal it are lacking.We simulated SCR data under six different detection functions, including the half-normal, to represent a wide range of space use patterns. We then fit three different SCR models, with the three simplest detection functions (half-normal, exponential and half-normal plateau) to each simulated data set. We evaluated the consequences of misspecification in terms of bias, precision and coverage probability of density and home range area estimates. We also calculated Bayesian p-values with respect to different discrepancy metrics to assess whether these can help identify misspecifications of the detection function.We corroborate previous findings that density estimates are robust to misspecifications of the detection function. However, estimates of home range area are prone to bias when the detection function is misspecified. When fitted with the half-normal model, average relative bias of 95% kernel home range area estimates ranged between −25% and 26% depending on the misspecification. In contrast, the half-normal plateau model (an extension of the half-normal) returned average relative bias that ranged between −26% and −4%. Additionally, we found useful heuristic patterns in Bayesianp-values to diagnose the misspecification in detection function.Our analytical framework and diagnostic tools may help users select a detection function when analyzing empirical data, especially when space use parameters (such as home range area) are of interest. We urge development of additional custom goodness of fit diagnostics for Bayesian SCR models to help practitioners identify a wider range of model misspecifications.