Intrinsic heterogeneity in detection probability and its effect on N-mixture models

Abstract

Estimating the abundance or density of animal populations is often a fundamental task in ecological research and species conservation. N-mixture models are widely used to estimate the detection probability of individual organisms that thusly leads to more accurate estimates of a species' true abundance. However, individuals likely vary in their probabilities of being detected. During a survey, heterogeneity (variation) in individual detection probability might arise due to conditions of the surveying process; this form of extrinsic heterogeneity can be accounted for by the use of appropriate covariates in the models. In contrast, intrinsic heterogeneity in the detection probabilities of individuals arises when intraspecific variation in behaviour results in individual organisms differing in their latent (inherent) probabilities of being detected. This form of heterogeneity is not tractable by the use of covariates and its possible effects on model performance have not been investigated to date. Using simulated data, we evaluated the performance of Poisson, negative binomial and zero-inflated Poisson versions of N-mixture models under the conditions of intrinsic heterogeneity in individual detection probability. Most versions of N-mixture models performed well in estimating abundance as indicated by relatively low root-mean-square-error values (RMSE < 1). Error distributions indicated a lack of substantial bias and relatively high precision and accuracy when simulated detection probabilities of individuals were high (>0·5) and heterogeneity was random. Otherwise, with structured heterogeneity (particularly positive density dependence) and low detection probabilities (<0·5), model performance was reduced (RMSE > 2). The poorest performing model was the zero-inflated Poisson version of N-mixture model applied to data from low survey effort. Our results suggest that N-mixture models are robust to intrinsic heterogeneity in individual detection probabilities except when the detection probabilities are low. When model-estimated detection probabilities are low (<0·5), model users should be aware that estimates of abundance could be erroneous if there was non-random intrinsic heterogeneity in individual detection probabilities during the surveys. Remedying this situation might require redesigning the basic survey protocol such that it does not rely on behavioural traits (as cues to detection) that are intrinsically variable among individuals.