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

Abstract

1. 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. 2. 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. 3. 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 (>0Á5) and heterogeneity was random. Otherwise, with structured heterogeneity (particularly positive density dependence) and low detection probabilities (<0Á5), 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. 4. 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 (<0Á5), 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.

Time‐for‐space substitution in N‐mixture modeling and population monitoring

“…In our application, the N ‐mixture model appeared to systematically underestimate population abundance in comparison to CMR; we obtained lower values in comparison with CMR in about 75% of years. Therefore, these findings seem to be more in line with the simulations of Veech et al (). The overall agreement between N ‐mixture and CMR estimates let us assume that identifiability problems and other major sources of bias, recently raised against these models (Barker et al , Link et al ), are not of concern, at least in this study.…”

A new parameterization for integrated population models to document amphibian reintroductions

“…Nevertheless, we envision this model being applied to a handful of donor and recipient populations. Unfortunately, N-mixture models produce biased estimates when capture probabilities are low and confounded with individual heterogeneity (Veech et al 2016), which is a common scenario for amphibian species. Their model uses concepts from the spatial capture-recapture literature to estimate initial spatially explicit abundances/densities, variation in abundance across time, as well as survival and per capita recruitment parameters.…”

Combining noninvasive genetics and a new mammalian sex‐linked marker provides new tools to investigate population size, structure and individual behaviour: An application to bats

“…Individuals with the highest philopatry, that is, females, are more likely to be detected. Beyond sex, individual detection probability may be heterogeneous due to a multitude of time‐ or site‐dependent extrinsic factors affecting the observation process itself (observers’ skills, timing and duration of censusing) and/or conditions (environmental factors restraining visibility or observers’ proximity to the animals and/or factors related to species biology and ecology; Kunz et al., ; Veech et al., ). Our results confirm that visual counts represent a reliable and cost‐effective method for censusing the more settled individuals within colonies (i.e., adult females) when only interested in bat demographic trends.…”

“…A common source of intraspecific variation is sex, with males and females displaying different behaviour that leads to large differences in detection probabilities (e.g., Christy, Yackel Adams, Rodda, Savidge, & Tyrrell, ; Ogutu, Piepho, Dublin, Reid, & Bhola, ; Singh, Qureshi, Sankar, Krausman, & Goyal, ). This observation leads to the development of statistical frameworks accounting for specific forms of intraspecific variation (e.g., Veech, Ott, & Troy, ), but the most obvious and efficient way of correcting potential bias is to a priori identify subsets of populations that differ in detection probabilities.…”

“…Pregnant and lactating females have stricter roost requirements than others (Speakman, Thomas, Kunz, & Fenton, ). Such possible intraspecific variations in roosting requirements and behaviour depending on sex or reproductive status could result in intrinsic heterogeneity in detection probabilities, and therefore, affect colony size (i.e., total number of adults) and fecundity (i.e., ratio juveniles/adults) measurements when estimated by visual counts (Safi, König, & Kerth, ; Veech et al., ). Here, we provide evidence that genetic approaches, including molecular sexing, are of great interest to elucidate the population structure of bat maternity colonies and to investigate possible differences in sex‐ and/or status‐related behaviours.…”