Accounting for non‐independent detection when estimating abundance of organisms with a Bayesian approach

Abstract

Summary1. Binomial mixture models use repeated count data to estimate abundance. They are becoming increasingly popular because they provide a simple and cost-effective way to account for imperfect detection. However, these models assume that individuals are detected independently of each other. This assumption may often be violated in the field. For instance, manatees (Trichechus manatus latirostris) may surface in turbid water (i.e. become available for detection during aerial surveys) in a correlated manner (i.e. in groups). However, correlated behaviour, affecting the non-independence of individual detections, may also be relevant in other systems (e.g. correlated patterns of singing in birds and amphibians). 2. We extend binomial mixture models to account for correlated behaviour and therefore to account for non-independent detection of individuals. We simulated correlated behaviour using beta-binomial random variables. Our approach can be used to simultaneously estimate abundance, detection probability and a correlation parameter. 3. Fitting binomial mixture models to data that followed a beta-binomial distribution resulted in an overestimation of abundance even for moderate levels of correlation. In contrast, the beta-binomial mixture model performed considerably better in our simulation scenarios. We also present a goodness-of-fit procedure to evaluate the fit of beta-binomial mixture models. 4. We illustrate our approach by fitting both binomial and beta-binomial mixture models to aerial survey data of manatees in Florida. We found that the binomial mixture model did not fit the data, whereas there was no evidence of lack of fit for the beta-binomial mixture model. This example helps illustrate the importance of using simulations and assessing goodness-of-fit when analysing ecological data with N-mixture models. Indeed, both the simulations and the goodness-of-fit procedure highlighted the limitations of the standard binomial mixture model for aerial manatee surveys. 5. Overestimation of abundance by binomial mixture models owing to non-independent detections is problematic for ecological studies, but also for conservation. For example, in the case of endangered species, it could lead to inappropriate management decisions, such as downlisting. These issues will be increasingly relevant as more ecologists apply flexible N-mixture models to ecological data.

Detecting diversity: emerging methods to estimate species diversity

“…This can lead to overinflation of counts and contrasts with the approach taken in distance sampling [21], which models the detectability of groups of individuals. However, a beta-binomial distribution can be applied to address nonindependence of detections of individuals [52,53].…”

Estimating abundance while accounting for rarity, correlated behavior, and other sources of variation in counts

“…As a remedy to this problem, Martin et al (2011) proposed an observation model wherein the beta distribution was used to specify random variation in detection probabilities among surveys. For example, suppose detection probability varies among repeated surveys of the same location and the source of variation cannot be measured.…”

Balancing Precision and Risk: Should Multiple Detection Methods Be Analyzed Separately in N-Mixture Models?

“…However, despite our efforts to mitigate for individual heterogeneity, the maximum per-cell abundance estimates from the hair trap-only analysis of males were unrealistically high (N = 150 in one cell). Other research [22] found that when detection of individuals is correlated, which could result from non-independent movement of animals, abundances were overestimated. Although it is unknown whether other forms of individual heterogeneity yield inflated abundance estimates, it seems likely that other forms of individual heterogeneity remain within our hair trap-only sample for males.…”