## Introduction

Recently developed binomial mixture models use repeated count data to estimate abundance (Royle 2004a,b). These models are becoming increasingly popular because they provide a simple and cost-effective way to account for imperfect detection (Kéry 2008). Accounting for detection probability is important to obtain reliable estimates of abundance and to make appropriate inferences (Williams, Nichols, & Conroy 2002). However, the standard binomial mixture model assumes that organisms are detected independently of each other (Royle & Dorazio 2008). This assumption may be violated when there is some correlation in the behaviour of animals, which can affect their probability of being detected by observers. For instance, several monitoring studies of birds and amphibians have used acoustic signals as a way to estimate abundance (Dawson & Efford 2009; McClintock *et al.* 2010), but it is reasonable to imagine that when one bird sings, its behaviour will influence the singing behaviour of its neighbours. In this case, these birds may not be detected independently of each other. Another example is the case of marine mammals that are monitored with aerial surveys (Edwards *et al.* 2007). In these surveys, the animals become available for detection when they come to the surface to breathe (Edwards *et al.* 2007). Our study was motivated by a monitoring program of manatees in Florida (*Trichechus manatus latirostris*), which are surveyed at warm water outfalls of power plants and in coastal areas (Edwards *et al.* 2007). In most instances, the water is too murky or too deep for observers to count manatees that are resting deep under the surface. It has been suggested that manatees may come to the surface in groups (Edwards *et al.* 2007).

Behaviour such as movement in groups (e.g. manatees surfacing in groups) may induce a correlation in detection probability of individuals. This may lead to biased estimates in a model that assumes independence of detections, such as the standard binomial mixture model. The beta-binomial distribution has been proposed as a method to account for correlated Bernoulli outcomes (Hisakado, Kitsukawa, & Mori 2006).

Here, we develop beta-binomial mixture models that account for correlated Bernoulli outcomes in the data (i.e. correlated detections of individuals) and examine the performance of the standard binomial and the beta-binomial mixture models under a range of scenarios including correlated outcomes, heterogeneity in detection, and zero inflation in abundance. We consider heterogeneity in capture probabilities and different levels of correlations (among Bernoulli outcomes) across sites. Zero inflation of abundance may result from the fact that in some ecological applications, many sampling units are unoccupied by the organism of interest (e.g. Wenger & Freeman 2008). We apply the binomial and beta-binomial mixture models to a case study with manatee aerial surveys and discuss the benefits and limitations of these approaches. Understanding how different sources of variation can affect estimates under N-mixture models (e.g. standard binomial and beta-binomial mixture models) is important given that these models are increasingly used for ecological research and also for decision-making regarding threatened and endangered species (e.g. Fonnesbeck *et al.* unpublished; Johnson 2010).