Estimating population size: The importance of model and estimator choice.

We consider estimator and model choice when estimating abundance from capture-recapture data. Our work is motivated by a mark-recapture distance sampling example, where model and estimator choice led to unexpectedly large disparities in the estimates. To understand these differences, we look at three estimation strategies (maximum likelihood estimation, conditional maximum likelihood estimation, and Bayesian estimation) for both binomial and Poisson models. We show that assuming the data have a binomial or multinomial distribution introduces implicit and unnoticed assumptions that are not addressed when fitting with maximum likelihood estimation. This can have an important effect in finite samples, particularly if our data arise from multiple populations. We relate these results to those of restricted maximum likelihood in linear mixed effects models.

A Bayesian Dirichlet process community occupancy model to estimate community structure and species similarity.

Community occupancy models estimate species-specific parameters while sharing information across species by treating parameters as sampled from a common distribution. When communities consist of discrete groups, shrinkage of estimates toward the community mean can mask differences among groups. Infinite-mixture models using a Dirichlet process (DP) distribution, in which the number of latent groups is estimated from the data, have been proposed as a solution. In addition to community structure, these models estimate species similarity, which allows testing hypotheses about whether traits drive species response to environmental conditions. We develop a community occupancy model (COM) using a DP distribution to model species-level parameters. Because clustering algorithms are sensitive to dimensionality and distinctiveness of clusters, we conducted a simulation study to explore performance of the DP-COM with different dimensions (i.e., different numbers of model parameters with species-level DP random effects) and under varying cluster differences. Because the DP-COM is computationally expensive, we compared its estimates to a COM with a normal random species effect. We further applied the DP-COM model to a bird data set from Uganda. Estimates of the number of clusters and species cluster identity improved with increasing difference among clusters and increasing dimensions of the DP; but the number of clusters was always overestimated. Estimates of number of sites occupied and species and community-level covariate coefficients on occupancy probability were generally unbiased with (near-) nominal 95% Bayesian Credible Interval coverage. Accuracy of estimates from the normal and the DP-COM was similar. The DP-COM clustered 166 bird species into 27 clusters regarding their affiliation with open or woodland habitat and distance to oil wells. Estimates of covariate coefficients were similar between a normal and the DP-COM. Except sunbirds, species within a family were not more similar in their response to these covariates than the overall community. Given that estimates were consistent between the normal and the DP-COM, and considering the computational burden for the DP models, we recommend using the DP-COM only when the analysis focuses on community structure and species similarity, as these quantities can only be obtained under the DP-COM.

Sources of variation in maternal allocation in a long-lived mammal.

Life history theory predicts allocation of energy to reproduction varies with maternal age, but additional maternal features may be important to the allocation of energy to reproduction. We aimed to characterize age-specific variation in maternal allocation and assess the relationship between maternal allocation and other static and dynamic maternal features. Mass measurements of 531 mothers and pups were used with Bayesian hierarchical models to explain the relationship between diverse maternal attributes and both the proportion of mass allocated by Weddell seal mothers, and the efficiency of mass transfer from mother to pup during lactation as well as the weaning mass of pups. Our results demonstrated that maternal mass was strongly and positively associated with the relative reserves allocated by a mother and a pup's weaning mass but that the efficiency of mass transfer declines with maternal parturition mass. Birthdate was positively associated with proportion mass allocation and pup weaning mass, but mass transfer efficiency was predicted to be highest at the mean birthdate. The relative allocation of maternal reserves declined with maternal age but the efficiency of mass transfer to pups increases, suggestive of selective disappearance of poor-quality mothers. These findings highlight the importance of considering multiple maternal features when assessing variation in maternal allocation.

Model selection for the North American Breeding Bird Survey.

The North American Breeding Bird Survey (BBS) provides data that can be used in complex, multiscale analyses of population change, while controlling for scale-specific nuisance factors. Many alternative models can be fit to the data, but most model selection procedures are not appropriate for hierarchical models. Leave-one-out cross-validation (LOOCV), in which relative model fit is assessed by omitting an observation and assessing the prediction of a model fit using the remainder of the data, provides a reasonable approach for assessing models, but is time consuming and not feasible to apply for all observations in large data sets. We report the first large-scale formal model selection for BBS data, applying LOOCV to stratified random samples of observations from BBS data. Our results are for 548 species of North American birds, comparing the fit of four alternative models that differ in year effect structures and in descriptions of extra-Poisson overdispersion. We use a hierarchical model among species to evaluate posterior probabilities that models are best for individual species. Models in which differences in year effects are conditionally independent (D models) were generally favored over models in which year effects are modeled by a slope parameter and a random year effect (S models), and models in which extra-Poisson overdispersion effects are independent and t-distributed (H models) tended to be favored over models where overdispersion was independent and normally distributed. Our conclusions lead us to recommend a change from the conventional S model to D and H models for the vast majority of species (544/548). Comparison of estimated population trends based on the favored model relative to the S model currently used for BBS summaries indicates no consistent differences in estimated trends. Of the 18 species that showed large differences in estimated trends between models, estimated trends from the default S model were more extreme, reflecting the influence of the slope parameter in that model for species that are undergoing large population changes. WAIC, a computationally simpler alternative to LOOCV, does not appear to be a reliable alternative to LOOCV.

Variation in the vital rates of an Antarctic marine predator: the role of individual heterogeneity.

Variation in life-history traits such as lifespan and lifetime reproductive output is thought to arise, in part, due to among-individual differences in the underlying probabilities of survival and reproduction. However, the stochastic nature of demographic processes can also generate considerable variation in fitness-related traits among otherwise-identical individuals. An improved understanding of life-history evolution and population dynamics therefore depends on evaluating the relative role of each of these processes. Here, we used a 33-yr data set with reproductive histories for 1,274 female Weddell seals from Erebus Bay, Antarctica, to assess the strength of evidence for among-individual heterogeneity in the probabilities of survival and reproduction, while accounting for multiple other sources of variation in vital rates. Our analysis used recent advances in Bayesian model selection techniques and diagnostics to directly compare model fit and predictive power between models that included individual effects on survival and reproduction to those that did not. We found strong evidence for costs of reproduction to both survival and future reproduction, with breeders having rates of survival and subsequent reproduction that were 3% and 6% lower than rates for non-breeders. We detected age-related changes in the rates of survival and reproduction, but the patterns differed for the two rates. Survival rates steadily declined from 0.92 at age 7 to 0.56 at the maximal age of 31 yr. In contrast, reproductive rates increased from 0.68 at age 7 to 0.79 at age 16 and then steadily declined to 0.37 for the oldest females. Models that included individual effects explained more variation in observed life histories and had better estimated predictive power than those that did not, indicating their importance in understanding sources of variation among individuals in life-history traits. We found that among-individual heterogeneity in survival was small relative to that for reproduction. Our study, which found patterns of variation in vital rates that are consistent with a series of predictions from life-history theory, is the first to provide a thorough assessment of variation in important vital rates for a long-lived, high-latitude marine mammal while taking full advantage of recent developments in model evaluation.

On the robustness of N-mixture models.

N-mixture models provide an appealing alternative to mark-recapture models, in that they allow for estimation of detection probability and population size from count data, without requiring that individual animals be identified. There is, however, a cost to using the N-mixture models: inference is very sensitive to the model's assumptions. We consider the effects of three violations of assumptions that might reasonably be expected in practice: double counting, unmodeled variation in population size over time, and unmodeled variation in detection probability over time. These three examples show that small violations of assumptions can lead to large biases in estimation. The violations of assumptions we consider are not only small qualitatively, but are also small in the sense that they are unlikely to be detected using goodness-of-fit tests. In cases where reliable estimates of population size are needed, we encourage investigators to allocate resources to acquiring additional data, such as recaptures of marked individuals, for estimation of detection probabilities.

On the reliability of N-mixture models for count data.

N-mixture models describe count data replicated in time and across sites in terms of abundance N and detectability p. They are popular because they allow inference about N while controlling for factors that influence p without the need for marking animals. Using a capture-recapture perspective, we show that the loss of information that results from not marking animals is critical, making reliable statistical modeling of N and p problematic using just count data. One cannot reliably fit a model in which the detection probabilities are distinct among repeat visits as this model is overspecified. This makes uncontrolled variation in p problematic. By counter example, we show that even if p is constant after adjusting for covariate effects (the "constant p" assumption) scientifically plausible alternative models in which N (or its expectation) is non-identifiable or does not even exist as a parameter, lead to data that are practically indistinguishable from data generated under an N-mixture model. This is particularly the case for sparse data as is commonly seen in applications. We conclude that under the constant p assumption reliable inference is only possible for relative abundance in the absence of questionable and/or untestable assumptions or with better quality data than seen in typical applications. Relative abundance models for counts can be readily fitted using Poisson regression in standard software such as R and are sufficiently flexible to allow controlling for p through the use covariates while simultaneously modeling variation in relative abundance. If users require estimates of absolute abundance, they should collect auxiliary data that help with estimation of p.

Bayesian cross-validation for model evaluation and selection, with application to the North American Breeding Bird Survey.

The analysis of ecological data has changed in two important ways over the last 15 years. The development and easy availability of Bayesian computational methods has allowed and encouraged the fitting of complex hierarchical models. At the same time, there has been increasing emphasis on acknowledging and accounting for model uncertainty. Unfortunately, the ability to fit complex models has outstripped the development of tools for model selection and model evaluation: familiar model selection tools such as Akaike's information criterion and the deviance information criterion are widely known to be inadequate for hierarchical models. In addition, little attention has been paid to the evaluation of model adequacy in context of hierarchical modeling, i.e., to the evaluation of fit for a single model. In this paper, we describe Bayesian cross-validation, which provides tools for model selection and evaluation. We describe the Bayesian predictive information criterion and a Bayesian approximation to the BPIC known as the Watanabe-Akaike information criterion. We illustrate the use of these tools for model selection, and the use of Bayesian cross-validation as a tool for model evaluation, using three large data sets from the North American Breeding Bird Survey.

A cautionary note on the discrete uniform prior for the binomial N.

Analysis of wildlife data frequently involves estimation of population size N based on binomial counts. Bayesian analysts often use a constant prior for N, the choice motivated by a desire to avoid an informative prior, and to let the data speak for themselves. For instance, data augmentation methods for model Mh posit a super-population of size M >> N with individual detection probabilities z(i)p(i), with p(i) sampled from a parametric family of interest, and z(i) an indicator of membership in the target population; thus, N = Sigma(i)z(i). Treating z(i) as independent Bernoulli trials with success rate psi and assigning a uniform prior to psi is equivalent to assigning a discrete uniform prior for N on {0, 1,2,..., M}; by setting M large enough, analysts approximate the improper constant prior on the positive integers. In this paper, I demonstrate some paradoxical and plainly unacceptable features of the constant prior. These defects are not shared by the scale prior, which has been recommended for its good performance as measured by frequentist criteria. I show how the scale prior can be approximated in program OpenBUGS, including data augmentation applications for individual covariates.

A flexible Bayesian hierarchical approach for analyzing spatial and temporal variation in the fecal corticosterone levels in birds when there is imperfect knowledge of individual identity.

Population cycles have long interested biologists. The ruffed grouse, Bonasa umbellus, is one such species whose populations cycle over most of their range. Thus, much effort has been expended to understand the mechanisms that might control cycles in this and other species. Corticosterone metabolites are widely used in studies of animals to measure physiological stress. We evaluated corticosterone metabolites in feces of territorial male grouse as a potential tool to study mechanisms governing grouse cycles. However, like most studies of corticosterone in wild animals, we did not know the identity of all individuals for which we had fecal samples. This presented an analytical problem that resulted in either pseudoreplication or confounding. Therefore, we derived an analytical approach that accommodated for uncertainty in individual identification. Because we had relatively low success capturing birds, we estimated turnover probabilities of birds on territorial display sites based on capture histories of a limited number of birds we captured. Hence, we developed a study design and modeling approach to quantify variation in corticosterone levels among individuals and through time that would be applicable to any field study of corticosterone in wild animals. Specifically, we wanted a sampling design and model that was flexible enough to partition variation among individuals, spatial units, and years, while incorporating environmental covariates that would represent potential mechanisms. We conducted our study during the decline phase of the grouse cycle and found high variation among corticosterone samples (11.33-443.92 ng/g [x=113.99 ng/g, SD=69.08, median=99.03 ng/g]). However, there were relatively small differences in corticosterone levels among years, but levels declined throughout each breeding season, which was opposite our predictions for stress hormones correlating with a declining population. We partitioned the residual variation into site, bird, and repetition (i.e., multiple samples collected from the same bird on the same day). After accounting for years and three general periods within breeding seasons, 42% of the residual variation among observations was attributable to differences among individual birds. Thus, we attribute little influence of site on stress level of birds in our study, but disentangling individual from site effects is difficult because site and bird are confounded. Our model structures provided analytical approaches for studying species having different ecologies. Our approach also demonstrates that even incomplete information on individual identity of birds within samples is useful for analyzing these types of data.

Evaluating the demographic buffering hypothesis with vital rates estimated for Weddell seals from 30 years of mark-recapture data.

1. Life-history theory predicts that those vital rates that make larger contributions to population growth rate ought to be more strongly buffered against environmental variability than are those that are less important. Despite the importance of the theory for predicting demographic responses to changes in the environment, it is not yet known how pervasive demographic buffering is in animal populations because the validity of most existing studies has been called into question because of methodological deficiencies. 2. We tested for demographic buffering in the southern-most breeding mammal population in the world using data collected from 5558 known-age female Weddell seals over 30 years. We first estimated all vital rates simultaneously with mark-recapture analysis and then estimated process variance and covariance in those rates using a hierarchical Bayesian approach. We next calculated the population growth rate's sensitivity to changes in each of the vital rates and tested for evidence of demographic buffering by comparing properly scaled values of sensitivity and process variance in vital rates. 3. We found evidence of positive process covariance between vital rates, which indicates that all vital rates are affected in the same direction by changes in annual environment. Despite the positive correlations, we found strong evidence that demographic buffering occurred through reductions in variation in the vital rates to which population growth rate was most sensitive. Process variation in vital rates was inversely related to sensitivity measures such that variation was greatest in breeding probabilities, intermediate for survival rates of young animals and lowest for survival rates of older animals. 4. Our work contributes to a small but growing set of studies that have used rigorous methods on long-term, detailed data to investigate demographic responses to environmental variation. The information from these studies improves our understanding of life-history evolution in stochastic environments and provides useful information for predicting population responses to future environmental change. Our results for an Antarctic apex predator also provide useful baselines from a marine ecosystem when its top- and middle-trophic levels were not substantially impacted by human activity.

Estimating age from recapture data: integrating incremental growth measures with ancillary data to infer age-at-length.

Estimating the age of individuals in wild populations can be of fundamental importance for answering ecological questions, modeling population demographics, and managing exploited or threatened species. Significant effort has been devoted to determining age through the use of growth annuli, secondary physical characteristics related to age, and growth models. Many species, however, either do not exhibit physical characteristics useful for independent age validation or are too rare to justify sacrificing a large number of individuals to establish the relationship between size and age. Length-at-age models are well represented in the fisheries and other wildlife management literature. Many of these models overlook variation in growth rates of individuals and consider growth parameters as population parameters. More recent models have taken advantage of hierarchical structuring of parameters and Bayesian inference methods to allow for variation among individuals as functions of environmental covariates or individual-specific random effects. Here, we describe hierarchical models in which growth curves vary as individual-specific stochastic processes, and we show how these models can be fit using capture-recapture data for animals of unknown age along with data for animals of known age. We combine these independent data sources in a Bayesian analysis, distinguishing natural variation (among and within individuals) from measurement error. We illustrate using data for African dwarf crocodiles, comparing von Bertalanffy and logistic growth models. The analysis provides the means of predicting crocodile age, given a single measurement of head length. The von Bertalanffy was much better supported than the logistic growth model and predicted that dwarf crocodiles grow from 19.4 cm total length at birth to 32.9 cm in the first year and 45.3 cm by the end of their second year. Based on the minimum size of females observed with hatchlings, reproductive maturity was estimated to be at nine years. These size benchmarks are believed to represent thresholds for important demographic parameters; improved estimates of age, therefore, will increase the precision of population projection models. The modeling approach that we present can be applied to other species and offers significant advantages when multiple sources of data are available and traditional aging techniques are not practical.

Uncovering a latent multinomial: analysis of mark-recapture data with misidentification.

Natural tags based on DNA fingerprints or natural features of animals are now becoming very widely used in wildlife population biology. However, classic capture-recapture models do not allow for misidentification of animals which is a potentially very serious problem with natural tags. Statistical analysis of misidentification processes is extremely difficult using traditional likelihood methods but is easily handled using Bayesian methods. We present a general framework for Bayesian analysis of categorical data arising from a latent multinomial distribution. Although our work is motivated by a specific model for misidentification in closed population capture-recapture analyses, with crucial assumptions which may not always be appropriate, the methods we develop extend naturally to a variety of other models with similar structure. Suppose that observed frequencies f are a known linear transformation f=A'x of a latent multinomial variable x with cell probability vector pi=pi(theta). Given that full conditional distributions [theta | x] can be sampled, implementation of Gibbs sampling requires only that we can sample from the full conditional distribution [x | f, theta], which is made possible by knowledge of the null space of A'. We illustrate the approach using two data sets with individual misidentification, one simulated, the other summarizing recapture data for salamanders based on natural marks.

An evaluation of density-dependent and density-independent influences on population growth rates in Weddell seals.

Much of the existing literature that evaluates the roles of density-dependent and density-independent factors on population dynamics has been called into question in recent years because measurement errors were not properly dealt with in analyses. Using state-space models to account for measurement errors, we evaluated a set of competing models for a 22-year time series of mark-resight estimates of abundance for a breeding population of female Weddell seals (Leptonychotes weddellii) studied in Erebus Bay, Antarctica. We tested for evidence of direct density dependence in growth rates and evaluated whether equilibrium population size was related to seasonal sea-ice extent and the Southern Oscillation Index (SOI). We found strong evidence of negative density dependence in annual growth rates for a population whose estimated size ranged from 438 to 623 females during the study. Based on Bayes factors, a density-dependence-only model was favored over models that also included environmental covariates. According to the favored model, the population had a stationary distribution with a mean of 497 females (SD = 60.5), an expected growth rate of 1.10 (95% credible interval = 1.08-1.15) when population size was 441 females, and a rate of 0.90 (95% credible interval = 0.87-.93) for a population of 553 females. A model including effects of SOI did receive some support and indicated a positive relationship between SOI and population size. However, effects of SOI were not large, and including the effect did not greatly reduce our estimate of process variation. We speculate that direct density dependence occurred because rates of adult survival, breeding, and temporary emigration were affected by limitations on per capita food resources and space for parturition and pup-rearing. To improve understanding of the relative roles of various demographic components and their associated vital rates to population growth rate, mark-recapture methods can be applied that incorporate both environmental covariates and the seal abundance estimates that were developed here. An improved understanding of why vital rates change with changing population abundance will only come as we develop a better understanding of the processes affecting marine food resources in the Southern Ocean.

Apparent tolerance of turkey vultures (Cathartes aura) to the non-steroidal anti-inflammatory drug diclofenac.

The nonsteroidal anti-inflammatory drug diclofenac is extremely toxic to Old World Gyps vultures (median lethal dose -0.1-0.2 mg/kg), evoking visceral gout, renal necrosis, and mortality within a few days of exposure. Unintentional secondary poisoning of vultures that fed upon carcasses of diclofenac-treated livestock decimated populations in the Indian subcontinent. Because of the widespread use of diclofenac and other cyclooxygenase-2 inhibiting drugs, a toxicological study was undertaken in turkey vultures (Cathartes aura) as an initial step in examining sensitivity of New World scavenging birds. Two trials were conducted entailing oral gavage of diclofenac at doses ranging from 0.08 to 25 mg/kg body weight. Birds were observed for 7 d, blood samples were collected for plasma chemistry (predose and 12, 24, and 48 h and 7 d postdose), and select individuals were necropsied. Diclofenac failed to evoke overt signs of toxicity, visceral gout, renal necrosis, or elevate plasma uric acid at concentrations greater than 100 times the estimated median lethal dose reported for Gyps vultures. For turkey vultures receiving 8 or 25 mg/kg, the plasma half-life of diclofenac was estimated to be 6 h, and it was apparently cleared after several days as no residues were detectable in liver or kidney at necropsy. Differential sensitivity among avian species is a hallmark of cyclooxygenase-2 inhibitors, and despite the tolerance of turkey vultures to diclofenac, additional studies in related scavenging species seem warranted.

Effects of methylmercury on reproduction in American kestrels.

Sixty breeding pairs of captive American kestrels (Falco sparverius) were exposed to a range of sublethal dietary concentrations of mercury (Hg), in the form of methylmercuric chloride, and their subsequent reproduction was measured. Egg production, incubation performance, and the number and percent of eggs hatched decreased markedly between 3.3 and 4.6 mg/kg dry weight of Hg (1.2 and 1.7 mg/kg wet wt), in the diet. The number of fledglings and the percent of nestlings fledged were reduced markedly at 0.7 mg/kg dry weight (0.3 mg/kg wet wt) and declined further between 2 and 3.3 mg/kg dry weight (0.7 and 1.2 mg/kg wet wt). Dietary concentrations of >or=4.6 mg/kg dry weight (1.7 mg/kg wet wt) were associated with total fledging failure. The estimated decline in fledged young per pair (24%, Bayesian regression) for kestrels consuming 0.7 mg/kg dry weight (0.3 mg/ kg wet wt) raises concerns about population maintenance in areas subject to high inputs of anthropogenic Hg. Mercury concentrations in 20 second-laid eggs collected from all groups were related to dietary concentrations of Hg, and the Hg concentrations in 19 of these eggs were related to eggs laid and young fledged. Concentrations of Hg in eggs from the highest diet group (5.9 mg/kg dry wt; 2.2 mg/kg wet wt) were higher than egg concentrations reported for either wild birds or for captive birds (nonraptors) fed dry commercial food containing 5 mg/kg methylmercury. Accumulation ratios of Hg from diets to eggs were higher than those reported for feeding studies with other species.

Bayesian multimodel inference for dose-response studies.

Statistical inference in dose-response studies is model-based: The analyst posits a mathematical model of the relation between exposure and response, estimates parameters of the model, and reports conclusions conditional on the model. Such analyses rarely include any accounting for the uncertainties associated with model selection. The Bayesian inferential system provides a convenient framework for model selection and multimodel inference. In this paper we briefly describe the Bayesian paradigm and Bayesian multimodel inference. We then present a family of models for multinomial dose-response data and apply Bayesian multimodel inferential methods to the analysis of data on the reproductive success of American kestrels (Falco sparveriuss) exposed to various sublethal dietary concentrations of methylmercury.

Seasonal components of avian population change: joint analysis of two large-scale monitoring programs.

We present a combined analysis of data from two large-scale surveys of bird populations. The North American Breeding Bird Survey is conducted each summer; the Christmas Bird Count is conducted in early winter. The temporal staggering of these surveys allows investigation of seasonal components of population change, which we illustrate with an examination of the effects of severe winters on the Carolina Wren (Thryothorus ludovicianus). Our analysis uses a hierarchical log-linear model with controls for survey-specific sampling covariates. Temporal change in population size is modeled seasonally, with covariates for winter severity. Overall, the winter-spring seasons are associated with 82% of the total population variation for Carolina Wrens, and an additional day of snow cover during winter-spring is associated with an incremental decline of 1.1% of the population.

Model weights and the foundations of multimodel inference.

Statistical thinking in wildlife biology and ecology has been profoundly influenced by the introduction of AIC (Akaike's information criterion) as a tool for model selection and as a basis for model averaging. In this paper, we advocate the Bayesian paradigm as a broader framework for multimodel inference, one in which model averaging and model selection are naturally linked, and in which the performance of AIC-based tools is naturally evaluated. Prior model weights implicitly associated with the use of AIC are seen to highly favor complex models: in some cases, all but the most highly parameterized models in the model set are virtually ignored a priori. We suggest the usefulness of the weighted BIC (Bayesian information criterion) as a computationally simple alternative to AIC, based on explicit selection of prior model probabilities rather than acceptance of default priors associated with AIC. We note, however, that both procedures are only approximate to the use of exact Bayes factors. We discuss and illustrate technical difficulties associated with Bayes factors, and suggest approaches to avoiding these difficulties in the context of model selection for a logistic regression. Our example highlights the predisposition of AIC weighting to favor complex models and suggests a need for caution in using the BIC for computing approximate posterior model weights.

Generalized site occupancy models allowing for false positive and false negative errors.

Site occupancy models have been developed that allow for imperfect species detection or "false negative" observations. Such models have become widely adopted in surveys of many taxa. The most fundamental assumption underlying these models is that "false positive" errors are not possible. That is, one cannot detect a species where it does not occur. However, such errors are possible in many sampling situations for a number of reasons, and even low false positive error rates can induce extreme bias in estimates of site occupancy when they are not accounted for. In this paper, we develop a model for site occupancy that allows for both false negative and false positive error rates. This model can be represented as a two-component finite mixture model and can be easily fitted using freely available software. We provide an analysis of avian survey data using the proposed model and present results of a brief simulation study evaluating the performance of the maximum-likelihood estimator and the naive estimator in the presence of false positive errors.