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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.

The goal of ecology is to understand interactions that determine the distribution and abundance of organisms. In principle, ecologists should be able to identify a small number of limiting resources for a species of interest, estimate densities of these resources at different locations across the landscape, and then use these estimates to predict the density of the focal species at these locations. In practice, however, development of functional relationships between abundances of species and their resources has proven extremely difficult, and examples of such predictive ability are very rare. Ecological studies of prey requirements of tigers Panthera tigris led us to develop a simple mechanistic model for predicting tiger density as a function of prey density. We tested our model using data from a landscape-scale long-term (1995-2003) field study that estimated tiger and prey densities in 11 ecologically diverse sites across India. We used field techniques and analytical methods that specifically addressed sampling and detectability, two issues that frequently present problems in macroecological studies of animal populations. Estimated densities of ungulate prey ranged between 5.3 and 63.8 animals per km 2 . Estimated tiger densities (3.2-16.8 tigers per 100 km 2 ) were reasonably consistent with model predictions. The results provide evidence of a functional relationship between abundances of large carnivores and their prey under a wide range of ecological conditions. In addition to generating important insights into carnivore ecology and conservation, the study provides a potentially useful model for the rigorous conduct of macroecological science. E cological investigations basically involve efforts to understand interactions that determine the spatial distribution and abundance of organisms (1-3). Ecologists strive for a predictive science in which they can identify key attributes as potential limiting factors for a focal species, measure these attributes at different locations, and make predictions about the abundance of the focal species based on these measured attributes. An alternative popular approach to the study of spatial distribution and abundance is to search for patterns in existing data and then to treat perceived patterns as phenomenological models to be used for making predictions. Regardless of research approach, the study of the distribution and abundance of organisms at large spatial scales (i.e., macroecological patterns) has received substantial emphasis recently (3)(4)(5)(6)(7)(8).Analyses directed at macroecological questions require data collected at a scale far beyond the typical study areas of most field ecologists. As a result, such analyses are usually based on either large-scale count surveys of animal populations (6) or on metaanalyses of results from numerous individual studies (8). However, most large-scale count surveys of animal populations fail to yield strong inferences for two reasons: they are based on raw count data (indices) bearing an unknown relationship to true anima...

We investigated the influence of age on survival and breeding rates in a long-lived species Rissa tridactyla using models with individual random effects permitting variation and covariation in fitness components among individuals. Differences in survival or breeding probabilities among individuals are substantial, and there was positive covariation between survival and breeding probability; birds that were more likely to survive were also more likely to breed, given that they survived. The pattern of age-related variation in these rates detected at the individual level differed from that observed at the population level. Our results provided confirmation of what has been suggested by other investigators: within-cohort phenotypic selection can mask senescence. Although this phenomenon has been extensively studied in humans and captive animals, conclusive evidence of the discrepancy between population-level and individual-level patterns of age-related variation in life-history traits is extremely rare in wild animal populations. Evolutionary studies of the influence of age on life-history traits should use approaches differentiating population level from the genuine influence of age: only the latter is relevant to theories of life-history evolution. The development of models permitting access to individual variation in fitness is a promising advance for the study of senescence and evolutionary processes.

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.

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Multinomial models with unknown index ("sample size") arise in many practical settings. In practice, Bayesian analysis of such models has proved difficult because the dimension of the parameter space is not fixed, being in some cases a function of the unknown index. We describe a data augmentation approach to the analysis of this class of models that provides for a generic and efficient Bayesian implementation. Under this approach, the data are augmented with all-zero detection histories. The resulting augmented dataset is modeled as a zero-inflated version of the complete-data model where an estimable zero-inflation parameter takes the place of the unknown multinomial index. Interestingly, data augmentation can be justified as being equivalent to imposing a discrete uniform prior on the multinomial index. We provide three examples involving estimating the size of an animal population, estimating the number of diabetes cases in a population using the Rasch model, and the motivating example of estimating the number of species in an animal community with latent probabilities of species occurrence and detection.