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.

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.

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.

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.

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.

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.

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.

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.

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).

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.

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.

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.

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).

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.

Individual covariation in life-history traits: seeing the trees despite the forest.

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.

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.

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.

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.

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).

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.

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.

Toxicity and hazard of vanadium to mallard ducks (Anas platyrhynchos) and Canada geese (Branta canadensis).

A recent Canada goose (Branta canadensis) die-off at a petroleum refinery fly ash pond in Delaware was attributed to vanadium (V) toxicity. Because of the paucity of V toxicity data for wild birds, a series of studies was undertaken using the forms of V believed to have resulted in this incident. In 7-d single oral dose trials with mallard drakes (Anas platyrhynchos), the estimated median lethal dose (LD50) for vanadium pentoxide was 113 mg/kg body weight, while the LD50 for sodium metavanadate was 75.

Modeling association among demographic parameters in analysis of open population capture-recapture data.

We present a hierarchical extension of the Cormack-Jolly-Seber (CJS) model for open population capture-recapture data. In addition to recaptures of marked animals, we model first captures of animals and losses on capture. The parameter set includes capture probabilities, survival rates, and birth rates.

Tigers and their prey: Predicting carnivore densities from prey abundance.

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.

Nonidentifiability of population size from capture-recapture data with heterogeneous detection probabilities.

Heterogeneity in detection probabilities has long been recognized as problematic in mark-recapture studies, and numerous models developed to accommodate its effects. Individual heterogeneity is especially problematic, in that reasonable alternative models may predict essentially identical observations from populations of substantially different sizes. Thus even with very large samples, the analyst will not be able to distinguish among reasonable models of heterogeneity, even though these yield quite distinct inferences about population size.