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W.A. Link

Publications and source records attributed to W.A. Link.

At least 37 records · Page 2Linked to original sources
USGS2006

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.

Ecology↗
USGS2006

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.

Ecology↗
USGS2004

Testing life history predictions in a long-lived seabird: A population matrix approach with improved parameter estimation

Life history theory and associated empirical generalizations predict that population growth rate (λ) in long-lived animals should be most sensitive to adult survival; the rates to which λ is most sensitive should be those with the smallest temporal variances; and stochastic environmental events should most affect the rates to which λ is least sensitive. To date, most analyses attempting to examine these predictions have been inadequate, their validity being called into question by problems in estimating parameters, problems in estimating the variability of parameters, and problems in measuring population sensitivities to parameters. We use improved methodologies in these three areas and test these life-history predictions in a population of red-tailed tropicbirds ( Phaethon rubricauda ). We support our first prediction that λ is most sensitive to survival rates. However the support for the second prediction that these rates have the smallest temporal variance was equivocal. Previous support for the second prediction may be an artifact of a high survival estimate near the upper boundary of 1 and not a result of natural selection canalizing variances alone. We did not support our third prediction that effects of environmental stochasticity (El Niño) would most likely be detected in vital rates to which λ was least sensitive and which are thought to have high temporal variances. Comparative data-sets on other seabirds, within and among orders, and in other locations, are needed to understand these environmental effects.

Oikos↗
USGS2004

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. 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.

Proceedings of the National Academy of Sciences↗
USGS2004

Some consequences of using counts of birds banded as indices to populations

In mist-net studies, it is often difficult to use capture-recapture methods to estimate number of birds present. Many investigators use number of birds captured as an index of population size. We investigate the consequences of using indices of bird abundance as surrogates for population size in hypothesis tests. Unless all of the birds present are captured, indices are biased estimates of local population size, and the amount of bias depends on the proportion of birds captured. We demonstrate the potential effects of bias on hypothesis tests based on indices. The bias generally causes type I error rates to be inflated. Investigators should either estimate the proportion of animals captured using capture-recapture methods or demonstrate that results of hypothesis tests based on indices are not consequences of bias in the indices.

Book chapter↗
USGS2004

Individual heterogeneity and identifiability in capture-recapture models

Individual heterogeneity in detection probabilities is a far more serious problem for capture-recapture modeling than has previously been recognized. In this note, I illustrate that population size is not an identifiable parameter under the general closed population mark-recapture model Mh. The problem of identifiability is obvious if the population includes individuals with pi = 0, but persists even when it is assumed that individual detection probabilities are bounded away from zero. Identifiability may be attained within parametric families of distributions for pi , but not among parametric families of distributions. Consequently, in the presence of individual heterogeneity in detection probability, capture-recapture analysis is strongly model dependent.

Animal Biodiversity and Conservation↗
USGS2004

Hierarchial mark-recapture models: a framework for inference about demographic processes

The development of sophisticated mark-recapture models over the last four decades has provided fundamental tools for the study of wildlife populations, allowing reliable inference about population sizes and demographic rates based on clearly formulated models for the sampling processes. Mark-recapture models are now routinely described by large numbers of parameters. These large models provide the next challenge to wildlife modelers: the extraction of signal from noise in large collections of parameters. Pattern among parameters can be described by strong, deterministic relations (as in ultrastructural models) but is more flexibly and credibly modeled using weaker, stochastic relations. Trend in survival rates is not likely to be manifest by a sequence of values falling precisely on a given parametric curve; rather, if we could somehow know the true values, we might anticipate a regression relation between parameters and explanatory variables, in which true value equals signal plus noise. Hierarchical models provide a useful framework for inference about collections of related parameters. Instead of regarding parameters as fixed but unknown quantities, we regard them as realizations of stochastic processes governed by hyperparameters. Inference about demographic processes is based on investigation of these hyperparameters. We advocate the Bayesian paradigm as a natural, mathematically and scientifically sound basis for inference about hierarchical models. We describe analysis of capture-recapture data from an open population based on hierarchical extensions of the Cormack-Jolly-Seber model. In addition to recaptures of marked animals, we model first captures of animals and losses on capture, and are thus able to estimate survival probabilities w (i.e., the complement of death or permanent emigration) and per capita growth rates f (i.e., the sum of recruitment and immigration rates). Covariation in these rates, a feature of demographic interest, is explicitly described in the model.

Animal Biodiversity and Conservation↗
USGS2003

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. The problem is illustrated with models for closed and open populations.

Biometrics↗
USGS2003

Estimation of change in populations and communities from monitoring survey data

Monitoring surveys provide fundamental information for use in environmental decision making by permitting assessment of both current population (or community) status and change in status, by providing a historical context of the present status, and by documenting response to ongoing management. Conservation of species and communities has historically been based upon monitoring information, and prioritization of species and habitats for conservation action often requires reliable, quantitative results. Although many monitoring programs exist for populations, species, and communities, as well as for biotic and abiotic features of the environment, estimation of population and community change from surveys can sometimes be controversial, and demands on monitoring information have increased greatly in recent years. Information is often required at multiple spatial scales for use in geographic information systems, and information needs exist for description of regional patterns of change in populations, communities, and ecosystems. Often, attempts are made to meet these needs using information collected for other purposes or at inappropriate geographic scales, leading to information that is difficult to analyze and interpret. In this chapter, we address some of the constraints and issues associated with estimating change in wildlife species and species groups from monitoring surveys, and use bird surveys as our primary examples.

Book chapter↗
USGS2003

Hierarchical models and the analysis of bird survey information

Management of birds often requires analysis of collections of estimates. We describe a hierarchical modeling approach to the analysis of these data, in which parameters associated with the individual species estimates are treated as random variables, and probability statements are made about the species parameters conditioned on the data. A Markov-Chain Monte Carlo (MCMC) procedure is used to fit the hierarchical model. This approach is computer intensive, and is based upon simulation. MCMC allows for estimation both of parameters and of derived statistics. To illustrate the application of this method, we use the case in which we are interested in attributes of a collection of estimates of population change. Using data for 28 species of grassland-breeding birds from the North American Breeding Bird Survey, we estimate the number of species with increasing populations, provide precision-adjusted rankings of species trends, and describe a measure of population stability as the probability that the trend for a species is within a certain interval. Hierarchical models can be applied to a variety of bird survey applications, and we are investigating their use in estimation of population change from survey data.

Ornis Hungarica↗
USGS2002

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. 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.

Brittany↗
USGS2002

Hierarchical modeling of population stability and species group attributes from survey data

Many ecological studies require analysis of collections of estimates. For example, population change is routinely estimated for many species from surveys such as the North American Breeding Bird Survey (BBS), and the species are grouped and used in comparative analyses. We developed a hierarchical model for estimation of group attributes from a collection of estimates of population trend. The model uses information from predefined groups of species to provide a context and to supplement data for individual species; summaries of group attributes are improved by statistical methods that simultaneously analyze collections of trend estimates. The model is Bayesian; trends are treated as random variables rather than fixed parameters. We use Markov Chain Monte Carlo (MCMC) methods to fit the model. Standard assessments of population stability cannot distinguish magnitude of trend and statistical significance of trend estimates, but the hierarchical model allows us to legitimately describe the probability that a trend is within given bounds. Thus we define population stability in terms of the probability that the magnitude of population change for a species is less than or equal to a predefined threshold. We applied the model to estimates of trend for 399 species from the BBS to estimate the proportion of species with increasing populations and to identify species with unstable populations. Analyses are presented for the collection of all species and for 12 species groups commonly used in BBS summaries. Overall, we estimated that 49% of species in the BBS have positive trends and 33 species have unstable populations. However, the proportion of species with increasing trends differs among habitat groups, with grassland birds having only 19% of species with positive trend estimates and wetland birds having 68% of species with positive trend estimates.

Ecology↗
USGS2002

A hierarchical analysis of population change with application to Cerulean Warblers

Estimation of population change from count surveys is complicated by variation in quality of information among sample units, by the need for covariates to accommodate factors that influence detectability of animals, and by multiple geographic scales of interest. We present a hierarchical model for estimation of population change from the North American Breeding Bird Survey. Hierarchical models, in which population parameters at different geographic scales are viewed as random variables, provide a convenient framework for summary of population change among regions, accommodating regional variation in survey quality and a variety of distributional assumptions about observer effects and other nuisance parameters. Markov chain Monte Carlo methods provide a convenient means for fitting these models and also allow for construction of estimates of derived variables such as weighted regional trends and composite yearly population indices. We construct an overdispersed Poisson regression model for estimation of trend and year effects for Cerulean Warblers (Dendroica cerulea), accommodating nuisance covariates for observer and start-up effects, and estimating abundance- and area-weighted annual indices at regional and continent-wide geographic scales. A goodness-of-fit test is also presented for the model. Cerulean Warblers declined at a rate of 3.04% per year over the interval 1966-2000.

Ecology↗
USGS2002

Scaling in sensitivity analysis

Population matrix models allow sets of demographic parameters to be summarized by a single value λ , the finite rate of population increase. The consequences of change in individual demographic parameters are naturally measured by the corresponding changes in λ ; sensitivity analyses compare demographic parameters on the basis of these changes. These comparisons are complicated by issues of scale. Elasticity analysis attempts to deal with issues of scale by comparing the effects of proportional changes in demographic parameters, but leads to inconsistencies in evaluating demographic rates. We discuss this and other problems of scaling in sensitivity analysis, and suggest a simple criterion for choosing appropriate scales. We apply our suggestions to data for the killer whale, Orcinus orca .

Ecology↗