The Challenge: Much of wildlife research consists of the description of variation in data. Some of the variation results from spatial and temporal change in populations, while some results from biologically irrelevant sampling variation induced by the process of data collection. Distinguishing relevant from irrelevant variation is the first task of statistical analysis, but the job does not end there. Even if the true values of population parameters were known, without the contamination of sampling variation, the investigation of population processes would require an evaluation of pattern among parameters.
The Science: Hierarchical models treat unknown population parameters as random variables, with probability distributions governed by hyperparameters. Knowledge of these stochastic relationships is fundamental to the understanding of demographic processes.
The analysis of hierarchical models has been facilitated by recent advances in Bayesian analysis, and computationally intensive techniques such as Markov Chain Monte Carlo. This study has been undertaken with the goal of promoting and developing hierarchical modeling solutions for demographic analysis.
For example, the demographic buffering hypothesis states that natural selection favors low temporal variability in population sensitive demographic parameters. An evaluation of this hypothesis using a 30-year mark-recapture data set for Weddell seals (Leptonychotes weddellii) required estimation not only of survival and recruitment rates, but also estimation of temporal variation and covariation among the rates.
The Future: Model selection and model criticism are important problems in statistical inference, and have been widely studied for simple models. These problems are more difficult for hierarchical models. Bayesian p-values and model weighting are tools for these tasks, but there is a need for further development of methods.
Work continues on the development and use of the Bayesian Predictive Information Criterion (BPIC) and a surrogate, the Watanabe/Akaike Information Criterion (WAIC). These are measures of the predictive ability of models, and are being used to compare trend models for the North American Breeding Bird Survey. BPIC is the gold standard, but is enormously computationally intensive, almost prohibitively so, even with parallel processing on fast multi-core computer systems. Work is in progress on combining the computational efficiencies of WAIC with the superior performance of BPIC.
Below are publications associated with this project.
Bayesian cross-validation for model evaluation and selection, with application to the North American Breeding Bird Survey
Individual heterogeneity in growth and age at sexual maturity: A gamma process analysis of capture–mark–recapture data
Truth, models, model sets, AIC, and multimodel inference: a Bayesian perspective
Modeling participation duration, with application to the North American Breeding Bird Survey
On thinning of chains in MCMC
Decision analysis for conservation breeding: Maximizing production for reintroduction of whooping cranes
Book review: Bayesian analysis for population ecology
Modeling misidentification errors that result from use of genetic tags in capture-recapture studies
Uncovering a latent multinomial: Analysis of mark-recapture data with misidentification
A Bayesian approach to identifying structural nonlinearity using free-decay response: Application to damage detection in composites
Below are partners associated with this project.
- Overview
The Challenge: Much of wildlife research consists of the description of variation in data. Some of the variation results from spatial and temporal change in populations, while some results from biologically irrelevant sampling variation induced by the process of data collection. Distinguishing relevant from irrelevant variation is the first task of statistical analysis, but the job does not end there. Even if the true values of population parameters were known, without the contamination of sampling variation, the investigation of population processes would require an evaluation of pattern among parameters.
The Science: Hierarchical models treat unknown population parameters as random variables, with probability distributions governed by hyperparameters. Knowledge of these stochastic relationships is fundamental to the understanding of demographic processes.
The analysis of hierarchical models has been facilitated by recent advances in Bayesian analysis, and computationally intensive techniques such as Markov Chain Monte Carlo. This study has been undertaken with the goal of promoting and developing hierarchical modeling solutions for demographic analysis.
For example, the demographic buffering hypothesis states that natural selection favors low temporal variability in population sensitive demographic parameters. An evaluation of this hypothesis using a 30-year mark-recapture data set for Weddell seals (Leptonychotes weddellii) required estimation not only of survival and recruitment rates, but also estimation of temporal variation and covariation among the rates.
The Future: Model selection and model criticism are important problems in statistical inference, and have been widely studied for simple models. These problems are more difficult for hierarchical models. Bayesian p-values and model weighting are tools for these tasks, but there is a need for further development of methods.
Work continues on the development and use of the Bayesian Predictive Information Criterion (BPIC) and a surrogate, the Watanabe/Akaike Information Criterion (WAIC). These are measures of the predictive ability of models, and are being used to compare trend models for the North American Breeding Bird Survey. BPIC is the gold standard, but is enormously computationally intensive, almost prohibitively so, even with parallel processing on fast multi-core computer systems. Work is in progress on combining the computational efficiencies of WAIC with the superior performance of BPIC.
- Publications
Below are publications associated with this project.
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 outstrAuthorsWilliam A. Link, John R. SauerIndividual heterogeneity in growth and age at sexual maturity: A gamma process analysis of capture–mark–recapture data
Knowledge of organisms’ growth rates and ages at sexual maturity is important for conservation efforts and a wide variety of studies in ecology and evolutionary biology. However, these life history parameters may be difficult to obtain from natural populations: individuals encountered may be of unknown age, information on age at sexual maturity may be uncertain and interval-censored, and growth daAuthorsWilliam A. Link, Kyle Miller HesedTruth, models, model sets, AIC, and multimodel inference: a Bayesian perspective
Statistical inference begins with viewing data as realizations of stochastic processes. Mathematical models provide partial descriptions of these processes; inference is the process of using the data to obtain a more complete description of the stochastic processes. Wildlife and ecological scientists have become increasingly concerned with the conditional nature of model-based inference: what if tAuthorsRichard J. Barker, William A. LinkModeling participation duration, with application to the North American Breeding Bird Survey
We consider “participation histories,” binary sequences consisting of alternating finite sequences of 1s and 0s, ending with an infinite sequence of 0s. Our work is motivated by a study of observer tenure in the North American Breeding Bird Survey (BBS). In our analysis, j indexes an observer’s years of service and Xj is an indicator of participation in the survey; 0s interspersed among 1s correspAuthorsWilliam A. Link, John R. SauerOn thinning of chains in MCMC
1. Markov chain Monte Carlo (MCMC) is a simulation technique that has revolutionised the analysis of ecological data, allowing the fitting of complex models in a Bayesian framework. Since 2001, there have been nearly 200 papers using MCMC in publications of the Ecological Society of America and the British Ecological Society, including more than 75 in the journal Ecology and 35 in the Journal of AAuthorsWilliam A. Link, Mitchell J. EatonDecision analysis for conservation breeding: Maximizing production for reintroduction of whooping cranes
Captive breeding is key to management of severely endangered species, but maximizing captive production can be challenging because of poor knowledge of species breeding biology and the complexity of evaluating different management options. In the face of uncertainty and complexity, decision-analytic approaches can be used to identify optimal management options for maximizing captive production. BuAuthorsDes H.V. Smith, Sarah J. Converse, Keith Gibson, Axel Moehrenschlager, William A. Link, Glenn H. Olsen, Kelly MaguireBook review: Bayesian analysis for population ecology
Brian Dennis described the field of ecology as “fertile, uncolonized ground for Bayesian ideas.” He continued: “The Bayesian propagule has arrived at the shore. Ecologists need to think long and hard about the consequences of a Bayesian ecology. The Bayesian outlook is a successful competitor, but is it a weed? I think so.” (Dennis 2004) Review info: Bayesian Analysis for Population Ecology. By RuAuthorsWilliam A. LinkModeling misidentification errors that result from use of genetic tags in capture-recapture studies
Misidentification of animals is potentially important when naturally existing features (natural tags) such as DNA fingerprints (genetic tags) are used to identify individual animals. For example, when misidentification leads to multiple identities being assigned to an animal, traditional estimators tend to overestimate population size. Accounting for misidentification in capture–recapture models rAuthorsJ. Yoshizaki, C. Brownie, K.H. Pollock, William A. LinkUncovering 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 bAuthorsW.A. Link, J. Yoshizaki, L.L. Bailey, K.H. PollockA Bayesian approach to identifying structural nonlinearity using free-decay response: Application to damage detection in composites
This work discusses a Bayesian approach to approximating the distribution of parameters governing nonlinear structural systems. Specifically, we use a Markov Chain Monte Carlo method for sampling the posterior parameter distributions thus producing both point and interval estimates for parameters. The method is first used to identify both linear and nonlinear parameters in a multiple degree-of-freAuthorsJ.M. Nichols, W.A. Link, K.D. Murphy, C.C. Olson - Partners
Below are partners associated with this project.