Development of Statistical Methods for Biological Applications

Science Center Objects

The Challenge: Wildlife science and management are guided by data, and it is unquestionably the case that the greatest success occurs when good data are analyzed by good statistical methods.

The Science:

This study provides the basis for collaboration between a mathematical statistician and quantitative ecologists.  One such collaboration led to the development of techniques for aging Dwarf crocodiles (Osteolaemus tetraspis), informed by model based analysis of two data sets, one consisting of young crocodiles of known age, another consisting of recapture data for older crocodiles of unknown age.  Methods developed for these crocodiles have been applied to wildebeest (Connochaetes taurinus albojubotus), frogs (Rana sierra) and even trees (Juniperus ashei).

A major product of the study has been publication of the book Bayesian Inference, with Ecological Applications by W.A. Link and R.J. Barker.  The Bayesian approach to statistical inference was first described in Thomas Bayes’  “An Essay towards solving a Problem in the Doctrine of Chances” published posthumously in 1763. Bayesian methods were largely ignored in the early twentieth century, but their usefulness for describing complex models, in concert with advances in computational capacity, has led to a surge of interest, which is revolutionizing statistical analysis.  A wildcard search for “Bayes*” in the text of publications of the Ecological Society of America provides an index to the phenomenon: 17, 29, 46, 69 and 85 publications are found for 1990-1994, 1995-1999, 2000-2004, 2005-2009 and 20101-2014.  Link and Barker's text has been well received, not only as an introduction to the Bayesian paradigm, but also for its presentations of Bayesian analysis of a variety of ecological and wildlife data.

The Future: The Bayesian paradigm is a mathematically sound and reliable basis for multimodel inference.  Bayesian multimodel inference has been and continues to be an important component of this study.   This study has addressed practical difficulties associated with choices of  objective prior distributions, and computational difficulties associated with Reversible Jump Markov chain Monte Carlo.

Research also continues on computational methods for Bayesian models describing complex latent structures.  Widely available and popular software packages such as OpenBUGS and JAGS are usually effective, but not always. Latent multinomial structures are problematic, requiring the selection of Markov bases for implementation of Gibbs sampling.  Applications have included models for growth and movement in closed populations based on removal data, and mark-recapture models accounting for misidentification.