Use of posterior predictive checks as an inferential tool for investigating individual heterogeneity in animal population vital rates
Article first published online: 20 MAR 2014
© 2014 The Authors. Ecology and Evolution published by John Wiley & Sons Ltd.
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Ecology and Evolution
Volume 4, Issue 8, pages 1389–1397, April 2014
How to Cite
Ecology and Evolution 2014; 4(8):1389–1397
- Issue published online: 22 APR 2014
- Article first published online: 20 MAR 2014
- Manuscript Accepted: 23 JAN 2014
- Manuscript Received: 14 JAN 2014
- Manuscript Revised: 14 JAN 2014
- National Science Foundation
- Division of Polar Programsn. Grant Number: ANT-1141326
- Bayesian inference;
- dynamic heterogeneity;
- fixed heterogeneity;
- individual variation;
- Leptonychotes weddellii;
- model checking;
- posterior predictive checking;
- state-space models
The investigation of individual heterogeneity in vital rates has recently received growing attention among population ecologists. Individual heterogeneity in wild animal populations has been accounted for and quantified by including individually varying effects in models for mark–recapture data, but the real need for underlying individual effects to account for observed levels of individual variation has recently been questioned by the work of Tuljapurkar et al. (Ecology Letters, 12, 93, 2009) on dynamic heterogeneity. Model-selection approaches based on information criteria or Bayes factors have been used to address this question. Here, we suggest that, in addition to model-selection, model-checking methods can provide additional important insights to tackle this issue, as they allow one to evaluate a model's misfit in terms of ecologically meaningful measures. Specifically, we propose the use of posterior predictive checks to explicitly assess discrepancies between a model and the data, and we explain how to incorporate model checking into the inferential process used to assess the practical implications of ignoring individual heterogeneity. Posterior predictive checking is a straightforward and flexible approach for performing model checks in a Bayesian framework that is based on comparisons of observed data to model-generated replications of the data, where parameter uncertainty is incorporated through use of the posterior distribution. If discrepancy measures are chosen carefully and are relevant to the scientific context, posterior predictive checks can provide important information allowing for more efficient model refinement. We illustrate this approach using analyses of vital rates with long-term mark–recapture data for Weddell seals and emphasize its utility for identifying shortfalls or successes of a model at representing a biological process or pattern of interest.