Model-based variance partitioning for statistical ecology

Abstract

Variance partitioning is a common tool for statistical analysis and interpretation in both observational and experimental studies in ecology. Its popularity has led to a proliferation of methods with sometimes confusing or contradicting interpretations. Here, we present variance partitioning in a model-based Bayesian framework as a general tool for summarizing and interpreting regression-like models to produce additional insight on ecological studies compared with what traditional parameter inference of these models on its own can reveal. For example, we propose predictive variance partitioning as a tool to extend sample-based analyses to analyses of whole populations or predictive scenarios. We also extend variance partitioning to encompass partitioning of variance within and between ecologically relevant subgroups of the observations, or the whole population of interest, to provide information on how the relative roles of processes underlying the study system may vary depending on the environmental or ecological context. We discuss the role of correlated covariates and random effects and highlight uncertainty quantification in variance partitioning. To showcase the utility of our approach, we present a case study comprising a simple occupancy model for a metapopulation of the Glanville fritillary butterfly. As a result, we demonstrate model-based variance partitioning as a general and rigorous statistical tool to gain more insight from ecological data.