Doors and corners of variance partitioning in 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 as a general tool in a model based Bayesian framework for summarizing and interpreting regression-like models. To demonstrate our approach we present a case study comprising of a simple occupancy model for a metapopulation of the Glanville fritillary butterfly. We pay special attention to the thorny issue of correlated covariates and random effects, and highlight uncertainty in variance partitioning. We recommend several alternative measures of variance, which jointly can be used to better interpret variance partitions. Additionally, we extend the general approach to encompass partitioning of variance within and between groups of observations, an approach very similar to analysis of variance. While noting that many troublesome issues relating to variance partitioning, such as uncertainty quantification, have been neglected in the literature, we likewise feel that the rather general applicability of the methods as an extension of statistical model-based analyses has not been fully utilized by the ecological research community either.