Reconsidering the Price equation: Benchmarking the analytical power of additive partitioning in ecology

Abstract

The Price approach allows the partitioning of composite variables into a set of additive components and has become an important tool in evolutionary and ecological research. However, because such components are not mutually independent and might be constrained by the inherent data structure, comparing and interpreting Price partitions among different datasets is not straightforward and has contributed to controversy in ecology.Here we discuss and develop null model approaches that might be used as statistical standards to normalise partition values and reduce collinearity between partitions. We use a simulation approach to estimate Price partitions of artificial data and their randomisations. Using structural equation modelling we then reveal the degree of collinearity between raw and standardised partitions.We first demonstrate that the degree of collinearity between partitions strongly depends on the data structure and then provide a general framework for null model selection. Null models that require limited additional information on the possible distribution of species richness and abundance perform best. These null models consistently reduce, but do not fully eliminate, collinearity between partitions. They assign separate type I and II error levels to each partition that differed among partitions.We argue in favour of null models that strike a balance between information need (simplicity) and complexity of additional information, but we discourage the use of simple permutation approaches that have been successful for analysing other biodiversity measures such as species richness. We highlight that the interpretation of additive partitions of complex ecological data will benefit from analyses of the dependence among partitions.