A game-theory–inspired decomposition of interspecific interaction matrices

Abstract

In evolutionary game theory, pair interactions are usually defined through so-called payoff matrices, which can be decomposed as linear combinations of basis matrices that represent just four different orthogonal interaction types. In this paper, we take the first steps in exploring the utility of this decomposition in ecology. We introduce the componental cosines of the irrelevant, external, coordination, and conflict components of matrices to measure the relative weight of the different interaction types, and use them to analyse the composition of 33 experimentally obtained interspecific interaction matrices compiled from the literature, which reveals statistically significant correlations both between different components and some components and community productivity and biodiversity.