Nonlinear averaging in 2D: intraspecific variation in two interacting species and consequences for population dynamics

Abstract

Interactions between two species, e.g. between a predator species and a prey species, can often be described as the sum of many individual-by-individual interactions whose outcomes depend on the traits of the interacting individuals. These traits often vary substantially among individuals in each species, and individuals do not always interact randomly, e.g. due to plastic responses to a shared environmental factor in a heterogeneous landscape. Here we investigate the impact of intraspecific trait variation (ITV) and such interspecific trait correlations on species interactions via nonlinear averaging. Building on past models that integrate over an interaction kernel to obtain the impacts of ITV, we develop a modeling framework that allows to model arbitrary species interactions, with interspecific trait correlations as novel feature. Based on two key ingredients, a joint trait distribution and a two-dimensional interaction function, the average interaction parameters (e.g. average predation rate) can be quantified numerically, approximated using an insightful Taylor approximation, and compared to cases without ITV. We highlight two applications of our framework. First, we study the quantitative and qualitative effects of ITV and trait correlations in a simple predator-prey model and show that even in the absence of evolution, variation and trait correlations among interacting individuals can make or break the coexistence between species. Second, we use simulated field data for a predator-prey system to show how the impact of ITV on an ecological interaction can be estimated from empirical data. HighlightsO_LIWe model how intraspecific trait variation in two species affects their interaction. C_LIO_LIOur framework allows correlations between the traits of interacting individuals. C_LIO_LITrait variation and correlations can strongly affect ecological interactions. C_LIO_LITrait variation and correlations can make or break coexistence. C_LIO_LIThe effect of intraspecific trait variation can be estimated from data. C_LI