Quantifying the effects of intraspecific trait variation and interspecific trait correlations on interacting populations—A nonlinear averaging approach

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 theoretical framework allowing the modeling of arbitrary species interactions, with interspecific trait correlations as a 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.