Decoding the interaction mediators from landscape-induced spatial patterns

TL;DR

This paper develops a novel method using the Feynman-Vernon decomposition to connect landscape-induced spatial patterns with underlying interaction mediators, enhancing understanding of ecological dynamics and nonlocal influences.

Contribution

It introduces a two-way bridge linking mediators' features with population spatial patterns via an interaction kernel, advancing ecological modeling techniques.

Findings

The interaction kernel captures nonlocal influences between individuals.

Concrete examples demonstrate the complexity of inferring mediators from spatial patterns.

The method provides a new approach to understanding landscape effects on populations.

Abstract

Interactions between organisms are mediated by an intricate network of physico-chemical substances and other organisms. Understanding the dynamics of mediators and how they shape the population spatial distribution is key to predict ecological outcomes and how they would be transformed by changes in environmental constraints. However, due to the inherent complexity involved, this task is often unfeasible, from the empirical and theoretical perspectives. In this paper, we make progress in addressing this central issue, creating a bridge that provides a two-way connection between the features of the ensemble of underlying mediators and the wrinkles in the population density induced by a landscape defect (or spatial perturbation). The bridge is constructed by applying the Feynman-Vernon decomposition, which disentangles the influences among the focal population and the mediators in a compact way. This is achieved though an interaction kernel, which effectively incorporates the mediators' degrees of freedom, explaining the emergence of nonlocal influence between individuals, an ad hoc assumption in modeling population dynamics. Concrete examples are worked out and reveal the complexity behind a possible top-down inference procedure.