Spatial moment dynamics and biomass density equations provide complementary, yet limited, descriptions of pattern formation in individual-based simulations

TL;DR

This study compares spatial moment dynamics and biomass density equations in their ability to approximate pattern formation in individual-based ecological models, revealing their complementary strengths and limitations across different parameters.

Contribution

It systematically evaluates the accuracy of SMD and biomass density models against individual-based simulations in a prototypical population dynamics system.

Findings

SMD and density models accurately predict population size and patterns in different regimes.

Neither approximation performs well in certain parameter regions, indicating need for improved models.

The two approaches complement each other by capturing different aspects of spatial dynamics.

Abstract

Spatial patterning is common in ecological systems and has been extensively studied via different modeling approaches. Individual-based models (IBMs) accurately describe nonlinear interactions at the organism level and the stochastic spatial dynamics that drives pattern formation, but their computational cost scales quickly with system complexity, limiting their practical use. Population-level approximations such as spatial moment dynamics (SMD) -- which describe the moments of organism distributions -- and coarse-grained biomass density models have been developed to address this limitation. However, the extent to which these approximated descriptions accurately capture the spatial patterns and population sizes emerging from individual-level simulations remains an open question. We investigate this issue considering a prototypical population dynamics IBM with long-range dispersal and intraspecific competition, for which we derive both its SMD and coarse-grained density approximations. We systematically compare the performance of these two approximations at predicting IBM population abundances and spatial patterns. Our results highlight that SMD and density-based approximations complement each other by correctly capturing these two population features within different parameter regimes. Importantly, we identify regions of the parameter space in which neither approximation performed well, which should encourage the development of more refined IBM approximation approaches.