Local dynamical equivalence of certain food webs

TL;DR

This paper introduces a method using generalized modeling to create coarse-grained representations of complex food webs that preserve local dynamics, demonstrated through examples and a conjecture on population grouping.

Contribution

It proposes a conjecture for grouping populations in food webs without altering local dynamics, advancing coarse-graining techniques in ecological modeling.

Findings

Food webs with different species counts can have identical local bifurcation diagrams.

A conjecture is formulated on which populations can be grouped without changing local dynamics.

Chaotic regions are shown to exist in the parameter space of certain multi-trophic food webs.

Abstract

An important challenge in theoretical ecology is to find good, coarse-grained representations of complex food webs. Here we use the approach of generalized modeling to show that it may be possible to formulate a coarse-graining algorithm that conserves the local dynamics of the model exactly. We show examples of food webs with a different number of species that have exactly identical local bifurcation diagrams. Based on these observations, we formulate a conjecture governing which populations of complex food webs can be grouped together into a single variable without changing the local dynamics. As an illustration we use this conjecture to show that chaotic regions generically exist in the parameter space of a class of food webs with more than three trophic levels. While our conjecture is at present only applicable to relatively special cases we believe that its applicability could be greatly extended if a more sophisticated mapping of parameters were used in the model reduction.