Analysis of trophic networks: an optimisation approach

TL;DR

This paper presents a convex optimization-based methodology to analyze matter flows in ecosystems, enabling efficient exploration of ecological networks and their stability using biomass data and biological constraints.

Contribution

It introduces a novel optimization approach for ecological network analysis that handles large systems and incorporates stability testing through differential equations.

Findings

Method is fast and scalable for large ecosystems

Flow decomposition reveals key pathways and circuits

Stability analysis confirms ecological feasibility

Abstract

We introduce a methodology to study the possible matter flows of an ecosystem defined by observational biomass data and realistic biological constraints. The flows belong to a polyhedron in a multi dimensional space making statistical exploration difficult in practice; instead, we propose to solve a convex optimization problem. Five criteria corresponding to ecological network indices have been selected to be used as convex goal functions. Numerical results show that the method is fast and can be used for large systems. Minimum flow solutions are analyzed using flow decomposition in paths and circuits. Their consistency is also tested by introducing a system of differential equations for the biomasses and examining the stability of the biomass fixed point. The method is illustrated and explained throughout the text on an ecosystem toy model. It is also applied to realistic food models.