Ranking species in complex ecosystems through nestedness maximization

TL;DR

This paper formulates the nested maximization problem for ranking species in complex ecosystems as a Quadratic Assignment Problem and introduces a physics-inspired algorithm to find optimal rankings, outperforming existing methods.

Contribution

It models species ranking as a Quadratic Assignment Problem and develops a novel physics-based algorithm for optimal solutions, surpassing current techniques.

Findings

Derived self-consistent equations for optimal rankings

Proposed an efficient algorithm outperforming existing methods

Framework generalizable to higher-order networks

Abstract

Identifying the rank of species in a social or ecological network is a difficult task, since the rank of each species is invariably determined by complex interactions stipulated with other species. Simply put, the rank of a species is a function of the ranks of all other species through the adjacency matrix of the network. A common system of ranking is to order species in such a way that their neighbours form maximally nested sets, a problem called nested maximization problem (NMP). Here we show that the NMP can be formulated as an instance of the Quadratic Assignment Problem, one of the most important combinatorial optimization problem widely studied in computer science, economics, and operations research. We tackle the problem by Statistical Physics techniques: we derive a set of self-consistent nonlinear equations whose fixed point represents the optimal rankings of species in an arbitrary bipartite mutualistic network, which generalize the Fitness-Complexity equations widely used in the field of economic complexity. Furthermore, we present an efficient algorithm to solve the NMP that outperforms state-of-the-art network-based metrics and genetic algorithms. Eventually, our theoretical framework may be easily generalized to study the relationship between ranking and network structure beyond pairwise interactions, e.g. in higher-order networks.