Dynamically evolved community size and stability of random Lotka-Volterra ecosystems

TL;DR

This paper investigates how the size and stability of ecological communities in Lotka-Volterra systems evolve dynamically, revealing that predator-prey relations enhance stability while interaction variability and complexity reduce community size.

Contribution

It introduces a dynamical approach to determine community size and stability based on interaction matrices, moving beyond fixed-size models and highlighting the role of interaction properties.

Findings

Prey-predator relations increase stability.

Interaction variability promotes instability.

Higher complexity reduces community size.

Abstract

We use dynamical generating functionals to study the stability and size of communities evolving in Lotka-Volterra systems with random interaction coefficients. The size of the eco-system is not set from the beginning. Instead, we start from a set of possible species, which may undergo extinction. How many species survive depends on the properties of the interaction matrix; the size of the resulting food web at stationarity is a property of the system itself in our model, and not a control parameter as in most studies based on random matrix theory. We find that prey-predator relations enhance stability, and that variability of species interactions promotes instability. Complexity of inter-species couplings leads to reduced sizes of ecological communities. Dynamically evolved community size and stability are hence positively correlated.