Specific non-monotonous interactions increase persistence of ecological networks

Abstract

The relationship between stability and biodiversity has long been debated in ecology due to opposing empirical observations and theoretical predictions. Species interaction strength is often assumed to be monotonically related to population density, but the effects on stability of ecological networks of non-monotonous interactions that change signs have not been investigated previously. We demonstrate that for four kinds of non-monotonous interactions, shifting signs to negative or neutral interactions at high population density increases persistence (a measure of stability) of ecological networks, while for the other two kinds of non-monotonous interactions shifting signs to positive interactions at high population density decreases persistence of networks. Our results reveal a novel mechanism of network stabilization caused by specific non-monotonous interaction types through either increasing stable equilibrium points or reducing unstable equilibrium points (or both). These specific non-monotonous interactions may be important in maintaining stable and complex ecological networks, as well as other networks such as genes, neurons, the internet and human societies.

Ecological non-monotonicity and its effects on complexity and stability of populations, communities and ecosystems

“…In the non-monotonic models with two interacting species, Zhang (2003) defined 11 possible equilibrium points. As compared to monotonic models, non-monotonic functions can increase species coexistences by producing stable equilibrium or reducing unstable equilibrium (Yan and Zhang, 2014, also see below).…”

“…Through simulation, Yan and Zhang (2014) found that four kinds of non-monotonic functions, shifting signs to negative or neutral interactions at high population density (Fig. 5d-f and i) increases persistence of ecological networks.…”

“…r2 indicate the per capita population increase rate of species 2. x1 indicate the population density of species 1. These relations are equal to the zero growth lines of species 2 against species 1 in which r2 is replaced with x2 (see Zhang, 2003, Yan andZhang, 2014). For simplification, the non-monotonic function is shown with two linear lines changing signs between positive, negative and neutral functions.…”

“…5d-i), Yan and Zhang (2014) investigated the persistence of three classic networks (i.e. randomly connected networks, cascade prey-predator networks and bipartite mutualistic networks).…”

“…It was found that shift between positive and negative interaction can increase competitive capacity and coexistence of two competing species. This shift of species interaction was then extended to ecological network models in which six kinds of non-monotonic interactions were defined, and four of them can promote persistence of models and then increase biodiversity (Yan and Zhang, 2014). During past decades, studies related to ecological non-monotonicity have begun to increase.…”