Ecological communities from random generalized Lotka-Volterra dynamics with nonlinear feedback

Abstract

We investigate the outcome of Lotka-Volterra dynamics of ecological communities with random interaction coefficients and non-linear functional response. We show in simulations that the saturation of Holling type-II response stabilises the dynamics. This is confirmed in an analytical generating-functional approach to Lotka-Volterra equations with piecewise linear saturating response. For such systems we are able to derive self-consistent relations governing the stable fixed-point phase, and to carry out a linear stability analysis to predict the onset of unstable behaviour. We investigate in detail the combined effects of the mean and variance of the random interaction coefficients, the cut-off parameter of the non-linear response, and a symmetry parameter. We find that stability and diversity increases with the introduction of functional response, where decreasing the functional response parameter has a similar effect to decreasing the symmetry parameter. We also find biomass and diversity to be less dependent on the symmetry of interactions with functional response, and co-operation to no longer have a detrimental effect on stability. *

Stochastic logistic models reproduce experimental time series of microbial communities

“…Large random networks tend to be unstable ( May, 1972 ). This problem is often solved by considering only weak interactions, sparse interaction matrices ( May, 2001 ) or by introducing higher-order interactions ( Grilli et al, 2017 ; Gavina et al, 2018 ; Sidhom and Galla, 2019 ). Although the stability of gLV models decreases with an increasing number of participating species, the stability only depends on the interaction matrix and not on the abundances ( Gibbs et al, 2018 ).…”

Why is cyclic dominance so rare?

“…Formulating the competition death rate as a function of the payoff , we connected evolutionary game theory to the competitive Lotka-Volterra type dynamics ( Huang et al, 2012 ; Huang et al, 2015 ; Park and Traulsen, 2017 ; Park et al, 2019 ; Sidhom and Galla, 2020 ). Note that is the payoff of an individual of type i from the interaction with an individual of type j .…”

Stochastic logistic models reproduce experimental time series of microbial communities

“…Large random networks tend to be unstable (May, 1972). This problem is often solved by considering only weak interactions, sparse interaction matrices (May, 2001) or by introducing higherorder interactions (Grilli et al, 2017;Gavina et al, 2018;Sidhom and Galla, 2019). Although the stability of gLV models decreases with increasing number of participating species, the stability only depends on the interaction matrix and not on the abundances (Gibbs et al, 2018).…”