Coexistence and Survival in Conservative Lotka-Volterra Networks
Johannes Knebel, Torben Kr\"uger, Markus F. Weber, Erwin Frey
TL;DR
This paper introduces a classification scheme for coexistence in conservative Lotka-Volterra networks, using the Pfaffian to analyze extinction processes and stability in multi-species ecological models.
Contribution
It presents a novel classification method for coexistence scenarios and quantifies extinction dynamics using the Pfaffian of the interaction matrix.
Findings
Global stability properties for four and five species systems
A generalized scaling law for extinction time
A new framework for analyzing long-term ecological dynamics
Abstract
Analyzing coexistence and survival scenarios of Lotka-Volterra (LV) networks in which the total biomass is conserved is of vital importance for the characterization of long-term dynamics of ecological communities. Here, we introduce a classification scheme for coexistence scenarios in these conservative LV models and quantify the extinction process by employing the Pfaffian of the network's interaction matrix. We illustrate our findings on global stability properties for general systems of four and five species and find a generalized scaling law for the extinction time.
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