Fixation in a cyclic Lotka-Volterra model
L. Frachebourg, P. L. Krapivsky
TL;DR
This paper analyzes a cyclic Lotka-Volterra model on a lattice, deriving an analytical critical number of species for fixation that matches simulation results, advancing understanding of species coexistence and fixation in ecological models.
Contribution
It provides an analytical determination of the critical number of species for fixation in a cyclic Lotka-Volterra model across different dimensions, validated by simulations.
Findings
Critical number of species N_c=5 in 1D
N_c=14 in 2D
N_c=23 in 3D
Abstract
We study a cyclic Lotka-Volterra model of N interacting species populating a d-dimensional lattice. In the realm of a Kirkwood approximation, a critical number of species N_c(d) above which the system fixates is determined analytically. We find N_c=5,14,23 in dimensions d=1,2,3, in remarkably good agreement with simulation results in two dimensions.
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Taxonomy
TopicsEvolution and Genetic Dynamics · Plant and animal studies · Mathematical and Theoretical Epidemiology and Ecology Models