Sympatric speciation by symmetry-breaking: The three-clade case
Abstract
In this paper we expand the concept of biological speciation by symmetry breaking of Golubitsky and Stewart to the case of three clades in which N populations following the same dynamical laws can separate. The underlying differential equation is based on a fifth order polynomial of a trait variable with first or second order coupling. We present some general strategies to find all possible steady states and their stabilities. Numerical data are given for a specific system. We show the locations of three-clade distributions in dependence on the coupling and an environmental parameter. The results show a decrease of the number of stable states with higher coupling and a higher probability of ending in a three-clade state for larger N. Limits and potentials of the approach if zero roots for the trait variable occur are discussed.
Keywords
Cite
@article{arxiv.2603.17026,
title = {Sympatric speciation by symmetry-breaking: The three-clade case},
author = {Giagkos-Ion Chlomoudis and Thomas Fuhrmann-Lieker and Meskerem A. Mebratie and Gokul B. Nair and Werner M. Seiler},
journal= {arXiv preprint arXiv:2603.17026},
year = {2026}
}
Comments
39 pages, 13 figures