Sympatric Speciation by Symmetry-Breaking: The Three-Clade Case

Co-author(s): Giagkos-Ion Chlomoudis, Thomas Fuhrmann-Lieker, Meskerem A. Mebratie, Gokul B. Nair

Reference: Preprint University Kassel (2026)

Description: 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.

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