Sympatric speciation by symmetry-breaking: The three-clade case
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917351063027712 |
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| author | Chlomoudis, Giagkos-Ion Fuhrmann-Lieker, Thomas Mebratie, Meskerem A. Nair, Gokul B. Seiler, Werner M. |
| author_facet | Chlomoudis, Giagkos-Ion Fuhrmann-Lieker, Thomas Mebratie, Meskerem A. Nair, Gokul B. Seiler, Werner M. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_17026 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sympatric speciation by symmetry-breaking: The three-clade case Chlomoudis, Giagkos-Ion Fuhrmann-Lieker, Thomas Mebratie, Meskerem A. Nair, Gokul B. Seiler, Werner M. Populations and Evolution 34C60, 34C14, 37C81, 37G10, 92D25 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. |
| title | Sympatric speciation by symmetry-breaking: The three-clade case |
| topic | Populations and Evolution 34C60, 34C14, 37C81, 37G10, 92D25 |
| url | https://arxiv.org/abs/2603.17026 |