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PreprintCC BY-SA 4.0HAL

Exponential convergence to a steady-state for a population genetics model with sexual reproduction and selection

  • Gaël Raoul
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Abstract

We are interested in the dynamics of a population structured by a phenotypic trait. Individuals reproduce sexually, which is represented by a non-linear integral operator. This operator is combined to a multiplicative operator representing selection. When the strength of selection is small, we show that the dynamics of the population is governed by a simple macroscopic differential equation, and that solutions converge exponentially to steady-states that are locally unique. The analysis is based on Wasserstein distance inequalities using a uniform lower bound on distributions. These inequalities are coupled to tail estimates to show the stability of the steady-states.

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Cite

BibTeXRIS
BibTeX
@misc{raoul2026exponential,
  title = {{Exponential convergence to a steady-state for a population genetics model with sexual reproduction and selection}},
  author = {Gaël Raoul},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  eprint = {2104.06089},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-03434278v1},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - Exponential convergence to a steady-state for a population genetics model with sexual reproduction and selection
AU  - Gaël Raoul
PY  - 2026
DA  - 2026/10/14
PB  - HAL
UR  - https://hal.science/hal-03434278v1
AB  - We are interested in the dynamics of a population structured by a phenotypic trait. Individuals reproduce sexually, which is represented by a non-linear integral operator. This operator is combined to a multiplicative operator representing selection. When the strength of selection is small, we show that the dynamics of the population is governed by a simple macroscopic differential equation, and that solutions converge exponentially to steady-states that are locally unique. The analysis is based on Wasserstein distance inequalities using a uniform lower bound on distributions. These inequalities are coupled to tail estimates to show the stability of the steady-states.
ER  -