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arXiv · 1409.1378

The general recombination equation in continuous time and its solution

Ellen Baake·Michael Baake·Majid Salamat
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Abstract

The process of recombination in population genetics, in its deterministic limit, leads to a nonlinear ODE in the Banach space of finite measures on a locally compact product space. It has an embedding into a larger family of nonlinear ODEs that permits a systematic analysis with lattice-theoretic methods for general partitions of finite sets. We discuss this type of system, reduce it to an equivalent finite-dimensional nonlinear problem, and establish a connection with an ancestral partitioning process, backward in time. We solve the finite-dimensional problem recursively for generic sets of parameters and briefly discuss the singular cases, and how to extend the solution to this situation.

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Ellen Baake, Michael Baake, Majid Salamat. 2015-07-14. The general recombination equation in continuous time and its solution. https://doi.org/10.3934/dcds.2016.36.63

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