The general recombination equationin continuous time and its solution

Ellen  Baake; Michael Baake; Majid  Salamat

doi:10.3934/dcds.2016.36.63

Article Contents

2016, Volume 36, Issue 1: 63-95. Doi: 10.3934/dcds.2016.36.63 open access

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The general recombination equation in continuous time and its solution

1.
Technische Fakultät, Universität Bielefeld, Postfach 100131, 33501 Bielefeld
2.
Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld

Received: August 2014

Revised: March 2015

Published: May 2017

Abstract / Introduction Related Papers Cited by

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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Mathematics Subject Classification: 34G20, 06B23, 92D10.

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