# American Institute of Mathematical Sciences

December  2016, 36(12): 6645-6656. doi: 10.3934/dcds.2016088

## Haldane linearisation done right: Solving the nonlinear recombination equation the easy way

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

Received  February 2016 Revised  July 2016 Published  October 2016

The nonlinear recombination equation from population genetics has a long history and is notoriously difficult to solve, both in continuous and in discrete time. This is particularly so if one aims at full generality, thus also including degenerate parameter cases. Due to recent progress for the continuous time case via the identification of an underlying stochastic fragmentation process, it became clear that a direct general solution at the level of the corresponding ODE itself should also be possible. This paper shows how to do it, and how to extend the approach to the discrete-time case as well.
Citation: Ellen Baake, Michael Baake. Haldane linearisation done right: Solving the nonlinear recombination equation the easy way. Discrete & Continuous Dynamical Systems - A, 2016, 36 (12) : 6645-6656. doi: 10.3934/dcds.2016088
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