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**Haldane linearisation done right: solving the nonlinear recombination equation the easy way.**
*(English)*
Zbl 1353.92064

Summary: 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.

### MSC:

92D10 | Genetics and epigenetics |

34G20 | Nonlinear differential equations in abstract spaces |

06B23 | Complete lattices, completions |

39A12 | Discrete version of topics in analysis |

### Keywords:

nonlinear recombination equation; continuous and discrete time; population genetics; measure-valued equations; closed solution
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\textit{E. Baake} and \textit{M. Baake}, Discrete Contin. Dyn. Syst. 36, No. 12, 6645--6656 (2016; Zbl 1353.92064)

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