an:06661522
Zbl 1353.92064
Baake, Ellen; Baake, Michael
Haldane linearisation done right: solving the nonlinear recombination equation the easy way
EN
Discrete Contin. Dyn. Syst. 36, No. 12, 6645-6656 (2016).
1078-0947 0133-0189 1553-5231
2016
j
92D10 34G20 06B23 39A12
nonlinear recombination equation; continuous and discrete time; population genetics; measure-valued equations; closed solution
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.