The general recombination equation in continuous time and its solution

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.

35 pages, 2 figures; revised version, with one additional section and various improvements

References in corpus (3)

• Single--crossover recombination and ancestral recombination trees
• Moment closure in a Moran model with recombination
• Unequal Crossover Dynamics in Discrete and Continuous Time

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• A probabilistic analysis of a continuous-time evolution in recombination
• Haldane linearisation done right: Solving the nonlinear recombination equation the easy way