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The process of recombination in population genetics, in its deterministiclimit, leads to a nonlinear ODE in the Banach space of finite measures on alocally compact product space. It has an embedding into a larger family ofnonlinear ODEs that permits a systematic analysis with lattice-theoreticmethods for general partitions of finite sets. We discuss this type of system,reduce it to an equivalent finite-dimensional nonlinear problem, and establisha connection with an ancestral partitioning process, backward in time. We solvethe finite-dimensional problem recursively for generic sets of parameters andbriefly discuss the singular cases, and how to extend the solution to thissituation.

The general recombination equation in continuous time and its solution