  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.
