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.
Cite
@article{arxiv.1409.1378,
title = {The general recombination equation in continuous time and its solution},
author = {Ellen Baake and Michael Baake and Majid Salamat},
journal= {arXiv preprint arXiv:1409.1378},
year = {2015}
}
Comments
35 pages, 2 figures; revised version, with one additional section and various improvements