Genetic recombination as a Generalised Gradient Flow

TL;DR

This paper extends the gradient flow framework of genetic recombination from two parents to multiple parents, revealing new structural insights and analyzing the backward-time process.

Contribution

It generalizes the gradient flow formulation of genetic recombination to any number of parents and studies the gradient structure of the backward process.

Findings

Recombination can be modeled as a generalized gradient flow for multiple parents.

The backward-time partitioning process also exhibits a gradient structure.

The classical two-parent case is extended to arbitrary parent numbers.

Abstract

It is well known that the classical recombination equation for two parent individuals is equivalent to the law of mass action of a strongly reversible chemical reaction network, and can thus be reformulated as a generalised gradient system. Here, this is generalised to the case of an arbitrary number of parents. Furthermore, the gradient structure of the backward-time partitioning process is investigated.