The general recombination equation in continuous time and its solution

Baake, Ellen; Baake, Michael; Salamat, Majid

doi:10.3934/dcds.2016.36.63

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2015

2021

Publication Types

Select...

Article4

Book1

Relationship

Self Cite3

Independent2

Authors

Journals

Cited by 5 publications

References 20 publications

(36 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

Genetic recombination as a generalised gradient flow

Alberti

2021

Monatsh Math

View full text Add to dashboard Cite

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.

show abstract

Genetic recombination as a generalised gradient flow

Alberti

2021

Monatsh Math

View full text Add to dashboard Cite

show abstract

Entropy production in nonlinear recombination models

Caputo¹,

Sinclair²

2018

Bernoulli

View full text Add to dashboard Cite

We study the convergence to equilibrium of a class of nonlinear recombination models. In analogy with Boltzmann's H theorem from kinetic theory, and in contrast with previous analysis of these models, convergence is measured in terms of relative entropy. The problem is formulated within a general framework that we refer to as Reversible Quadratic Systems. Our main result is a tight quantitative estimate for the entropy production functional. Along the way we establish some new entropy inequalities generalizing Shearer's and related inequalities.

show abstract

Erratum and addendum to: The general recombination equation in continuous time and its solution

Baake¹,

Baake²,

Salamat³

2015

DCDS-A

Self Cite

View full text Add to dashboard Cite

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 finitedimensional problem recursively for generic sets of parameters and briefly discuss the singular cases, and how to extend the solution to this situation.

show abstract

The general recombination equation in continuous time and its solution

Cited by 5 publications

References 20 publications

Genetic recombination as a generalised gradient flow

Genetic recombination as a generalised gradient flow

Entropy production in nonlinear recombination models

Erratum and addendum to: The general recombination equation in continuous time and its solution

Contact Info

Product

Resources

About