A carregar...
Projeto de investigação
Sem título
Financiador
Autores
Publicações
Gradient Flow Formulations of Discrete and Continuous Evolutionary Models
Publication . Chalub, Fabio A. C. C.; Monsaingeon, Léonard; Ribeiro, Ana Margarida; Souza, Max O.; CMA - Centro de Matemática e Aplicações; DM - Departamento de Matemática; Springer Science Business Media
We consider three classical models of biological evolution: (i) the Moran process, an example of a reducible Markov Chain; (ii) the Kimura Equation, a particular case of a degenerated Fokker-Planck Diffusion; (iii) the Replicator Equation, a paradigm in Evolutionary Game Theory. While these approaches are not completely equivalent, they are intimately connected, since (ii) is the diffusion approximation of (i), and (iii) is obtained from (ii) in an appropriate limit. It is well known that the Replicator Dynamics for two strategies is a gradient flow with respect to the celebrated Shahshahani distance. We reformulate the Moran process and the Kimura Equation as gradient flows and in the sequel we discuss conditions such that the associated gradient structures converge: (i) to (ii), and (ii) to (iii). This provides a geometric characterisation of these evolutionary processes and provides a reformulation of the above examples as time minimisation of free energy functionals.
Unidades organizacionais
Descrição
Palavras-chave
Contribuidores
Financiadores
Entidade financiadora
Fundação para a Ciência e a Tecnologia
Programa de financiamento
3599-PPCDT
Número da atribuição
PTDC/MAT-STA/28812/2017