TY - JOUR
T1 - Fitness potentials and qualitative properties of the Wright-Fisher dynamics
AU - Chalub, Fabio A. C. C.
AU - Souza, Max O.
N1 - FACCC was partially supported by FCT/Portugal Strategic Project UID/MAT/00297/2013 (Centro de Matematica e Aplicacoes, Universidade Nova de Lisboa) and by a "Investigador FCT" grant. MOS was partially supported by CNPq under grants # 486395/2013-8 and # 309079/2015-2. We also thank two anonymous reviewers, whose comments helped us to improve the paper. In particular, one of the reviewers pointed out to us the potential connection to mutation models.
PY - 2018/11/14
Y1 - 2018/11/14
N2 - We present a mechanistic formalism for the study of evolutionary dynamics models based on the diffusion approximation described by the Kimura Equation. In this formalism, the central component is the fitness potential, from which we obtain an expression for the amount of work necessary for a given type to reach fixation. In particular, within this interpretation, we develop a graphical analysis — similar to the one used in classical mechanics — providing the basic tool for a simple heuristic that describes both the short and long term dynamics. As a by-product, we provide a new definition of an evolutionary stable state in finite populations that includes the case of mixed populations. We finish by showing that our theory – rigorous for two types evolution without mutations– is also consistent with the multi-type case, and with the inclusion of rare mutations.
AB - We present a mechanistic formalism for the study of evolutionary dynamics models based on the diffusion approximation described by the Kimura Equation. In this formalism, the central component is the fitness potential, from which we obtain an expression for the amount of work necessary for a given type to reach fixation. In particular, within this interpretation, we develop a graphical analysis — similar to the one used in classical mechanics — providing the basic tool for a simple heuristic that describes both the short and long term dynamics. As a by-product, we provide a new definition of an evolutionary stable state in finite populations that includes the case of mixed populations. We finish by showing that our theory – rigorous for two types evolution without mutations– is also consistent with the multi-type case, and with the inclusion of rare mutations.
KW - Diffusive approximations
KW - Fitness potential
KW - Mechanistic interpretation
KW - Replicator dynamics
KW - Wright-Fisher dynamics
UR - http://www.scopus.com/inward/record.url?scp=85052308234&partnerID=8YFLogxK
U2 - 10.1016/j.jtbi.2018.08.021
DO - 10.1016/j.jtbi.2018.08.021
M3 - Article
C2 - 30125575
AN - SCOPUS:85052308234
VL - 457
SP - 57
EP - 65
JO - Journal Of Theoretical Biology
JF - Journal Of Theoretical Biology
SN - 0022-5193
ER -