The canonical equation of adaptive dynamics: a mathematical view
Champagnat, Nicolas ; Ferrière, Régis ; Ben Arous, Gérard
HAL, inria-00164767 / Harvested from HAL
Text on HAL
The Darwinian evolution of a quantitative adaptive character is described as a jump process. As the variance of the distribution of mutation steps goes to zero, this process converges in law to the solution of an ordinary differential equation. In the case where the mutation step distribution is symmetrical, this establishes rigorously the socalled canonical equation first proposed by Dieckmann and Law (1996). Our mathematical approach naturally leads to extend the canonical equation to the case of biased mutations, and to seek ecological and genetic conditions under which evolution proceeds either through punctualism or through radiation.
Publié le : 2001-07-05
Classification:  adaptive dynamics,  branching,  canonical equation,  diffusion,  jump process,  mutation-selection process,  scaling,  [MATH.MATH-PR]Mathematics [math]/Probability [math.PR],  [SDV.GEN.GPO]Life Sciences [q-bio]/Genetics/Populations and Evolution [q-bio.PE] 
@article{inria-00164767,
     author = {Champagnat, Nicolas and Ferri\`ere, R\'egis and Ben Arous, G\'erard},
     title = {The canonical equation of adaptive dynamics: a mathematical view},
     journal = {HAL},
     volume = {2001},
     number = {0},
     year = {2001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/inria-00164767}
}

Champagnat, Nicolas; Ferrière, Régis; Ben Arous, Gérard. The canonical equation of adaptive dynamics: a mathematical view. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/inria-00164767/