Biology – Quantitative Biology – Populations and Evolution
Scientific paper
2008-11-03
Biology
Quantitative Biology
Populations and Evolution
18 pages, 3 figures
Scientific paper
We study the large population limit of the Moran process, assuming weak-selection, and for different scalings. Depending on the particular choice of scalings, we obtain a continuous model that may highlight the genetic-drift (neutral evolution) or natural selection; for one precise scaling, both effects are present. For the scalings that take the genetic-drift into account, the continuous model is given by a singular diffusion equation, together with two conservation laws that are already present at the discrete level. For scalings that take into account only natural selection, we obtain a hyperbolic singular equation that embeds the Replicator Dynamics and satisfies only one conservation law. The derivation is made in two steps: a formal one, where the candidate limit model is obtained, and a rigorous one, where convergence of the probability density is proved. Additional results on the fixation probabilities are also presented.
Chalub Fabio A. C. C.
Souza Max O.
No associations
LandOfFree
From discrete to continuous evolution models: a unifying approach to drift-diffusion and replicator dynamics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with From discrete to continuous evolution models: a unifying approach to drift-diffusion and replicator dynamics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and From discrete to continuous evolution models: a unifying approach to drift-diffusion and replicator dynamics will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-233244