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math.AP2006★ 13 cited
Discrete versus continuous models in evolutionary dynamics: from simple to simpler -- and even simpler -- models
Fabio A. C. C. Chalub, Max O. Souza
There are many different models--both continuous and discrete--used to describe gene mutation fixation. In particular, the Moran process, the Kimura equation and the replicator dyn…
math.AP2006★ 7 cited
The continuous limit of the Moran process and the diffusion of mutant genes in infinite populations
Fabio A. C. C. Chalub, Max O. Souza
We consider the so called Moran process with frequency dependent fitness given by a certain pay-off matrix. For finite populations, we show that the final state must be homogeneous…