A rigorous model study of the adaptive dynamics of Mendelian diploids.

@article{Collet2013ARM,
  title={A rigorous model study of the adaptive dynamics of Mendelian diploids.},
  author={P. Collet and Sylvie M{\'e}l{\'e}ard and Johan A. J. Metz},
  journal={Journal of mathematical biology},
  year={2013},
  volume={67 3},
  pages={569-607}
}
Adaptive dynamics (AD) so far has been put on a rigorous footing only for clonal inheritance. We extend this to sexually reproducing diploids, although admittedly still under the restriction of an unstructured population with Lotka-Volterra-like dynamics and single locus genetics (as in Kimura's in Proc Natl Acad Sci USA 54: 731-736, 1965 infinite allele model). We prove under the usual smoothness assumptions, starting from a stochastic birth and death process model, that, when advantageous… CONTINUE READING
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