A probabilistic view on the deterministic mutation–selection equation: dynamics, equilibria, and ancestry via individual lines of descent

@article{Baake2018APV,
  title={A probabilistic view on the deterministic mutation–selection equation: dynamics, equilibria, and ancestry via individual lines of descent},
  author={Ellen Baake and Fernando Cordero and Sebastian Hummel},
  journal={Journal of Mathematical Biology},
  year={2018},
  volume={77},
  pages={795-820}
}
We reconsider the deterministic haploid mutation–selection equation with two types. This is an ordinary differential equation that describes the type distribution (forward in time) in a population of infinite size. This paper establishes ancestral (random) structures inherent in this deterministic model. In a first step, we obtain a representation of the deterministic equation’s solution (and, in particular, of its equilibria) in terms of an ancestral process called the killed ancestral… 
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