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General selection models: Bernstein duality and minimal ancestral structures
TLDR
It turns out that multiple ancestral processes are associated to the same forward dynamics and the set of optimal ancestral structures is characterised and a recipe to construct them from the drift is provided and allows to recover well-known ancestral structures of the literature.
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Common ancestor type distribution: a Moran model and its deterministic limit
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A probabilistic view on the deterministic mutation–selection equation: dynamics, equilibria, and ancestry via individual lines of descent
TLDR
The deterministic haploid mutation–selection equation with two types is reconsidered and ancestral structures inherent in this deterministic model are established, including the pruned lookdown ancestral selection graph and an alternative characterisation in terms of a piecewise-deterministic Markov process.
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The deterministic limit of the Moran model: a uniform central limit theorem
We consider a Moran model with two allelic types, mutation and selection. In this work, we study the behaviour of the proportion of fit individuals when the size of the population tends to infinity,…
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Λ-coalescents arising in populations with dormancy
TLDR
It is shown that because an individual that wakes up unusually early can have a large number of surviving descendants, for some choices of model parameters the genealogy of the population will be described by a Λ-coalescent, and the beta coalescent can describe theGenealogy when the rate at which individuals wake up increases exponentially over time.
Lines of descent in the deterministic mutation-selection model with pairwise interaction
TLDR
With the help of the stratified ancestral selection graph, the mutation-selection differential equation with pairwise interaction is considered and results about the ancestral type distribution in the case of unidirectional mutation are obtained.
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Natural selection and the advantage of recombination
TLDR
It is shown that on average: 1) natural selection amplifies poorly-matched gene combinations and 2) creates time-averaged negative associations in the process.
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Asymptotic proportion of arbitrage points in fractional binary markets
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On the stationary distribution of the block counting process for population models with mutation and selection
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Natural selection promotes the evolution of recombination 2: during the process of natural selection*
TLDR
It is shown that natural selection acting on standing heritable variation always creates conditions favoring the evolution of recombination, in expectation, and that sex and recombination may have evolved more as a byproduct than as a catalyst of natural selection.
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