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Résumé |
We briefly introduce the field of population genetics, that deals with genetic
variations among individuals. We present some fundamental models that apply to
well-mixed populations, where all individuals interact equally. While these models
can be theoretically analyzed, they are of limited interest to describe natural
systems, where spatial structure plays an important role (e.g. microbial
communities or ecological systems). In particular, we are interested in the impact
of structure on the spread of a mutant, i.e. an individual that has a higher
fitness, defined as an ability to spread or reproduce. We introduce a new model of
population on graphs, where subpopulations are placed on the nodes of a graph
structure and can migrate along the edges of the graph, following Markovian
updates. We apply a branching process approximation, a stochastic process analysis
that allows us to derive several results on the dynamics of the spread of a
mutant.
In particular, we compute the key quantity of the fixation probability of a
mutant, i.e. how likely it is for mutants to take over the whole graph population,
for any graph structure. We show that any graph structure makes it more likely for
mutants to take over the population.
Reference: Alia Abbara and Anne-Florence Bitbol, Frequent asymmetric migrations
suppress natural selection in spatially structured
populations, PNAS Nexus (2023). |
