The effect of linkage on establishment and survival of locally beneficial mutations

The effect of linkage on establishment and survival of locally beneficial mutations
Simon Aeschbacher, Reinhard Buerger
(Submitted on 25 Nov 2013)

When organisms adapt to spatially heterogeneous environments, selection may drive divergence at multiple genes. If populations under divergent selection also exchange migrants, we expect genetic differentiation to be high at selected loci, relative to the baseline caused by migration and genetic drift. Indeed, empirical studies have found peaks of putatively adaptive differentiation. These are highly variable in length, some of them extending over several hundreds of thousands of base pairs. How can such `islands of differentiation’ be explained? Physical linkage produces elevated levels of differentiation at loci close to genes under selection. However, whether this is enough to account for the observed patterns of divergence is not well understood. Here, we investigate the fate of a locally beneficial mutation that arises in linkage to an existing migration-selection polymorphism and derive two important quantities: the probability that the mutation becomes established, and the expected time to its extinction. We find that intermediate levels of recombinations are sometimes favourable, and that physical linkage can lead to strongly elevated invasion probabilities and extinction times. We provide a rule of thumb for when this is the case. Moreover, we quantify the long-term effect of polygenic local adaptation on linked neutral variation.

2 thoughts on “The effect of linkage on establishment and survival of locally beneficial mutations

  1. I really enjoyed this paper. It put together a bunch of stochastic process tools in a sensible way to look at this tricky problem.

    I was interested to see it started out motivating things by the “islands of speciation” idea; but didn’t think this idea was returned to as much as it could have been, in interpreting the results. The thing I would have liked to have seen was an assessment of how much correlation between locally adaptive alleles there is (and hence, the size of any “islands”) under some distribution of fitness effects. Sort of figure 2, but integrated over the DFE. And/or a 2-D histogram of the probability of establishment as a function of recombinationrate and effect size.

    It also occurs to me that the paper establishes how likely new alleles are to establish at
    distances from existing alleles, and how long they stick around for; are there tools from general dynamical point processes that could be used to work out how clustered the resulting stationary version is?

    • Thanks, Peter, for these comments! You are right, there is much more to be done here and we are thinking of such steps. However, the paper seemed very long to us already. We will look into this. I think your first point should be straightforward to do. The second needs more thinking…

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