How recombination and changing environments affect new mutations

Blog author: David Lawrie was a graduate student in Dmitri Petrov’s lab. He is now a postdoc at USC.

I recently sat down with Oana Carja, a graduate student with Marc Feldman, to discuss her paper published in the journal of Theoretical Population Biology entitled “Evolution with stochastic fitnesses: A role for recombination”. In it, the authors Oana Carja, Uri Liberman, and Marcus Feldman explore when a new mutation can invade an infinite, randomly mating population that experiences temporal fluctuations in selection.

The one locus case

This work builds off of previous research in the field on how the fluctuations in fitness over time (i.e., increased variance of fitness) affect the invasion dynamics of a mutation at a single locus. For a single locus, it has been shown that the geometric mean of the fitness of the allele over time determines the ability of an allele to invade a population. This effect is known as the geometric mean principle. Fluctuations in fitness increase the variance and therefore decrease the geometric mean fitness. The variance of the fitness of the allele over time thus greatly impacts the ability of that allele to invade a population.

What if there are two loci?

In investigating a two locus model, the researchers split the loci by their effect on the temporally-varying fitness: one locus only affects the mean, while the other controls the variance. The authors demonstrate through theory and simulation that:

1)    allowing for recombination between the two loci increases the threshold for the combined fitness of the two mutant alleles to invade the population beyond the geometric mean (see figure).

2)    periodic oscillations in the fitness of the alleles over time lead to higher fitness thresholds for invasion over completely random fluctuations (see figure).

3)    edge case scenarios allow for the maintenance of polymorphisms in the population despite clear selective advantages of a subset of allelic combinations.

Temporally changing environments and recombination thus make it overall more difficult for new alleles to invade a population.

Invasibility thresholds as a function of recombination rate. Recombination makes it more difficult for new alleles to invade a population.

Invasibility thresholds as a function of recombination rate. If there is no recombination (the left-most edge of the figure), the geometric mean of the pair of new alleles needs to be higher than 0.5 to allow for invasion, because the resident alleles’ geometric mean fitness is set to 0.5. However, as recombination between the two loci increases, the geometric mean needed for invasion increases rapidly. If there is free recombination (r = 0.5) then  invasion can only happen if the new alleles’ geometric mean fitness is twice the resident alleles’ geometric mean fitness (light grey area). If the environment is changing periodically, it is even harder for new alleles to invade a population (dark grey area).

The evolution of models of evolution

This work is important for addressing the evolutionary dynamics of loci controlling phenotypic variance – in this case, controlling the ability of a phenotype to maintain its fitness even if the environment is variable. Most environments undergo significant temporal shifts from the simple changing of the seasons to larger scale weather changes such as El Niño and climate change, in which species must survive and thrive. For organisms in the wild, many alleles that confer a benefit in one environment will be deleterious when the environment and selective pressures change. There may be modifier-loci which buffer the fitness of those loci in the face of changing environments. Such modifier-loci have been recently found in GWAS studies and may be important for overall phenotypic variance. Thus modeling the patterns of evolution for multiple loci in temporarily varying environments is a key component to advancing our understanding of the patterns found in nature.

Future work

Epigenetic modifiers are a hot area of research and one potential biological mechanism to control phenotypic variance. The evolution of such epigenetic regulation is a particular research interest of Oana. Future work will continue to explore the evolutionary dynamics of epigenetic regulation and focus on applying the above results to finite populations.

Paper author: Oana Carja is a graduate student with Marc Feldman

Reference

Oana Carja, Uri Liberman, Marcus W. Feldman, Evolution with stochastic fitnesses: A role for recombination, Theoretical Population Biology, Volume 86, June 2013, Pages 29-42, ISSN 0040-5809.

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