The probability of parallel evolution

Orr (2005) considers the likelihood of the same mutants being fixed in two populations as a function of parallel selection, compared to drift. The model used is a very simple one, basically involving a single locus in each population with a limited number of advantageous mutants that may be presented to both populations.

The argument for the idea that beneficial mutations are limited is probably right:

Throughout this analysis, I make a major assumption: the number of beneficial mutations is small. This will almost certainly be true for two reasons. First, environments are autocorrelated through time, making it unlike [sic] that a previously highly fit wild-type allele would suddenly plummet in relative fitness; second, random changes in a functional protein are much more likely to worsen than to improve protein function (216).

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The result of the paper is that parallel evolution is likely under such circumstances. This is not especially surprising, and the innovative aspects of the paper are the demonstration that this is true under many models of the distribution of fitnesses of mutations. The equations in the paper are derived from extreme value theory, with the basic theme being that the fittest possible new mutations are also the rarest, so these will preferentially be incorporated into populations.

Does this study apply to natural populations? Even most closely related populations typically differ in ecology in some respects, so it is hard to say that the model where mutations have the same fitness characteristics in two different populations is always relevant. Likewise, over the long term it is likely that a natural population will be as near to an optimum allele as is practicable. That is to say, the argument above that wild-type alleles are unlikely to plummet in relative fitness, carried to its logical extreme, would predict that any natural population of substantial size would already have had the opportunity to explore all the adaptive space available to it by recurring mutations.

Only in fairly unusual circumstances will populations be limited from achieving higher fitness (for any single gene) because mutations don't occur often enough. Instead, they will be limited by the fact that the mutations that do occur are never more adaptive than the current wild-type. The unusual circumstances would include cases in which the adaptive landscape really is complex; for example, where the phenotypic characters influenced by the gene are themselves subject to complex patterns of stabilizing selection. Here, the possibility for stepped advantages among many genes creates the opportunity for a progression of mutations. That is to say, many genes that interact with each other are all highly optimized and adaptive mutations at each of them are incredibly rare. But when an adaptive mutation occurs at one of these genes, it may shift the interaction in ways that make a new (perhaps recurring and previously neutral or deleterious) mutation at one or more of the other genes more likely to be adaptive. In this way, a highly polygenic trait might be mutation-limited in its evolution, while no individual gene can be said to be mutation-limited.

References:

Orr HA. 2005. The probability of parallel evolution. Evolution 59(1):216-220.