Adaptive Tracking and Rare Alleles

  1. In my lab we are experimenting with evolution at high mutation rates and examining populations as they respond to alternating environments.
  2. I/we need to read more and more deeply.
  3. This blog exists and can be a commitment device.

Today I will start with the task of providing summaries of relevant literature by discussing Dean et al. (2017) Fluctuating Selection in the Moran (published one month ago in Genomics).

When thinking about changing environments a lot of the evolutionary fun would appear to be related to various flavours of bet hedging. The less exciting possibility is adaptive tracking in which populations respond to changing contingencies with changing allele frequencies. The conditions under which balancing selection maintains diversity are thought to be quite restricted, essentially frequency-dependent selection in haploids + heterozygote advantage in diploids. Without frequency-dependent selection, haploid organisms bearing alleles with lower fitness would be driven to extinction. (Recall that bet hedging is the interesting corner in which an allele with a lower arithmetic mean fitness, but a higher geometric mean fitness, across environments, is favoured.) This paper shows that frequency dependence can occur in a dynamic system in a manner that permits the persistence of alleles over time and this results in quite a radical conclusion about how polymorphism is affected by fluctuating selection.

The authors begin by making the interesting point that when populations are growing towards a carrying capacity this implicitly favours rare alleles. In a simple two allele model, when the fitter allele is rare, the population takes longer to reach the carrying capacity so a large time slice is available for the rare allele to increase in frequency. If the fitter allele is more common (and the rare allele is less fit) the population will grow faster and the time slice, during which the rare allele reduces in frequency, is shorter. This can increase the residence time of rare alleles and favour their persistence if the selective contingencies reverse when carrying capacity is reached. The authors show that this is empirically supported by serial transfer experiments. The key point here is that there is a kind of frequency dependence, but it is time not growth rate that varies. (This point is subtle and reminds me of the distinction between Allen Orr’s argument about risk aversion (owing the inherent payoff asymmetries in relative fitness) versus the specific adaptations implied by conservative bet hedging.)

The rest of the paper takes this into more dynamic territory. Working with continuous, time-overlapping models they look at what happens in a chemostat in which organisms remain at a starving quasi-steady state. The analogous point applies. The growth rates of organisms slows to match the wash out rate as they become dominant in a population. Again it is not the intrinsic growth rate (unconstrained by resources) associated with an allele that varies with its frequency, but there is a frequency dependence in their realised growth. Doublings increase for all genotypes when fit alleles are rare (helping them on the way up), and decrease when less fit alleles are rare (slowing down their exit from the population). And so far we haven’t changed the environment.

Now the authors allow changes in the environment during which intrinsic (resource-independent) growth rates can vary more or less and may correlate (between alleles) more or less. Unsurprisingly, tightly correlated and invariant rates result in loss of polymorphism as alleles that are less fit overall are driven to extinction. However if you dial up the frequency of environmental shifts you can rescue those rare alleles. Using a mixture of simulations and analytical results, they show, among other things, that overlapping fitness distributions allow an allele with lower fitness overall (averaging across environments) to persist.

The Moran of the title comes in when they look at models with finite population size, something expected to disfavour rare alleles as they are stochastically lost. Similarly to the carrying capacity and steady-state models above, birth and death events are paired. They begin with strict symmetrical fitness between alleles in two types of environment. In this model the persistence times of rare alleles can be hugely increased by modest frequencies of switching. This is actually favoured by Goldilocks level of selection against the (temporarily) less fit allele. Too high and it gets nixed in one period, too low and drift will kick it out. With varying durations between switching events, the presence of a single long period will drive out polymorphism. Similar conclusions also apply to the equilibrium condition (eventual loss/fixation).

Of course real evolution includes mutation adding new alleles into the population. So how does fluctuating selection affect our expectations here? It drives up polymorphism, but, intriguingly, a high mutation rate is an opposing force owing to clonal interference between alleles. Strong selection also promotes polymorphism – again perhaps surprisingly, and perhaps because it enhances the time slice asymmetries discussed above and allows recent deleterious mutations to stick around for a bit.

Finally the authors allow neutral alleles and here the conclusions become very interesting. Fluctuating selection, because it introduces frequent bottlenecks, has the interesting property of purging neutral variation. Given the ubiquity of seasonal and weather-based fluctuations this certainly changes the expectations for wild populations!

This is an interesting paper and has me thinking about (dynamic) equilibria and the striking complexity introduced when you add even the most basic bits of ecology into the evolutionary mix. Now let’s see if we can add an evolving distribution of fitness effects into their models!

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