Natural Selection Fails to Optimize Mutation Rates

Rich Lenski's group published this paper in PLoS Computational Biology less than two weeks ago:
Clune J, Misevic D, Ofria C, Lenski RE, Elena SF, Sanjuán, R. (2008). Natural Selection Fails to Optimize Mutation Rates for Long-Term Adaptation on Rugged Fitness Landscapes. PLoS Comput Biol 4(9). PLoS Computational Biology, 4 (9).

In the Ph.D. program I'm in we are required to give a journal club talk once per semester (the result of which is that that's exactly how many we give), and I chose to do this one for last Wednesday because it is something I worked on briefly in the NK-landscape a while back^*.

Clune et al. used AVIDA to investigate if natural selection is sufficient to evolve mutation rates that are close to the static mutation rates that optimize fitness. First they do a bunch of runs with different mutation rates to find which one optimizes fitness, and find a genomic mutation rate of U_opt=4.641 (figure 1). Then they allow the value of the mutation rate to change by mutation, and compare the evolved mutation rates and resulting fitness to that of the static ones. They find that the evolved mutation rate is much lower than U_opt, and that the average population fitness is also much lower than that obtained for U_opt. In other words, a population left to evolve by natural selection does not evolve a mutation rate that benefits the population the most.

Figure 1: Population average fitness of with static mutation rates (solid black line) compared to evolving mutation rates (red and blue dots). Initial conditions were U=1 (red) and U=10^-3 (blue).

Their hypothesis to explain this puzzling observation is that selection against the mutational load wins over the adaptive benefit of a high mutation rate. When a population sits on top of a local peak in the fitness landscape, it has two choices: Either evolve a low mutation rate, so that it avoids deleterious mutations, which lowers the average population fitness, or it evolves a high mutation rate, so that it can locate another higher peak somewhere not so far away in genotype space. Their result suggest that the former strategy wins. The short-term effect of minimizing the mutational load wins over the long-term benefit of adaptation.

They then went on to hypothesize that it is the topology of the fitness landscape the decides which of these alternatives wins. In AVIDA the fitness landscape is very rugged, meaning it has many fitness peaks and valleys. They therefore constructed an explicit landscape in which they could manually adjust the size of a valley that the population would need to cross in order to adapt. Since adaptation is fast, they also switched the landscape every 300 generations between two "seasons" (figure 2). This has the effect of needing more beneficial mutations to optimize fitness, resulting in a longer time of adaptation (which leads to better statistics). As can be seen in this figure, when there is no valley, the population does indeed evolve a mutation rate identical to the static optimal mutation rate. But with a valley size of 2 or 3, both the mutation rate and the resulting fitness is lower than that of a population with the optimal static mutation rate.

Figure 2: Explicit fitness landscapes. First and second column show how the fitness landscape alternate between the two "seasons". The third column is the reulting fitness as a function of the mutations rate. Solid line are static mutation rates, and red and blue points are for simulations with evolving mutation rates. The greater the valley is, the harder is is for natural selection to evolve the optimal mutation rate, and it thus fails to optimize fitness when the landscape is rugged.

What does that mean for us? For one thing is means that when using evolutionary algorithms to find solutions to human problems we need to be careful setting the mutation rate so that optimal solutions are found.

It also suggest there is a barrier preventing real populations of living organisms to optimize their reproductive output when their mutation rates can evolve. Mutation rates do vary between species and individuals. When errors are made by the DNA copying machinery during meiosis and mitosis, there are ways to correct for it. How well that is done depends on proteins that are products of genes, that themselves are prone to copying-errors. It is practically impossible to attain a 100% fidelity (i.e. zero mutation rate), but it is in principle straightforward to select for a machinery that allows more mutations to slip through uncorrected. But alas, the landscape dictates the dynamics and prevents high mutation rates.

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^* In the NK-landscape I found that I could only avoid fixation of a mutator-lcous with zero mutation rate by updating the environment every ten generations. This has the effect of requiring the population to continuously adapt. This was for K=3, which means there is a fair amount of epistasis - the landscape has many local peaks.