Bad mutations are good for you

Bonus: homemade video included!

Years ago I was vexed by creationists claiming that because most mutations (that aren't neutral) are deleterious, and only few are beneficial, then evolution cannot happen, because for every beneficial mutation there are many deleterious, thus, goes the inference, making adaptation impossible. (See GLOSSARY OF EVOLUTION below.) This (mis)understanding totally ignores selection, and the fact that not all individuals would be hit by deleterious mutations. And even if they did all suffer deleterious mutations, once in a while the combined effect of one or a few deleterious mutations and one beneficial might be an increase in fitness, in which case the deleterious mutations could go to fixation together with the beneficial (this is known as hitchhiking).

But, ignoring creationists (mostly a good call), many evolutionary biologists also assume that deleterious mutations are prohibitive for evolution, leading them to neglect the benefit that deleterious mutation can have. Weinreich et al. (2006), for example, tacitly assume that proteins can adapt only by fixing beneficial mutations. There are, of course (because it is the truth), exceptions, such as Ortlund et al. (2007), who found that epistasis permits proteins to evolve new functions.

Epistasis is the interaction between genes. Imagine you have a quantitative trait (i.e. a physical trait of an organism that is determined by more than one gene). The trait could be size, for example, to which many genes contribute. The population then might find itself in an environment where it is great to be 0.2 meters long. Smaller and bigger individuals suffer a disadvantage, ensuring that whenever offspring change to be shorter or longer, they are selected against. The result is that the population is stable at 0.2 meters. However, it might just be that a length of 0.8 meters is even better, and if it would be possible to suffer the lower fitness of the intermediate sizes between 0.2 and 0.8 for a while, then the population could attain greater fitness. However, that would require some individuals to go through a fitness valley in between the two peaks at 0.2 and 0.8. Assuming that it is not possible for an individual of size 0.2 m to have an offspring of size 0.8 m, then at least one lineage must cross the valley, suffering a cost in fitness. And this always carries the risk of being the end of that lineage, and that the valley cannot be crossed.

However, whether it is possible to cross a valley in the fitness landscape is a matter of certain parameters. Though deleterious, if the cost of crossing the valley isn't very high, then it might not be too difficult to cross. Or, if the two peaks aren't that far from each other - if the number of mutations needed to cross the valley isn't great - then it becomes more likely that a lineage can tolerate the lower fitness and make it to the other side. The mutation rate is also important: the higher the rate the more mutations there are, and the more likely it is that the right ones occur at all, but a too high mutation rate can increase the mutational load (the cost of mutations on fitness) so much that offspring fitness is always low. And then there is population size. On the one hand, the larger the population is, the more offspring are created per generation, and thus the more mutations are tried, and therefore the higher the chance that the right mutations to find the other peaks occur at all. On the other hand, the larger the population size is, the stronger selection is, making deleterious mutations more disadvantageous. In small populations, random sampling has a bigger effect, just as when flipping a coin only 10 times might get you 3 heads and 7 tails, while flipping a thousand coins is much less likely to get far from the expected 50/50 distribution.

Enough talk. Here I have made a simulation of a population evolving in a fitness landscape. There are two traits that independently can vary between 0 and 1, and both of the traits have two peaks at approximately 0.2 and 0.8. This results in a two-dimensional landscape with four peaks. I start with a homogeneous population of 100 individuals who all have trait values of 0 and 0. I show a snapshot of the population every ten updates (the number on top of the landscape).

Now go!



So what happens? After 6000 updates (with overlapping generations), we see that the population crosses not one but two valleys, and ends up on the highest peak (alas, on the far side of it). If deleterious mutations were not allowed, the population would have stayed at [0.2, 0.2]. Thus, deleterious mutations are actually beneficial.

This simulation has a mutation rate per locus of 0.2, and every mutation changes the trait value by a random number drawn from a Gaussian distribution with zero mean and 0.07 standard deviation (this results in the mean effect (positive or negative) being 0.056, which means that it takes more than seven mutations to climb the second peak, and that's assuming the lineage goes the straight path across the valley, which it of course never does). At every update ten percent of the population is killed randomly (without considering fitness), and then those dead individuals are replaced by offspring of the survivors. Who gets to leave offspring is affected by their fitness, such that the higher fitness an individual has, the higher the chance that it will procreate. However, selection is not deterministic, but stochastic; that an individual has the highest fitness does not imply that it gets to reproduce more, though it does make it more likely to have offspring than everyone else.

GLOSSARY OF EVOLUTION
Organism: A uni- or multi-cellular automaton with the ability to reproduce.
Fitness: A measure of the organism's ability to reproduce.
Genotype: The genetic make-up of the organism; the particular DNA.
Phenotype: The physical characteristics of an organism.
Mutation: Any change in the organism's genotype (recombination, insertions, deletions, SNPs, inversions, duplications, translocations, etc.).
Beneficial mutation: Having an advantageous effect on fitness.
Deleterious mutation: Having a detrimental effect on fitness.
Neutral mutation: Effectively no change in fitness.
Population: A competing group of organisms of the same species.
Species: Don't even go there.
Trait: A characteristic of an organism encoded by part of the genotype.
Selection: The increase of genotypes or traits in a population due to their fitness advantage.
Drift: A random fluctuation of genotypes or traits in a population.
Fixation: The event of a mutation becoming universal or very common within a population.
Substitution: A mutation that has gone to fixation.
Adaptation: The process by which the population increases its fit to the environment.

Glossary reproduced and expanded with permission from Carnival of Evolution #16.

References:
Weinreich DM, Delaney NF, Depristo MA, & Hartl DL (2006). Darwinian evolution can follow only very few mutational paths to fitter proteins. Science (New York, N.Y.), 312 (5770), 111-4 PMID: 16601193
Ortlund EA, Bridgham JT, Redinbo MR, & Thornton JW (2007). Crystal structure of an ancient protein: evolution by conformational epistasis. Science (New York, N.Y.), 317 (5844), 1544-8 PMID: 17702911