The Fate of the Lone Mutant

... or the hopes of a poor monster.

A sci-fi movie? Nop. When I was studying (ahem) for geneticist, I found a Population Genetics book (I don't recall which one of the many I read) that had a chapter with such a heading. Yes, I know that, the guys of PG are nuts. The story is that under that heading that was exactly what it was described, i.e. which is the evolutionary fate of a mutation recently arisen in a population (that bit about the hopes not, I added that myself; you'll see why later).

A number of years ago, before I started takin PG lessons, I met a guy nick-named Xac Mazo. We talked a lot in some public discussion forums (at terra.es) and one thing led to another and in the end we discovered that both of us had had experimented with simulations of the evolution of populations. I'll let himself to explain, if he wants to, what kind of madness made him do so; my answer is something I read when I was younger.

It was an article in PCmania ('Temas Informágicos') dealing with population dynamics as an example of an ordered deterministic-chaos system. A simple BASIC program allowed me to play with the parameters of the logistic growth equation. Since luck favours the trained mind, it took me a long number of years to finally develop the idea any further.

I did so when I (thanks to Mazo) discovered that you can generate recursive functions in MS Excel. Te idea was to simulate the fate of two sympatric populations that have a difference in reproduction rate. The result, the obvious one.

We started simulating evolutionary genetics scenarios, including the fate of the lone mutant. Especially that one, I must say, because the point we were trying to prove in a discussion of that time was what chances had a "hopeful monster" of giving birth a new species. Under "normal" circumstances, the chances were really tiny...

What is needed in order to get the newly arisen allele fixed in a stable frequency (and somehow significant)? First, we start from only an heterozygous individual (every new mutation appears first in an heterozygote by definition). The heterozygote will try to reproduce and for that it needs a couple that, obviously, will be homozygous "normal". Therefore, its descendence would be half heterozygous, half homo-normal. Asuming random mating, until a "critical mass" is reached, the heterozygotes will always mate with homo-normals, so there are never homo-mutants until that point in which it's possible for a heterozygote to mate another heterozygote by random mating.

That means that a number of generations have to pass by since the mutation appears until the first homozygotic mutant individual appears. In the meanwhile, the mutation has to survive in heterozygosity, and that's not easy due to the high death rates. In fact, both the theory and the simulations predict that the fate of a mutation is its desappearence. Well, the classic theory says that always an heterozygous individual must remain, but if we take into account 'real-life' parameters such as finite population size, gene frequencies always rational (x/N, x and N being natural numbers), then sooner or later the mutation will be lost.

However that's not true always. By pure chance alone, it can happen that the cumulative effect of random sampling (unavoidable in finite-size populations) end up leading to the complete fixation of the new allele. This very seldom happens.

Selection can help. In 'the selective brake' I argued that selection indeed does accelerate the fixation of beneficial mutations, and here I will explain that a bit more. I've just mentioned that by sampling error, frequencies may vary randomly (Hardy-Weinberg law, the equilibrium of gene frequencies, is maintained in a stadistic fashion: the number of populations (or repetitions if this is a simulation) in which the mutant becomes fixed is proportional to the mutant gene frequency in the original population (1/2N); that is, we need N repetitions/sample populations for the mutation to become fixed in one). Therefore, it's possible that in a good luck strike the heterozygote's frequency rises high enough to reach the 'critical-mass' level and homozygous mutant individuals start appearing in the population. And then selection can see their mutant phenotype and fight against the rampant randomness.

But no matter how high the favorable selection coefficiente is, the fate of the mutation is still under the power of the blind, sheer, luck, since it has to survive the heterozygous period "dormant". The hopeful monster is against all odds.

But what about if heterozygotes do have a selective advantage? There are 4 possible scenarios.
Let's use w for fitness, and the sub-index will tell which genotype it's referring: (m) homozygous mutant, (h) heterozygote, (n) homozygous normal; w_m>w_n

1. w_m > w_h = w_n
2. w_m > w_h > w_n
3. w_m = w_h > w_n
4. w_m < w_h > w_n

We have commented already the first one, the heterozygote not having any selective advantage, only homo-mutant does. Next case is the one in which the heterozygot has some advantage over the homo-normal, but not as much as the homo-mutant (codominant heredity, incomplete heredity). In case number 3 the heterozygote has the same advantage as the homozygous mutant (dominant heredity). The last one is the most extreme situation, the heterozygote has more selective advantage than either kind of homozygotes (heterosis, also known as heterozygote superiority; most famous example is HbS and falciform anemy).

In theory and in silico, the higher the fitness of the heterozygote, the faster the mutation spreads. From this Mazo concludes that if there isn't any selection favouring the heterozygote (all except the number 1), the mutant doesn't have much of a fate.

But those aren't all the possibilities there are. We are assuming random mating, so what happens if there's inbreeding? The initial heterozygote has mixed descendence, but if they do mate between themselves, since the F2 there can be homozygous mutants showing up the new phenotype. Of course, consanguinity will rise, but then it's a matter of balancing the selection against the genetic load with the advantage of the new mutation. And there are several degrees of inbreeding. In nature there's a tendency to mate in the whereabouts an individual was born, so seldom times there's panmixia (even in those cases with high dispersion of seeds or gametes, the chances of mating close to the parent are quite higher than not doing so). The consequence is that, if the species doesn't have much mobility, then the locality is enriched with the new allele and therefore new homo-mutants can appear more often.

The second way of avoiding panmixia is called 'assortative mating'. The individuals don't choose randomly who to mate with, they have their preferences (even pollen grains have their ways to tell who are they mating with). If we can imagine an individual able to distinguish those who bear the mutant allele (for good or bad) and decide to mate accordingly, then the chances of heterozygotes meeting each other rise and therefore homozygous mutants appear sooner.

I like the later a lot, because even without any selective advantage for the heterozygotes, it's possible to produce two populations living alongside, or even one displacing the other! The combination of non-random mating (inbreeding or assortative mating) and positive selection for the recesive mutant is powerful enough as for beating the effect of random sampleing and achieving that, in the end, the lone mutant be a hopeful one.