Wright’s Shifting Balance Process revisited one last time

It is shaping up to a busy summer, mostly because I am packing up my house so I can go to Brazil for a year. And that is my rather lame excuse for neglecting my blog.

In any case, what I did so many weeks ago was go through the three phases of Wright’s shifting balance process one at a time. Perhaps it is time to do a summary post.

To review, the three phases are (1) the phase of random drift, (2) the phase of mass selection, and (3) the phase of interdeme selection. As I pointed out before Wright’s initial model is undoubtedly naïve, nevertheless, it forms a good basis for thinking about evolution. Importantly, Wright thought all three of the phases were acting simultaneously, so in a sense the phases might be thought of as a human construct based on our need to categorize things. The question becomes how can all of these phases be acting simultaneously when they apparently have very different requirements, what with drift working best with small population size, and selection working best with large population size, and needing isolated demes for phase one, and differential migration for phase three, etc. Any way, if other people can tell just so stories so can I. The scenario I am going to paint may work, then again, it may not. I am not going to defend it either way.

I am inclined to suspect that the answer may lie in how additive genetic variances change over the adaptive topography. In particular consider the adaptive topography. If we choose an adaptive topography in which the axes are phenotypic then at any point we can take the tangent to the multidimensional surface, and I would argue that the slope of that tangent is the phenotypic variance for fitness. If we then projected that on to axes of the heritable components of the phenotype and again made an adaptive topography then the tangent would be the (effective) additive genetic variance for fitness.

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The reason that this is important for the shifting balance process is that this is the element that has been missing from discussions of the shifting balance process. The point being that what is important is not population size or strength of selection per se, but rather the ratio of selection to drift. When NeS <<1 a gene is effectively neutral. In words if the effective population size (Ne) times the strength of selection (S) is much less than one the gene can be considered effectively neutral. There is an interesting subtext here, in that Ohta was thinking about selection acting directly on genes (yea, we phenotypic selectionists don’t believe in such nonsense), so in effect the heritability in this case is one. In the case of traits should neutrality be related to Ne(h2S)? I am at my in-laws, so I don’t have time or facilities to work that out.

The important point is that Ne(h2S) can become small either by Ne becoming small (what is typically being considered), or by h2S becoming small. Thus, in the region of selective peaks and valleys Neh2S will be small. At peaks although the population size is large, the tangent is very small, and fitness is nearly neutral. In valleys both Ne and Ne(h2S) will be small, and again the trait will be nearly neutral. It is mainly on the slopes of the peaks that the effective additive genetic variance will be large enough that selection, and thus phase 2 will be important. This makes the point that phase one and phase two can coexist, with phase one being dominant at peaks and valleys, and phase two being dominant on slopes.

This still leaves the problem of escaping from a local adaptive peak, but I suspect there may be some ways around that as well. To me the big problem is getting a metapopulation in which there are populations on more than one peak. My first thought is that this may be in some sense fractal. That is, populations differing on different tiny peaks within a major overall local adaptive peak may be common, but populations differing in major adaptive peaks may be quite rare. Thus, the probability of metapopulations with subpopulations on different peaks probably depends on how different the peaks are. That said, there are a number of ways that such metapopulations might arise. The easiest to imagine is a changing environment in which a former adaptive peak suddenly becomes much lower. Such changes need not be permanent. For example, an unusual weather year might effectively change selection enough that a peak temporarily disappears leaving the populations free to drift. Alternatively, even if an environmental change didn’t change the height of a peak it could lower population sizes enough to decrease NeS sufficiently that phase one becomes important. Finally, it is quite possible that environmental variation could increase dramatically for what ever reason. This would have the effect of increasing the phenotypic variance, and lowering the heritability. This could lower Ne(h2S), and allow genetic drift to become the dominant force.

Once we get a metapopulation with subpopulations spread over several adaptive peaks then phase three can start participating. As pointed out in my previous post, this requires differential migration, which can be a force that overwhelms selection. That is, populations that export migrants will have a powerful influence on populations that import migrants. Also as I pointed out last week, whether a migrant can enter a population will depend on the fitness of the individual (not their offspring). Thus, a net exporter of migrants can be that simply because they have a larger population size and export more migrants, or because their migrants have a higher fitness, and are always able to invade the other population. Once the migrants invade they will mate and produce offspring. If the subpopulations are truly on different adaptive peaks than their offspring will be of low fitness, and there will be a general increase in non-additive variance (due to decreased inbreeding, and the introduction of new alleles). The net result is that the migrants will pull the subpopulation down the slope, decrease the heritability, and generally set up the population to be more susceptible to genetic drift. As a result this interpopulation migration may in fact support phase one due to its effect on population size and variance components. Remember, one migrant every four generations is optimal for speciation to occur!

I have run out of space, so I will sum this up by pointing out that the argument that the three phases or Wright’s shifting balance process have difficulty coexisting may have more to do with our emphasis on additive models and our lack of understanding of the effects of non-additivity and less to do with real problems with how this process actually works in the real world.

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