No, this should not be in the "Physical Science" category. By hypersphere I'm thinking of the model that R.A. Fisher popularized as opposed to Sewall Wright's conception of the adaptive landscape, a multidimensional sphere within which was located a position which was the adaptive optimum. While Wright's landscapes were rugged, and so opened up the possibility that gene-gene interactions and some level of stochasticity and meta-population dynamics were critical factors in evolution over the long term, Fisher's more symmetrical model focuses on the power of selection operating on loci of independent effect in driving inevitable frequency changes. The image to the left is simply a 2-dimensional rendering of Fisher's idea, as a population converges upon the adaptive peak the mutations should be of smaller and smaller effect so that they do not result in an "overshoot" and a decrease in fitness. The implication clear: initial mutations may be of large effect, but over time as selection for a trait affects change across the genome subsequent mutations should be of smaller fitness effect. Additionally, if the ecological pressures remain the same it seems plausible that the selection coefficient of the initial mutant which drives the population toward the optimal phenotype will be greater than the selection coefficients of subsequent mutations, which after all arise in a situation where other mutants already exist.
That's the theory. Why do I bring this up? It's about the evolution of skin color. I've posted quite a bit on this topic, and have read many of the recent papers coming out of genomics labs. In short over the past 5 years a lot has come into clearer focus and we seem to know the half a dozen or so genes of large effect which control most of the world wide variation in pigmentation. These genes and their allelic variants come in many flavors and combinations which result in the range of phenotypes we see around us, a continuous variable controlled by discrete genetic components. There are many of these genes. SLC24A5, SLC45A2/MAPT/AIM1 (yes, it has three names that I can tell), KITLG, OCA2, MC1R and ATRN, these are just some of the candidates which have been fingered so far. Note that some genes seem to be responsible for between population variation in some comparisons but not in others (e.g., SLC24A5 can account for about 1/3 of the difference between Europeans and Africans, it can account for none of the difference between East Asians and Africans). Additionally note that some of these genes are definitely responsible for other traits. OCA2 and KITLG seem to have associations with variation on eye color and hair color, while some MC1R alleles cause red hair.
So we have this laundry list of genes. We have a general sense of their effects. We have a rough sense of distribution. Additionally, many of these loci show strong selection signals. There are two issues that have been nagging at me though. First, the big one: when did the selection events occur? Specifically, when did the derived alleles which result in lighter skin show up? Well, there is some work which suggests that the rise in frequency of SLC24A5 might be as recent as 6,000 years ago! This is pretty wild because this variant is fixed in Europeans, that is, almost at 100%. Another allele, SLC45A2, has given up a slighter older selection event, perhaps around 11,000 years. The ranges on these numbers are often quite large though. There isn't much on the other genes. I actually emailed someone who is a position to know more about this area and they basically confirmed that the dates don't exist, or they're very fuzzy. There isn't much to go on. So why I am bothered? SLC45A2 & SLC24A5. First, the meager data we have suggests that SLC24A5 is younger and has been subject to extremely high selection coefficients (on the order of 10%), and might be the largest effect locus in producing the light skin of Europeans (as much as 38% of the difference between Africans and Europeans). Additionally, SLC24A5 is very widespread, pushing into southern India (more on this later). In contrast, SLC45A2 is somewhat older, possibly of smaller effect, more geographically restricted, and at lower frequency. Do you see the confusion here? Why is the younger allele of larger effect, why is it fixed, why does it have a larger effect? Shouldn't new mutations be converging upon an adaptive optimum through increments of smaller magnitude?
A second issue goes back to geography. Look at the map and note how much more widespread SLC24A5 is compared to SL45A2. While the former is fixed in Europe and reaches frequencies of 50% in its derived form in southern India, the latter is already at 50% derived in the Levant. Imagine that the selection pressure here is skin color, northern Europeans are at higher latitudes so they need to produce more Vitamin D via lighter skin. Since these genes tend to act in an additive and independent manner it stands to reason that Europeans will have more substitutions of the derived forms than Africans. But, populations like those of the Middle East may have an adaptive optimum somewhere in the middle. One can conceive of an evolutionary narrative where there are mutants in the background of human populations, and as we move north those that result in light skin fix. Once the adaptive optimum has been reached in the Middle East the new mutants in the background will be purged by negative selection, but in Europe there might still be "room to grow," so to speak. Europeans will have more substitutions than Middle Easterners, who will have more than Africans. That's what you see. But it may be that the substitution shared between Middle Easterners and Europeans, to a greater extent, is the most recent! It is almost as if instead of emerging in situ within populations as they moved north, light skin swept down south from Europe. In fact, the SLC24A5 derived allele is extant at frequencies of 80% or more in northwest India and remains as high as 50% across much of the southern half of the subcontinent. If this allele is very recent it is peculiar that light skin was necessary within the last 6,000 years in the Indian subcontinent, and it is notable that SLC45A2 and TYR variants are extant at far lower frequencies.
Enough speculation, let me offer my caution. The distribution of alleles I'm pretty certain of. The signatures of selection are there, though whether they are real or not I'm less certain of. The effects of loci such as SLC24A5 and KITLG have been pretty well confirmed, I'm more certain that the regions around these genes have something to do with skin color than that any given test of selection is making the accurate inference. The big wild card are the ages of the selective events, the sweeps, we don't have precise dates, and those which give up a number have large ranges. I don't have that strong a confidence that SLC24A5 is the most recent skin lightening sweep. The fact that several of these genes show up in tests which detect recent events suggest that much of it has occurred within the last 10,000 years, but I can't put a time on KITLG vs. TYR. If it turns out that SLC24A5 is an older sweep event than SLC45A2, then this post will have been baseless speculation to some extent, as the latter is less widespread, not even fixed in some European populations, and of somewhat smaller phenotypic effect (perhaps). But if the hints we are getting now are correct it makes you wonder what's going on. The geographic distribution of SLC24A5 is extremely perplexing, it is extant within the dark skinned populations of South Asia, but totally absent among the lighter populations of East Asia. So far the model I've held to implicitly implies that skin color is the target of selection, but what if it's not? What if like blue eyes skin color itself is a byproduct? At this point we know so much more than we did a few years ago, but as always that's just led to more questions.
Note: Acceleration does offer a nice "out" if SLC24A5 is the most recent, doesn't it?
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How many different types of mutation/trait relationships exist? These types should have different adaptive landscapes. Here are some example types:
Constrained by physical laws: Improves one trait but at a cost. (E.g., brain size vs. metabolic cost.)
Balanced: Improves one trait, harms a different trait. Balance point is determined by environment. (E.g., vitamin D production vs. UV protection.) In some cases if the traits are sufficiently important then the traits may eventually de-couple.
Unconstrained: For rapid adaptation to the environment, the trait is relatively free to change without affecting other traits. (E.g., some immune system genes. Skeletal adaptations such as jaw or tooth structure.)
Network constraints: The trait depends on a complex regulatory gene network, metabolic pathway, or peripheral nerve-brain-hormone feedback control. Many other traits are affected by the same systems. The trait will depend on hundreds or thousands of "nodes" and hundreds of other traits are likewise affected. The biological system has evolved to be robust and canalized. Trait values are constrained by multiple, redundant feedback controls. Genetic variation is often masked, not obviously appearing in the phenotype. Some highly connected or highly important nodes are severely constrained, conserved for hundreds of millions of years.
I find the network constraints type most interesting. Suppose having more intelligence increases fitness. There are potentially thousands of mutations that could increase intelligence. But a mutation of large effect might well disrupt other important traits. Instead I'd expect to see a long series of mutations of modest effect that slowly push the network in a direction that increases the desirable trait. Now consider the recent paper on accelerated human adaptation and imagine large numbers of mutations of modest effect arising and sweeping local populations. What does this suggest with regard to DNA variants associated with intelligence variance? Or groups that have a mental abilities, personalities, and behaviors shaped by different environments for thousands of years? (Gene flow between groups will have mitigated this process somewhat.)