A few days ago I was browsing Haldane’s Sieve,when I stumbled upon an amusing discussion which arose on it’s “About” page. This “inside baseball” banter got me to thinking about my own intellectual evolution. Over the past few years I’ve been delving more deeply into phylogenetics and phylogeography, enabled by the rise of genomics, the proliferation of ‘big data,’ and accessible software packages. This entailed an opportunity cost. I did not spend much time focusing so much on classical population and evolutionary genetic questions. Strewn about my room are various textbooks and monographs I’ve collected over the years, and which have fed my intellectual growth. But I must admit that it is a rare day now that I browse Hartl and Clark or The Genetical Theory of Natural Selection without specific aim or mercenary intent.
R. A. Fisher
Like a river inexorably coursing over a floodplain, with the turning of the new year it is now time to take a great bend, and double-back to my roots, such as they are. This is one reason that I am now reading The Founders of Evolutionary Genetics. Fisher, Wright, and Haldane, are like old friends, faded, but not forgotten, while Muller was always but a passing acquaintance. But ideas 100 years old still have power to drive us to explore deep questions which remain unresolved, but where new methods and techniques may shed greater light. A study of the past does not allow us to make wise choices which can determine the future with any certitude, but it may at least increase the luminosity of the tools which we have iluminate the depths of the darkness. The shape of nature may become just a bit less opaque through our various endeavors.
Figure from “Directional Positive Selection on an Allele of Arbitrary Dominance”, Teshima KM, Przeworski M
So what of this sieve of Haldane? As noted at Haldane’s Sieve the concept is simple. Imagine two mutations, one which expresses a trait in a recessive fashion, and another in a dominant one. The sieve operates by favoring the emergence out of the low frequency zone where stochastic forces predominate of dominantly expressing variants (i.e., even if an allele confers a large fitness benefit, at low frequencies the power of random chance may still imply that it is highly likely to go extinct). An example of this would be lactase persistence, which in the modal Eurasian variant seems to exhibit dominance. The converse case, where beneficial mutations are recessive in expression suffer from a structural problem where their benefit is more theoretical than realized.
The mathematics of this is exceedingly simple, a consequence of the Hardy-Weinberg dynamics of diploid random mating organisms. Let’s use the gene which is implicated in variation in lactase persistence as an example, LCT. Consider two alleles, LP and LNP, where the former confers persistence (one can digest lactose sugar as an adult), and the latter manifests the conventional mammalian ‘wild type’ (the production of lactase ceases as one leaves the life stage when nursing is feasible). LP is clearly the novel mutant. In a small population it is not unimaginable that by random chance the frequency of LP rises to ~10%. What now? At HWE you have:
p2 + 2pq + q2 = 1, where q = LP allele. At ~10% the numbers substituted would be:
(0.90)2 + 2(0.90)(0.10) + (0.10)2
This is where dominance or recessive expression is highly relevant. The reality is that LP is a dominant trait. So in this population the frequency of LP as a trait would be:
(0.10)2 + 2(0.90)(0.10) = 19%
Now imagine a model where LP is favored, but it expresses in a recessive fashion. Then the frequency of the trait would equal q2, the homozygote LP-allele proportion. That is, 1%. Though population genetics is often constructed on an algebraic foundation, the results lend themselves to intuition. A structural parameter endogenous to the genetic system, dominant or recessive expression, can have longstanding consequences in terms of the likely trajectory of the alleles. Selection only “sees” the trait, so a recessive trait with sterling qualities may as well be a trait with no qualities. In contrast, a dominantly expressed allele can cut like a scythe through a population, because every copy “counts.”
In preparation for this post I revisited the selection on Haldane’s Sieve in the encyclopediac Elements of Evolutionary Genetics. The authors note that this phenomenon, though of vintage character as these things can be reckoned is a field as young as evolutionary genetics, is still a live one. The dominance of favored mutations in wild populations, or the recessive character of deleterious ones in laboratory stock, may reflect the different regimes which these two genes pools are subject to. The nature of things is such that is easier to generate recessive mutations than dominant ones (i.e., loss is easier than gain), so the preponderance of dominant variants in wild stocks subject to positive selective pressure lends credence to the idea that evolutionary rather than development forces and constraints shape the genetic character of many species.
And yet things are not quite so tidy. Haldane’s Sieve, and the framework of dominant versus recessive alleles, operates differently in the area of sex chromosomes. In many lineages there is a ‘heterogametic sex’ which carries only one functional chromosome for most of the genome. In mammals this is the male (XY), while in birds this is the female (ZW). As males have only one functional copy of most genes on the sex chromosome, the masking effect of recessive expression does not apply to them in mammals. This may imply that because of the exposure of many deleterious recessive variants to natural selection within the heterogametic sex one would see different allelic distributions and genetic landscapes on these chromosomes (e.g., more rapid adaptation because of the exposure of nominally recessive alleles in the heterogametic sex, as well as more purifying selection on deleterious variants). But the reality is more complex, and the literature in this area is somewhat muddled. More precisely, it seems phylogenetically sensitive. Validation of the theory in mammals founders once one moves to Drosphila.
And that is why research in evolutionary genetics continues. The theory stimulates empirical exploration, and is tested against it. Much of the formal theory of classical evolutionary genetics, which crystallized in the years before World War II, is now gaining renewed relevance because of empirical testability in the era of big data and big computation. This is an domain where the past is not simply of interest to historians. Scientists themselves, chasing the next grant, and producing the expected stream of publications, may benefit from a little historical perspective by standing upon the shoulders of giants.