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41eAv4GeGqL._SY344_BO1,204,203,200_ Sometimes what you infer about history is totally wrong. How often? Sometimes we find out. As I’ve outlined on this blog over the course of years inferences made in historical population genetics using extant variation have often turned out to be totally wrong. How do we know? Time machines. Ancient DNA.

Yesterday I received a copy of Sewall Wright and Evolutionary Biology. I read it about 10 years ago, but I didn’t know as much about evolutionary biology back then. So I wanted to get a copy of it (unlike R. A. Fisher: The Life of a Scientist there are actually affordable copies). I decided to get straight to the section which covered the general time period of the Wright-Fisher controversies, when two of the great eminences involved in the development of the field of population genetics were hashing out somewhat different perspectives.

41qS+5MyBmL._SY344_BO1,204,203,200_ Rather than getting into that, what I want to recount is the passage the author, Will Provine, offers up from Sewall Wright’s personal correspondence which reproduced R. A. Fisher’s last letter to him. One interesting sidebar here is that R. A. Fisher, from all the biographical information I’ve been able to gain an impression from, was a much more flawed person than Sewall Wright. Fisher was the greater scientist (seeing that he made original contributions to statistics), but Wright was the greater human. After a period of somewhat frequent correspondence Fisher and Wright ceased their direct interaction, right at a time when their differences were being highlighted, leading to decades of ill feeling. In particular, there had been a mixed review of The Genetical Theory of Natural Selection which Wright had submitted to Genetics.

From everything Will Provine knew beforehand he was expecting a rather cold and unfriendly last letter from Fisher to Wright due to the nature of the review. His expectations were totally off base. R. A. Fisher was entirely gracious and good-natured, and seemed appreciate of the review despite its dissents. The lesson that Provine takes from this is that we don’t truly know what we don’t truly see, and we should have greater humility about the darkness outside of the bounds of our direct perception.

 
• Category: Science • Tags: Sewall Wright 
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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.

(Republished from Discover/GNXP by permission of author or representative)
 
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adaptive_landscape_labelledLast week I took an intellectual road trip back nearly a century and explored the historical context and scientific logic by which R. A. Fisher definitively fused Mendelian genetics with quantitative evolutionary biology. In the process he helped birth the field of population genetics. While the genetics which we today are more familiar with begins at the biophysical substrate, the DNA molecule, and the phenomena which emerge from its concrete structure, population genetics starts with the abstract concept of the gene. This abstraction and its variants are construed as algebraic quantities from which one can infer a host of dynamics. These are the processes which are the foundations of evolutionary change, as population genetics flows into evolutionary genetics, and ultimately the raw material of natural history.

ResearchBlogging.org Fisher’s accomplishments were a function of both his abilities and his passions. He was a mathematical prodigy, with the ability to distill natural processes down to highly general abstractions. And like many English gentlemen of his age he had a passion for evolutionary biology, and cherished his copy of The Origin Of Species. His ultimate aim was to transform evolutionary biology into a discipline with the same analytical rigor as physical chemistry. But he wasn’t the only major figure on the scene in his era.

Sewall_WrightSewall Wright was an American physiological geneticist with a background in animal breeding. While Fisher was a mathematician who sought to apply his skills to evolutionary biology, Wright was a biologist who taught himself mathematics to further his own understanding of evolutionary processes. The two were in many ways the Yin and the Yang of early population genetics, with their conflicts and disagreements being termed the Wright-Fisher controversies, and the common formal framework which they converged upon becoming the ubiquitous Wright-Fisher model. Wright’s life spanned 99 years, from 1889 to 1988. His biography, both personal and scientific, are explored in rich detail in Will Provine’s Sewall Wright and Evolutionary Biology. Because of the length and breadth of his influence in evolution it’s worth reading just to get a sense of how Wright shaped the Modern Neo-Darwinian Synthesis behind the scenes. Provine seems to indicate that Wright was the primary theoretical influence on Theodosius Dobzhansky,* who mentored a whole generation of evolutionary biologists to come (e.g., Dobzhansky → Lewontin → Coyne).

If I may make recourse to analogy, if R. A. Fisher was the Alfred Marshall of evolution, Sewall Wright’s mentality seems more characteristic of Thorstein Veblen’s work. Fisher’s aim was to formulate elegant and simple general principles which would explain evolutionary process top to bottom. His fundamental theorem of natural selection, “The rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time,” was perhaps the best example of Fisher’s grand general ambitions. Wright, by origin an experimental biologist, certainly aimed for grandeur, but I can not perceive in him the yearning for a clean concise elegance which discards the sloppiness he saw in evolution as it played out in the laboratory. This inability to ignore the detail was a “bug” which he in some ways turned into a feature when it came to his theorization of evolutionary process.

Many of the ideas which would be the focus of Wright’s career, and later shape the outlook of his acolytes, can be found in a 1932 paper The roles of mutation, inbreeding, crossbreeding and selection in evolution. In this paper Wright introduces concepts which are still with us today, and reviews the state of knowledge at the time. Some of his observations are almost amusing now 80 years later. He suggests that multicellular organisms likely have more than 1,000 genes. Wright also alludes to concepts such as allopatric speciation and postzygotic reproductive isolation which have spawned an enormous literature, and are the stuff of careers..

FitnessLandscapeBut the core of the paper seem to be the adaptive landscape and the shifting balance. What is the adaptive landscape? If you follow Will Provine’s reading no one really knows! OK, to be fair, the landscapes usually describe a topography where fitness is on the vertical y-axis, and x and z are frequencies of genes, or perhaps phenotypes. But are they frequencies within a whole population? Or do they represent genotypic combinations within individuals? Over the decades of the utilization of the metaphor Provine indicates that Wright and his students had different ideas of what the metaphor was in the specifics, suggesting its Rashomon-like aspects. The idea of landscapes across which evolution traverses over time is a very easy to visualize, but making use of the framework in a concrete sense is more difficult. This was especially so in the days before computer programs which could produce beautiful multi-dimensional visualizations.

wrightlandTo the right you see a primitive representation of a fitness landscape from Wright’s paper. The y & x axis are different genes, and at their intersection you have a gene-gene combination. There are several ideas at work in these evolutionary landscapes. The first of them are gene-gene interactions, epistasis. It is often asserted that Wright and Fisher disagreed on the importance of epistasis in evolution, with Wright arguing that these interactions were critical, and Fisher dismissing their long term importance. There are other interpretations, and much of the disagreement may actually have been more about fine weights than the basic thrust of their positions. But the general sketch is that biologists in the Fisherian tradition emphasize gradual continuous evolution through selection on additive genetic variance across genes of small effect through natural selection (I understand that this is somewhat a caricature of Fisher’s own views, and most of his intellectual descendants view this description as the creation of their critics, but that’s the perception). The Wrightian tradition is more pluralistic, and frankly somewhat confused because different thinkers have different spins (e.g., epistasis vs. drift). But in general it suggests that factors such as population substructure, gene-gene interaction, and random genetic drift, all play crucial roles in evolution. The partisans of contingency in evolutionary process and the importance of specific genetic architecture in constraining and shaping the arc of change would likely get more sympathy from Wright.

shiftbalFor Sewall Wright the specific nature of the fitness topography is critical in shaping how evolution plays out on the genetic level. If the topography is “rugged” so that there are many fitness peaks and valleys of disparate values along the y-axis, then populations may become “trapped” on a lower peak which is separated from the higher one by a valley. The movement of a population along the adaptive landscape clearly has a temporal interpretation, and so one can see how contingency and history are critical. Where you start out from may constrain where you can end up. At least, if you rely on conventional deterministic processes such as natural selection on a single locus. This is where Wright suggests that populations structured so that their effective sizes are smaller can evolve much faster, and leap across the valley’s so to speak, through the action of random genetic drift. It may be that to attain a given gene-gene combination (or gene-gene-gene-gene, etc.) is nearly an impossible proposition in a deterministic framework where one has to proceed on a step-by-step basis, but through the luck of random genetic drift one can envisage the odds being reduced by a few chance deviations in allele frequency.

Because Wright posits that much of evolution occurs by scaling a sequence of distinct and disparate adaptive peaks, he implicitly rejects gradualism and embraces discontinuity and rapid bursts of evolution. This sort of process occurs in a situation with moderate population substructure, so that effective population size is reduced within demes which then can “peak shift” more frequently, but, with enough population-to-population interaction that inbreeding does not drive mutational meltdown or pedigree collapse. When a subpopulation reaches a particularly fortuitous adaptive peak, then it enters a phase of demographic expansion, and it can replace all the other demes of conspecifics (or at least genetically assimilate them to a great degree). This is where Sewall Wright introduces intergroup selection, or more colloquially group selection. Here Wright and Fisher part company again, naturally. Fisher believed that individual level selection was sufficient to explain evolutionary process, while Wright clearly did not. The debate between those who believe that group selection is a significant force in evolution, and those who do not, continues to this day (group selectionists now have a more general model, multilevel selection theory).

Epistasis. Drift. Moderate population structure and migration. Add to the mix mutation and selection, as well as the fact that the adaptive topography itself is in constant flux, and Wright already has the beginnings of a strong brew in The roles of mutation, inbreeding, crossbreeding and selection in evolution. I’ve only glanced over a few of the points. In other sections Wright touches upon what would one day become mutational meltdown, as well as the nature of speciation. There are many disparate threads here which would eventually lead into a range of disparate research programs.

So with that I want to get to my “human obsession.” Near the end of the paper Sewall Wright seems to offer that the emergence of our own species could be well characterized by a shifting balance model. I suspect that Wright may be right on this. The movement out of Africa was a great pulse, where one human lineage seems to have rapidly replaced or genetically assimilated all the others. Human populations do have substructure, but they also exchange genes, and leapfrog each other. Our cultures may be the perfect vehicles for intergroup selection on the memetic, if not genetic, level (between group variance in memes can be much greater than on genes). I suspect this is not going to be age where elegant one-size-fits-all theories are going to be of particular use, so we might want to dig back into Wright’s diverse set of ideas.

humanexpansion* More directly though he came out of the Morgan lab.

Citation: Sewall Wright (1932). The roles of mutation, inbreeding, crossbreeding and selection in evolution Proceedings of The Sixth International Congress of Genetics, 1

Related:

Notes on Sewall Wright: The Shifting Balance Theory – Part 1
Notes on Sewall Wright: The Shifting Balance Theory (Part 2)
R. A. Fisher and the Adaptive Landscape
R. A. Fisher and Epistasis
Notes on Sewall Wright: the Adaptive Landscape
Notes on Sewall Wright: Migration
Notes on Sewall Wright: Population Size
Notes on Sewall Wright: Wright’s F-statistics
Notes on Sewall Wright: Genetic Drift
Notes on Sewall Wright: the Measurement of Kinship
Notes on Sewall Wright: Path Analysis
Wright, Fisher, Haldane, and odds and ends

Image Credits: Evolutionary Systems Biology, Wikimedia, Scholarpedia, Science

(Republished from Discover/GNXP by permission of author or representative)
 
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Razib Khan
About Razib Khan

"I have degrees in biology and biochemistry, a passion for genetics, history, and philosophy, and shrimp is my favorite food. If you want to know more, see the links at http://www.razib.com"