Sewall Wright

Peter Visscher and colleagues present a long review paper on the concept and use of heritability in the current Nature Reviews Genetics.

Heritability allows a comparison of the relative importance of genes and environment to the variation of traits within and across populations. The concept of heritability and its definition as an estimable, dimensionless population parameter was introduced by Sewall Wright and Ronald Fisher nearly a century ago. Despite continuous misunderstandings and controversies over its use and application, heritability remains key to the response to selection in evolutionary biology and agriculture, and to the prediction of disease risk in medicine. Recent reports of substantial heritability for gene expression and new estimation methods using marker data highlight the relevance of heritability in the genomics era.

There's nothing particularly new here -- the "genomics" in the title doesn't amount to much beyond a discussion of how to estimate heritability from SNP-inferred relationships instead of pedigrees. But much that is old is worthwhile.

It reads like twelve pages out of Falconer -- if Falconer were in a new edition -- and if you don't have Falconer, well, you might do well to read these twelve pages. They include a box about the "heritability of IQ controversy" as well as a discussion of the basic mystery about heritability in natural populations -- why should additive genetic variance be as high as it is?

References:

Visscher PM, Hill WG, Wray NR. 2008. Heritability in the genomics era -- concepts and misconceptions. Nature Rev Genet 9:255-266. doi:10.1038/nrg2322

Last year around this time, I noted that I happened to be reading Sewall Wright during a TV episode that mentioned Sewall Wright. It's not so unusual for me to be reading Wright, but in this instance I was directed to something I hadn't paid much attention to before.

I'm reminded of the article today because I talked about its basic theme during a lecture, and also because I'm writing up some stuff about effective population size, a concept attributed to Wright.

John Gillespie's 2000 article, "Genetic drift in an infinite population," introduced the concept of pseudohitchhiking, or "genetic draft." An important thing about pseudohitchhiking is that it behaves as a stochastic force very much like genetic drift. The formal difference between the two is that the stochasticity of a pseudohitchhiking locus depends on recombination and selection, while genetic drift depends on neither. Gillespie's paper considered to what extent pseudohitchhiking led to similar predictions for the change in allele frequency. This is a connection he made more explicit in his 2001 article, "Is the population size of a species relevant to its evolution?" by drawing out the first and second moments of neutral evolution under both drift and pseudohitchhiking. For drift, these are (Gillespie 2001:2161, eqs. 1 and 2):

The first equation means that the expected change in allele frequency under drift is zero. This is otherwise known as the deterministic component. Under selection, the expected change in allele frequency depends on the current frequency and the fitnesses of genotypes. Under drift all genotypes have equal fitnesses and the only possible changes are stochastic, therefore the expected change is zero irrespective of the current allele frequency.

The second equation describes the variance of the change in allele frequency. You might think this variance would be zero, since the expected amount of change is zero. But the variance represents the magnitude of possible changes from the expected value due to random sampling a finite number of individuals. This is the stochastic component of allele frequency evolution.

The magnitude of these stochastic changes is directly proportional to heterozygosity and inversely proportional to population size. Larger populations have smaller potential changes in allele frequency due to random sampling. Intermediate allele frequencies (near 50 percent) can change more due to random sampling than high or low frequencies. These relations are embodied by the second equation above -- and if you're keeping score, this second equation is used in defining the variance effective population size.

The two equations help to frame the discussion of effective population size. The size of a population is relevant to its evolution only under certain contexts. If the deterministic change in allele frequencies is the dominant pattern of evolution, then population size is irrelevant to the outcome. In contrast, if random sampling is the most important cause of allele frequency changes, then the outcome (fixation or loss) may be indeterminate, but the population size is very important to the rate of the process.

As Gillespie's article makes clear, genetic drift is not the only stochastic process affecting the evolution of allele frequencies. His mechanism of pseudohitchhiking is one. And there are many others -- all non-deterministic in that their outcomes cannot be predicted from the frequencies of alleles or their phenotypic effects. The rate of these processes depends on different things: some internal to the population and some external. Genetic drift depends on the size of the population and its allele frequencies; genetic draft depends on the rate of recombination, the rate of generation of new favorable mutations, and the relative fitnesses of these mutations. Environmental stochasticity depends on the demography of other species as well as physical factors such as water availability and the weather.

Sewall Wright tried to categorize these stochastic processes, as well as the deterministic ones, making a catalog of of the processes that can cause evolutionary changes. Those of us who teach intro classes are well accustomed to talking about the "forces of evolution" -- selection, drift, gene flow, and mutation. These are important because they constitute different patterns of change in allele frequencies. But Sewall Wright went beyond this four-fold categorization, linking different aspects of these patterns with their stochastic and deterministic effects.

First, he defines the problem in terms of allele frequencies:

As is now generally appreciated, the seemingly very diverse factors that must be taken into account in population genetics can best be brought under a common viewpoint by considering their effects on gene frequency (Wright 1955:17).

Then he provides a full breakdown of different patterns of evolutionary change, or "modes" of change of the gene frequencies in a population:

Modes of Change of Gene Frequency

I. Immediate
1. Directed processes (mean change in allele frequencies determinate in principle)
a. Recurrent mutation
b. Recurrent immigration and crossbreeding
c. Mass selection

2. Random processes (variance in change in allele frequencies determinate in principle)
a. Fluctuations in mutation
b. Fluctuations in immigration
c. Fluctuations in selection
d. Accidents of sampling

3. Unique events
a. Novel favorable mutation
b. Unique hybridization
c. Swamping by mass immigration
d. Unique selective incident
e. Unique reduction in numbers

II. Secular change in system of coefficients
1. From internal causes (control by new adaptive peak)
2. From changes in environment
a. In home territory
b. In colonized territory

This breakdown clearly separates the deterministic factors of evolution (here, category 1, "Directed processes") from the stochastic factors (everything else). I find a couple of things very interesting from this perspective:

1. Wright makes a distinction between recurrent mutation, whose effect is more or less deterministic on allele frequencies, and "novel favorable mutation", each of which is a random, unlikely event. Both are distinguished from "fluctuations in mutation," which might be described as an intermediate between the two -- although writing in 1955 it is plausible that Wright may actually have meant alterations in the propensity toward mutations due to variation in radiational or chemical processes. This is one indication of the difference between Wright and Fisher, who felt that novel mutations might become more or less predictable in large populations.

I also noticed how many of Wright's "unique events" have been marshalled by one or another researcher to explain human evolution.

Another point of interest, reflecting the several instances of interesting evolutionary trends under domestication that I've linked this week, is Wright's accommodation of artificial selection within this scheme:

It may be noted here that artificial selection also imposes a new system of peaks toward one of which mass selection may be expected to drive the population rapidly. Since the peak attained is not a natural one, progress is almost inevitably at the expense of fecundity and viability. On relaxation, the population may be expected to return toward the original peak, or to another, and usually lower one, if the artificial selection has driven it across what was naturally a valley (Wright 1955:17).

This should be amended, in that selection comes at the expense of fecundity and viability in the previous environment, not the new artificially selected one. But the prediction that artificial selection should decrease fitness in the species' natural environment comes straightforwardly considering the nature of selection as a deterministic force. If the species was initially well adapted to its natural environment, any changes resulting from artificial selection would likely make it worse, not better.

Wright's well-known idea was that the stochastic factors might play an important role allowing a population to explore the adaptive landscape. In his "shifting balance" formulation, the division of an abundant species into many small subpopulations tends to maximize the species' ability to evolve toward higher fitness peaks, because a small group might have a fortuitous combination of alleles allowing it to move to a higher fitness peak. This model has been controversial even up to the present day, because of our lack of knowledge about the characteristics of "fitness landscapes".

But it is worth pointing out Wright's definition of the stochastic factors here, each of which might operate in conjunction with genetic drift in the shifting balance model. It is clear from the list that the balance between these different factors might itself change over time -- for instance, in our acceleration idea, the incidence of novel mutations is greatly accelerated in a growing population, ultimately increasing the scope of the deterministic process.

References:

Gillespie JH. 2000. Genetic drift in an infinite population: the pseudohitchhiking model. Genetics 155:909-919.

Gillespie JH. 2001. Is the population size of a species relevant to its evolution? Evolution 55:2161-2169.

Wright S. 1955. Classification of the factors of evolution. Cold Spring Harbor Symp Quant Biol 20:16-24.

Last year, the show had several anthro-related episodes, but this year it has been mostly network theory and the like. Until last night, when Sewall Wright was mentioned by name!

That's right, folks. US network drama. Friday night. Sewall Wright.

Sweeeeeeeet!

Why Sewall Wright? Well, our intrepid mathematician, Charlie, had to calculate the inbreeding coefficient for a monomaniacal polygamist cult leader. His pedigree for five generations or so was sewn into a quilt, and neither Charlie nor his attractive mathematician girlfriend knew what the symbols represented -- until Charlie's department chair, played by Kathy Najimy, for goodness sake, (who happened to be in Charlie's house because she is getting it on with Charlie's dad -- you know, Judd Hirsch -- recognized the pedigree symbols from cattle breeding!

Is this a great show, or what?

Of course, they followed that moment with some genetic nonsense about how the cult leader couldn't conceive with any of his highly related wives, so he had to have a particular unrelated female to mate with. I say, "nonsense," mainly because it was irrelevant to the plot, and didn't really convey a correct understanding of "recessive" alleles.

But how much can I ask for, really? Especially when I happened to be reading Sewall Wright at that very moment!

This morning, my irritation level about this Neandertal women hunting story finally reached its boiling point. I unleashed a Neandertal-style cry of anguish -- which if you've never heard one, sounds remarkably like a Wookie-style cry of anguish.

Am I a simple misogynist? Does the idea of deerstalking Neandertal women threaten my manhood? Maybe, although Gretchen assures me I'm not. Mostly, I'm irritated because a full-text search of the paper yields no mention of any possible test of their idea.

I hate being so critical of this idea. I really like Kuhn's and Stiner's other work. But over half of people think that all our raving about ancient humans is fantasy anyway, so I try to be as critical as I can. And this is a real doozy.

It's bad enough for something like this to hit the New York Times. But this one has even invaded Instapundit. Clearly something must be done!

So, I told my class I was incapable of giving a normal lecture, and would continue on the subject of sexual division of labor until they found a satisfactory means of testing Kuhn and Stiner's hypothesis.

Unfortunately, my students actually like seeing me rant and tear out my hair, so they had a positive disincentive to find the right answer. So, if you want a job done right...

Testing the hypothesis

In case you've missed it, the proposition by Steven Kuhn and Mary Stiner -- excellent archaeologists, both -- is that Neandertal women were incapable of the kind of sex-based division of labor found in most human societies, and instead spent their time helping Neandertal men to find and kill large animal prey.

So let me approach this hypothesis with a skeptical eye. What exactly does it entail?

1. Kuhn and Stiner propose that modern humans had a fitness advantage because they mobilized female labor to find and process high-effort plant resources and small animals.

2. Neandertals were so committed to large-animal hunting that they required assistance from their women, compromising their ability to collect low-quality but dependable plant and small animal resources.

3. In Kuhn and Stiner's view, these differences meant that modern humans and Neandertals were locked onto different adaptive peaks, and Neandertals were constrained from adopting the modern human pattern of division of labor, even though it allowed greater population growth.

Why is the adaptive peak story (number 3) necessary? Here's why: if the behavior of Neandertal women was very flexible, then they could have adopted the broader dietary strategy easily. There would be no rugged fitness landscape, because behavioral plasticity would smooth the fitness differences.

In other words, condition (3) is absolutely necessary to the hypothesis that sexual division of labor was the fitness advantage of modern humans over Neandertals.

Testing the adaptive landscape condition

I think that the adaptive landscape assumption is the greatest flaw in this hypothesis. Kuhn and Stiner's hypothesis depends on the assumption that sexual division of labor is quite rigid, so that Neandertals did not adopt a modern organizational strategy even though such a strategy was adaptive for modern humans in the same habitat.

That is a very strong claim, but necessary to their hypothesis. If Neandertal social organization strategies were actually flexible, then cultural variation among Neandertal groups would have enabled some of them to find the high-fitness strategy. Once a few groups reached the high-fitness sexually divided labor strategy, they would have proliferated. That is precisely the logic behind Sewall Wright's shifting balance theory, and it applies here equally well. Plasticity enables a population to explore the fitness landscape.

So if Neandertal foraging behavior was actually flexible, then there would have been no impediment to Neandertal females exploiting collected plants and small animals. In fact, if you showed that Neandertals actually did collect plants and eat small animals, it seems to me that the entire argument about social organization is moot.

As noted in several of the comments on the Kuhn and Stiner paper, Neandertals did collect small animals, marine resources, and plants at many sites. They did use grinding stones occasionally in Eastern Europe. They did collect grass seeds in the Levant, and nuts in Spain. In other words, Neandertals did have substantial dietary flexibility. This evidence for flexibility is currently best outside northwestern and north-central Europe, at least from faunal and plant remains.

The flexibility is also evident in dental microwear, which includes individuals from northwest and north-central Europe (Pérez-Pérez et al. 2003, Lalueza 1996). Based on the dates of specimens with different wear patterns, Pérez-Pérez and colleagues suggested not only that Neandertals had great dietary flexibility, but also that they may have relied on plants more during colder climatic periods. Since the early Upper Paleolithic was one of the colder periods, this seems relevant to the apparent contrast in subsistence strategies. In any event, the idea that Neandertals were invariantly carnivorous is simply inconsistent with the pattern of data.

Let's consider for a moment what would cause Neandertals to continue to pursue a low-fitness hunting strategy when they obviously were capable of acquiring high-fitness plant foods, they experimented with high-fitness plant foods, and many of them ate enough of the high-fitness plant foods to mark up their teeth. It seems quite implausible that Neandertals were locked into a strategy of perpetual experimentation and sampling of a high-fitness resource!

I think we're forced to conclude that either (a) further exploitation of plant foods did not provide a high-fitness strategy, or (b) Neandertals were stupid. Right? All this rigmarole about organizational strategies becomes another way to describe Neandertal stupidity.

Human ecology

The best explanation for why Neandertals didn't use more plant foods is that they didn't pay. Here's what Kuhn and Stiner wrote about plant acquisition:

Vegetable foods may well have been part of Middle Paleolithic diets in Eurasia, but these were more like salads, snacks, and desserts than energy-rich staples. (Grinding stones are known from the contemporaneous Middle Stone Age in Africa, a point we will return to later.)

...Large underground storage organs are common among plant taxa in arid sub-Saharan Africa, but the high-yield edible plant foods of temperate and Mediterranean Eurasia tend to be seeds and nuts that, while potentially nutritious, require more effort to collect and process and thus afford low net yields (Kuhn and Stiner 2006:957).

So Neandertals were using the most energy-rich resource available in Europe, and this is a problem? Many of us like salads, snacks and desserts. If they were making effective use of the available plant foods, then there is no basis whatsoever to suggest that Upper Paleolithic people were pursuing a more effective strategy. As I hint below, Upper Paleolithic people and modern hunter-gatherers both may share demographic pressures that forced a reduction in diet quality and trophic level. We should attend to the ecological changes that made the Upper Paleolithic adaptation work.

The same argument applies to the changes in social ecology, including the use of needles in the Upper Paleolithic. As Soffer ably demonstrates elsewhere (with Adovasio and colleagues), Upper Paleolithic people used needles because they had fabric. Neandertals didn't. That was a technological innovation that changed human ecology.

Somebody might be tempted to say that if Neandertal women had adopted a fundamentally Upper Paleolithic social organization, they would have invented fabric. But that argument doesn't apply to any recent technological innovation (if only 1970's office workers had more time on their hands, they would have invented the spreadsheet!), so I don't see how it can sensibly apply to Neandertals.

The deerstalking women

Note that these observations say nothing about what Neandertal women actually did. In other words, we have shown that condition (3) is very unlikely, but we haven't addressed condition (2). Maybe, as part of their dietary flexibility, Neandertal women really did help with hunting some of the time.

At its boundary -- Neandertal women hunted occasionally -- this idea is nothing more than an untestable suggestion. We cannot negate such a broad suggestion. Besides, in broad form it is likely true. Who could deny that a hungry Neandertal woman might help her male groupmates drive animals into an ambush?

But I think we can at least test the idea that Neandertal women were habitual hunters. I am willing to make one assumption: Neandertal hunting strategies involved a higher mortality risk than Upper Paleolithic hunting strategies.

That assumption is justifiable in terms of technology -- Neandertals killed with close ambush methods because they did not have projectile weapons; Upper Paleolithic people did have projectile weapons, and they apparently also used more logistical hunting strategies. Also, the assumption is justifiable by mortality and injury data -- Neandertals died younger, and they died with lots of healed injuries.

Still, the mortality risk of Neandertal hunting was not uniformly distributed. Some roles were riskier than others. It may well have been that women could participate in hunting, as drivers for example, while bearing a lower mortality cost than men. This is, of course, a sexual division of labor, but such a division would not involve separate male and female collection strategies.

But if Neandertal women could bear a lower mortality cost while participating in hunting, then so could Upper Paleolithic women. And if Neandertal men could spend less time hunting and have a higher return rate with female help, then so could Upper Paleolithic men. And if Neandertal women didn't need to stay in camp to tend their children, then neither did Upper Paleolithic women.

In other words, if hunting was less risky for Neandertal women than for Neandertal men, it was even less risky for Upper Paleolithic women! Upper Paleolithic women should have been more likely to hunt than Neandertal women.

You see, the caloric return of different food sources (meat versus plants, big animals versus small animals) for Neandertals and Upper Paleolithic people would have been precisely the same, assuming the same success rate and risks. So to explain a difference between the two groups in adaptive terms, we need to posit a difference in their success rates or their risks.

We have four options:

a. Upper Paleolithic women achieved a higher return than Neandertal women from plants and small animals.

b. Upper Paleolithic hunting returns were much higher than Neandertal hunting returns, so women had plenty of free time to collect plants and small animals.

c. Upper Paleolithic hunting returns were much lower than Neandertal hunting returns, so women were forced to collect plants and small animals, despite their lower caloric value.

d. Upper Paleolithic camps were intrinsically more dangerous than Neandertal camps, requiring more women (and possibly men) to stay close to defend children and new mothers.

Each of these four options reduces to a very simple proposition. For example, under option (a), Upper Paleolithic women could have achieved higher return rates from plant foods if they had better technology. Option (b) implies that hunting technology increased Upper Paleolithic returns. Option (c) implies that demographic growth placed greater stress on local resources in the Upper Paleolithic (it is very similar to the "broad spectrum" idea as applied to the development of agriculture). And option (d) would imply that demographic growth resulted in more warfare between neighboring groups, also consistent with the increase in social markings and regional tool differentiation in the Upper Paleolithic.

Notice that all of these options come down to technological or demographic changes. None of them give an important causal role to sexual division of labor. Instead, the aspects of division of labor that can be observed in the archaeological record emerge as a result of basic technological or demographic conditions.

I view the demographic factors as more important than technological ones, but I have no strong rationale for this preference. To me, the most important point is that the risk factors constraining the adoption of full-time hunting for recent human women must have been even stronger for Neandertal women. This means if we want to find hunting women, we should look at recent human foragers. And they aren't there.

Technological or demographic conditions may have altered this picture, increasing the likelihood that Neandertal women did hunt. But there is no evidence that they did.

Final lessons

So the idea can be tested! It wasn't even that hard!

To the extent that we can compare with living and prehistoric humans, there is no support for the idea that Neandertals went extinct because their women spent too much time hunting. There are positive reasons that refute this idea -- most importantly, the demonstrated dietary flexibility of Neandertals and other archaic humans, which would have enabled Neandertal women to exploit a systematic plant and small animal collection strategy if it actually had increased their fitness. The fact that they did not do so is probably a reflection of their ecology, not their social organization.

It remains difficult or impossible to refute mere possibilities on the basis of the archaeological and fossil record. But we should remember that such mere possibilities are not testable hypotheses.

Certainly, some Neandertal women may have hunted along with Neandertal men. Maybe they were Neandertal Amazons who severed a breast to better thrust spears into roaming bison. After all, we know that they were capable of amputating limbs, so why not?

The "why not" in this case is, obviously, that Neandertal Amazons are a product of fantasy. Sure, the fossil record cannot rule out the possibility that they existed. But comparisons with our everyday experience and our knowledge of variation in other species both tend to indicate that such a curious adaptation would be unlikely.

The same is true of Kuhn and Stiner's model. A deerstalking Neandertal woman is by no means impossible. Maybe they spent a lot of time hunting, who knows? The problem is that there is no evidence that they did so.

References:

Bamforth DB. 2002. Evidence and metaphor in evolutionary archaeology. Am Antiq 67:435-452.

Kuhn SL, Stiner MC. 2006. What's a mother to do? The division of labor among Neandertals and modern humans in Eurasia. Curr Anthropol 47:953-980.

Lalueza C, Pérez-Pérez A, Turbon D. 1996. Dietary inferences through buccal microwear analysis of Middle and Upper Pleistocene human fossils. Am J Phys Anthropol 100:367-387.

Pérez-Pérez A, Bermúdez de Castro JM, Arsuaga JL. 1999. Nonocclusal dental microwear analysis of 300,000-year-old Homo heidelbergensis teeth from Sima de los Huesos (Sierra de Atapuerca, Spain). Am J Phys Anthropol 108:433-457. Abstract

Pérez-Pérez A, Espurz V, Bermúdez de Castro JM, de Lumley MA, Turbón D. 2003. Non-occlusal dental microwear variability in a sample of Middle and Late Pleistocene human populations from Europe and the Near East. J Hum Evol 44:497-513. DOI link

A subset of evolutionary theorists are specifically concerned with how the evolution of multiple characters of organisms are linked to each other by genetic correlations. A handful of those theorists actually think about human evolution. There is a little bit of matrix algebra involved; maybe that explains why the number is so small -- I don't know.

But the problem is of fundamental importance to quantitative evolution, because the power of selection to change a feature is constrained by the genetic relationships of that feature to other features of the organism.

For example -- want to make the brain bigger? Then you have to deal with the fact that some of the same genes that make brains bigger also make bodies bigger. Want to make the neocortex bigger in particular? It will be hard to do it without increasing the size of the brain, the size of the body, the size of the teeth, and so on. All these sizes are genetically correlated to some extent, the actual extent being described by the genetic variance-covariance matrix (often called G). Each of these characters has its own pattern of (often stabilizing) selection, so if you push on one very much, others will pull against you.

Massimo Pigliucci (2006) knows a lot of quantitative genetics. He even has a textbook about it. He also has a paper in Biology and Philosophy, titled "Genetic variance-covariance matrices: a critique of the evolutionary quantitative genetics research program." So this attracted my interest -- what is a well-known quantitative geneticist doing critiquing the research project of quantitative genetics?

It has a pretty provocative abstract:

This paper outlines a critique of the use of the genetic variance-covariance matrix (G), one of the central concepts in the modern study of natural selection and evolution. Specifically, I argue that for both conceptual and empirical reasons, studies of G cannot be used to elucidate so-called constraints on natural selection, nor can they be employed to detect or to measure past selection in natural populations - contrary to what assumed by most practicing biologists. I suggest that the search for a general solution to the difficult problem of identifying causal structures given observed correlation's has led evolutionary quantitative geneticists to substitute statistical modeling for the more difficult, but much more valuable, job of teasing apart the many possible causes underlying the action of natural selection. Hence, the entire evolutionary quantitative genetics research program may be in need of a fundamental reconsideration of its goals and how they correspond to the array of mathematical and experimental techniques normally employed by its practitioners (Pigliucci 2006:1).

That's some big talking -- "fundamental reconsideration of its goals". Do his specific critiques of the application of the genetic variance-covariance matrix support this conclusion?

His first point is that the theoretical work on "the" G matrix leaves very open the structure of particular G matrices that one might study in one or another organism. Some covariances among characters are stable at high taxonomic levels, like the family level, and other covariances may be very different from one population of a species to another. He writes:

The upshot of this is that quantitative geneticists who focus on stamens in Brassicaceae are likely to reach completely different conclusions about the stability of the genetic variance-covariance matrix from their colleagues who instead study leaf evolution in semi-aquatic plants. Indeed, research by Waldmann and Andersson (2000) in populations of Scabiosa columbaria and S. canescens found, among other patterns, that 'the magnitude of (co)variances was more variable among characters than among populations,' i.e., the results of a given study of G depend more strongly on which traits the investigators choose to focus on then it does on the species selected! Again, this ought to be obvious, but much of the literature is written in a way that implies that the evolution of G is a single kind of thing, and that it makes sense to think of G itself, somewhat independently of the particular traits used to calculate it (Pigliucci 2006:8).

I think that does pose a theoretical problem (i.e., what is the relationship of theory to empirical results-on-the-ground), but it doesn't pose any particular problem for people studying specific traits in a specific group of organisms -- for instance, cranial form in the hominids. At that level, we don't care about G matrices in general, or even the total genetic variance-covariance matrix for the human body, as long as we can estimate the variances and covariances of the characters we are studying. So the global problem may not affect the specific implementations.

Pigliucci's second point carries more force, and to my mind is really a concatenation of two separate issues. First, we have some practical means that we may use to estimate genetic variances and covariances -- such as half-sib breeding designs. But we have no justification for the further assumption that the variances and covariances obtained from such experiments actually apply to any natural populations. The second, and related, issue is that the "true" G matrix in a natural population depends on its breeding structure.

If anything, these points have more force applied to the specific example of human evolution than to the general case. For one thing, for most characteristics we don't even have any studies of the genetic variance and covariance with other characters. A lot of studies just substitute the phenotypic variance-covariance matrix, assuming that it is "more or less" like the genetic matrix.

And there is an awful lot of simply using phenotypic variances and covariances without mentioning genetics at all! As in, "population X and Y cluster phenotypically near each other, therefore they are genetically close to each other."

The second part is something to consider more closely. Have hominids changed their breeding structure in ways that would make difference to the genetic correlations among traits? Hard to say. Seems like changes in group size and within-group relatedness would make a difference, but I'm not sure about the scale.

Pigliucci's third point concerns the use of G, which is always a local estimate, to examine long-term patterns of evolution:

As with h², if the available genes or the gene frequencies in the population change, so too might G; similarly, in a different range of environments (or if the population becomes differently distributed among the environments encountered), G might well change. Given this, if one wants to make use of G in simulations of long-term evolution (e.g., Via 1987), one must assume that the matrix stays constant (or at least proportional) to the ancestral state over the time period one is investigating (generally thousands of generations). But several authors (e.g., Turelli 1988; Pigliucci and Schlichting 1997) have pointed out that this is highly unlikely on first principles, because evolution de facto changes gene frequencies, and therefore G itself; nor is it unreasonable to suppose that over such time periods the environment encountered by the population may change as well. Therefore, while it is sensible to assume near-constancy of G for short-term applications (e.g., crop or animal breeding, artificial selection experiments, or perhaps even evolution in wild populations over few generations), the hypothesis of approximate constancy becomes less and less likely the more widely separated the relevant populations are in time and/or space (Pigliucci 2006:10-11).

He notes that the same argument applies to variation in environments, as does to time.

I would personally say that this is the most serious problem. If the genetic variance-covariance matrix evolves, as it must for phenotypic evolution to occur, then it cannot be assumed constant. I have many times heard the argument that we can estimate variances and covariances for fossil humans by using large samples of living humans -- because living humans are more or less similar in their variances and covariances to ancient humans. (These are, of course, phenotypic variances and covariances, since the idea of genetics rarely enters!) But this idea is simple nonsense, particularly since it is usually made in an effort to show just how different some fossil sample is from living people!

Pigliucci's fourth point is best described in his own words:

More philosophically interesting are problems concerning G that cut to the core of why biologists use the concept to begin with. Let us start with the notion that the predictability of future phenotypic evolution is predicated on G revealing 'constraints' on evolutionary change imposed by the 'genetic architecture' underlying complex phenotypes. The idea is that trade-offs between traits to which an organism can allocate available resources (for example, between survival and reproduction) should manifest themselves as observable (negative) genetic covariances between the traits in question. If this were true, studies of G matrices could reveal features of the underlying trade-offs that influence the direction of phenotypic evolution, a major goal of evolutionary biology. Unfortunately, work by Houle (1991) and Gromko (1995) has dealt what should have been devastating blows to these uses of G in evolutionary theory; oddly, despite these key papers being published in Evolution, the premier journal in the field, their arguments have scarcely made a dent in the literature (Pigliucci 2006:12).

He goes on to describe the results. Houle demonstrated mathematically that trade-offs do not always give rise to negative genetic covariances, because the genetic covariances depend on the genetic variances and the number of genes involved. Large variances at many genes may outweigh even strong negative covariances at few genes. Gromko demonstrated many different pleiotropic mechanisms might generate the same G matrix, and that the pattern of covariances cannot distinguish between different possible evolutionary outcomes. In particular, covariances near zero might occur for systems that nevertheless are highly constrained in their coevolution.

More than other problems, this one would seem to reveal a conflict between evolutionary developmental (evo-devo) approaches and standard quantitative genetic approaches. Where standard approaches might view the genetic variance-covariance matrix as the genetic structure, evo-devo looks for the mechanisms that give rise to the stucture. Since different functional relationships among genes might give rise to the same covariances, this gives some reason for caution in applying the covariances to predict long-term evolution.

Pigliucci's fifth point is that G matrices don't provide much help in distinguishing the effects of selection from those of genetic drift. This is an important theoretical problem in biology and one that has been applied to evolutionary transitions in human evolution (e.g., the cranial form of early Homo). Pigliucci gives a review of the predictions of standard theory (viz., selection should affect different sets of characters differently, drift should affect the entire matrix in a proportional way), and then describes Drosophila experimental work that raises problems for the theory:

When these authors [Phillips et al., 2001] considered the average G across populations (a statistically useful, but biologically meaningless, construct), this did indeed follow Roff's expectations: the populations that had undergone drift had an average G that was proportional to that of the founding population, as predicted by the theory for a set of replicated populations (i.e., when one actually knows the historical path of evolution). If these results had held for the individual populations that underwent drift, rather than for the statistical construct created by averaging them, this would have been good news indeed. But alas, when Phillips and collaborators examined the Gs of individual populations that had undergone drift, they found that most were not proportional to their control at all: i.e., these matrices appeared to have been produced by selection, not drift, even though there was no significant selection going on! (Pigliucci 2006:16, emphasis in original).

In other words, instances of the evolutionary process don't look like averages over many instances. This is a problem with inferring selection as opposed to drift (i.e., drift in a single population may look like selection), but I would guess there is a corresponding problem inferring drift (i.e., selection in a small sample may look like drift, due to the inaccuracies in estimating covariances). The problem of sample size and covariances is one I may take up again later.

Pigliucci's sixth and final point is that biologists often confuse individual-level versus population-level processes when they talk about "selection on" G matrices. I can see this point, as he describes it:

When considering natural selection, it is clear that physical interactions at the individual level may result in predictable statistical patterns at the population level, and yet this does not imply that the reverse move (from population to individual) is just as straightforward. The point has been made more generally by Shipley (2000), who - in the context of discussing the relationship between causation and correlation in biology - concluded that biologists can test hypothesized causal models by comparing them with their predicted statistical 'shadows,' but cannot reasonably go from the latter to the former. Alas, that is exactly what a great part of the research project in evolutionary quantitative genetics is all about! To put it into another fashion, we can calculate the statistics, but what sort of biological questions are they answering, if any? (Pigliucci 2006:17).

But I'm having trouble thinking of a concrete example that shows why it is a problem, beyond being a conceptual problem.

In any event, that summarizes the critique. It is hard for me to imagine the multivariate study of fossil hominids that answers all these points convincingly. There is maybe some feeling that studies of fossil hominids are imperfect, but will get better if the samples increase in numbers, etc., etc. But Pigliucci has some nice turns of phrase that I like as answers to this idea. For example:

[B]y now it should be clear that quantitative evolutionary biologists ought not to think of these statistical constructs as 'first approximations' to be refined by further research; the difficulty with these constructs is not that they are imprecise (and, therefore, amenable to 'refinement'), but that they do not answer the questions we wish answered (Pigliucci 2006:19).

After his critique, Pigliucci tries to outline ways that might advance our understanding and avoid these conceptual problems. I can't say he has much success at it, since ultimately somebody is going to have to invent new methods to answer the problems.

Additionally, I would say that the problems studying hominid evolution go a lot deeper. Many studies uncritically apply multivariate techniques to samples of five or ten individuals. Keep in mind that these samples are insufficient for estimating variances with reasonable error. Now consider that people are using them to estimate covariances among twenty or more characters. That's a different scale of problem from the ones Pigliucci is describing, but it borders and grades into them.

I do want to quote one part of the conclusion of the paper, because it will be interesting to students of the Fisher-Wright controversy:

The conceptual reason [for commitment to multivariate regression], of more philosophical interest, can be traced back to the rationale that went into the publication of Lande and Arnold's (1983) paper: the main goal there was to provide not just a way to statistically quantify natural selection in action, but to do so while obtaining coefficients of selection that could be directly plugged into the standard quantitative genetics equations for the prediction (or post-diction) of phenotypic evolution. It turns out that, until now, nobody has figured out a way to use path coefficients for the same purpose (but see Scheiner et al. 2000 for the beginning of such an attempt). This implies that a theoretical goal has been for all effective purposes overriding serious conceptual and methodological limitations of the techniques used. What makes this a possible dead end for the entire field is that there are good reasons to believe that the theoretical goal in question - the long-term prediction of evolutionary trajectories - is simply not achievable because of the problems of locality and liability of G discussed above (Pigliucci 2006:20).

That's interesting because, of course, the usual multivariate techniques owe their origin to Fisher, while path analysis was Sewall Wright's solution to some of these genetic problems. Personally, I would say that path analysis is more logical in many ways, but yet it is pretty difficult to implement. A connection between evo-devo genetics and path analysis would be pretty interesting to see.

References:

Pigliucci M. 2006. Genetic variance-covariance matrices: a critique of the evolutionary quantitative genetics research program. Biology and Philosophy 21:1-23. DOI link

Two hypotheses, discussed by Burke and Arnold (2001):

The role of epistasis in adaptive evolution has been a controversial issue ever since Sewall Wright and R.A. Fisher first formalized their views in the early 1930s. According to Wright (113, 114), natural selection retains favorably interacting gene combinations. Therefore, as a result of the highly integrated nature of the genome, selection may lead to the production of what Dobzhansky (43) has termed "coadapted" gene complexes. In contrast, Fisher (48) argued that natural selection acts primarily on single genes, rather than on gene complexes. In Fisher's view, therefore, selection favors alleles that elevate fitness, on average, across all possible genetic backgrounds within a lineage. Such alleles have been termed "good mixers" (75). Regardless of the role of epistasis within lineages, however, negative epistasis in a hybrid genetic background, or hybrid incompatibility, is fully consistent with both the Wrightian and Fisherian worldviews. This is because allelic fixation occurs in any one lineage without regard to the compatibility (or lack thereof) of new alleles with those in any other lineage. Hybridization then produces a vast array of recombinant genotypes that have never before been subjected to selection. On average, these genotypes will be less well adapted than their parents, giving rise to some level of selection against hybrids.

Hybrid breakdown, or the reduction in fitness of segregating hybrid progeny that often results from intercrossing genetically divergent populations or taxa, has long been taken as evidence of unfavorable interactions between the genomes of the parental individuals (e.g., 39, 42, 43, 75, 80). The most widely accepted genetic model for the occurrence of such incompatibilities was first described by Bateson (15, as cited in 83), and later by Dobzhansky (39) and Muller (79, 80). In short, the Bateson-Dobzhansky-Muller (BDM) model assumes that an ancestral population consisting solely of individuals of the genotype aa/bb is broken into two parts that are temporarily isolated from each other. In one subpopulation, a new allele (A) is then assumed to arise at the first locus. Meanwhile, a new allele (B) is assumed to arise in the other subpopulation. Because individuals of the genotype aa/bb, Aa/bb, and AA/bb can interbreed freely, the A allele can then spread to fixation in the first subpopulation; likewise, individuals of the genotype aa/bb, aa/Bb, and aa/BB can interbreed freely, and the B allele spreads to fixation in the second subpopulation. However, although A is compatible with b, and B is compatible with a, the interaction of A with B is assumed to produce some sort of developmental or physiological breakdown, such that hybridization between the two subpopulations leads to the production of offspring with decreased levels of viability and/or fertility. Although this model focuses on negative interactions between differentiated regions of the nuclear genome, similar interactions between one or more regions of the nuclear genome and some component of the cytoplasm (e.g., the chloroplast or mitochondrial genome) could also play an important role in hybrid incompatibility. Unfortunately, the BDM model does not provide any mechanistic explanation as to how mutations that are neutral (or beneficial) within a given lineage will produce strongly disadvantageous incompatibilities when combined in a hybrid background (Burke and Arnold 2001, emphasis added).

References:

Burke JM, Arnold ML. 2001. Genetics and the fitness of hybrids. Annu Rev Genet 35:31-52. DOI link

Razib at Gene Expression has a very informative post referring to the edited volume Epistasis and the Evolutionary Process (Wolf et al. 2000). I'm posting a reference myself because I want to remember and return to the topic later.

It's full of Sewall Wright goodness.

References:

Wolf JB, Brodie ED III, Wade MJ. 2000. Epistasis and the evolutionary process. Oxford University Press, New York.

I'm trying to resist becoming a hotbed of female orgasm blogging, but I just heard a promo for the story on the local news, so it seems impossible to avoid. Moreover, the issue has become a genuinely interesting debate about the role and method of evolutionary analysis. On this, I have a small contribution to make.

The Guardian is running a story on research by Kate Dunn and colleagues (2005) into the heritability of sexual response in women. Here's the abstract:

Orgasmic dysfunction in females is commonly reported in the general population with little consensus on its aetiology. We performed a classical twin study to explore whether there were observable genetic influences on female orgasmic dysfunction. Adult females from the TwinsUK register were sent a confidential survey including questions on sexual problems. Complete responses to the questions on orgasmic dysfunction were obtained from 4037 women consisting of 683 monozygotic and 714 dizygotic pairs of female twins aged between 19 and 83 years. One in three women (32%) reported never or infrequently achieving orgasm during intercourse, with a corresponding figure of 21% during masturbation. A significant genetic influence was seen with an estimated heritability for difficulty reaching orgasm during intercourse of 34% (95% confidence interval 27-40%) and 45% (95% confidence interval 38-52%) for orgasm during masturbation. These results show that the wide variation in orgasmic dysfunction in females has a genetic basis and cannot be attributed solely to cultural influences. These results should stimulate further research into the biological and perhaps evolutionary processes governing female sexual function.

At the Philosophy of Biology weblog, Elisabeth Lloyd (author of aforementioned book on female orgasm evolution) has a post generally supportive of the paper itself, but very critical of press accounts of it. She directs her greatest criticism toward the following comments by study senior author Tim Spector, which appear in the Guardian article:

Tim Spector of St Thomas's hospital in London, who led the research, said: "The theory is that the orgasm is an evolutionary way of seeing if men can prove themselves to be likely good providers or dependable, patient and caring enough to look after the kids."

Women who orgasm very easily may be more likely to be satisfied with poor quality men.

"Perhaps women who had orgasms too easily weren't very good selectors," Professor Spector said. "It paid women to be more fussy and this is one way of doing it. The simple fact is that it takes women on average 12 minutes and men two and a half minutes to reach orgasm. Adjusting to that imbalance is a test."

Lloyd has done a lot of thinking about this hypothesis, and she has a lot of ammo to unload on it. I quote from her post to give her deconstruction with some of its original clarity:

As the Guardian article makes clear, Spector is (re-)proposing a theory that orgasm is a mate-selecting device; he claims that the fact that orgasm during intercourse is difficult to attain is an evolutionary adaptation itself, making the well-known variability in orgasm among women an adaptation.

But we run into trouble immediately. The proposed adaptive state is a conditional response to quality males - have an orgasm if he's a good guy, don't if he's not - and under this theory, clearly the population of women was under selection pressure to have moved towards that optimum peak (balanced by the usual energetic costs, and so on). So why would that be an argument for the variability of orgasmic response, and not an argument for the standard result of a directional selection regime, namely, a peak at the optimum?

She goes on to summarize the data from the study, which fairly convincingly show that all females cannot have been selected to pursue this strategy -- their variability is too extensive:

If selection has been of any appreciable strength, and has been going on at least since the advent of archaic humans, we should expect that nearly all women would have such a conditional response to intercourse, and thus that nearly all women would be capable of orgasm with intercourse under the right conditions. The bad news is that there is no evidence for such a peak at all, that a full third of women rarely or never have orgasm with intercourse, and that as many as one out of ten women don't have an orgasm even once in their lives. There is a small peak in the distribution, but it is located at the non-orgasmic segment of the distribution. In other words, this is the kind of variability he needs to support his theory, and his own data show that the supporting evidence just isn't there, as I'll detail in a moment.

But there's another kind of variability, namely, that some women never have orgasm with intercourse, some women always do, and some women sometimes do and sometimes don't. This kind of variability is the kind that they do document in their study, and this kind of variability would not be selected for under his proposed hypothesis, but perversely, he implies that it would.

Heritability and alternative strategies

But I'm not sure that Lloyd and Spector are really talking about the same hypothesis. (Disclaimer: Hey, I don't know, maybe they are, in which case Lloyd's critique is more valid than I suggest.) The prologue to the Spector quote taken from the Guardian reads as follows:

The findings suggest the failure of some women to orgasm regularly is not a dysfunction, but a sophisticated mate-selection strategy that evolved during prehistoric times.

When I read that, I believed that Spector was arguing that some women (namely the ones with rarer orgasms) may have had an adaptive strategy for conditional response to male quality, leaving unstated the obvious corollary that other women may pursue different adaptive strategies.

After all, the idea that all women follow the conditional response strategy is ridiculous on its face: it cannot explain the women who reach orgasm easily and quickly most of the time, regardless of partner. If female orgasm is an adaptation, clearly there must be at least two distinct strategies: one in which orgasm is difficult and arrived at only through certain efforts, and one in which orgasm is readily achieved. There is no reason why these alternative strategies may not competed with each other in ancient human populations, considering each may have distinct advantages and drawbacks. A quick orgasm may make sex very compelling, possibly resulting in a higher frequency of inseminations -- possibly from multiple male partners. This strategy would reduce the risks associated with partnering with a single male (especially the risk of male infertility), while increasing the genetic diversity of a woman's offspring. In contrast, the conditional response strategy might have the predicted effects in encouraging female choice for male quality. Please remember that neither of these strategies has been tested, nor has the effect of their conjunction; I merely say that the hypothesis is conceivable that both of them coexisted as genetic variants within ancient human populations.

Indeed, there is no reason why there should not have been a large number of different adapted strategies toward female orgasms in past human societies. Human sexual experience must have been highly heterogenous, and the selective consequences of partially heritable mating strategies would interact in a complex way. It has the makings of a very interesting evolutionary problem.

Now, I agree that the uncritical acceptance of these hypotheses is not warranted. And I agree with Lloyd that a nonadaptive hypothesis is also very credible. The data do not point one direction or another at this point. But it is far too soon to discount the possibility that there are multiple adapted sexual strategies in human females that incorporate orgasm in differing ways.

Considering the hypothesis of alternative strategies, Lloyd's critique is mostly hollow. Consider the following passage:

The fact that this new study establishes a heritability of .45 for orgasm with masturbation (which is much more revealing than orgasm with intercourse, as far as basic orgasmic capacity goes), is also very damaging to any adaptationist account, and I'm surprised that technical people aren't saying so. Traits that are species-adaptations, such as, for example, having the capacity for language, or starting off with a good sense of taste, or having a massive brain, have heritabilities near zero. Nearly all the variability has been used up, selected out. This is just the end result of what I've just recited about the peaks in distributions. If selection is strong enough and goes on for long enough, variability around the peak gets weeded out through selection, and we're left with just one type plus random mutation and somatic, developmental, and environmental accident. Traits with heritabilities near .5 are not even close to being decent candidates for species-wide adaptations, for just this reason, as is widely known (I thought...).

FOURTH CONCLUSION: Spector's own heritability results also indicate that female orgasm is not an adaptation. Is it only population geneticists who know that species-wide adaptations have heritabilities near zero? How can it be that an expert on heritability like Spector doesn't know this? I guess this piece of knowledge might be a casualty of over-specialization.

I guess I'm as "technical" a person as has considered the issue lately, and Lloyd is just wrong about this. Certainly it is true that Fisher's Fundamental Theorem predicts that the heritability of a trait will decrease under directional selection, but Lloyd has provided us no reason to suppose that selection on female orgasm need have been directional in its pattern. Even if it were true that female orgasm were centered around a single strongly selected peak, it is far more likely that this peak would be the product of stabilizing selection rather than directional selection. The persistence of genetic variation (and thereby heritability) in such a scenario would depend on the effects of the genes themselves (e.g., is there heterosis? epistasis? antagonistic pleiotropy?). There is no simple answer to these questions, we have no knowledge whatever about the genes influencing female orgasm, and hence, it is impossible to make categorical statements about the likely heritability of the character after a history of selection.

If, as I think is a more likely scenario, there are alternative adaptive strategies toward female orgasm in humans, then it is not only likely, but necessary that the trait have substantial heritability. Unless offspring are similar to their parents, there is no sense in which alternative adaptive strategies can exist as adaptations (although under such circumstances they may well exist as cultural strategies without necessary genetic correlates).

"Species-wide adaptations"

Likewise, Lloyd's "fourth conclusion" confusingly states that "species-wide adaptations have heritabilities near zero." Remember that heritability is simply the proportion of phenotypic variance explained by genetic variance. Heritability may be near zero if phenotypic variance is high while genetic variance is very low. It may also be near zero if phenotypic variance is very low -- if the population just does not vary in the trait under consideration.

What does Lloyd mean by a "species-wide adaptation"? This is not clear to me, because her examples clearly are different in terms of variability. Humans today universally have language, and they universally have large brains (compared to, say, chimpanzees). But while the heritability of linguistic capacity is unknown, the heritability of brain size is very high in today's humans (> 0.9). Thus, it is desirable that we should be very careful in describing a trait as a "species-wide adaptation," at least if by this we mean to include some limit to the degree of potential heritability.

The example of language would seem to imply a discrete feature that differs categorically between species. A simpler example (that does not beg the question of ape linguistic capacity) is one of the human adaptations for obligate bipedality: an adducted big toe. Almost no humans have an opposable big toe; almost no chimpanzees have an adducted one. The distribution of variation of such traits nearly completely separates different species from each other, and within a species their heritability is near zero -- because their variation is near zero.

If this is the kind of trait Lloyd refers to, then it is true but trivial that such traits have heritabilities near zero. The fact that their phenotypic variance within a species is near zero allows no other conclusion. It is equally true that if we assert that female orgasm is a "species-wide adaptation" in the sense of being categorically absent from other species, then we must conclude that its heritability within humans as a categorical trait must be near zero.

But there is no reason to think that any aspect of female (or male) sexuality is a "species-wide adaptation" like an adducted big toe. As Lloyd's example of brain size makes clear, many species-typical adaptations have substantial within-species heritabilities. For example, humans have a high valgus angle, meaning the angle at the knee joint between the long axes of the femur and tibia. This angle facilitates bipedal locomotion by placing the tibia beneath the body's center of gravity during single-legged stance. This trait is clearly species-typical: human femora can easily be differentiated from chimpanzee femora by the valgus angle. But at the same time, the valgus angle itself is variable within humans. That is to say, the distribution of this continuous variable both separates humans from chimpanzees and distinguishes humans from each other. Within humans, much of the phenotypic variance is explained by underlying genetic factors, through the phenotypic correlations with other traits, such as stature, leg length, and pelvis width. Thus, this human-specific trait is moderately heritable within humans.

Human-specific traits in which alternative strategies underlie variation likewise are extensively heritable. As a case in point, human intelligence is substantially different from intelligence in any other hominoid species. Although some (hypothetical) measurement of intelligence might show some slim overlap between humans and chimpanzees in its distribution, the mean values of the two species are so different that they defy scaling. Even so, intelligence is both substantially variable in humans and substantially heritable. This heritability of intelligence may have many causes, but one of them must be the fact that intelligence itself comprises many different mental abilities that each have separate adaptive consequences. It is widely believed that such adaptive variation may in part predispose people to differing behavioral strategies, including variation in personality.

I tend to think this is not very far from the mode of evolution of human sexuality. Dunn et al. (2005:3) in fact consider mental factors as potential behavioral mediators:

Other potentially imoprtant biological factors include androgen levels or receptors, or natural variations in pleasure centres in the brain, resulting from dopamine or other psychological mood effects. All of these processes are probably mediated to some extent by genetic variations. Other associated factors, such as differences between individuals in anxiety and depression, also have heritable components and may partly contribute to the genetic component of orgasmic ability reported here.

It seems shortsighted to consider the evolution of female sexuality in isolation from the complex neurological factors that mediate female social behavior. A low frequency of orgasm during masturbation has little meaning as an adaptive character. The response to social situations, nonsexual interactions with female peers and potential male -- and female -- sexual partners, and long-term stresses must be considered in a full account of the biology of sexuality. The story does not begin or end at the clitoris, but must ultimately focus on the human as a psychological whole.

After all, the first lesson in health class is that the most important sexual organ is the one between the ears.

UPDATE 6/10/05: Elisabeth Lloyd has been kind enough to comment on this post in the comments to her original post on the subject. This has cleared up much confusion, particularly concerning the state of adaptive hypotheses for female orgasm.

Apparently, although I would never have guessed it, my hypothesis of multiple alternative strategies is novel. It seemed almost too obvious to be worth posting to me, since most of my recent thinking has been about brain evolution where these kinds of alternative strategies are common parlance. If you are a scientist reading this, take note: this is one of the great advantages of blogging, since what seems obvious to you may not be so to someone in a different field, and vice-versa.

In her comment, Lloyd acknowledges my point that only directional selection necessarily reduces heritability, but informs us that adaptive hypotheses concerning female orgasm have been framed exclusively assuming directional selection. In this case, her arguments certainly do apply to those hypotheses. This is one of the drawbacks of contemporary adaptationism that is not included in Gould and Lewontin's classic essay, "The Spandrels of San Marco": the frequent assumption that adaptations are the result of directional selection rather than other patterns. It is also a frequent confusion as applied to Sewall Wright's concept of adaptive peaks, which are not maintained by direcional selection, nor are they necessarily reached by it.

At any rate, as I mention above, I scarcely think the hypothesis of alternative strategies is testable. By introducing the possibility of many additional parameters, the hypothesis conceivably may be consistent with almost any distribution of orgasm incidence or facility. The important question is whether the hypothesized strategies may be biologically justifiable, and this will necessarily remain an impossible question to answer as long as the other behavioral correlates of such strategies are unknown. Lloyd's comment points out the problems with some such strategies as applied to the evidence. This is a bouncing ball in a sense: whenever one strategy is demonstrated to be biologically problematic, one might still propose a different set of strategies that would be commensurate with the same observations. At some point this becomes a reductio ad absurdum, but there is little chance that even the first level of two contrasting adaptive strategies can be tested with data now available.

Also note, that the more we consider correlates of female orgasm, the more we approach a non-adaptive hypothesis. That is to say, if female orgasm depends for its frequency, pattern, and existence upon other psychological or behavioral qualities, then it is possibly much simpler to argue that it is selection upon these qualities rather than orgasm itself that has shaped its distribution.

So again, this is a very much more interesting evolutionary problem than at first it might appear, and very intimately connected to the evolutionary history of the human mind.

Many thanks to Elisabeth Lloyd for her gracious and thoughtful comment. I'll never snark about orgasm-blogging again!

References:

Dunn KM, Cherkas LF and Spector TD. 2005. Genetic influences on variation in female orgasmic function: a twin study. Biol Lett (advance online). Royal Society Publications online