Tag Archives: quantitative genetics

On Genetics and Human Behavioral Biology

Nicholas Wade, former science reporter for the New York Times has written a book, A Troublesome Inheritance, in which he argues that large-scale societal differences (e.g., the existence of capitalist democracies in the West or of paternalistic, authoritarian political systems in Asia) may be attributable to small genetic differences that were fixed at a population level through the action of natural selection since the emergence of anatomically modern humans and their subsequent dispersal from Africa. The fixation of these gene variants happened because the continents of Europe, Asia, and Africa (homes of the major “racial” groups) differed in systematic ways. David Dobbs recently reviewed it in the Sunday Review of Books, which prompted a kind of amicus brief letter-to-the-editor from over 120 population geneticists, affirming that Wade’s writing misrepresents the current science of genetics. A full list of the signatories of this letter can be found here. It is a veritable who’s who of contemporary population genetics.

As you might imagine, A Troublesome Inheritance has been quite controversial. A great deal has already been written on this book, both in formal publications and in the science (and economics) blogging ecosystem. To name just a few, Greg Laden, my old homie and fellow TF for Irv DeVore‘s famous Harvard class, Science B-29, Human Behavioral Biology, wrote a brief review here for American Scientist. Columbia statistician and political scientist, Andrew Gelman, wrote a review for Slate.com. Notre Dame professor and frequent contributor of popular work on human evolution, Agustin Fuentes, wrote a critique for Huffington Post, while UNC-C anthropology professor Jonathan Marks wrote a critique for the American Anthropological Association blog, which also appears in HuffPo.

Honestly, I think that Wade’s book is so scientifically weak and ideological (despite his protestations that science should be apolitical) that it is likely to have a very short half-life in contemporary discourse on human diversity and science more broadly. In fact, I have advocated to the editorial boards of professional societies to which I belong not to do anything special about this book since I’m confident it will be soon forgotten for its sheer scientific mediocrity. I find it interesting that the great majority of the people who like the book seem not to be scientists but comment on Wade’s “bravery” for spurning “political correctness” and the like. There are substantial parallels here to public debate over climate change or vaccination: the professional conclusions of the scientists who actually work on the topic only matter when they correspond with the social, political, or economic interests of the parties engaging in the debate. What do geneticists know about genetics anyway? So, it is with some hesitancy that I write about it, but my colleagues’ letter has reminded me of a larger beef I have with the contemporary state of human evolutionary studies. This beef boils down to the fact that most contemporary students of human evolutionary biology know next to nothing about genetics. I’ve actually encountered a number of leading figures in human behavioral biology who maintain an outright hostility toward genetics. This is a topic that my colleague Charles Roseman and I have grumbled about for a few years now. We keep threatening to do something about it, but haven’t quite gotten around to it yet. Perhaps this is a humble start…

This state of affairs is extremely problematic since genetics is the material cause (in the Aristotelean sense) or one of the mechanistic causes (in the Tinbergian sense) of much of the diversity of life. If we are going to make a scientific claim that some observed trait is the result of natural selection, we should be able to have a sense for how such a trait could evolve in the first place. The standard excuse for ignoring genetics in the adaptive analysis of a trait of interest is what Alan Grafen termed the “phenotypic gambit.” The basic idea behind the phenotypic gambit is that natural selection is strong enough to overcome whatever constraints may be acting on it. The phenotypic gambit is a powerful idea and it has yielded some productive work in behavioral ecology. I use it. However, a complete evolutionary explanation of a trait’s existence needs to consider all levels of explanation. In modern terms, and as nicely outlined a letter by Randolph Nesse, we need to answer questions about mechanism, ontogeny, phylogeny, and function. Explanations relying on the phenotypic gambit only address the functional question (i.e., fitness, or what Tinbergen called the “survival value” of the trait).

I could go on about this for a long time, so I will limit myself to three points: (1) complex traits will generally not be created by a single gene, (2) heritability and the response to selection are regularly misunderstood and misapplied, (3) we need to think about the strength of selection and the constancy of selective regimes when making statements about the adaptive evolution of specific traits.

First, we need to get over the whole one-gene thing. Among other things, the types of adaptive arguments that are made particularly for recent human behavioral innovations are simply highly implausible for single genes. There are a variety of formulae for calculating the time to fixation of advantageous alleles that depend on the particulars of the system (e.g., details about dominance, initial frequency, mutation rate). Using the approximation that the number of generations that it takes for the fixation of a highly advantageous allele with selection coefficient s is simply twice the natural logarithm of s divided by s, we can calculate the expected time to fixation for an advantageous allele. With a (very) substantial average selection coefficient of s=0.05 (think of lopping of 5% of the population each generation), the time to fixation of such a highly advantageous allele is about 120 generations generations. That’s over 3,000 years for humans. This is interesting, of course, because it makes the type of recent evolution the John Hawks or Henry Harpending have discussed more than plausible. It makes it hard to imagine how the large changes in presumably complex behavioral complexes in historical time suggested by authors such as Wade or Gregory Clark, author of Farewell to Alms (which I actually find a fascinating book), pretty implausible.

In addition to the population-genetic implausibility of single-locus evolutionary models, complex traits are polygenic, meaning that they are constructed from multiple genes, each of which typically has a small effect. Now, this doesn’t even address the issue of epigenetics, where genotype-environment interactions profoundly shape gene expression and can produce fundamentally different phenotypes in the absence of significant genetic difference, but that’s another post. In many ways, this is good news for people who study whole organisms in a naturalistic context (like human behavioral ecologists!) because it means that we can work with quantitatively-measured trait values and apply regression models to understanding their dynamics. In short, the math is easier though, admittedly, the statistics can be pretty tricky. Further good news: there are lots of people who would probably be happy to collaborate and there are plenty of training opportunities in quantitative genetics through short courses, etc.

The masterful review paper that Marc Feldman and Dick Lewontin wrote for Science in 1975 amid the controversy surrounding Arthur Jensen’s work on the genetics of intelligence, and its implications for racial educational achievement differentials, still applies. Heritability is a systematically misunderstood concept and its misuse seems to surface in policy debates approximately every twenty years. Heritability, in the strict sense, is a ratio of the total phenotypic variance that is attributable to additive genetic variance (i.e., the variance contributed by the mean effect of different alleles). Because total variance of the phenotype is in the denominator of this ratio, heritability is very much a population-specific measure. If a population has low total phenotypic variance because of a uniformly positive environment, for instance, there is more potential for a greater fraction of the total variance to be due to additive genetic variance. Think, for example, about children’s intelligence (as measured through psychometric tests) in a wealthy community with an excellent school district where most parents are college-educated and therefore have the motivation to guide their children to high scholastic achievement, the resources to supplement their children’s school instruction (e.g., hiring tutors or sending kids to enrichment programs), and the study skills and knowledge base to help their children with homework, etc. I have used this example in prior post. Given the relative uniformity of the environment, more of the variation in test scores may be attributable to additive genetic contributions and heritability would be higher than it would be in a more heterogeneous population. This is a hypothetical example, but it illustrates the rather constrained meaning of heritability and the problems associated with its application to cross-population comparisons. It is also suggestive of the problem of effect sizes of different contributions to phenotypic variance. The potential for environmental variance to swamp real additive genetic variance is quite large. What’s a better predictor of life expectancy: having a genetic predisposition to high longevity or living in a neighborhood with a high homicide rate or a endemic cholera in the drinking water supply?

Heritability essentially measures the potential response to selection, everything else being equal. The so-called Breeder’s Equation (Lush 1937) states that the change in a single quantitative phenotype (e.g., height) from one generation to the next is equal to the product of heritability and the force of selection. If there is lots of additive variability in a trait but not much selective advantage to it, the change in the mean phenotype will be small. Similarly, even if selection is very strong, the phenotype will not change much if the amount of additive variance is low. A famous, but frequently misunderstood result, known as Fisher’s Fundamental Theorem shows that the change in fitness is directly proportional to variance in fitness. This is really just a special case of the breeder’s equation, as shown in great detail in Lynch and Walsh’s textbook (and their online draft chapter 6) or in Steve Frank’s terrific book, in which the trait we care about is fitness itself. An important implication of Fisher’s theorem is that selection should deplete variance in fitness — and this makes sense if we think of selection as truncating a distribution. A corollary of Fisher’s theorem is that traits which are highly correlated with fitness should not have high heritability. Oops. Does this mean that intelligence, with its putatively very high heritabilities is not important for fitness?

Everything in the last paragraph applies to the case where we are only considering a single trait. When we consider the joint response of two or more traits to selection, we must account for correlations between traits (technically, additive genetic covariances between the traits). Sometimes these covariances will be positive; sometimes they will be negative. When the additive genetic covariance between two traits is negative, it means that selection to increase the mean of one will reduce the mean of the other. In their fundamental (1983) paper, my Imperial College colleague Russ Lande and Steven Arnold generalized the breeder’s equation to the multivariate case. The response to selection becomes a balancing act between the different force of selection, additive genetic variance, and additive genetic covariance for all the traits. Indeed, this is where constraints come from (or it’s at least one place). Suppose there are two traits (1 and 2) that share a negative covariance. Further suppose that the force of selection is positive for both but is stronger on trait 1 than it is on trait 2. Depending on the amount of genetic variance present, this could mean that the mean of trait 2 will not change or even that the mean could decrease from one generation to the next.

The work of Lande and Arnold (and many others) has spawned a huge literature on evolvability (something that Charles has moved into and that we have some nascent collaborative work on in the area of human life-history evolution). This work is very important for understanding things like the evolution of human psychology. Consider the hypothesis, popular in evolutionary psychology, that the mind is divided into a large number of specific problem-solving “modules,” each of which is the product of natural selection on the outcome of the problem-solving. How do you create so many of these “organs” in a relatively short time frame? Humans last shared a common ancestor with chimpanzees and bonobos around five million years ago and most likely human ancestors until about 1.8 million years ago seem awfully ape-like (and therefore probably not carrying around anything like the human mental toolkit in their heads). One of the key processes responsible for the creation of complex phenotypes is known as modularity (which is a bit confusing since this is also the term that evolutionary psychologists use for these mental organs!) and one of the fundamental mechanisms by which modularity is achieved is through the duplication of sets of genes responsible for existing structures. These duplicated “modules” are less constrained because of their redundancy and can evolve to form new structures. However, the fact that modules are duplicated means that they should experience substantial genetic correlation with their ancestral modules. This makes me skeptical that the diversity of hypothetical structures posited by the massive modularity hypothesis could be constructed by directional selection on each module. There is just bound to be too much correlation in the system to permit it to move in a fine-tuned way toward to phenotypic optimum for each module.

Trade-offs matter for the evolution of phenotypes. While I suspect that very few human evolutionary biologists would argue with that, I think that we generally fall short of considering the impact of trade-offs for adaptive optima. The multivariate breeders’ equation of Lande and Arnold gives us an important (though incomplete) tool for looking at these trade-offs mechanistically. A few authors have done this. The example that comes immediately to mind is Virpi Luumaa and her research group, who have done some outstanding work on the quantitative genetics of human life histories using Finnish historical records.

My third, and last (for now), point addresses the constancy of selection. This is related to the concept of the Environment of Evolutionary Adaptedness (EEA), central to the reasoning of evolutionary psychology. A few years back, I wrote quite a longish piece on this topic and its attendant problems. Note that when we use population-genetic models like the one we discussed above for the expected time to fixation of an advantageous allele, the selection coefficient s is the average value of that coefficient over time. In reality, it will fluctuate, just as the demography of the population selection is working on will vary. Variation in vital rates can have huge impacts on demographic outcomes, as my Stanford colleague Shripad Tuljapurkar has spent a career showing. It can also have enormous effects on population-genetic outcomes, which shouldn’t be too surprising since it’s the population of individuals which is governed by the demography that is passing genetic material from on generation to the next!

When I read accounts of rapid selection that rely heavily on EEA-type environments or the type of generalizations found in the second half of Wade’s book (e.g., Asians live in paternalistic, autocratic societies), my constant-environment alarm bells start to sound. I worry that we are essentializing societies. One of the all-time classic works of British Social Anthropology is Sir Edmund Leach’s groundbreaking Political systems of Highland Burma. Leach found that the social systems of northern Burma were far more fluid than anthropologists of the time typically thought was the case. One of the key results is that there was a great deal of interchange between the two major social systems in northern Burma, the Kachin and and Shan. Interestingly, the Shan, who occupied lowland valleys, practiced wet-rice agriculture, and whose social systems were highly stratified were seen by western observers as being more “civilized” than the Kachin, who occupied the hills, practiced slash-and-burn agriculture, and had much more egalitarian social relations. Leach (1954: 264) writes, “within the general Kachin-Shan complex we have, I claim, a number of unstable sub-systems. Particular communities are capable of changing from one sub-system into another.” Yale anthropologist/political scientist James Scott has extended Leach’s analysis in his recent book, The Art of Not Being Governed, and suggested that the fluid mode of social organization, where people alternate between hierarchical agrarian states, and marginal tribes depending on political, historical, and ecological vicissitudes is, in fact, the norm for the societies of Southeast Asia.

The clear implication of this work for our present discussion is that a single lineage may find some of its members struggling for existence in hierarchical states where the type of docility that Wade suggests should be advantageous would be beneficial, while descendants just a generation or two distant might find themselves in egalitarian societies where physical dominance, initiative, and energy might be more likely to determine evolutionary success. I don’t mean to imply that these generalizations regarding personality-type and evolutionary success are necessarily supported by evidence. The key here is that the social milieux of successive generations could be radically different if the models of Leach and Scott are right (and the evidence brought to bear by Scott is impressive and leads me to think that the models are right). At the very least, this will reduce the average selection differential on the putative genes for personality types that are adapted to particular socio-political environments. More likely, I suspect, it will establish quite different selective regimes — say, for behavioral flexibility through strong genotype-environment interactions!

These are some of the big issues regarding genetics and the evolution of human behavior that have been bothering me recently. I’m not sure how we go about fixing this problem, but a great place to start is by fostering more collaborations between geneticists and behavioral biologists. Of course, this would be predicated on behavioral biologists’ motivation to fully understand the origin and maintenance of phenotypes and I worry that the institutional incentives for this are not in place.

Response to Selection

I’m done now with the first week of the Spring quarter. It was a bit challenging because I had to attend the PAA meetings in Washington, DC for the latter part of the week, but Brian Wood ably covered for me on Thursday. I thought that I would use the blog as a tool for summarizing one of the key points I want students to take away from this fist week in which we discussed evolution and natural selection.

We spent a good deal of lecture time talking about adaptation.  Specifically, we discussed how adaptation can serve as a foil to typology and essentialism. Adaptation is local and must be seen within its specific environmental and historical context. Adaptations are dynamic because environments are.

Adaptationist thinking is powerful, but can easily be overdone. This is why I also think it is essential to understand the mechanics of selection, something that I’m afraid is not often addressed in introductory evolutionary anthropology classes.  So, in the very first lecture of class, I throw some quantitative genetics (and, thus, some math) at students.  Of course, these are Stanford students, so I’m confident they can handle a little techie-ness every now and then. We specifically discuss the multivariate breeder’s equation, sometimes known as Lande‘s equation:

\Delta \mathbf{\bar{z}} = \mathbf{G \beta}

,

where \Delta \mathbf{\bar{z}} is the change in the mean fitness of a multivariate trait, \mathbf{G} is the additive genetic variance-covariance matrix, and \beta is the selection gradient on \mathbf{\bar{z}}.

In effect, \beta is a vector pointing in the direction of the optimal change in the phenotype. The matrix \mathbf{G} does two things to this gradient pushing \mathbf{\bar{z}} toward its optimum: (1) it scales the response depending on how much additive variance there is in each trait and (2) it rotates it as a function of the covariances between traits. I won’t get too much into matrix multiplication here (this is a very nice reference too). The key point is that \mathbf{G} is a square k \times k matrix (where k is the number of traits we’re looking at) the diagonal elements of which are variances and the off-diagonal elements of which, g_{ij} represent the covariances between traits i and j.   Selection requires variance. Without sufficient variance, even strong selection won’t change the phenotype much between generations.  But variance isn’t all there is to it. When the covariances are positive, there will be substantial indirect selection, and when they are negative, you have genetic constraints at work. Selection may be pointing in a particular direction, but the structure of the trade-offs could very easily mean that you can’t actually get there.

Let’s consider three quick (toy) examples.  Say we have two traits, maybe “length” and “width” (this could be something less vague and insipid: Lande (1979) looks at brain mass and body mass in a serious two-trait example). We will assume that the selection gradient is \mathbf{\beta} = \{0.5, 0.25\}?. That is, the force of selection is twice as high on length as it is on width, but it is pretty strong and positive on both. We’ll demonstrate the effect of variance and constraint in three ways:  (1) more variance in the trait under weaker selection (\mathbf{G_1}), (2) positive covariance between the two traits (\mathbf{G_2}), and (3) negative covariance between the two traits (\mathbf{G_3}).

 \mathbf{G_1} = \left( \begin{array}{cc} 0.33 & 0.00 \\ 0.00 & 0.67 \end{array} \right)

 \mathbf{G_2} = \left( \begin{array}{cc} 0.33 & 0.33 \\ 0.33 & 0.67 \end{array} \right)

 \mathbf{G_3} = \left( \begin{array}{cc} 0.33 & -0.33 \\ -0.33 & 0.67 \end{array} \right)

The figure below plots the response to selection in the three different types of genetic architecture.  The direction of selection is indicated in the grey arrow. If the variances of the two traits were equal to 1 and there were zero covariances, this is where selection would move the phenotype pair (try it). We can see that the response to selection moves toward width (the trait under weaker selection) even when covariances are zero (black arrow).  Why? Because there is more variance for width than there is for length (0.67 \times 0.25 > 0.33 \times 0.5).  This effect becomes more pronounced when there is positive covariance between the traits (blue arrow) — the selection toward width is 0.33 \times 0.5 +0.67 \times 0.25 = 0.3325. When the covariances are negative, we see something cool (red arrow).  The response to selection is small and moves (almost) entirely in the direction of length. This is because the negative covariance between length and width, when acted on by the strong selection on length, all but cancels out the positive response to selection (-0.33 \times 0.5 + 0.67 \times 0.25 = 0.0025).

selection-constraint-plot

This simple demonstration shows that the response to selection can be complex. Making an argument that some trait would be under selection is not sufficient to say that it actually evolved (or will evolve) that way.  Entirely plausible arguments for the direction of selection are made all the time in evolutionary anthropology.  Here is one from a very important paper in paleoanthropology (Lovejoy 1981: 344):

Any behavioral change that increases reproductive rate, survivorship, or both, is under selection of maximum intensity. Higher primates rely on social behavioral mechanisms to promote survivorship during all phases of the life cycle, and one could cite numerous methods by which it theoretically could be increased.  Avoidance of dietary toxins, use of more reliable food sources, and increased competence in arboreal locomotion are obvious examples. Yet these are among the many that have remained under stadong selection throughout much of the course of primate evolution, and therefore unlikely that early hominid adaptation was a product of intensified selection for adaptations almost universal to anthropoid primates.

Arguing for selection without considering trade-offs can get you into trouble.  Selection in the presence of quantitative genetic constraints (or even differential variance in the traits) can produce counter-intuitive results. (Selectionists, don’t dispair. There are ways to deal with this, but it will have to wait for another post). In the case of Lovejoy’s argument, there are good reasons to think that survivorship and reproductive rate are, indeed, strongly negatively correlated. Which is under stronger selection? Which has more additive variance? How strong are the negative covariances?

When we make selectionist or adaptationist arguments, we should always keep in the back of our minds the three questions:

  1. How strong is the force of selection?
  2. How much variance is there on which selection can act?
  3. How is the trait constrained through negative correlations with other traits?

References

Lande, R. A. 1979. Quantitative genetic analysis of multivariate evolution applied to brain: body size evolution. Evolution. 33:402-416.

Lovejoy, C. O. 1981. The origin of man. Science. 211:341-350.

Genetic Architecture of Maize Flowering Time

There is a really cool paper by Buckler and colleagues in the current issue of Science.  The basic gist of this paper is that flowering time in maize (Zea mays) is not controlled by any large-effect genes (actually quantitative trait loci or QTLs — these are positions in the genome that are associated with genes underlying a particular trait).  Instead, flowering time is controlled by lots of different QTLs, all with small effect.  I know what you’re saying: “this fool anthropologist has really gone off the deep end this time. Why would he ever care about such boring stuff?!” Ah, but this is anything but boring and it has a very clear relevance to the evolution of life histories, human included.

Genes are discrete entities.  Yet we know that they code for things that can essentially vary continuously like stature or age at first reproduction. Probably the simplest (and remarkably general, even though this isn’t how we learn about genetics in high school) way to think of genes is on-off switches.  At a particular locus, if you have allele A you get a +1 on your phenotype.  If you have allele a you get a +0.  For a locus that has just these two alleles, the possible phenotypes (assuming no environmental inputs, gene-gene interactions, or anything exotic) are 0,1, and 2 corresponding to aa, Aa/aA, and AA genotypes respectively.  You get twice as many individuals with phenotype=1 because there are two ways of making the heterozygote but only one way of making each of the homozygotes.  This is more or less high school biology.

Now, let’s say that our phenotype is controlled by not one locus but many.  If we can reasonably assume that the different loci are independent of each other (not a hard-and-fast assumption), then a famous result from probability theory has important bearing on the question at hand.  In particular, I’m referring to the normal approximation of the binomial distribution. The binomial distribution is the coin-flipping distribution: how many tails will you get if you toss a coin (with a probability of tails = p) n times.  It turns out that when the product np is greater than 5 (a very rough rule of thumb as there are other mild conditions) the binomial distribution — a discrete probability distribution — is very well approximated by a normal distribution — a continuous one.  This is essentially how we get continuous phenotypes from discrete genotypes. The normal distribution is the limiting distribution whenever we have lots of small things drawn independently from the same process acting in an additive way (this is the mechanistic explanation of why the binomial can be approximated so well by the normal when np gets large).   Lots of loci, each acting in an additive way with small effect, leads to a normal distribution of a phenotype. When we have a few loci acting with large effect and possibly with strong interactions between loci (i.e., epistasis), the distribution of phenotypes is more likely to be more discrete (as with the one-locus, two-allele model).

Maize lives in a broad range of environments and, like us, it reproduces sexually. Unlike us, some plants can “self.” That is, they don’t need two to tango — they reproduce sexually but a single individual provides both sets of gametes. The genetic architecture of flowering in two other genetically well-studied plants, rice and Arabidopsis (the ubiquitous mustard plant that is the favored model system of many developmental geneticists), does not show the same design as maize.  Both rice and Arabidopsis are selfing species.  It turns out that their genetic architecture resembles that of the simple additive system — one with major gene effects and a more discrete distribution of flowering times. In these species, there is more evidence for gene-gene interactions and environmental inputs in the flowering time phenotype as well.

The fact that flowering time in maize is controlled by many loci with small additive effects means that the distribution of flowering time in any sizable population of maize will be approximately normally distributed.  There will be approximately continuous variation across the possible range of phenotypes and there will be far more individuals with phenotypes near the mean of the population.  In fact, about 95% of the phenotypes will be within ± 2 standard deviations of this mean.  Variation is the stuff of natural selection.  In order for evolution to occur by natural selection you need three things: (1) variation in the phenotype, (2) a heritable basis for this variation, and (3) differential fitness as a result of the variation.  No variation in the phenotype, no response to selection.  A trait with a nice continuous distribution — as apparently maize flowering time is — can respond with exquisite precision to selection imposed by the environment (assuming the population is big enough so that random events don’t interfere). Maize shows an amazing degree of phenotypic diversity.  Flowering date is no exception with a range — the landraces of maize vary in their developmental time between an astounding 2 and 11 months.

So there is plenty of phenotypic variation in maize to respond to selection.  Another important implication of the normal distribution of flowering time also means that local variation will fall into a fairly restricted range (that 95% of variation falling within ± 2 standard deviations thing).  If the distribution were more discrete, a field might contain two completely different flowering phenotypes.  In a species that requires out-crossing, producing gametes at two completely different times doesn’t do you much good.  When you have a nice normal distribution of flowering times, there is variation, but it is not too extreme — particularly in any local area.  This trait architecture allows maize to thread the evolutionary needle: enough variation to allow response to selection but not so much as to make reproduction impossible.

This type of architecture — lots of small effects from independent genes — is common in two other laboratory favorites, fruit flies and mice. It is also common in humans according to Flint & Mcckay (2009). Human stature, in particular, is a trait that has this kind of architecture. We know from the work of Rebecca Sear at the London School of Economics and her colleagues, that height predicts  reproductive success in humans (albeit in complex ways). Whether age at first reproduction (the human equivalent to flowering) is constructed the same way as maize flowering or human stature is an open question but I seriously doubt that we will find it to be controlled by a couple genes with large effect.  Such quantitative genetic architecture in complex life history traits bodes well for prediction.  We have a very well-developed theory that relates response to selection to the genetic variation in quantitative traits and the force of selection acting on those traits.  In order for this prediction to work well though, we need to also understand how life history traits are related to each other. That is, we need to not just know the means and standard deviations of one trait (like stature or age at sexual maturity).  We also need to know how traits are related to each other.  In other words, we need to measure the covariances between traits.  Fortunately, the normal approximation that we use for one trait can easily be extended to multiple traits, providing a nice framework for both estimation and prediction. I am working at this very moment on estimating the quantitative genetic relationships between human life history traits using a large genealogical database of a historical population.  More on this later…