Quantitative genomics, adaptation, and cognitive phenotypes

Posted on September 10, 2017September 10, 2017 by Razib Khan

The human brain utilizes about ~20% of the calories you take in per day. It’s a large and metabolically expensive organ. Because of this fact there are lots of evolutionary models which focus on the brain. In Richard Wrangham suggests that our need for calories to feed our brain is one reason we started to use fire to pre-digest our food. In Geoffrey Miller seems to suggest that all the things our big complex brain does allows for a signaling of mutational load. And in Robin Dunbar suggests that it’s social complexity which is driving our encephalization.

These are all theories. Interesting hypotheses and models. But how do we test them? A new preprint on bioRxiv is useful because it shows how cutting-edge methods from evolutionary genomics can be used to explore questions relating to cognitive neuroscience and pyschopathology, Polygenic selection underlies evolution of human brain structure and behavioral traits:

…Leveraging publicly available data of unprecedented sample size, we studied twenty-five traits (i.e., ten neuropsychiatric disorders, three personality traits, total intracranial volume, seven subcortical brain structure volume traits, and four complex traits without neuropsychiatric associations) for evidence of several different signatures of selection over a range of evolutionary time scales. Consistent with the largely polygenic architecture of neuropsychiatric traits, we found no enrichment of trait-associated single-nucleotide polymorphisms (SNPs) in regions of the genome that underwent classical selective sweeps (i.e., events which would have driven selected alleles to near fixation). However, we discovered that SNPs associated with some, but not all, behaviors and brain structure volumes are enriched in genomic regions under selection since divergence from Neanderthals ~600,000 years ago, and show further evidence for signatures of ancient and recent polygenic adaptation. Individual subcortical brain structure volumes demonstrate genome-wide evidence in support of a mosaic theory of brain evolution while total intracranial volume and height appear to share evolutionary constraints consistent with concerted evolution…our results suggest that alleles associated with neuropsychiatric, behavioral, and brain volume phenotypes have experienced both ancient and recent polygenic adaptation in human evolution, acting through neurodevelopmental and immune-mediated pathways.

The preprint takes a kitchen-sink approach, throwing a lot of methods of selection at the phenotype of interest. Also, there is always the issue of cryptic population structure generating false positive associations, but they try to address it in the preprint. I am somewhat confused by this passage though:

Paleobiological evidence indicates that the size of the human skull has expanded massively over the last 200,000 years, likely mirroring increases in brain size.

From what I know human cranial sizes leveled off in growth ~200,000 years ago, peaked ~30,000 years ago, and have declined ever since then. That being said, they find signatures of selection around genes associated with ‘intracranial volume.’

There are loads of results using different methods in the paper, but I was curious note that schizophrenia had hits for ancient and recent adaptation. A friend who is a psychologist pointed out to me that when you look within families “unaffected” siblings of schizophrenics often exhibit deviation from the norm in various ways too; so even if they are not impacted by the disease, they are somewhere along a spectrum of ‘wild type’ to schizophrenic. In any case in this paper they found recent selection for alleles ‘protective’ of schizophrenia.

There are lots of theories one could spin out of that singular result. But I’ll just leave you with the fact that when you have a quantitative trait with lots of heritable variation it seems unlikely it’s been subject to a long period of unidirecitional selection. Various forms of balancing selection seem to be at work here, and we’re only in the early stages of understanding what’s going on. Genuine comprehension will require:

– attention to population genetic theory
– large genomic data sets from a wide array of populations
– novel methods developed by population genomicists
– and funcitonal insights which neuroscientists can bring to the table

Why you should learn some population genetics

Posted on June 27, 2017June 27, 2017 by Razib Khan

From reader surveys I know a substantial portion of the people who will see this post are financially well off (of those who aren’t, a large number are students). Therefore, you can invest in some books.

Often people ask me questions related to population genetics in the comments (sometimes I get emails). That is all well and good. But it is always better to be able to fish than have to ask for fish. Additionally, learning some population and quantitative genetics allows you to develop some tacit schemas through which you can process information coming at you, and through with you can develop some general intuition.

If you have a modest level of mathematical fluency and and the disposable income, here are three indispensable books which are like the keys to the kingdom:

*
*
* .

If you don’t have the cash to spare, there are online notes which are pretty good:

* Graham Coop’s Population Genetics notes
* Joe Felsenstein’s Theoretical Evolutionary Genetics

There are others online resources, but they are not as comprehensive. John Gillespie’s is good as very gentle introductions go, but if you are going to spend money, I think just plumping down for a more comprehensive textbook (which will have more genomics in it) is better over the long run.

The goal of getting these books isn’t to make you a population geneticist, but, if you are interested in evolutionary questions it gives you a powerful toolkit. Really nothing in evolutionary process makes sense except in the light of population genetics.

Dost thou know the equilibrium at panmixia?

Posted on April 25, 2017April 26, 2017 by Razib Khan

If you read a blog about Biblical criticism from a Christian perspective it would probably be best if you were familiar with the Bible. You don’t have to have read much , rather, just the . Barring that, at least the !

At this point, with over 400 individuals responding to the reader survey, it is strange to consider that more people believe they have a handle on what F_st is than the Hardy-Weinberg Equilibrium. First, F_st is a more subtle concept than people often think it is. And second, because the HWE is so easy, important, and foundational to population genetics. I mean $p^2 + 2pq + q^2 = 1$ . Could it be simpler???

So a quick ask. If you are one of the people who doesn’t understand HWE or why it is important, please get yourself a copy of John Gillespie’s . I understand that not everyone has the time, interest, or money for , or any of the more “hardcore” texts. But will surely suffice to follow anything on this blog.

Or, barring that, please review the online resources which you have available. Two examples:

Graham Coop’s Notes on Population Genetics or Joe Felsenstein’s unpublished textbook Theoretical Evolutionary Genetics.

Why the rate of evolution may only depend on mutation

Posted on April 23, 2017April 24, 2017 by Razib Khan

Sometimes people think evolution is about dinosaurs.

It is true that natural history plays an important role in inspiring and directing our understanding of evolutionary process. Charles Darwin was a natural historian, and evolutionary biologists often have strong affinities with the natural world and its history. Though many people exhibit a fascination with the flora and fauna around us during childhood, often the greatest biologists retain this wonderment well into adulthood (if you read W. D. Hamilton’s collections of papers, , which have autobiographical sketches, this is very evidently true of him).

But another aspect of evolutionary biology, which began in the early 20th century, is the emergence of formal mathematical systems of analysis. So you have fields such as phylogenetics, which have gone from intuitive and aesthetic trees of life, to inferences made using the most new-fangled . And, as told in , in the 1920s and 1930s a few mathematically oriented biologists constructed much of the formal scaffold upon which the Neo-Darwinian Synthesis was constructed.

At the highest level of analysis evolutionary process can be described beautifully. Evolution is beautiful, in that its end product generates the diversity of life around us. But a formal mathematical framework is often needed to clearly and precisely model evolution, and so allow us to make predictions. R. A. Fisher’s aim when he wrote was to create for evolutionary biology something equivalent to the laws of thermodynamics. I don’t really think he succeeded in that, though there are plenty of debates around something like Fisher’s fundamental theorem of natural selection.

But the revolution of thought that Fisher, Sewall Wright, and J. B. S. Haldane unleashed has had real yields. As geneticists they helped us reconceptualize evolutionary process as more than simply heritable morphological change, but an analysis of the units of heritability themselves, genetic variation. That is, evolution can be imagined as the study of the forces which shape changes in allele frequencies over time. This reduces a big domain down to a much simpler one.

Genetic variation is concrete currency with which one can track evolutionary process. Initially this was done via inferred correlations between marker traits and particular genes in breeding experiments. Ergo, the origins of the “the fly room”.

But with the discovery of DNA as the physical substrate of genetic inheritance in the 1950s the scene was set for the revolution in molecular biology, which also touched evolutionary studies with the explosion of more powerful assays. Lewontin & Hubby’s 1966 paper triggered a order of magnitude increase in our understanding of molecular evolution through both theory and results.

The theoretical side occurred in the form of the development of the neutral theory of molecular evolution, which also gave birth to the nearly neutral theory. Both of these theories hold that most of the variation with and between species on polymorphisms are due to random processes. In particular, genetic drift. As a null hypothesis neutrality was very dominant for the past generation, though in recent years some researchers are suggesting that selection has been undervalued as a parameter for various reasons.

Setting the live scientific debate, which continue to this day, one of the predictions of neutral theory is that the rate of evolution will depend only on the rate of mutation. More precisely, the rate of substitution of new mutations (where the allele goes from a single copy to fixation of ~100%) is proportional to the rate of mutation of new alleles. Population size doesn’t matter.

The algebra behind this is straightforward.

First, remember that the frequency of the a new mutation within a population is $\frac{1}{2N}$ , where $N$ is the population size (the $2$ is because we’re assuming diploid organisms with two gene copies). This is also the probability of fixation of a new mutation in a neutral scenario; it’s probability is just proportional to its initial frequency (it’s a random walk process between 0 and 1.0 proportions). The rate of mutations is defined by $\mu$ , the number of expected mutations at a given site per generation (this is a pretty small value, for humans it’s on the order of $10^{-8}$ ). Again, there are $2N$ gene copies, so you have $2N\mu$ to count the number of new mutations.

The probability of fixation of a new mutations multiplied by the number of new mutations is:

$$ \frac{1}{2N} $ \times 2N\mu = \mu$

So there you have it. The rate of fixation of these new mutations is just a function of the rate of mutation.

Simple formalisms like this have a lot more gnarly math that extend them and from which they derive. But they’re often pretty useful to gain a general intuition of evolutionary processes. If you are genuinely curious, I would recommend . It’s not quite a core dump, but it is a way you can borrow the brains of two of the best evolutionary geneticists of their generation.

Also, you will be able to answer the questions on my survey better the next time!

Why overdominance probably isn’t responsible for much polymorphism

Posted on April 14, 2017 by Razib Khan

Hybrid vigor is a concept that many people have heard of, because it is very useful in agricultural genetics, and makes some intuitive sense. Unfortunately it often gets deployed in a variety of contexts, and its applicability is often overestimated. For example, many people seem to think (from personal communication) that it may somehow be responsible for the genetic variation around us.

This is just not so. As you may know each human carries tens of millions of genetic variants within their genome. Populations have various levels of polymorphism at particular positions in the genome. How’d they get there? In the early days of population genetics there were two broad schools, the “balance” and “classical.” The former made the case for the importance of balancing selection in maintaining variation. The latter suggested that the variation we see around us is simply a transient between fixation of a favored mutation from a low a frequency or extinction of a disfavored variant (perhaps environmental conditions changed and a high frequency variant is now disfavored). Arguably the rise of neutral theory and empirical results from molecular evolution supported the classical model more than the balance framework (at least this was Richard Lewontin’s argument, and I follow his logic here).

But even in relation to alleles which are maintained at polymorphism through balancing selection, overdominance isn’t going to be the major player.

Sickle cell disease is a classic consequence of overdominance; the heterozygote is more fit than the wild type or the recessive disease which is caused by homozygotes of the mutation. Obviously polymorphism is maintained despite the decreased fitness of the mutant homozygote because the heterozygote is so much more fit than the wild type. The final proportion of the alleles segregating in the population will be conditional on the fitness drag of the homozygote in the mutant type, because as per HWE it will be present in the population ~q².

The problem is that this is clearly not going to scale across loci. That is, even if the fitness drag is more minimal than is the case with the sickle cell locus, one can imagine a cummulative situation. The segregation load is just going to be too high. Overdominance is probably a transient strategy which fades away as populations evolve more efficient ways to adapt that doesn’t have such a fitness load.

So how does balancing selection still lead to variation without heteroygote advantage? W. D. Hamilton argued that much of it was due to negative frequency dependent selection. Co-evolution with pathogens is the best case of this. As strategies get common pathogens adapt, so rare strategies encoded by rare alleles gain in fitness. As these alleles increase in frequency their fitness decreases due to pathogen resistance. Their frequency declines, and eventually the pathogens lose the ability to resist it, and its frequency increases again.

Why only one migrant per generation keeps divergence at bay

Posted on April 8, 2017 by Razib Khan

The best thing about population genetics is that because it’s a way of thinking and modeling the world it can be quite versatile. If is a way to analyze the world rationally, thinking like a population geneticist allows you to have the big picture on the past, present, and future, of life.

I have some personal knowledge of this as a transformative experience. My own background was in biochemistry before I became interested in population genetics as an outgrowth of my lifelong fascination with evolutionary biology. It’s not exactly useless knowing all the steps of the Krebs cycle, but it lacks in generality. In his I recall Isaac Asimov stating that one of the main benefits of his background as a biochemist was that he could rattle off the names on medicine bottles with fluency. Unless you are an active researcher in biochemistry your specialized research is quite abstruse. Population genetics tends to be more applicable to general phenomena.

In a post below I made a comment about how one migrant per generation or so is sufficient to prevent divergence between two populations. This is an old heuristic which goes back to Sewall Wright, and is encapsulated in the formalism to the left. Basically the divergence, as measured by Fst, is proportional to the inverse of 4 time the proportion of migrants times the total population + 1. The mN is equivalent to the number of migrants per generation (proportion times the total population). As the mN become very large, the Fst converges to zero.

The intuition is pretty simple. Image you have two populations which separate at a specific time. For example, sea level rise, so now you have a mainland and island population. Since before sea level rise the two populations were one random mating population their initial allele frequencies are the same at t = 0. But once they are separated random drift should begin to subject them to divergence, so that more and more of their genes exhibit differences in allele frequencies (ergo, Fst, the between population proportion of genetic variation, increases from 0).

Now add to this the parameter of migration. Why is one migrant per generation sufficient to keep divergence low? The two extreme scenarios are like so:

Large populations change allele frequency very slowly due to drift, so only a small proportion of migration is needed to prevent them from diverging
Small populations change allele frequency very fast due to drift, so a larger proportion of migration is needed to prevent them from drifting

Within a large population one migrant is a small proportion, but drift is occurring very slowly. Within a small population drift is occurring fast, but one migrant is a relatively large proportion of a small population.

Obviously this is a stylized fact with many details which need elaborating. Some conservation geneticists believe that the focus on one migrant is wrongheaded, and the number should be set closer to 10 migrants.

But it still gets at a major intuition: gene flow is extremely powerful and effective at reducing differences between groups. This is why most geneticists are skeptical of sympatric speciation. Though the focus above is on drift, the same intuition applies to selective divergence. Gene flow between populations work at cross-purposes with selection which drives two groups toward different equilibrium frequencies.

This is why it was surprising when results showed that Mesolithic hunter-gatherers and farmers in Europe were extremely genetically distinct in close proximity for on the order of 1,000 years. That being said, strong genetic differentiation persists between Pygmy peoples and their agriculturalist neighbors, despite a long history of living nearby each other (Pygmies do not have their own indigenous languages, but speak the tongue of their farmer neighbors). In the context of animals physical separation is often necessary for divergence, but for humans cultural differences can enforce surprisingly strong taboos. Culture is as strong a phenomenon as mountains or rivers….