”These are all fairly obvious” (says Sewall Wright)

I was checking a quote from Sewall Wright, and it turned out that the whole passage was delightful. Here it is, from volume 1 of Genetics and the Evolution of Populations (pages 59-60):

There are a number of broad generalizations that follow from this netlike relationship between genome and complex characters. These are all fairly obvious but it may be well to state them explicitly.

1) The variations of most characters are affected by a great many loci (the multiple factor hypothesis).

2) In general, each gene replacement has effects on many characters (the principle of universal pleiotropy).

3) Each of the innumerable possible alleles at any locus has a unique array of differential effects on taking account of pleiotropy (uniqueness of alleles).

4) The dominance relation of two alleles is not an attribute of them but of the whole genome and of the environment. Dominance may differ for each pleiotropic effect and is in general easily modifiable (relativity of dominance).

5) The effects of multiple loci on a character in general involve much nonadditive interaction (universality of interaction effects).

6) Both ontogenetic and phylogenetic homology depend on calling into play similar chains of gene-controlled reactions under similar developmental conditions (homology).

7) The contributions of measurable characters to overall selective value usually involve interaction effects of the most extreme sort because of the usually intermediate position of the optimum grade, a situation that implies the existence of innumerable different selective peaks (multiple selective peaks).

What can we say about this?

It seems point one is true. People may argue about whether the variants behind complex traits are many, relatively common, with tiny individual effects or many, relatively rare, and with larger effects that average out to tiny effects when measured in the whole population. In any case, there are many causative variants, alright.

Point two — now also known as the omnigenetic model — hinges on how you read ”in general”, I guess. In some sense, universal pleiotropy follows from genome crowding. If there are enough causative variants and a limited number of genes, eventually every gene will be associated with every trait.

I don’t think that point three is true. I would assume that many loss of function mutations to protein coding genes, for example, would be interchangeable.

I don’t really understand points six and seven, about homology and fitness landscapes, that well. The later section about homology reads to me as if it could be part of a debate going on at the time. Number seven describes Wright’s view of natural selection as a kind of fitness whack-a-mole, where if a genotype is fit in one dimension, it probably loses in some other. The hypothesis and the metaphor have been extremely influential — I think largely because many people thought that it was wrong in many different ways.

Points four and five are related and, I imagine, the most controversial of the list. Why does Wright say that there is universal epistasis? Because of physiological genetics. Or, in modern parlance, maybe because of gene networks and systems biology. On page 71, he puts it like this:

Interaction effects necessarily occur with respect to the ultimate products of chains of metabolic processes in which each step is controlled by a different locus. This carries with it the implication that interaction effects are universal in the more complex characters that trace such processes.

The argument seems to persists to this day, and I think it is true. On the other hand, there is the question how much this matters to the variants that actually segregate in a given population and affect a given trait.

This is often framed as a question of variance. It turns out that even with epistatic gene action, in many cases, most of the genetic variance is still additive (Mäki-Tanila & Hill 2014, Huang & Mackay 2014). But something similar must apply to the effects that you will see from a locus. They also depend on the allele frequencies at other loci. An interaction does nothing when one of the interaction partners are fixed. If they are nearly to fixed, it will do nearly nothing. If they’re all at intermediate frequency, things become more interesting.

Wright’s principle of universal interaction is also grounded in his empirical work. A lot of space in this book is devoted to results from pigmentation genetics in guinea pigs, which includes lots of dominance and interaction. It could be that Wright was too quick to generalise from guinea pig coat colours to other traits. It could be that working in a system consisting of inbred lines draws your attention to nonlinearities that are rare and marginal in the source populations. On the other hand, it’s in these systems we can get a good handle on the dominance and interaction that may be missed elsewhere.

Study of effects in combination indicates a complicated network of interacting processes with numerous pleiotropic effects. There is no reason to suppose that a similar analysis of any character as complicated as melanin pigmentation would reveal a simpler genetic system. The inadequacy of any evolutionary theory that treats genes as if they had constant effects, favourable or unfavourable, irrespective of the rest of the genome, seems clear. (p. 88)

I’m not that well versed in pigmentation genetics, but I hope that someone is working on this. In an era where we can identify the molecular basis of classical genetic variants, I hope that someone keeps track of all these A, C, P, Q etc, and to what extent they’ve been mapped.

Literature

Wright, Sewall. ”Genetics and the Evolution of Populations” Volume 1 (1968).

Mäki-Tanila, Asko, and William G. Hill. ”Influence of gene interaction on complex trait variation with multilocus models.” Genetics 198.1 (2014): 355-367.

Huang, Wen, and Trudy FC Mackay. ”The genetic architecture of quantitative traits cannot be inferred from variance component analysis.” PLoS genetics 12.11 (2016): e1006421.

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Yours truly outside the library on Thomas Bayes’ road, incredibly happy with having found the book.

Annonser

Morning coffee: null in genetics

coffee

Andrew Gelman sometimes writes that in genetics it might make sense to have a null hypothesis of zero effect, but in social science nothing is ever exactly zero (and interactions abound). I wonder whether that is actually true even for genetics. Think about pleiotropy. Be it universal or modular, I think the evidence still points in the direction that we should expect any genetic variant to affect lots of traits, albeit with often very small effects. And think of gene expression where genes always show lots of correlation structure: do we expect transcripts from the same cells to ever be independent of each other? It doesn’t seem to me that the null can be strictly true here. Most of these differences have to be too small for us to practically be able to model them, though — and maybe the small effects are so far below the detection limit that we can pretend that they could be zero. (Note: not trying to criticise anybody’s statistical method or view of effect sizes here, just thinking aloud about the ”no true null effect” argument.)

Morning coffee: pleiotropy

kaffekatt

In the simplest terms pleiotropy means genetic side-effects: a pleiotropic gene is a gene that does several things and a pleiotropic variant is a variant that makes its carrier different from carriers of other variants in more than one trait. It’s just that the words ‘gene’ , ‘trait’ and ‘different’ are somewhat ambiguous. Paaby & Rockman (2013) have written a nice analytical review about the meaning of pleiotropy. In their terminology, molecular gene pleiotropy is when the product of a gene is involved in more than one biological process. Developmental pleiotropy, on the other hand, deals with genetic variants: a variant is developmentally pleiotropic if it affects more than one trait. This is the sense of the word I’d normally think of. Third, selectional pleiotropy is deals with variants that affect several aspects of fitness, possibly differently for different individuals.

Imagine that we have found a variant associated with two variables. Have we got a pleiotropic variant on our hands? If the variables are just different measures of the same thing, clearly we’re dealing with one trait. But imagine that the variables are actually driven by largely different factors. They might respond to different environmental stimuli and have mostly separate genetic architectures. If so, we have two different traits and a pleiotropic variant affecting both. My point is that it depends on the actual functional relationship between the traits. Without knowing something about how the organism works we can’t count traits. With that in mind, it seems very bold to say things about variants in general and traits in general. Paaby & Rockman’s conclusion seems to be that genetic mapping is not the way to go, because of low power to detect variants of small effect, and instead they bring up alternative statistical and quantitative genetics methods to demonstrate pleiotropy on a large scale. I agree that these results reinforce that pleiotropy must be important, in some sense of the word. But I think the opposite approach still has value: the way to figure out how important pleiotropy is for any given suite of traits is to study them mechanistically.

(Zombie kitty by Anna Nygren.)