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Wednesday, August 31, 2011

Epistasis vs additivity

Continuing the discussion from my previous post: strong interactions at the level of individual genes do not preclude a linear (additive) analysis of population variation and natural selection.

On epistasis: why it is unimportant in polygenic directional selection

[Phil. Trans. R. Soc. B (2010) 365, 1241–1244 doi:10.1098/rstb.2009.0275]

James F. Crow*
Genetics Laboratory, University of Wisconsin, Madison, WI 53706, USA

There is a difference in viewpoint of developmental and evo-devo geneticists versus breeders and students of quantitative evolution. The former are interested in understanding the developmental process; the emphasis is on identifying genes and studying their action and interaction. Typically, the genes have individually large effects and usually show substantial dominance and epistasis. The latter group are interested in quantitative phenotypes rather than individual genes. Quantitative traits are typically determined by many genes, usually with little dominance or epistasis. Furthermore, epistatic variance has minimum effect, since the selected population soon arrives at a state in which the rate of change is given by the additive variance or covariance. Thus, the breeder’s custom of ignoring epistasis usually gives a more accurate prediction than if epistatic variance were included in the formulae.

Why did Crow have to write this 2010 paper? Don't evo-devo folks understand population genetics? Why do they find the dominance of additive heritability to be so counter-intuitive? Which of the two groups of scientists has a better understanding of how evolution works? Evo-devo folks seem to be from the traditional "revel in complexity" branch of biology: perfectly happy to find that living creatures are too complicated to be modeled by equations. (But are they?)

Some excerpts from the paper:

... Recent years have seen an increased emphasis on epistasis (e.g. Wolf et al. 2000; Carlborg & Haley 2004). Students of development and evo-devo, as well as some human geneticists, have paid particular interest to interactions. For those in these fields, epistasis is an interesting phenomenon on its own and studying it gives deeper insights into developmental and evolutionary processes. Ultimately one wants to know which individual genes are involved, and if one is studying the effects of such genes, it is natural to con- sider the ways in which they interact. Historically, among many other uses, epistasis has provided a means for identifying steps in biochemical and developmental sequences. More generally, including epistasis is part of the description of gene effects. So epistasis, despite methodological challenges, is usually welcomed as providing further insights. Students of development or evo-devo typically study genes of major effect. Of course, genes with major effects are more easily discovered, so they may be providing a biased sample. But we can say that at least some of the genes involved have large effects. And such genes typically show considerable dominance and epistasis.

In contrast, animal and plant breeders have traditionally regarded epistasis as a nuisance, akin to noise in impeding or obscuring the progress of selection. It may seem surprising that the traditional practice of ignoring epistasis has not led to errors in prediction equations. Why? It is this seeming paradox that I wish to discuss.

Continuously distributed quantitative traits typically depend on a large number of factors, each making a small contribution to the quantitative measurement. In general, the smaller the effects, the more nearly additive they are. Experimental evidence for this is abundant. This is expected for reasons analogous to those for which taking only the first term of a Taylor series provides a good estimate. ...

The most extensive selection experiment, at least the one that has continued for the longest time, is the selection for oil and protein content in maize (Dudley 2007). These experiments began near the end of the nineteenth century and still continue; there are now more than 100 generations of selection. Remarkably, selection for high oil content and similarly, but less strikingly, selection for high protein, continue to make progress. There seems to be no diminishing of selectable variance in the population. The effect of selection is enormous: the difference in oil content between the high and low selected strains is some 32 times the original standard deviation.

... Students of development, evo-devo and human genetics often place great emphasis on epistasis. Usually they are identifying individual genes, and naturally the interactions among these are of the very essence of understanding. The individual gene effects are usually large enough for considerable epistasis to be expected.

Quantitative genetics has a contrasting view. The foregoing analysis shows that, under typical conditions, the rate of change under selection is given by the additive genetic variance or covariance. Any attempt to include epistatic terms in prediction formulae is likely to do more harm than good. Animal and plant breeders who ignored epistasis, for whatever reasons, good or bad, were nevertheless on the right track. And prediction formulae based on simple heritability measurements are appropriate.

The power of using microscopic knowledge (genes) to develop macroscopic theory (phenotypes), whereby phenotypic measurements are used to develop prediction formulae, is beautifully illustrated by quantitative genetics theory.

Can we understand evolution without mathematics? Two more useful references:

Statistical Mechanics and the Evolution of Polygenic Quantitative Traits

The Evolution of Multilocus Systems Under Weak Selection

Note I am at BGI right now so there may be some latency in communication.

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