Friday, July 08, 2005

Through the rugged roads of gene land   posted by Razib @ 7/08/2005 10:51:00 PM

Several years back David wrote about Sewall Wright's Shifting Balance Theory. If you know much about the history of mathematical genetics you know that R.A. Fisher and Wright's disputes over the importance of population substructure, genetic drift and the adaptive landscape was a simmering pot looming in the background of the emergence of the Modern Synthesis. One of the points that Fisher and Wright clashed over was the relative evolutionary importance of epistasis. I want to emphasize the evolutionary importance, because of course R.A. Fisher did not reject mechanistic epistasis as a background feature of a specie's genetic architecture, rather he was skeptical of its relevance as a driver of evolution. It was the average effect of a single allele against a genetic background which resulted in phenotypic adaptation according to Fisher. Each beneficial mutation would be driven by directional selection toward fixation, while the vast majority of mutations would be purified from the genetic background. In contrast, Wright conceived of an evolutionary landscape where epistatic interactions across loci would result in isolated adaptive peaks cordoned off by depressed regions of reduced fitness. This pluralistic scenario would result in balancing selection that would maintain more variation within the genetic background than in Fisher's model. Then in the late 1960s the Lewontin and Hubby papers reported such high levels of allozyme polymorphism that both the "Classical" (Fisher) and "Balancing" (Wright) schools of the Modern Synthesis were sent scrambling.1 The elucidation of The Neutral Theory of gene substitution by Mootoo Kimura explained away the relative lack of fixation on the molecular level, heterozygosity and polymorphism were simply the transitory states of the dynamic system where neutral alleles were progressively substituted for each other by random walk genetic forces. Nevertheless, after reading Speciation my mind wandered back to the possibilities inherent in epistasis, coadapted gene complexes, supergenes and all the assorted detritus that remains after you remove Fisher's additive genetic effects.

With my questions in hand I decided to dive into Epistasis and the Evolutionary Process, an anthology of recent research on the issue of epistasis and its relationship to evolution.2 My first hurlde was that I had to move beyond my reflexive mechanistic/molecular view of epistasis. To me, epistasis, the interaction between two or more loci on the genome, was always accompanied by an image of molecular products entering into scripted regulatory dances with each other. This is of course ubiquitious in eukaryotic organisms, interlocking cascades of regulation and the precipitous acceleration of combinatorical possibility explains how manifold complexity can emerge from a relatively small number of genes. It was peculiar for me to realize that epistasis on a population genetic level can occur between loci in different individuals when fitness is the dependent variable. Consider maternal effects, an interaction the between genotype of the mother and the genotype of the offspring which shapes the final offspring phenotype, mediated by the uterine environment. Or the variation in fitness of individuals in disparate social groups of conspecifics. The point is that epistasis means many things, and unmodified it is lacking in precision (please note that there is obviously overlap with norm of reaction if other genes are considered the "environment" in which a given gene expresses a phenotype).

The first two chapters of Epistasis and the Evolutionary Process are a rough and ready introduction to the paradigm that the researchers who contributed the 16 chapters of the book are working within. Obviously they think epistasis is important in evolutionary genetics, but, they do not necessarily hew to the view that the Shifting Balance is the most accurate model in which epistatic processes are necessarily relevant. Though the book is filled with equations there is repeated reference to one particular evocative graphical metaphor, that of the wrinkled and rugged surface of the adaptive landscape. Geometrically speaking, at any given time, the Fisherian landscape is conceived of as a constant slope. Contrastingly the epistatic landscape is characterized by relatively flat "canals" and arcs that represent the nonlinear fitness and phenotypic effects that are the hallmark of epistasis (though over a small enough area curved epistatic surfaces can become flat additive ones!). More plainly an adaptive landscape characterize by widespread epistatic effects would be rugged, while that characterized by staid additive effects would be gently sloping. With this visual metaphor the smorgasbord of dancing definitions floats before your eyes, mechanistic epistasis is the direct interaction of genetic products across loci, statistical epistasis is what remains after additive, dominance and environmental variation are accounted for, additive genetic mechanisms can have epistatic statistical effects, while epistatic genetic mechanisms can have additive statistical effects!

I have read most of the chapters (after chapter 2 you can skip around due to tightly constrained topicality as opposed to sequential contingency), but I want to simply introduce a few definitions and get to the "epistatic explanation of sex."

Here is the list of "terms" from chapter 2 (Table B2.1):3

For deleterious mutations:
Synergistic - Negative fitness deviation, double mutant less fit than predicted by additive effects of single mutants.
Diminishing returns - Positive fitness deviation, double mutant more fit than predicated by additive effects of single mutants, but still less fit than a single mutant.
Compensatory - Positve fitness deviation, double mutant more fit than single mutant, less fit than wild type.
Supercompensatory - Positve fitness deviation, double mutant more fit than wild type.

For advantageous mutations (these mutations increase the s):
Synergistic - Positive fitness deviation, double mutant more fit than predicted by additive effects.
Diminishing returns - Negative fitness deviation, double mutant less fit than predicted by additive effects, but still more fit than a single mutant.
Decompensatory - Negative fitness deviation, double mutant less fit than single mutant.

(please plug in various s values into the equation listed in notation 3 to get a more intuitive feel if the jumble above is confusing)

For synthetic mutations, where one allele masks the other:
Synthetic deleterious - Negative fitness deviation, double mutant less fit than single mutant and wild type (both the latter are equal fitness).
Synthetic advantageous - Positive fitness deviation, double mutant more fit than single mutant and wild type (both the latter are equal fitness).

Obviously this alphabet soup of definitions is not unrelated to other concepts in genetics. "Synthetic" mutations induce dominant or recessive phenotypes, depending on what vantage point you approach from. Additionally, keep in mind that one locus may have various epistatic interactions with numerous other loci, so in one context it might increase fitness, and another context decrease fitness, depending on what other alleles are present. The authors argue in fact that this variance of epistasis implies that geneticists must look "beyond the average" of the genetic background (a la Fisher) because the mean effect of a locus in reference to epistatic interactions obscures context dependent information (the mean epistatic effect might be a deviation of zero, but if there is a great deal of variance in that deviation over time, space and individuals, that is clearly relevant).

Since I am a bit overlong at this point I wish to hit a few quick points and gloss over the important connection (possibly) between negative epistasis and sex (particularly recombination). First, in reference to mutational load some analytic models imply that low epistatic variance combined with synergistic epistasis can purge mutations. Others in reference to Muller's Ratchet imply that synergistic epistasis can amplify deleterious effects (so allowing selection to purge the mutation and halt possible substitution). Additionally, variance of epistatic effects and the flipping of the sign of deviation can switch double mutants into a net positive (Synergistic → Supercompensatory). And of course epistasis can be crucial in the formation of coadapted gene complexes which throw up fitness valleys that eventually result in speciation.4

But, to sex. The basic idea is that mild negative epistasis builds up negative linkage disequilibrium (because extreme, that is double mutant, gene combinations are disfavored) which only recombination can break apart so as to generate variation which selection can work with (favorable, but extreme, genotypes are generated). Too much epistasis is problematic because the generation of less fit genotypes from recombination reducing linkage disequilibria can have too great a fitness short term fitness hit. Additionally, the variation of epistasis as a function of time can be incorporated into the "Red Queen" hypothesis put forward by William Hamilton, with a series of epistatic oscillations playing the starring role given to frequency dependence.

I will have more to say on various chapters later, though if you are curious about a "human payoff" I suggest chapter 3 by Alan Templeton. Some of the medically salient traits Templeton highlights are often discussed on the Epistasis Blog, I suggest you check it out.

Jason Wolf's website has several papers related to the topics above in PDF form.

1 - Though I admire Richard Dawkins I do feel that in some ways his fidelity to the rhetoric of Classical Selectionism is a bit much sometimes and his attempts to simply coopt Neutral Theory or Punctuated Equilibria by slight of verbal redefinition ("We believed that all along!") is a bit lame, though perhaps not as inexecusable as the more extreme pronouncements from Neutral Theory champions or S.J. Gould's initial "revolution" against "Ultra-Darwinianism" (and yes, flirtation with Saltationism).

2 - This book is searchable, and after the first two chapters all the others are rather stand alone, so, if something interests you it is entirely possible to read up on a topic without ponying up a red cent.

3 - The authors present a simple two-locus model for illustrative purposes. The fitness, Wab, of a double mutant haplotype is (1 + sa)*(1 + sb) + ε, where ε is the epistatic deviation and the s is the selection coefficient. Note also the "additive effects" are actually multiplicative, so that if the s for each mutation was 0.2, with no epistasis the fitness would be 0.64, 0.8*0.8.

4 - For the record, I tend to believe that allopatric speciation is the norm. I don't think alleles random walk in frequency through gene space and just "lock" at some point into a new complex and speciate sympatrically.