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51C2YXWQKDL._SY344_BO1,204,203,200_ Today I was running with a friend and we were talking about some details in relation to perceptions of particular definitions on the part of biologists. My friend is a molecular biologist, whose work is primarily in biochemistry, and she reminded me that there’s a strange confusion in relation to the term epistasis. A problem that I’m at the root of in her case. Back when she was prepping for her qualifying exams a professor who was helping her study asked her what epistasis was. When we were going over this term almost everyone defined epistasis in a fashion which was recognizable to molecular biologists. That is, as interactions between genes which are concretely mediated by upstream and downstream pathways and produce discrete alternative phenotypes. But there is another way to conceptualize epistasis, and that is in an evolutionary/statistical sense, often interpreted as deviation from additivity of genetic effect. I immediately brought up this distinction, and when my friend relayed this during her prep session the professor had no idea what she was talking about. Now the issue is coming to the fore again, as it is clear from talking to undergraduates that they’re totally unfamiliar with the evolutionary/statistical definition of epistasis, in part because many of their professors are not aware of it. Not only that, but they tend to take the molecular pathways model (see slide 8) so literally that they’d likely not recognize Bateson’s original definition which relied on phenotypes.

Now, I understand that DNA is a big deal. I read The Double Helix. Molecular genetics changed everything, including the study of evolution. But with genomics I would argue that a more quantitative and formal perspective needs to come back into the discipline in a more thoroughgoing manner. The neglect of evolutionary/statistical frameworks in favor of purely molecular/biochemical ones in undergraduate education due to the nature of the training of some researchers is going to be an issue down the line.

With that in mind, see Epistasis—the essential role of gene interactions in the structure and evolution of genetic systems, in Nature Reviews Genetics. Box 1 has the definitions which I’m alluding to above. And below is a post I wrote in 2005, based on reading of Epistasis and Evolutionary Process.

Note: The following is a re-post from 2005.

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.

Related: 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, W ab, of a double mutant haplotype is (1 + s a)*(1 + s b) + 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.

• Category: Science • Tags: Epistasis, Genetics 
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An old argument going back to the origins of theoretical population genetics has to do with the nature of the genetic effects which control traits and are subject to change in allele frequency due to adaptation. Often these are bracketed as part of the controversies between R. A. Fisher and Sewall Wright (see Sewall Wright and Evolutionary Biology). In short, Fisher contended that most evolution through adaptation was driven by selection operating upon additive genetic variation. That is, variation due to alleles across the genome, each having independent and additive effects on the trait. One might think of these as linear effects. In contrast Wright’s views were more complex or confused, depending upon your perspective on the sum totality of his theories. In the domain of genetic architecture he presented a model where gene-gene interactions, epistasis, played an important role in the evolutionary trajectory of populations, which traversed ‘adaptive landscapes’ in a contingent fashion.

The point is not to revisit old and somewhat stale controversies. It is to suggest that filaments of these nearly century old debates persist down to the present in a vividly relevant manner. Evolutionary biology is a progressive science, but the arc of the initial narrative initiated by the fusion of biometrics, Darwinism, and Mendelism, has not concluded. Last year a group suggested that much of the “missing heritability” may actually be found in the interaction term across genes. In many quantitative genetic treatments this component may be collapsed into the “environmental” component, as opposed to the “narrow-sense” heritability, which is defined by additive genetic variance. If this epistatic component can be thought to be more complex and non-linear it stands to reason that biologists would focus on the additive component of variance first. But, there is the possibility that additive genetic variation is somewhat like looking under the lamp post, because that is where the light is.

A new paper in PLoS Genetics takes the argument even further, An Evolutionary Perspective on Epistasis and the Missing Heritability. Let me jump to the first paragraph of the discussion:

The architecture of genetic variation must be understood if we are to make progress in fields such as disease risk prediction, personalised medicine, and animal and crop breeding. This study sought to examine the potential for epistasis to maintain genetic variation under selection, and thus to inform GWA strategies based on these results.

Though the paper seemed to shift between a broad evolutionary perspective and salient within biomedically focused GWAS studies, I found the treatment of the former rather elliptical. Using a range of gene-gene interaction models they concluded that deleterious genetic variation could be maintained to a far greater extent than with an additive paradigm. Ergo, the extant genetic variation across many traits which may seem to violate the fundamentals of evolutionary process (fitness maximization and erasure of genetic variation). This makes some sense, in that additive genetic variation should be effective in purging deleterious variants, and fixing advantageous ones. In contrast, interaction effects are such that benefits and demerits may be more conditional, at least in regards to their magnitude (from what I recall this was one reason for Fisher’s dismissal of their important to the overall evolutionary arc of a population; see R.A. Fisher: The Life of a Scientist). One technical aspect that concerns me about the arguments outlined in the above paper is the emphasis on overdominance and heterozygote advantage. Though they are aware of the problem of segregation load multiplied across loci, where homozygotes are generated in a context where heterozygotes are most fit, the authors still emphasize scenarios in their two-locus models where this is critical. Intuitively I have difficultly believing that this can be any major part of explaining “missing heritability.” But the broader issue in regards to epistasis is well taken, and it is a reality that epistatic and additive variance can emerge from the same loci conditional upon the overall genetic architecture. On the evolutionary canvas the two may be interchangeable as a function of time.

Their treatment of problems with GWAS was more straightforward. This is the method whereby associations are found between traits/diseases and particular genetic variants by looking at differences between discrete populations with differences in traits/diseases of interest. It seems that their models illustrate that the power to detect epistatic variance, and its impact on trait value, is masked by the fact that linkage disequilibrium between markers and causal variants must be very high for it to be detected. In contrast additive effects are less sensitive to decay in linkage disequilibrium, which measures the association of alleles across genes, so that one marker may serve as a signal for the presence of another variant down or up the genome.

Part of the answer is probably here. But how much? Though no “letter” to Nature I felt that this paper could be fleshed out somewhat, as some of the inferences seem to be rather underdeveloped. They have demonstrated complexity and lack of generality. But what now? I suppose we’ll see.

Citation: Hemani G, Knott S, Haley C (2013) An Evolutionary Perspective on Epistasis and the Missing Heritability. PLoS Genet 9(2): e1003295. doi:10.1371/journal.pgen.1003295

Addendum: For those curious about epistasis and evolution, see if your college library has Epistasis and the Evolutionary Process.

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Ornithomimosaurian dinosaur & ostrich, image credit Nobu Tamura & James G. Howes

ResearchBlogging.orgThe Pith: This post explores evolution at two different scales: the broad philosophical and the close in genetic. Philosophically, is evolution a highly contingent process which is not characterized by much replication of form and function? Or, is evolution at the end of the day aiming for a few set points which define the most optimal fitness positions possible? And how do both of these models relate to the interaction across genes, epistasis? In this post I review a paper which shows exactly how historical contingency could work through gene-gene interactions on the molecular genetic scale.

Imagine if you will a portal to another universe which you have access to. By fiat let’s give you a “pod” which allows you to move freely throughout this universe, and also let’s assume that you can travel fast enough to go from planet to planet. What if you see that on all the planets there’s a sludgy living “goo” of some sort? To complexify the issue imagine that upon further inspection the goo is divided between a predominant photosynthetic element, and “parasitic” heterotrophs. But aside from these two niches there’s little diversity to be seen in this cosmos. The “climax ecology” of all the planets resemble each other, in case after case convergent evolution toward the one-morphology-to-out-fit-them-all. We could from these observations construct a general theory of evolution which deemphasizes the role of contingency. In other words, there are broad general dynamics which shape and prune the tree of life in this hypothetical universe so that there is always a final terminal steady-state of the most fit morphology.

A model of evolution as a process of very general principles which converges upon a small finite range of optimal solutions has been promoted by paleontologists such as Simon Conway Morris. Stephen Jay Gould was a famous expositor of the inverse position, which emphasized chance and contingency. Gould’s suggestion was that if you ran the evolutionary experiment anew the outcomes each time would likely differ. In The Ancestor’s Tale Richard Dawkins leans toward the former position, insofar as he does assent to the proposition that evolutionary dynamics do inevitably forward certain broad trends, irrespective of the specific historical sequence of states antecedent to the terminus. More fanciful and speculative extrapolations of this logic are used to justify the ubiquity of a humanoid morphology in science fiction. The theory goes that a bipedal organism whose upper limbs are free to manipulate tools is going to be the likely body plan of intelligent aliens (though they will also have easy to add nose frills and such).

Until we meet those aliens these speculations are going to remain just that. And the debates about morphology, in particular body plan, are constrained by the fact that we have only one “natural experiment” to go on. So that’s why it is interesting to look at genetics, which is after all the modern fundamental characterization of the basic of evolutionary process in regards inheritance of traits. In particular looking at molecular genetics and evolution can be illustrative of the grounding of broader process. Neutral theory, which was stimulated by an understanding of evolution on the molecular level, has reordered our perception of the nature of larger scale morphological characters, in terms of both their potential utility and ultimate origin. Similarly, an inspection of the interactions of genotypes can put a spotlight on the adaptive landscape, an abstraction of the dimension of fitness explored by combinations of genetic variants.

A new paper in PLoS Genetics explores the specific question of the role of epistasis in the dance between contingency and determinism. The more common conceptualization of epistasis is mechanistic or biophysical, describing concrete gene-gene interactions on a molecular genetic scale. In this context we are more curious about the fitness and phenotypic implications of gene-gene interactions. This is evolutionary or statistical epistasis. You can think of this sort of phenomenon as simply the non-linearities in the mapping from genotype to phenotype.

Evolutionary genetics in the early 20th century was formulated by R. A. Fisher to avoid these non-linearities. Rather, it fixated on a model of change of allele frequency one locus at a time, averaging the “genetic background.” These were evolutionary genetic architectures which were additive and independent (multiplicative effects remain linear, and can be rescaled easily). Statistical epistasis is describing genetic architectures which are not additive and independent. Fisher’s intellectual rival Sewall Wright was more concerned with these interaction effects in his “Shifting Balance Theory,” but even Will Provine, Wright’s biographer, admitted that there was a certain incoherency and lack of clarity in his thoughts on gene-gene interactions and adaptive landscapes.

So where are we now? In the PloS Genetics paper, Initial Mutations Direct Alternative Pathways of Protein Evolution, the authors suggest that interlocking gene-gene interactions can shape the path of evolution via the constraints which prior states place upon later ones. In other words the adaptive landscape is not simple in its topography, characterized by a clear and distinct fitness peak, but is rugged so that there are multiple points upon which the populations may converge upon.

Here’s the author summary:

A long-term goal of evolutionary biology is to understand the factors that govern the outcome of evolution. Epistasis (i.e. the situation in which the fitness effect of a mutation depends on its genetic background) is one such factor. Epistasis not only affects the dynamics of evolution, it may also direct its outcome by affecting the type and order of selected mutations. This effect is particularly strong under sign epistasis, which occurs when the sign of a mutation’s fitness effect depends on its genetic background. Here, we demonstrate how epistasis causes divergence of mutational pathways of an antibiotic resistance enzyme, TEM-1 β-lactamase. First, we use in vitro mutagenesis followed by selection for cefotaxime resistance to demonstrate that alternative mutational pathways towards highly resistant variants exist in addition to the main pathway that was previously described. Next, to test whether negative interactions between alternative initial substitutions govern this diversification, we start identical evolution experiments with alleles containing initial substitutions from the deviating lines. These alleles consistently evolve to lower adaptive peaks and acquire different mutations than those in the main pathway. Our results demonstrate that sign epistasis between alternative initial substitutions may force evolution to follow different mutational pathways.

This is not a paper gifted with easy to comprehend figures. The one to the left though is rather informative. It shows what we should expect in regards to evolutionary arcs: populations converge upon a fitness peak and enter a phase of stasis after rapid evolution. Each of the lines denotes different mutational lineages, and the height on the y-axis illustrates how resistant these lineages are to antibiotics. The x-axis is time. In this series of directed evolution experiments they seem to have increased the mutation rate so that genetic variation was not a limiter on the action of evolution through natural selection (remember, the power of selection is proportional to genic variance). This is to some extent old school genetics. We’re not talking thousands of SNPs. But I honestly had a hard time keeping in mind the alphabet soup of different loci. But the broad insights are derived from a narrow range of results:

– An initial set of experiments which allowed for the evolution of antibiotic resistance show the emergence of a similar genetic profile in most of the lines. This illustrates the power of convergence given the same exogenous adaptive pressure, the antibiotic. The authors argue that this highlights epistasis’ role in constraining the mutational space across the genome which can be modified to allow for antibiotic resistance.

– But, there were exceptions in several lineages. Two lack the G238S substitution. These two lines had reduced ability to resist the antibiotic. Forcing the G238S variant onto the background of the lineages which lacked it resulted in the finding that this substitution did not have a fitness improving impact, in contrast to the other cases. This shows the importance of genetic background, as the nature of other genes affects the selective advantage or lack thereof of a particular allele. Additionally, the lineages which lacked G238S tended to plateau at a lower of level of resistance. These would be lower fitness peaks, but separated from the higher G238S peak by “valleys.”

– Also, in these lineages there seem to be an excess of mutations as opposed to the G238S bearing trials. The authors offer the hypothesis that this selection of mutants in this novel background is evidence that the evolutionary process is taking a different route to solving the same problem because of shifted initial conditions (i.e., genetic variants which block the selection of G238S).

– Aside from the key initial mutations the authors also noted that there was a tendency to specific joint mutational pairs, as well as negative correlations across others. In other words, if mutation X was present, mutation Y tended not to be present, and vice versa. This suggests that the mutational path toward a fitness peak is not a series of independent steps, but a varied set of circumlocutions until an avenue toward the goal is sighted.

– Finally, forcing different pairs of negatively epistatic variants also resulted in different outcomes contingent upon the magnitude of the interaction. In a case where there was very strong negative epistasis (sharply reduced fitness, and reduced expression of the phenotype) there was a rapid reversion back to a state where such epistasis was mitigated. Remember, the mutational rates here were high, so back mutations are possible. But a second case with far weaker epistasis showed that such reversions were not always inevitable. In these cases weak epistatic interactions may eventually have been masked by modifier variants in the genetic background.

So is evolution contingent, or is it inevitable? Do gene-gene interactions play a major long-term role in evolution, or is epistatic variance inevitably converted to additive genetic variance? I think the answer is that it depends. Instead of dichotomously binning the possible space of answers one just has to acknowledge that the nature of the parameters are important. In a universe of near infinite population size and stable environmental conditions one suspects that contingency is rather less important, as natural selection can explore an enormous range of genotypic combinations over long periods of time. A contrasting situation would be one where environmental pressures are protean, and populations constrained in size. If evolution by natural selection is thought of as a tinkerer, you’d naturally see a lot more ad hoc contingent creations when you limit the raw materials (population size) and reduce the time to create (by changing selection pressures).

Citation: Salverda ML, Dellus E, Gorter FA, Debets AJ, van der Oost J, Hoekstra RF, Tawfik DS, & de Visser JA (2011). Initial mutations direct alternative pathways of protein evolution. PLoS genetics, 7 (3) PMID: 21408208

🔊 Listen RSS Does the chart above strike you as strange? What it shows is that the mean fitness of a population drops as you increase the rate of deleterious mutation (many more mutations are deleterious than favorable)…but at some point the fitness of the population bounces back, despite (or perhaps because of?) the deleterious mutations! This would seem, to me, an illustration of bizzaro-world evolution. Worse is better! More is less! Deleterious is favorable? By definition deleterious isn’t favorable, so one would have to back up and check one’s premises.

And yet this seems just what a new paper in PLoS ONE is reporting. Purging Deleterious Mutations under Self Fertilization: Paradoxical Recovery in Fitness with Increasing Mutation Rate in Caenorhabditis elegans:

Compensatory mutations can be more frequent under high mutation rates and may alleviate a portion of the fitness lost due to the accumulation of deleterious mutations through epistatic interactions with deleterious mutations. The prolonged maintenance of tightly linked compensatory and deleterious mutations facilitated by self-fertilization may be responsible for the fitness increase as linkage disequilibrium between the compensatory and deleterious mutations preserves their epistatic interaction.

Got that? OK, you probably need some background first….

The authors used C. elgans as a model organism. This “worm” is ubiquitous in biology. There’s an enormous community of developmental biologists, geneticists, and neuroscientists, who work with elegans as a model organism. For the purposes of evolutionary genetics you need to know a few things about elegans though. The vast majority of reproduction of elegans occurs through “selfing.” That is, most elegans are hermaphrodites who fertilize themselves. They’re obviously not asexual, but their habits are straight out of South Park. A small minority of reproductive events among elegans are sexual in a conventional manner, because a few of the worms in any given generation are males. For the purposes of this experiment you need to ignore this aspect; they’re focusing on the selfing. To do this they removed males out of the equation, either by introducing a male killing mutation, xol-1, or, manually removing them.

So now we have just the selfers. If you pick up a standard pop gen text, e.g. Principles of Population Genetics, you’ll find out that selfers tend to have some peculiar and interesting properties when it comes to the long term arc of evolutionary genetics. In particular, they “purge” “genetic load” like crazy. What this means is that deleterious alleles get removed from selfing populations very fast through negative selection. Why? How?

Let’s go back to genetics 101. Imagine a locus where an individual is a heterozygote, and carries an allele which is “wild type” and another which is deleterious, and recessively expressed. Cystic fibrosis is a recessive disease that is common among Europeans. 1 out of 25 Europeans is a heterozygote, and there is a 1 out of 25 chance that these individuals will mate with someone who is also a carrier. Out of these pairings, 50% of the offspring will also be carriers, 25% will be wild type homozygotes, and 25% will express the cystic fibrosis disease because they’re homozygotes for the deleterious allele. With the numbers given that means 1 out of 2,500 births will result in a child with cystic fibrosis.

Cystic fibrosis is a lethal disease which sharply reduces fitness (many individuals are just infertile). This is negative selection against the deleterious allele. But, the selection is relatively weak. Why? Take a look at the ratio between those who carry the allele, but have normal fitness, and those who carry two copies and have reduced fitness. It’s 100 to 1. Most copies of the deleterious allele are “masked” from any negative fitness consequences because they’re paired up with a normal wild type which complements and compensates the function of the mutant variant. This is one reason why we carry so many deleterious alleles; they’re often paired up with a “good” copy which prevents the fitness of the individual from cratering.

Now let’s bring this back to selfing. In a human population we pair up with others. So you have to multiply independent probabilities, 1/25 × 1/25, to produce a Punnett square where two heterozygotes are crossed. In a scenario of selfing the probabilities are different. There’s perfect assorting of genotype to genotype for selfers, because the genotypes are simply being crossed with themselves. If you’re a fertile hermaphrodite who carries the mutant cystic fibrosis allele there’s a 25% chance that you’re offspring will be homozygotes for cystic fibrosis, because you know that the cross will be with another heterozygote (yourself). Now imagine that the whole population consists of selfers. Instead of 1 out of 100 copies being exposed to selection, 1 out of 2 copies are exposed to selection! This is how selfers purge genetic load so well. When selection only operates on homozygotes, their tendency to produce homozygotes means that deleterious alleles are far more exposed to selection. Why do selfing populations in the aggregate produce so many homozygotes? Heterozygotes mating with heterozygotes produce both heterozygotes and homozygotes. Homozygotes mating with homozygotes produce only homozygotes. The “toy” chart I’ve put together shows what happens when you take a uniform population of heterozygote selfers in generation 1, and allow them to reproduce down the generations. Each generation the proportion of heterozygotes, those individuals where deleterious alleles are masked and so protected from the purging power of natural selection, decreases. Selection becomes more and more efficacious in purging genetic load from the population.

There are still two other concepts important to understanding the implications of this paper. Epistasis and genetic linkage. But let’s move on to some results first, and then digest them with a further helping of conceptual condiments. Here’s figures 3 & 4, which I’ve reedited a bit. On the left you see fitness (fecundity) as a function of the concentration of mutagen. In other words, as you move up the mutagen concentration on the x-axis the mutation rates are increasing. On the right you see a plot which shows the mean fitness after x # of generations, which each set of data points represent differing concentrations of the mutation. I’ve highlighted the lines with no mutagen, and maximal mutagen.

The bizarro aspect is the jump between 80 mM and 100 mM. As mutation rates increase there is a bounce back of fitness. Imagine that you were rolling a boulder up an incline which got progressively steeper in its grade. Common sense and basic physics would tell you that you’d have to use more and more force to move the boulder the same distance. Now imagine that beyond a certain grade of steepness you actually had to use less force! That would make no sense. In some ways that’s what’s going on here. But then, evolutionary processes may not be so linear and predictable as Newtonian mechanics.

Of course there could be some straightforward reasons for this strange behavior. For example, the xol-1 mutant which produced maleless populations may have had pleiotropic effects. To test for this they manually removed males from a population without the mutation, and obtained similar results. Additionally, they also took a divergent elegans line with the xol-1 mutant and performed the same experiments, and again the same pattern recapitulated itself. Finally, there’s always the possibility that resistance to the mutagen had developed above a certain concentration. If resistance to the mutagen had developed presumably taking the population which had exhibited the increased fitness ~100 mM, and placing it back into lower concentration environments, would produce a different response curve than we saw before. That is not what occurred, as you can see in figure 6.

Now that we have the core results under our belt, let’s move on to trying to make sense of how water can flow uphill like this. So back to the concepts, genetic linkage, and epistasis. The first is easy. Genes are arrayed along physical DNA strands. The closer the physical position of the genes, the more likely they are inherited together in a straightforward fashion. The kink in the expectation is recombination. In diploid organisms you have two copies of each gene on the two strands. Recombination can shuffle specific gene copies from one strand to the other (or, more accurately, break and recombine strands in a fashion so that both differ from the state before the event). The further the distance between any two gene copies on a physical strand, the greater the likelihood for recombination to separate the two. When two copies are very close there’s only a small physical distance across which recombination might operate to separate them. Therefore, the closer the copies the more “linked” the genes are.

Before explaining why this matters, let’s talk about epistasis. Epistasis can be thought of generally as gene-gene interaction. In the mechanistic molecular sense you’re referring to biophysical processes whereby one gene has some interaction with another gene. But there’s another way to think about: fitness or trait value. In this sense epistasis as gene-gene interaction introduces non-linearities into the mapping of genotype to phenotype, as well as genotype to fitness. This is what matters for the purposes of this paper. In particular, epistasis manifesting as compensatory deleterious mutations.

So how does this matters for selfers? Recall that above we were talking about how selfers purge deleterious genetic load by cranking up the proportion of homozygotes exposed to negative selection. Implicitly our model was single locus. We were looking at one gene, and one mutant. But how about if you had a large number of mutants? Can selfers produce all those homozygotes simultaneously, and so purge the load efficiently? Purging load through natural selection entails reduced fitness for many members of a population; purge too much and the population crashes and you’re liable to just go extinct through mutational meltdown. This where linkage and recombination come back to the fore. Recombination is often thought of as a way to create new genetic combinations. But in homozygous selfing lineages recombination doesn’t live up to that promise: there’s not enough heterozygosity within the genomes of these organisms so that the shuffling of the strands across each other produces anything new! Selfing lineages exhibit very strong linkage between sequences of genetic variants across loci because of the inability of recombination to break apart associations. So, if you have two genes, A and B, which are linked, and A is very fit and B is moderately unfit, if they are co-inherited B may sweep up to fixation with A. As you crank up mutation rates then the theory predicts that deleterious alleles will simply swamp out the ability of selfing lineages to purge the load fast enough to prevent ultimate extinction. Even if the genetic background wasn’t homozygous, too many mutations within the genome would be swapping out deleterious copies for other deleterious copies during recombination.

That theory was born out more or less at concentrations of the mutagen below 100 mM. But then expectation was confounded. Why? This is where epistasis steps into the picture. In the previous model we implicitly assumed an additive model. Imagine the fitness of allele 1 at gene A ~ 3 and the fitness of allele 2 and gene B ~ -2. Summing them together ~1. And so on. Epistasis confuses this simple picture because it implies non-linear computations. The fitness value of A and B may be conditional on the state of a third gene, C. In any case, a compensatory mutation is one where more deleterious is in fact less deleterious. Precisely, having two deleterious mutations may actually have less of a fitness hit than having one deleterious mutation! In some ways this becomes a matter of semantics and analytic philosophy. -10 + – 10 > – 10 is just incoherent.

Since this is not a philosophy blog, how does this relate to selfing lineages? It goes back to linkage. Recall that tight linkage may produce situations where recombination can not break apart unhealthy associations where favorable variants are linked with unfavorable ones, and the latter may hitchhike with the former in selective sweeps (in populations with more heterozygosity recombination would increase the range of combinations across which selection operated; see Muller’s ratchet). This is the bad. But in the case of compensatory mutations the inability of recombination to break apart associations may be a positive. These epistatic interactions are contingent on robust combinations persisting. Recombination would break apart those combinations, preventing the fitness gains from persisting across generations. But in these selfing linages the homogenized genetic backgrounds are relatively fixed palettes against which these mysterious genetic interactions which turn expectations upside down can perform their magic.

This paper had some moderately weird results. The response to mutagen concentration increases seemed robust within their set of experiments, but who knows how general this phenomenon is? A reliance on compensatory mutation also strikes me as only less weird because the results were so weird. In the last paragraph the authors seem to acknowledge the general strangeness at work:

Regardless of the mechanism driving the fitness increase exhibited by populations exposed to 100 mM EMS, the result is a testament to the resiliency of the genome. Consistent exposure to high mutation rates should wreak havoc on the genome, and repeated exposure to 80 mM EMS (Figure 5) appears to do just that. However, the genome is able to recover a large proportion of the fitness lost at 80 mM EMS when exposed to 100 mM EMS (Figure 3). This result is quite surprising and challenges the long-held beliefs concerning the relationship between mutation rates and fitness.

The long-held belief presumably being that high mutation rates are correlated with decreased mean fitness, and ultimately likely extinction. A great deal of post-apocalyptic fiction from the Cold War period was predicated on just this assumption. And clearly in most cases this seems to be a warranted axiom. On the other hand, sometimes in biology the minor exceptions are more important in explaining the patterns of diversity we see around us. If there was a veil of ignorance over us and we had to predict the nature of replicating organisms on this planet would we predict the incredible diversity we see all around us? Would we predict intelligent life? I suspect that there would be the preference for a simple and elegant model where life on earth was optimized toward extremely simple and highly robust rapid replicators. Prokaryotes. And to a first approximation that logical inference based on Darwinian assumptions would be correct. Prokaryotes are omnipresent. In fact, some estimate that there are 10 times as many bacterial cells within a human body as human cells. But obviously there are creatures on the Earth besides prokaryotes. And we care a great deal about this “residual” from the expected trend line….

Citation: Morran LT, Ohdera AH, & Phillips PC (2010). Purging Deleterious Mutations under Self Fertilization: Paradoxical Recovery in Fitness with Increasing Mutation Rate in Caenorhabditis elegans. PloS one, 5 (12) PMID: 21217820

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Snapdragon,_smallOne of the main criticisms of the population genetic pillar of the modern evolutionary synthesis was that too often it was a game of “beanbag genetics”. In other words population geneticists treated genes as discrete independent individual elements within a static sea. R.A. Fisher and his acolytes believed that the average effect of fluctuations of genetic background canceled out as there was no systematic bias, and could be ignored in the analysis of long term evolutionary change. Classical population genetics focused on genetic variation as abstract elementary algebras of the arc of particular alleles (or several alleles). So the whole system was constructed from a few spare atomic elements in a classic bottom-up fashion, clean inference by clean inference. Naturally this sort of abstraction did not sit well with many biologists, who were trained in the field or in the laboratory. By and large the conflict was between the theoretical evolutionists, such as R. A. Fisher and J. B. S. Haldane, and the experimental and observational biologists, such as Theodosius Dobzhansky and Ernst Mayr (see Sewall Wright and Evolutionary Biology for a record of the life and ideas of a man who arguably navigated between these two extremes in 20th century evolution because of his eclectic training). With the discovery that DNA was the specific substrate through which Mendelian genetics and evolutionary biology unfolded physically from generation to generation a third set of players, the molecular biologists, entered the fray.

The details of genetics, the abstract models of theorists, the messy instrumentalism of the naturalists, and the physical focus of the molecular researchers, all matter. Through the conflicts between geneticists, some arising from genuine deep substantive disagreement, and some from different methodological foci, the discipline can enrich our understanding of biological phenomena in all its dimensions. Genomics, which canvasses the broad swaths of the substrate of inheritance, DNA, is obviously of particular fascination to me, but we can also still learn something from old fashioned genetics which narrows in on a few genes and their particular dynamics. A new paper in PLoS Biology, Cryptic Variation between Species and the Basis of Hybrid Performance, uses several different perspectives to explore the outcomes of crossing different species, in particular the impact on morphological and gene expression variation. You’ve likely heard of hybrid vigor, but too often in our society such terms are almost like black-boxes which magically describe processes which are beyond our comprehension (hybrid vigor and inbreeding depression freely move between scientific and folk genetic domains). This paper attempts to take a stab at peeling pack the veil and gaining a more fundamental understanding of the phenomenon. First, the author summary:

A major conundrum in biology is why hybrids between species display two opposing features. On the one hand, hybrids are often more vigorous or productive than their parents, a phenomenon called hybrid vigor or hybrid superiority. On the other hand they often show reduced vigour and fertility, known as hybrid inferiority. Various theories have been proposed to account for these two aspects of hybrid performance, yet we still lack a coherent account of how these conflicting characteristics arise. To address this issue, we looked at the role that variation in gene expression between parental species may play. By measuring this variation and its effect on phenotype, we show that expression for specific genes may be free to vary during evolution within particular bounds. Although such variation may have little phenotypic effect when each locus is considered individually, the collective effect of variation across multiple genes may become highly significant. Using arguments from theoretical population genetics we show how these effects might lead to both hybrid superiority and inferiority, providing fresh insights into the age-old problem of hybrid performance.

There are various ways one presumes that hybrid vigor could emerge. One the one hand the parental lines may be a bit too inbred and therefore have a heavier than ideal load of deleterious alleles which express recessively. Since two lineages will likely have different deleterious alleles, crossing them will result in immediate complementation and masking of the deleterious alleles in heterozygote state. Another model is that two different alleles when combined in heterozygote state have a synergistic fitness effect. We generally know of heterozygote advantage in cases where there’s balancing selection, so that one of the homozygotes is actually far less fit than the other, but the fitness of the heterozygote is superior to both homozygotes. But that is not a necessity, and presumably there could be cases where both homozygotes are of equal fitness, but the heterozygote is of marginally greater fitness.

As for hybrid inferiority, a simple model for that is that lineages have co-adapted complexes of genes which are enmeshed in gene-gene networks. These networks are finely tuned by evolution and introduction of novel alleles from alien lineages may lead in destabilization of the sensitive web of interconnections. This model taken to an extreme is a scenario whereby speciation could occur if two lineages become mutually exclusive on a particular genetic complex which is “mission critical” to biological machinery (imagine that the gene involved in spermatogenesis is effected).

These stories are fine as it goes, but they do have something of an excessively ad hoc aspect. A little light on formalization and heavy on exposition. In this paper the authors aim to fix that problem. To explore genetic interactions in hybrids, and how they effect gene expression, they selected the genus Antirrhinum as their model. These are also known as “snapdragons.” Like many plants Antirrhinum species can hybridize rather easily across species barriers. They observe the effect of taking genes from a set of species and placing them in the genetic background of another. In particular they are focusing on A. majus, hybridizing it with a variety of other Antirrhinum species, as well as introgressing alleles from the other species onto a A. majus genetic background (so an allele on a specific gene is placed within the genome of A. majus).

Just as they focus on a specific genus of organism, so they also focus on a specific set of genes and the molecular and developmental genetic phenomenon associated with those genes. The genes are CYC and RAD, which are located near each other genomically, with CYC being a cis-acting regulator of RAD. In other words, CYC modulates the expression of RAD which is on the same chromosome. Variance in gene expression simply defines the concrete difference in levels of protein product. Mutant variants of CYC and RAD, cyc and rad, are created by insertion of transposons. Insertion of transposons can abolish gene expression, resulting in removal or alteration of function. What is that function? I’m rather weak on botanical morphology, so I’m going to be cursory on this particular issue lest a reader correct me strenuously for misapplication of terminology. So I’ll show you a figure:


I added the labels. C is basically what majus should look like, while G is a totally “ventralized” mutant. B and F approach wild type, but the other outcomes are more mixed. Note the genotypes in the small print. Table 1 measures the expression levels of the gene product for the various genotype:

journal.pbio.1000429.t001 (1)

Look at the first row; mutant variants of CYC which are nonfunctional reduce normal copies of RAD down to 20% levels of gene expression. That’s because CYC is a transcriptional regulator of RAD. The process is not reversed. RAD lacking functionality does not impact CYC (last row). Finally, the heterozygote states does result in reduced dosage of the gene product. Though the phenotypes might be closer to wild type than the mutant, the molecular expression of the gene is substantially changed. This is one of the issues which is always important to remember: the extent of dominance exhibited by a sequence of phenotypes consequent from a particular genotype may vary dependent on which phenotype you are a highlighting. On a molecular level there is incomplete dominance. Additive effects. On the level of exterior morphology there is more perceived dominance. This is not even addressing the issue of pleiotropy, where the same gene may have dominant and recessive expression on two different traits simultaneously in inverted directions (i.e., the recessively expressed allele in trait A may be dominant in B, and vice versa).

Figure 1 shows the different allelic expression levels in hybrids of Antirrhinum species. But what about the impact of the combinations on phenotype? I’ve reedited figure 4 so it fits better on this page:


Here’s the text description for the figure:

GEM spaces for CYC and RAD, showing location of various genotypes and species.

(A) Dorsalisation index for each position in GEM space using values from Table 1. Standard errors for DIcor and expression levels are shown (if error bars are not visible, they are smaller than the symbols). A smooth surface has been fitted to the data (see Materials and Methods for details of surface fitting). Note that the wild-type, C, lies on a plateau while the double heterozygote, E, is on the slope. (B) Top view of the GEM space, incorporating the relative expression values from the species taken from Figure 1 (circles). These values were adjusted assuming that A. majus (red circle) is at position (1, 1) in gene expression space. Triangles indicate expected gene activity values in the double heterozygote (CYC = x×0.6; RAD = y×0.5; see Table 1E). Some of the double heterozygotes are predicted to have DI values above or below the position of A. majus. Triangles pointing upwards indicate species showing notch phenotype. (C) Enlargement of rectangle in (B). bra, A. braun-blanquetii; cha, A. charidemi; lat, A. latifolium; lin, A. linkianum; maj, A. majus; meo, A. meonanthum; pul, A. pulverulentum; str, A. striatum; tor, A. tortuosum; cha-BC, introgression of A. charidemi into A. majus background.

GEM = gene expression–morphology (GEM) space. As I note above the mapping between the manifestation of genetic variation on the molecular level and on the gross morphological level may be subtle. Figure 4 has the two genes under consideration forming a plane through the x and z-axes, while gross morphology is illustrated on y-axis. What’s on the y-axis is actually a principal component which serves as an abstract representation of the morphological variation of the petal structure illustrated in the earlier figure. They call it the “dorsalization index” (D i). The wild type = 1 and the expressed mutant = 0. So the interval 0 to 1 in phenotype space is a good gauge as to the deviation of the morphology from wild type.

The letters in panel A are representations of the letters in the first and second figures within this post. G represents the double homozygote mutant. It stands to reason that its D i is ~ 0. C, B, F, and to some extent E, form a “plateau” where gene expression may vary a fair amount but the morphology remains relatively stable. A, D, H and I represent intermediate cases on the “slope” where changes in genetic architecture produce large shifts in phenotype. The idea of dominance and recessiveness already indicate that not all genetic variation is created equal, and that there are non-linearities in the interaction of genetic variation and phenetic variation. Here using D i and quantitative levels of gene expression one can take the verbal/qualitative insight and translate it into a quantitative relation.

Panel B seems to be similar to L. L. Cavalli-Sforza’s synthetic maps of PC variation of gene frequencies. It’s taking the y-axis in A and transforming it into the clinal grade on the plane. The circles in panel B represent conventional hybrids between A. majus and other species within its genus. There is variation in gene expression levels within these hybrids, but note that they reside on the phenotypic plateau. In contrast, the triangles show double heterozygotes: (CYC RAD)/(cyc cyc). The heterozygote combinations are for a variety of species, as indicated in the figure text. Note that they explore more of the phenotype type space, as evident in panel C, which is just an zoom of the rectangle in panel B.

So far they’ve shown that homozygote mutants abolish the wild type morphology, while heterozygotes of various combinations move over phenotype space. RAD‘s expression is contingent on CYC, so that can explain some of the unpredictability of the variation when viewed in light of a simple qualitative model. Additionally, wild type hybrids move in the gene expression dimension, but not in the phenotype space. So next they looked at the impact of a particular species CYC and RAD genes against the majus genetic background in the doubly heterozygote state. In other words we’re not talking about a hybrid where half of the total genome content is from each parental species. We’re talking about introgression of alleles at a specific locus from species A to species B, so that the nature of the total genome content is of species B, except at a particular locus or set of loci, where they are from A. Figure 5 shows the results of such a cross:


The result of these studies show that alleles from A. charidemi are much more efficacious in maintaining wild type phenotype in the heterozygote state than A majus. This is because of underlying gene expression differences across species. Observe that CYCchar is particularly relevant because of the dependence on the RAD locus upon CYC in terms of gene regulation. The presence of charidemi and majus derived alleles on the same chromosome, so that cis--acting dynamics were operative, was achieved through recombination. A further exploration of the expression of each allele individually confirmed that CYCchar had a 30% higher expression than CYCmaj.

OK, so at this point we’ve examined the general topology of GEM. The relation between morphology and gene expression, the nature of the landscapes which describe their relationship. Next, we’ll move to GEF, gene expression–fitness (GEF) spaces. Genes/gene expression, phenotypes, and fitness, are the three-legged-stool of evolution, and specifically natural selection and adaptation. In a proximate sense the relationship between genes and phenotypes are physically mediated by a sequence of developmental pathways over life history. In an ultimate, evolutionary, sense, the relationship between genes and phenotypes are mediated by fitness, with variation in phenotypes over time being driven by variation in genotypes via the engine of fitness differentials. The distinction between evolutionary and non-evolutionary genetics, the abstract/theoretical and concrete/empirical, crops up with something like epistasis. On the one hand epistasis refers to physical relationships between genes. On the other hand it can also describe the variation in trait value which emerges from the interlocus interactions. And finally, it can refer to non-linear fitness effects due to combinations of alleles across loci.

In this case we’ve already seen how variation on the molecular level of gene expression due to genetic differences at two loci do not always translate into variation in morphology. The plateau in GEM space is simply due to the invariance in the morphological dimension. Once variance shows up you see the plane tilt and become steep. GEF space is exactly analogous, except that we are looking at variation in fitness on the y-axis. This is the domain of evolution, the ultimate. This section has only one figure:


GEM was based on concrete observation and experiment. GEF space is more theoretical, insofar as from what I can tell they didn’t measure fitness in actual lineages, but rather hypothesized distributions of fitness from parameters which might give us insight into hybrid vigor and/or breakdown. Red is obviously increased fitness and blue decreased. The surface of the landscape is simply where the gene expression values intersect with realized fitness. There are several alternative topologies here. I’ll quote the figure text:

Gene expression levels for two genes are plotted along the horizontal plane while fitness is along the vertical axis. (A) Radially symmetrical peak. (B) 2-D Projection of (A) showing location of effectively neutral zone and position of two parental genotypes (P1, P2 triangles), the resulting F1 (square) and additional genotypes observed in the F2 (diamonds). The F1 in this case is nearer to the centre of the peak while the F2s have similar fitness to the parents. (C) Diagonal ridge. (D) 2-D projection of diagonal ridge showing tilted elliptical neutral zone. The F1 is nearer to the peak than the parents but some F2 genotypes may now have lower fitness and fall outside the neutral zone. (E) Curved ridge. (F) 2-D projection of curved ridge showing banana-shaped neutral zone. Some F1 genotypes may have lower fitness and fall outside the neutral zone.

First, one has to introduce the concept of ‘drift load.’ A population of a particular genotype has an expected fitness, while in the best-of-all-world’s there is an idealized fitness peak. Random genetic drift will drive the population away from the peak because variance which shifts the gene frequencies from generation to generation. The power of drift to alter gene frequencies is inversely proportional to effective population size, N e, the proportion of the population contributing to the genes of the next generation (often a rule of thumb is 1/3 of the census size, though this probably applies for human-scale organisms; usually it is much smaller than census). The drift load is the drag on fitness induced by drift, and is defined by the equation: ~1/(4N e). In other words, as N → ∞ the drift load disappears because sample variance is eliminated. But this load is applicable at each loci, so if you sum up across many genes then small increments can produce a non-trivial fitness decrement simply due to the vicissitudes of generation-to-generation variance.

In the figure above the dark red zone is neutral. That means there’s no fitness variance. That’s the “fitness plateau” equivalent to the phenotypic plateau observed above. P1 and P2 are parental generations, different lineages. F1 are hybrids, while F2 are crosses of the hybrid generation. The deviation of P1 and P2 in all the panels from the center of the fitness plateau are indications of drift load. The shape and nature of the fitness plateau are critical in determining the outcomes for the F1 and F2 generation, and consequent vigor or breakdown. Geometrically you see the rationale for hybrid vigor in panel A and B, as F1’s are closer to the center of the fitness plateau as drift load is dampened on the cross. In the text the authors note that ‘the variance around the optimum of the mean of two independent populations is half that of either one, and so the “drift load” is half as great.’ So instead of ~1/(4N e), you have ~1/(8N e). This is a gain in fitness which can be substantial over many loci. Over 1,000 genes it would be a gain of 0.125, which is very large, and can explain heterosis. But as many farmers know the F2 generation often exhibits a regress in fitness. “Hybrids do not breed true.” In a Mendelian model some of the offspring of the hybrids will segregate the alleles so that homozygotes will reappear. In panel A the F2 have about the same fitness as the parental cases. In panel B this is not the case; new genotypic combinations presumably are produced which lay outside of the fitness plateau, and this leads to a major hybrid breakdown. In panel C the F1 are slightly below the parental populations in fitness, while the F2 are far below them.

In the discussion they then work back from the theoretical digression to its relevance to observed variation, and their particular model taxon:

The phenotype and fitness of species hybrids will reflect the extent to which these various GEF scenarios apply to the many thousands of genes in the genome. Radial or elliptical neutral domains, centred around a common position in GEF space, would be expected for loci that are under similar normalising selection in multiple environments. This situation likely applies to the CYC and RAD genes as all species in the Antirrhinum group have similar asymmetric closed flowers. It would also be expected for many loci controlling basic physiology and growth. F1 hybrids would therefore be expected to show higher fitness and increased performance with respect to these traits. This provides an explanation for hybrid vigour that avoids the pitfalls of previous models that require fixation of loci with major deleterious effects or that invoke special mechanisms for heterozygote advantage. A similar explanation has been proposed to account for the origin of hybrid vigour between domesticated inbred lines…Hybrid vigour is usually lost in F2s or recombinant inbred lines, indicating that many of the loci involved interact to give tilted rather than untilted neutral zones.

Although hybrid vigour is commonly observed for physiological traits, the overall fitness of species hybrids is often lower than that of the parents, with sterility or other dysgenic effects being observed. This observation may partly reflect adaptation to different environments and thus shifts in the shape of fitness surfaces that drive changes in genotype. However, it may also reflect loci that interact to give curved or L-shaped neutral zones…Such zones will be prevalent for traits that involve more complicated epistatic interactions, perhaps accounting for the dysgenic effects observed in F1s. The negative contribution of loci with curved neutral zones is likely to increase with time, as loci drift towards the extremities of the banana-shaped neutral domains.

Remembering that there is a possible association between cis-elements and physiological traits,. it is interesting to observe that one may be able to infer fitness landscapes from patterns of morphological and genetic variation. I don’t know how robust the generalizations above are, and obviously this particular paper is more about setting up a testable framework than validating that framework, but we’ve come a long way from “beanbag genetics.”

Citation: Rosas U, Barton NH, Copsey L, Barbier de Reuille P, & Coen E (2010). Cryptic Variation between Species and the Basis of Hybrid Performance. PLoS biology, 8 (7) PMID: 20652019

Image Credit: Wikimedia

• Category: Science • Tags: Epistasis, Evolution, Genetics 
Razib Khan
About Razib Khan

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