Saturday, March 04, 2006

Why Sex Is Good (and not for the obvious reasons)

A new paper in Nature helps explain why sex is so ubiquitous.

The existence of sexual reproduction is one of the great mysteries of evolutionary biology. It’s widespread, but there is no consensus on what benefits it confers over asexual reproduction, which seems to be a perfectly respectable way to go about reproducing (there are many asexual species, and some species have even gone from sexual to asexual reproduction). This is not for want of candidate explanations — it is just very difficult to get the relevant evidence to adjudicate between to competing theories (1). A recently published paper in Nature, from Ricardo Azevedo and colleagues, now provides some clues to explain the conundrum of sex.

So why is sex such a puzzle? In the 1970s, John Maynard Smith and George C. Williams independently explored the problems posed by sex, which Maynard Smith summed up as the ‘twofold cost of sex’. Jeremy Cherfas and John Gribbin have summarised the problem like this:
[I]magine a population of male and female animals happily reproducing by means of sex…Now imagine that a mutant female arises, that is, one who differs genetically from the bulk of the population. She can do without males and still have young. Her offspring will all be female who, like their mother, can reproduce without the help of males, by a process called parthenogenesis (from the Greek for virgin birth). Because she does not produce males, such a female would have twice as many daughters as the other females; and because only daughters put much effort into raising offspring the mutation would spread very rapidly indeed. Within a very few generations all the females will be asexual. There is the cost of sons, dramatically brought out into the open: they halve a female’s capacity to reproduce.
This drives home the message that females that reproduce parthenogenetically (or asexually) and produce more parthenogenetic females will, other things being equal, push out sexual reproducers. But the idea that sex halves a “female’s capacity to reproduce” is perhaps worth expanding on, as phrased like that it might be misleading.

Imagine a population of 100 females and 100 males. In this idealised population, each male mates with one female, and between them have two offspring, which the female raises. This occurs generation after generation. After 5 generations, a given female would have left 32 descendants, as would each male. Now imagine a parthenogenetic female, who through virgin birth can leave 2 females as descendants; again, after 5 generations, a parthenogenetic female would leave 32 descendants, which, in terms of counting offspring, is exactly the same as in the sexual situation. This makes it clear that it is not the capacity to reproduce per se that is halved by sex, or doubled by asexual (parthenogenetic) reproduction (that is, females on average will still leave the same number of descendants. Sex does, however, reduce the per capita reproductive rate, as sex requires that two individuals get together to make one offspring, whereas in an asexual situation each individual produces each offspring alone.

The cost of sex can be expressed in different though fundamentally similar terms: by considering the fate of genes influencing sexual and asexual reproduction (the strategy made so famous by Richard Dawkins in The Selfish Gene).

Think of a simplistic model in which one gene determines whether a female reproduces sexually or asexually. Let’s assume that there are 100 females in a population (and 100 males), all of which reproduce sexually. Any given gene in a female has a 50% probability of being passed on to her offspring, so that all offspring are 50% related to their mothers and, of course, 50% related to their fathers. Now a mutant gene arises in a female that causes her to reproduce asexually. In this situation, she will be 100% related to her offspring (and the offspring will be 100% related to their mothers) — after all, she passes on all her genes to her offspring (and the mother is the only source of the offspring’s genes).

Such a gene for asexual reproduction would be present in 100% of her offspring, a guaranteed ticket to the future. This stands in stark contrast to the fate of genes in a sexual reproducer — only 50% of her genes would then be eligible for entry into future generations. For any given gene in a sexual species, including those determining whether to engage in sex or not, there is a 50% chance of being passed on. In other words, a gene for sex reduces by half the likelihood that it, and all other genes in the genome, will make it into the next generation. Therefore asexual reproduction increases by twofold the genetic representation of female genes in future generations; this, then, highlights the twofold cost of sexual reproduction. I’ve belaboured the point at bit, but it’s important to get clear on this.

In both the model suggested by Cherfas and Gribbin, and the ones sketched above, although the actual numbers of offspring left by females is the same in asexual and sexual populations, the proportion of asexual females relative to sexual females and sexual males will rise, and with it the genes for asexual reproduction instead of sexual reproduction. Extrapolated over time, the genes for sexual reproduction would be displaced by asexual variants and disappear, and all reproduction would be asexual. This leads to the same conclusion that Cherfas and Gribbin arrive at — namely, that producing sons is not in the genetic interest of females. So the problem of sex is the question of why sexual reproduction is so ubiquitous in nature. What benefits does it provide to offset its costs?

There are, as noted above, a variety of hypotheses as to what these benefits are. One strong contender is the ‘mutational deterministic hypothesis’, devised by Alexey Kondrashov (2), and it is this model that the current paper in Nature draws on.

The basic idea of the mutational deterministic hypothesis is that sex can bring harmful mutations present in two parents together in a single individual; if this individual then dies, this eliminates harmful mutations (deleterious mutations, in the argot of geneticists) from the population. Imagine a group of asexual organism reproducing away. Then a deleterious mutation arises in one individual. All descendants of this mutant will inherit the harmful gene, and carry the cost. The only way this cursed lineage can get rid of its bad ‘genetic load’ is to die out, or wait for the unlikely event of a mutation that exactly reverses the original deleterious mutation. If this lineage suffers another genetic hit, then it will be doubly afflicted, with as little scope for escape.

Sex changes this. Imagine two sexual parents, each of which carries one harmful genetic variant. If the parents have more than one offspring, then, through the lottery of sexual inheritance, some might inherit one, both or neither of the harmful mutations. The mutation-free offspring have clearly benefited from sex, and those that inherit one have fared no worse than under asexual reproduction. But what about those that get a double dose of bad mutations? What happens to them? Well, it depends on whether the effects of the mutations interact with each other, a process known as epistasis.

These genetic interaction can take a number forms. If there is no interaction, or neutral epistasis, then the combined effects of the two mutations will be the sum of the independent mutations (that is, if each mutation carried a cost of –5 ‘survival points’, having both would cost –10). Alternatively, the mutations can interact positively, or antagonistically (this nomenclature is a bit counter-intuitive, as antagonism sounds negative, so you have to pay attention!). In this case the combined effects cancel each other out to a degree, such that the overall effect may be less than the sum of the individual effects (say, anywhere between –9 and –6 survival points), or even their individual costs (anywhere between 0 and –4 survival points). Finally, the effects may interact negatively, or synergistically, in which cause the combined effect is greater than the sum (a lower number than –10 survival points: –11, –12 and so on).

If harmful mutations interact synergistically — that is, enhance the effects of each other — then sex can potentially pay the two-fold cost it imposes over asexual reproduction by purging lineages of harmful mutations. Here’s how. If possessing either mutation A or B alone merely lowers fitness (survival plus reproduction), these mutations may hang around in lineages for a while and continually lower the fitness of all individuals in that lineage, constantly dragging each individual down. Synergy between the mutations provides a way out of this. In the most extreme case, individuals that get a double dose, or multiple doses, of mutations are absolutely unviable, and die right away. In this case, a whole clutch of bad mutations can be wiped out in one go. At the same time, other offspring may, through the luck of sexual inheritance, be mutation free — in which case, the bad genes have be removed from that lineage. This is a potentially powerful benefit for maintaining sexual reproduction.

One obvious question in light of all this is whether epistatic interactions between mutations are typically positive, neutral or negative. The answer is that in experiments you see all sorts of interactions, which hasn’t exactly helped to clarify what role epistatic interactions might play in the evolution of sex.

Previous work using computational models of evolution has suggested that natural selection can shape the nature of epistatic interactions, so under some (artificial) selective regimes natural selection can favour positive (antagonistic) epistasis, and in another negative (synergistic) epistasis. One way that the evolution of epistasis can be affected is if the genomes of organisms — that is, their entire collection of genes — and the networks of protein products they encode are selected to be ‘robust’. Robust in this sense means being insensitive to the effects of mutations. Selecting for robustness affects the nature of epistatic interactions.

Robustness is a good design feature: if you’ve got a complex system with lots of interacting parts, you don’t want the fate of the entire system to be placed in the hands of every single part. It’s good to have some mechanism for coping when parts go wrong.

It turns out that if you select for robustness in computer simulations, you produce as a correlated response increased negative (synergistic) epistasis. Another way of saying this is that robustness is negatively correlated with the ‘direction of epistasis’: when robustness is positive, epistasis is negative (taking positive and negative to represent different directions)*.

Genomes in sexually reproducing species do not only need to be robust against mutations. They also need to be robust against the genetic shuffling that occurs between generations when sperm and eggs recombine and mix their genes, process that is characteristic of sexual reproduction. This is ‘recombinational’ robustness. It has been proposed that sexual reproduction, which essentially means more recombination, imposes stronger selection for genetic robustness than asexual reproduction does.

And this is where the new study comes in — it probes this very idea. It’s not an experiment, at least not in the sense of involving real organisms with real genes. Instead, the researchers have used a computational model of artificial gene networks to get some purchase on whether sex (or recombination) selects for increased robustness.

The details of the model used in the new paper are complicated, but a few salient points should be noted. The model basically simulates a population of individuals (actually gene networks), and there is a certain amount of genetic variation between ‘individuals’ for evolution to work on. Individuals can also mutate to create new variation, and in sexual versions of the population recombination between individuals (mixing up of parental genes) takes place.

This model has previously been shown to produce, or evolve, genetic robustness if the gene networks are selected on the basis of whether they produce stable patterns of gene expression. Genes encode protein products, and these can in turn affect the activity of other genes (and sometimes also the activity of the genes encoding them). Genetic networks evolve to produce patterns of gene expression that achieve functional ends, like building limbs and regulating our metabolism. If these are easily perturbed they’ll have difficulty producing the desired outcome. And so gene-expression patterns should be stable, or at least respond in appropriate ways when perturbed, to produce functional organisms, or at least functional gene networks. When gene networks that produce stable gene-expression patterns are selected for, robustness emerges — that is, the networks evolve the capacity to maintain stable patterns of gene expression if the face of perturbations.

In this particular application of the model, the role of recombination in producing robustness was explored, using gene networks selected for their capacity to produce stable gene-expression patterns. What’s more, the researchers also looked at whether recombination, through producing robustness, could influence the direction of epistatic interactions (that is, whether there were positive, neutral or negative) that evolved.

Because of the way the model was set up, populations should be subjected to selection for both mutational robustness (insensitivity to mutations) and recombinational robustness (insensitivity to the effects of bring genes into new combinations through genetic recombination).

By tweaking the model, Azevedo and colleagues were able to tease apart the effects of sexual reproduction on selection for mutational and recombinational robustness. They found that to the extent that mutational robustness evolved in sexual populations, it was not as a result of direct selection for this type of robustness. Instead, mutational robustness was found to be a correlated response to selection for recombinational robustness. So selection for recombinational robustness produces a correlated response of mutational robustness. Another important finding is that in sexual populations in which mutational robustness evolved, negative, or less positive, epistasis also evolved. As the authors conclude:
“Taken together, these results confirm that mutational robustness and negative epistasis both evolved in response to selection for recombinational robustness.”
There are obviously limitations to this study. Firstly, it is very simple compared to the complexity of the genomes of multi-cellular plants and animals. Secondly, recombination is already present in the model — so this, the central feature of sex, did not have to evolve but was already there. Perhaps in this regard the paper contributes more to our understanding of the maintenance of sex, rather than its origins.

However, it is an interesting thought that sexual reproduction seems to create conditions that favour its own maintenance. Perhaps sex evolved in part because recombination lead to the evolution of genetic robustness, enabling extremely complex genomes to evolve, and this robustness resulted in a correlated evolution of negative (or synergistic) epistasis. Then sex could deliver the benefits spelled out by the mutational deterministic hypothesis. The synergistic interaction of harmful mutations would enable sex to purge them from the genomes of sexually reproducing organism — and therefore to pay its way.

*This might seem odd. Let me explain if it doesn’t. Mutational robustness, or insensitivity to mutations, is a capacity to dampen down the harmful effects of mutations. So any mechanism that did that would seem to be associated with robustness. And that seems to be what positive (antagonistic) epistasis does — the harmful effects of combined mutations antagonise each other, and cancel one another out to an extent. This is a sort of damping down. But in fact negative epistasis is seen to emerge alongside robustness.

The reason for this is difficult to explain, but it seems to be a reliable finding. One possibility is that if genomes have on average only one or two mutations, then mutational robustness can evolve through positive epistasis for the smaller number of mutations. This has the effect of changing the shape of a graph plotting fitness against mutational load (if we assume that previously there was no directional epistasis - that is,
neutral epistasis ). In fact, the new curve looks like a curve of negative epistasis, but from a different starting point. This isn’t, I realise, terribly helpful without some images. But in sum, genomes might evolve to be more robust to the presence of the small average number of mutations but pay the price of being less robust in the face of many mutations (thanks to Ricardo Azevedo for this point, personal communication).

1. A relatively accessible introduction to some of the ideas about the evolution can be found in: Cherfas, J. & Gribbin, J. The Mating Game: In Search of the Meaning of Sex (Penguin, 2001).

2. Kondrashov, A. S. Deleterious mutations and the evolution of sexual reproduction. Nature 336, 435–440 (1988).


Anonymous Anonymous said...

I think epistatis is a red herring in determining the benefits of sex.

From the selfish gene point of view, recombination provides no net benefit. The effects of epistatis make no difference to the likelihood of a random gene surviving in the long run in an intra-species context (it's a zero-sum game). However it provides (after undergoing selection) fitter genomes which benefit the (sub-)species in iter-species competition, at last in the short term. Thus its benefits depend on group selection.

The issue of unequal parental investment doesn't apply to hermaphrodite species, and in any case is offset or negated by the increased opportunity for specialisation provided by sexual dimorphism. Sexual reproduction persists in many species with unequal parental investment, so there must be significant countervailing benefits.

Toby Kelsey

4:34 pm GMT  
Blogger brainbark said...

Very stimulating reading -- thanks!

9:59 pm GMT  
Anonymous Jeremy said...

Hey. Thanks for the plug. I need to read the Nature paper and think about it, but it sounds very interesting.

11:09 pm GMT  
Blogger Ricardo Azevedo said...

Toby Kelsey wrote: "I think epistatis is a red herring in determining the benefits of sex. From the selfish gene point of view, recombination provides no net benefit [...] its benefits depend on group selection."

The point of Weismann's hypothesis (of which the mutational deterministic hypothesis is a particular version) is that recombination increases the variance in fitness, not mean fitness. As for the group selection argument, here's what Austin Burt had to say in his review of Weismann's hypothesis (Evolution 54: 337-351, 2000):

"Weismann's hypothesis has often been criticized as requiring group selection, with the accompanying suggestion that what is required is to find an individual-level advantage to sex, but such criticisms are misguided on several counts: (1) group selection (or, more precisely, clade selection) is exactly what is involved in competition between sexual species and obligately asexual clones; (2) individuals are not necessarily expected to benefit from the adaptations they display (recall the evolution of kin-directed altruism and of meiotic drive); and (3) the Weismannian principle also applies to genes segregating within populations: if recombination makes selection more effective, then genes for recombination will find themselves in fitter than average genomes and so increase in frequency when rare."

11:54 pm GMT  
Anonymous Anonymous said...

Its been a while since I've followed the evolution of sex debate, but I seem to remember everyone being happy with the idea that if the mutation rate is "high" enough, sex has an immediate benefit by purging deleterious mutations from one's offspring (regardless of epistatis effects). No group selection required. The late '90's produced an outflow of papers trying to estimate critical values for that mutation rate (it varies for different generation times and genome sizes) and to empiricially determine mutation rates from yeast to humans. Bottom line was that you needed somewhere in the range of 1-1000 mutations per genome per generation to make sex pay, and that eukaryotes were somewhere within that range.

4:59 pm GMT  
Blogger Ricardo Azevedo said...

Anonymous said: '[...] I seem to remember everyone being happy with the idea that if the mutation rate is "high" enough, sex has an immediate benefit by purging deleterious mutations from one's offspring (regardless of epistatis effects).'

The "idea" you recall that prompted that rush to measure the deleterious mutation rate (U) in the 1990s was actually the mutational deterministic hypothesis. This proposes essentially what you stated, except that the efficacy of the "purging" requires negative epistasis. If epistasis is positive and U is high (say, between 1 and 5), sexual populations will experience "mutational meltdown" within a few generations.

11:55 pm GMT  
Blogger Giordano said...

What? no mention of Bill Hamilton?
How soon we forget.
Bill's idea that the species pool contains strategies against parasites remains the only convincing explanatipon for sex. The 'Red Queen'
Other explanations seem to be secondary

6:12 am GMT  
Blogger Dan Jones said...

You're right, Bill Hamilton's ideas deserve mention - they're given good coverage in the popular book (The Mating Game) that I mentioned in my original post for anyone wanting an intro to them.

9:43 am GMT  

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