AUSTRALIAN FRONTIERS OF SCIENCE, 2005
Walter and Eliza Hall Institute of Medical Research, Melbourne, 12-13 April
The genetic limits to evolutionary change
Associate Professor Mark Blows, School of Life Sciences, University of Queensland
One of my main interests is genetic limits to evolutionary change. What I am going to do today is to get that interest across to you in a particular context, the lek paradox.
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I am going to be talking about two things today. The first is male exaggerated traits, like this peacock’s tail. Lots and lots of species that we see out in nature have these kinds of exaggerated male traits. The inference is that it is these traits that are responsible for male mating success. So a lot of my talk is going to be describing the genetic basis of these kinds of traits.
The other part of my talk – which is probably the more important part but, like many important parts of talks, is not going to be discussed very much – is the female preference. It is really the maintenance of female preference in natural populations which this talk is about, although most of the data is on male traits. I am not going to be talking much about the female preference expressed in this cartoon, but what I will be talking about is a preference that females have for genetic quality. These exaggerated male traits are supposed to be honest indicators of general genetic quality of males, and it is that pleiotrophic genetic link between the exaggerated trait and genetic quality in general that I am going to be discussing.
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So what is the lek paradox? When we see males like the bird pictured in this slide, with many exaggerated traits that obviously have no benefit to the individual at all except for gaining mates, the suspicion is that these sorts of traits should signal genetic quality in some way. If that is true, it means that both sexual selection (females choosing those traits) and natural selection (genetic quality) are operating in the same direction. So an allele that both increases the size of the trait and increases genetic quality – has a pleiotrophic effect on both sets of traits – is going to be under positive selection. It is going to drive to fixation fairly quickly.
Once it goes to fixation, of course, it means that all males in the population are the same at that particular locus, there is no variation being expressed at that locus. And so what we expect is that this kind of selection should deplete genetic variance in the male trait. If it is the case that all males are the same, then when females step up to the plate and choose, there is no longer any benefit for doing so, because the females are choosing amongst – at this particular locus – genetically identical males.
We have the question, then: why do females continue to choose, when we expect the genetic variance in male traits, and therefore the genetic benefits for females, to be so low? What is maintaining these obvious female preferences in the population? This is what is called the lek paradox. We know that females choose, we know that these traits signal genetic quality in many systems, so what is maintaining that when there are no genetic benefits for doing so?
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We think we have got a solution to that paradox. At the moment, the evolution of condition-dependence is put forward in the literature as the explanation for resolving the lek paradox. It works something like this.
The male trait, be it plumage, colour or tail length, is going to have relatively few genes contributing to it. So it represents a small mutational target.
When the alleles at these loci that code for larger trait size move to fixation, what we then expect to happen is that a mutation which allows males to trade off some other aspect of their quality, to make even larger trait sizes, will be faded. What we then have is the evolution of condition-dependence for that trait. There is now a genetic link between general quality, trading that off, into the exaggerated trait.
General condition is expected to have a large mutational target – many, many processes will contribute to general condition of an organism. If that is the case, what we then have is genic capture of the genetic variance in condition by this male trait. The inference is that having a large mutational target will result in higher genetic variance. If there are lots and lots of loci involved, it is very difficult for selection to take all that variance and fix it in the population.
Indeed, when we go out in the natural populations and do the genetic experiments, what we find is that these male traits do have much higher genetic variance than general morphology or life history traits or even other behaviours. So there does seem to be some evidence for these exaggerated male traits having unusually high levels of genetic variance.
And so at the moment, as a field, we are quite comfortable with the fact that the lek paradox has been resolved and we can move on to something else.
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What I want to put forward today, though, is a complication of that story. I will be arguing, in fact, that it this not the right time to dismiss the lek paradox as being resolved.
Here is a simple thought experiment, where we have not one male trait but two male traits, two dimensions to this male exaggerated trait. Most traits are going to be either two- or three-dimensional in reality, but in the way that we measure traits they can be of much higher dimension. If we take 10 morphological measures, for instance, on body size, that is going to be a 10-dimensional trait to deal with later on. So multidimensionality is an empirical certainty, if you like.
This slide depicts two traits, and if you imagine the rectangle in the left-hand panel to be genetic space, what we have here is the genetic variance in trait 2, along the horizontal axis, and the genetic variance in trait 1 along the vertical axis. You can see that there is some kind of positive pleiotrophic relationship between these two traits. They covary in a positive manner; there is a positive genetic correlation between them. I am going to use that term ‘genetic correlation’ a fair bit during the talk.
So you can see that, no matter in which direction sexual selection, female choice, is operating, there is always going to be genetic variance in this particular case. But it doesn’t have to be that way. Here in the right-hand panel is another example, where you can see that the genetic variance in each of the two traits is exactly the same as in this example here, but the covariance between the two traits is such that there is a lot of genetic variance along one axis – which would be called the first eigenvector of this particular two-dimensional system – but there is not much genetic variance at all in the other direction.
So when there are multiple dimensions, considering limits to evolutionary change needs to be thought of with respect to these genetic constraints in the number of dimensions that you have measured the trait in. Looking at individual heritabilities of male traits, the level of genetic variance in natural populations, may not be sufficient to resolve the lek paradox after all.
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I was interested in trying to define the lek paradox statistically in an empirical system. Unfortunately, animals like the bird I showed you in connection with the lek paradox don’t fit into the bottles that I have in the lab, but this other guy does. This is Drosophila serrata, which is a native of Australia. It is found along the east coast in the rainforests and associated habitats. You can see that, at least initially, it is not a very good candidate for sexual selection studies. There are no obvious male exaggerated traits here to deal with.
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But in reality these guys have a very complex communication system. The way that they communicate between males and females, and indeed with other species, is through a contact pheromone system.
This slide shows a gas chromatograph of a single male individual. You take the male, you wash him in hexane, which is a solvent that strips off the waxes which are these contact pheromones, and jam it into the GC. Here I have labelled 10 individual compounds which you find, ranging in size from about C24 to about C30. And it is the area under the curve in each case that tells you the concentration of that particular chemical on that particular individual.
So here is my multidimensional male phenotype, if you like. The data represents the concentration of each of these chemicals, going through integration of those curves.
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What do we know, then, about these ‘cuticular hydrocarbons’ in this animal?
The first thing we know is that they are sexually dimorphic. Males and females look different for these cuticular hydrocarbons. They all have the same chemicals, but they have them in different concentrations. And that is obviously a prerequisite for some kind of sexually selected system: males have to look different from females.
The way that you get males and females looking different is to lower the genetic correlation between the expression of the trait in males and females. If the same loci are expressed in exactly the same fashion in males and females, they will be the same. To evolve sexual dimorphism, you need to lower that correlation, new loci need to start to contribute to the traits in the two sexes. You can measure that, and these genetic correlations are quite low for these chemicals in males and females.
We also know that these cuticular hydrocarbons act as a display trait. So males have control over their cuticular profile, and within minutes they can display to a female by changing the hydrocarbon profile on their cuticle – to such an extent, in fact, that depending on the girl standing in front of them, they will change the way that they display. You can actually observe indirect genetic effects on the male phenotype. You can actually see the effect on the sire of the female, you can see the effect of her genes on his phenotype, because he is looking so closely at her, making some judgment about her and then altering his display. So these are classical display traits, although they don’t look that way initially when you look at a gas chromatograph.
We also know that these CHCs possibly signal genetic quality. We know that because male CHCs are genetically correlated with offspring fitness. If you mate a series of males to a number of random females, and genetically associate his phenotype with the productivity of those random females, you find a significant association. So these CHCs have important life history consequences for the individuals that carry them.
Finally, we have been able to observe these CHCs evolve in natural populations. So we know that they respond to selection and they respond to selection that is generated on mate recognition. So when this particular beast, Drosophila serrata, comes into contact with a closely related species in the field, their communication system evolves away from that second species to avoid confusion and making mistakes. That is called a process of reinforcement, and we have been able to see that on these particular CHCs.
So we have a pretty good idea that this communication system can evolve, that it operates in the way of an exaggerated male display, and that it signals genetic quality. We are now in a position to ask: can we see whether the lek paradox has been resolved in this particular case?
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It is pretty easy to do that. All you need to do is first quantify sexual selection – take a female, give her a choice between two males, do that hundreds and hundreds and hundreds of times – use multiple regression then to estimate the strength of sexual selection on each of eight cuticular hydrocarbons. So β1 to β8 is the vector of linear selection gradients, the formal analysis of linear selection.
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Visually, we can take that eight-dimensional problem and bring it down into three dimensions so that we can see what is going on. Here on the y-axis is male attractiveness, and these two axes at the base are what are called the first two canonical axes of that eight-dimensional fitness surface that we can get from that experiment.
What you can see here is individuals – they are individual cuticular hydrocarbon phenotypes. We have males that were chosen, males that were rejected. And the thing to note about this thin plate spline surface is that there is not much curvature on it. It is a sloping plane going from bottom up to top. It is this sloping plane that represents the strong female choice – strong sexual selection in an open-ended fashion. So we can quantify sexual selection quite effectively.
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To do the genetics, all we need to do is set up a breeding design – pretty straightforward. I am not going to go into the particular breeding designs used here, but what I do want to concentrate on for a moment is the genetic covariance matrix, which is the way that we are going to quantify the relationships between all those traits.
Once again, for a two-trait system we have got the variance in trait 1, the genetic variance in trait 2, and the genetic covariance between them. When we have got more than two traits, we simply arrange those numbers in matrix form: the variance in trait 1, the variance in trait 2, the covariance between them, et cetera. This, then, is a symmetrical variance/covariance matrix, which is absolutely fundamental to most multivariate statistics but also allows us to conveniently summarise the genetic basis of multiple traits.
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How, then, can we see the lek paradox? Here is that fitness surface, looking down from on top now. So this is a contour plot of the same diagram. Once again, sexual selection is running from ugly males up to attractive males.
Because I knew the parentage of each of these males, I can look at what is called the breeding value of their fathers, the fathers’ genetic value, if you like. And because those values are basically means, they occupy a much smaller space on the surface – take the means of anything and they tend to contract, in accordance with the central limit theorem – and what you find is that on these two axes (remember this is an eight-dimensional system and I am only showing you two axes) the major axis of genetic variance is orthogonal to the axis of sexual selection.
So here it is starting to look as though we have got that case where we have got lots of genetic variance in each of the eight traits, but there doesn’t seem to be much genetic variance at all in the direction that sexual selection wants to go.
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That is a visual way of doing it. A more accurate way is to do it algebraically. What we need to do here is to associate that vector of linear selection with that G matrix. The way we can do that is to use some techniques from linear algebra. You see here the standard projection matrix. We have first to estimate a subspace of that G matrix, and the way we do that is to take the first four eigenvectors of the matrix.
Those first four eigenvectors describe over 99 per cent of the genetic variance in that eight-dimensional system.
What we can then do is ask: given the vector of female choice, how much of the genetic variance lies in that particular direction? We can get an idea of that by calculating the angle between the direction of selection and the projection of genetic variance that is closest to that direction. What we find, under both lab conditions and field conditions, is that the closest available genetic variance to the direction of selection is over 70° away.
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What does that mean? Basically, it means that over 99 per cent of the genetic variance in this eight-dimensional system is in one direction, but sexual selection wants to go in the other direction. So what I am saying is that here is a statistical demonstration of the existence of the lek paradox in the natural population.
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If that is the case, we need to ask: why are females continuing to choose?
I don’t know the answer to that question, but there are at least two possibilities here. The first is that perhaps the balance between mutation and selection is such that females get just enough of a benefit as new mutations occur. That is, females often don’t get a benefit but when those mutations do occur they will drive them out of the population if they are deleterious, and in the very unlikely event that they are favourable, they will go through to fixation.
Another possibility is that female preferences evolve continually, and they are continually looking for new aspects of male genetic quality which is signalled through some aspect of the signalling system. I don’t know of any evidence for that at the moment.
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Briefly, I would just like to thank two of the people in my lab, Emma Hine, who is a PhD student, and Steve Chenoweth, who is a postdoc. Emma has great skills in mathematics, Steve is a fantastic computational biologist, and they have been instrumental in developing this work with me.
