Friday, January 25, 2013

Experimental test of a genetic constraint hypothesis

We have recently posted a (heavily revised) manuscript to arXiv detailing how we used the fruit fly Drosophila melanogaster (you can read here about why these little flies are so wonderful) to test a particular hypothesis about a genetic constraint, and more generally how our knowledge of development may inform us about the structure of the genetic variance-covariance matrix, G. Also we developed a really cool set of statistical models that evaluated our explicit hypotheses (more on that right at the end of the post)!

As a quick reminder (or introduction), G summarizes both how much genetic variation particular traits have, as well as how much traits co-vary genetically. This covariation can be due to "pleiotropy" which is a fancy word for when a gene (or a mutation in that gene) influences more than one trait. ie. a mutation might influence both your eye and hair colour). These traits can also covary together when two or more alleles (each influencing different traits) are physically close to each other (linked) and recombination has not had enough time to break these combinations apart. I highly recommend Jeff Conner's recent review in Evolution for a nice review of these (and other concepts related to some issues I discuss below).

Evolutionary biology, in particular evolutionary quantitative genetics thinks a lot about the G-matrix, and how it interacts with natural selection (or drift) to generate evolutionary change. This is summarized by the now famous equation linking change in trait means(Δ) as a function of both genetic variation (and covariation) and the strength of natural selection (usually measured as a so-called selection gradient, β). This is the multivariate (more than one trait) version of the breeders equation (made most famous by all of the seminal work by R. Lande).


Why do we care so much about this little equation? It encapsulates many pretty heady ideas.  First and foremost that you can not have evolutionary change without genetic variation. That's right, natural selection by itself is not enough. You can have very strong selection for traits (such as running speed) to survive better with a predator around, but if there is no heritable variation for running speed, no (evolutionary) change will happen in the proceeding generations (and good luck with that tiger coming your way). However, once you have to consider multiple traits (running speed, endurance and hearing), we have to think about whether there is available genetic variations for combinations of traits, and whether these are "oriented" in a similar direction to natural selection. If not, it may be that evolutionary change with be slowed considerably (even if each traits seems to have lots of heritable variation). Of course if the genetic variation for all of these traits is pointing in the same direction as selection, then evolution may proceed very quickly indeed! The ideas get more interesting and complex from there, but they are not the for this discussion (the paper above by Jeff Conner, and this great review by Katrina McGuigan are definitely worth reading for more on this).

In any case, much thought has been given to how this G matrix can change both by natural selection and by other factors such as new mutation. Depending on how G changes, future evolutionary potential might change, which is pretty cool if you think about it! How might G change then? These are important ideas, because while we can estimate what G looks like, and how it might change (in particular due to natural selection), it is much harder to know what it will look like far in the future, making our ability to predict long term evolutionary change more difficult.
So what might help us predict G? One idea is that our knowledge of developmental biology will help us understand the effects of mutations, and thus G. If so, developmental biology could be a particularly powerful way of predicting the potential for evolutionary change, or lack there of (a so called developmental constraint).

To test this idea, I decided to use a homeotic mutation. Homeosis is the term used for when one structure (like an arm) is transformed (during development) to another (related) structure like a leg.  In fruitflies homeotic mutations are the stuff of legend (and nobel prizes), in particular for the wonderful cases of the poor critters growing with legs (instead of antenna) out of their heads, or four winged flies. You can see wonderful examples of mutations causing such homeotic changes in flies and other critters here.

In our case we used a much weaker and subtler homeotic mutation Ubx1, which causes slight, largely quantitative changes. For example with this mutation, the third set of legs on the fly would be expected to resemble (in terms of lengths of the different parts of the leg) the second set of legs (flies like all insects have 3 sets of legs as adults). We wanted to know whether when we changed the third legs to look like second legs, would the G for the transformed third leg look that of a normal third leg or a normal second leg? Thus we were trying to predict changes in G based on what we know (a priori) of development and genetics in the fruitfly.

So what did we find? The most important points are summarized in figure 2 and table 3 (if you want to check out the paper that is). The TL'DR version is this: Yes, the legs homeotically transformed like we expected, but G of the mutant legs did not really change very much from that of a normal third leg. In other words, our knowledge of development did not really help us much in understanding changes in G. There are a few reasons why (which we explain in the paper), but I think that it is an interesting punchline, and I will leave it up to you to decide what it means (and if our experiment, analysis and interpretation are reasonable and logically consistent).

I also really want to give a shout out to one of the co-authors (JH) who developed the particular statistical model that we ended up using. He developed a set of explicit models that really helped us test our specific hypotheses directly with the data and experimental design at hand. This is sadly rarely done with statistics, so it is worth reading just for that! I really think (hope?) that this combination of approaches can be very useful for evolutionary genetics. Let me know what you think!

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