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I recently got the opportunity to give a talk at both UNC and Eastern Carolina University on my current research project. The talk is available over at figshare if you’d like to scrutinize the details. I’ll give you some of the background here since the talks have no narration.

For starters I’m interested in males that provide only potential genetic benefits to their offspring; I’m also looking at the model where females are assessing male genetic quality based on a male morphological trait (such as an ornament, weapon or body size). This means that females expect to have offspring that are both more sexy and who survive better when she mates with a highly ornamented male, rather than a less well-ornamented male. The problem in this setting is the “lek paradox,” where eventually a female will do just as good to mate randomly as she would to be choosy, since there will be no genetic variation in ornamentation or condition. Usually in models we use mutation to maintain genetic variation for condition; I think I’ve found that being more specific about the type of mutation gives us a good theory that will resolve the lek paradox (yet again!).

The bighorn sheep is Alberta's provincial animal

The bighorn sheep is Alberta’s provincial animal (Photo credit: Wikipedia)

My question specifically deals with the scenario where males all start out with the same trait value and then grow that trait throughout their lives (I call this an age-dependent trait). Females can’t tell who is in good condition when looking just at young males. Several models have shown that age-dependent traits are a good strategy for males with relatively good health. They will have more matings over their lifetimes if they ramp up their signaling over their lifetimes. One particular model showed that if males are in good health, they should delay as long as possible, so as not to incur the wrath of natural selection, until they have had lots of opportunities to mate. Lower condition males should adopt a “hope I die before I get old” strategy and be as sexy as possible, as soon as possible.

The problem with these models is that they assume the full range of strategic variation is present in a particular population. They don’t represent changes over time; they just say what the best strategies are. I showed in a previous model that in a population-genetic simulation an age-dependent trait that starts out small will lead to the evolution of preferences and age-dependent traits. This makes sense from a dynamical point of view because selection is weaker at older ages: since older-aged males are only a small fraction of the population, any genetic variation in those males will not contribute much to the whole pot of variation. Selection can’t do much with genetic variation in older males, hence they are relatively free to be as extravagant as they want.

But what if old, sexy males are carrying mutations in their sperm that females cannot detect? I assumed that males will contribute harmful (deleterious) mutations to their offspring at a rate that is basically their age times a per-age mutation rate. I also assumed that the trait increases linearly. This is not realistic, as a lot of traits grow up to a point and then stop or even decline in old age. However, it gets the point across that young males are similarly sized and old males vary in their traits depending on their condition.

The results I have as of yet show that this process actually ensures continued genetic variation in the overall condition trait. The equilibrium female preference hovers above the equilibrium trait size, ensuring that females will always be going for the older, sexier males that carry mutations in their sperm. Mate choice therefore reinforces the process that keeps genetic variation in the population. I hope this result holds up under further mathematical scrutiny, because it’s a nice surprise.

I have a few snags to work out before I write this up; the feedback I got from the talks was invaluable. A few people had really great ideas, like a female strategy to screen sperm for deleterious mutations, and a research strategy to scan sperm samples for such mutations. Although my first reaction was “that’s going to be a lot of work!” my host chimed in that someone actually is doing this already. Wow!