Yesterday's post on evolutionary speed limits and Haldane's Dilemma has sparked some interesting discussion, and some of the comments have already started to move beyond the very simple scenario that I outlined. Next week, I'll post a couple of more complex examples, and look at the effect of things like a lower frequency of mutants in the starting population, what can happen with two mutations being selected at the same time, and whether mutations need to be fixed to be evolutionarily meaningful. I'll also go over a couple of basic concepts that might help in understanding those scenarios.
Today, I'm just going to respond to part of one of the comments that was left on the last post. This is mostly because it's an interesting question that deserves a thorough response, partly because the question involves some basic concepts that should be explained before I dive into more detail, and partly because it's Friday and I really don't want to spend the time plugging numbers in to work up another example.
Caligula, fairly early on in the comments, raises a point that involves a concept that is very basic to evolutionary biology: fitness:
Now let's apply your scenario. Assume the initial fitness 1.0, and assume that a benefical mutation occurs. But what is the physical interpretation of a mutation which increases one's absolute fitness beyond 1.0? Now, I do think that such an interpretation is possible, and it does not need to be ridiculous. In terms of viability, absolute fitnesses 1.1 and 1.0 behave the same, of course. There is no 110% chance of survival, after all. However, fitness 1.1 means that the offspring of a sexual parent can afford to lose a beneficial allele in segregation without necessarily suffering from reduced viability. So, under gene selection, fitness above 1.0 might still make a difference.
A distinction needs to be made here between relative fitness and absolute fitness. Absolute fitness measures (in some form - there are a couple of different measures that are possible) the reproductive output of a given form. Relative fitness measures how well different forms of the same trait do when compared with each other. The two measures look at very different things, and cannot be compared.
I'm going to write a post this weekend on fitness, as part of the series of basic concepts posts here at Scienceblogs. (John Wilkins has already written one, but he's looking at the concept from a slightly different perspective, so I'm going to do another. ) For the moment, the important thing to note is that the comment above seems to be confusing relative and absolute fitness a bit.
But even if fitness beyond 1.0 might be somewhat useful, I believe you understand my point. I think your scenario is a mirror image of Haldane's, rather than something qualitatively new. You likely are not suggesting that fitness can climb beyond 1.0. In order to ensure this, you must implicitly assume that the population is less-than-optimally adapted. So, when you say the a beneficial mutation with coefficient 0.1 occurs, you are probably implicitly assuming that the mean fitness of the population at that moment is at most 0.9. Compare to Haldane's scenario above to see that the math is now identical, even if the biological "background story" might be slightly different.
I see no problem at all with assuming that the population is not "optimally" adapted. Actually, I see more of a problem with assuming that any population is ever optimally adapted. All of the members of a population might, at a particular point in time, have the best available genetic makeup for a particular trait, but that does not necessarily mean that they have the best possible genotype.
This is actually where the difference between relative and absolute fitness becomes very important, because it shows a situation where the relative fitness of a geneotype can change without the need for any corresponding change in the absolute fitness. This is exactly what happened in the second example I showed, where the size of the population increased rapidly because of the increased number of survivors among those carrying the mutation. The absolute fitness of the old population did not change at all. The offspring of the "normal" individuals were just as likely to survive to reproduce ten generations in as they were before the first "mutant" showed up. The relative fitness of the old population, on the other hand, changed a great deal. Initially, it was the most fit genotype present (becuase it was the only genotype present). When the new form appeared, however, it was more fit than the "normal" form, and therefore had a higher relative fitness.