A phenotypic view of evolution Evolution in Structured Populations

A conversation with a physicist: Some thoughts on fitness

This past week I went over to the university at a nearby city, and talked to some physicists interested in complex systems, and among other things, biology. As seems to be the nature of physicists turned biologists, I was impressed with some of their ideas, but also impressed with their lack of knowledge of biology, and, to be blunt, their view that biologists were basically inept when it came to theoretical issues. Perhaps the most impressive simple example was one (note no names, but an American, not a Brazilian) wanted to publish a paper showing that the Fisher’s fundamental theorem was not universal. Now that is a paper that would be met with a large yawn. Aside: I find FFT to be a fun mathematical truism, given a set of assumptions, but I seriously doubt anybody has taken its universality seriously in a very long time.

FFT equation 7

Fisher’s fundamental theorem is a mathematical truism, but only if the underlying assumptions are met. It is well known that these assumptions will only rarely be exactly met in real systems, and that this theorem should be used to guide intuition, rather than to make quantitative predictions.

However, there were two issues that came up that I want to cover more seriously. Today I will talk about fitness, and next week I will talk about variance in evolution.

I was telling this physicist about some of my ideas, and in the process talking about “fitness”. In the course of this discussion I was repeatedly told that unless we really understood terms we couldn’t proceed. So as a result I kept being more and more specific, sadly, about everything but fitness. It was only later that it dawned on me that he didn’t think I knew what I meant by fitness. I actually think that this is one of the problems that physicists have with biologists. They tend to come up with wacky examples of where a naïve concept they attribute to biologists doesn’t apply, and then say that because this definition does not apply in this case we have no idea what we are talking about. This is, of course, a bit disturbing for somebody who has published models in which naïve definitions of fitness don’t apply (e.g., Goodnight et al. 2008. Complexity 13(5): 23-44). In short, I think I have a pretty danged good idea of what I mean by fitness.


I might just know something about fitness!      bankai.    (from http://pt.wikipedia.org/wiki/Ichigo_Kurosaki)

What this physicist was missing is that when I talk about “fitness” it is in fact shorthand for “temporal component of fitness”. Please bear with me on this, since I have never attempted to define fitness in a way that I would apply to all situations. But if I were to attempt to define fitness it would define it to be something along the lines of:

Fitness is the probability that an organism will start a lineage that will persist for an arbitrary period into the future.

I think a good boundary would be speciation, thus, I might narrow the definition of fitness to be:

Fitness is the probability that an organism will start a lineage that will eventually participate in the founding of a new species.

Obviously, this is an unworkable definition, but still, there are reasons why a truly general definition would need to be something along these lines. For example in the paper cited above (Goodnight et al. 2008. Complexity 13(5): 23-44) we examined the dynamics of a predator that was subject to mutations with how aggressive it was. What we found was that the optimal aggressiveness was a balance between growing quickly, but not so quickly that a lineage exhausted its prey and went extinct. The interesting thing was that in the short term these “optimal” lineages were always invasible by a more aggressive mutation, but in the long term these more aggressive lineages always went extinct. The point is that very aggressive lineages had an apparent high fitness over the course of a few generations, but a low fitness over a longer term. A true definition of fitness would have to incorporate this.


long term pred prey study

τ is a measure of aggressiveness, or how quickly the predator consumes the prey. Note that in this example a highly aggressive (cyan and dark blue) predator appears, but eventually burns out and goes extinct. (Figure from Goodnight et al. 2008. Complexity 13(5): 23-44.)

So, how do we deal with this obviously unworkable definition of fitness? The answer that my colleague did not understand is that we work with components of fitness. As Arnold and Wade (1984. Evolution 38: 709-718)pointed out so long ago, as long as episodes of selection are described in a multiplicative manner (that is conditional probabilities) it is valid to study a component of selection. In the predator prey example, it is perfectly valid to define a component of fitness that is lifetime reproductive success. If you did this you would discover that for this fitness component, the “fitness” of an aggressive mutant was very high. A biologist who chose their words very carefully would acknowledge that there may well be other later selective events that would counter the effects of this fitness component, but that would not invalidate conclusions about differences within lifetime fitnesses.

Since we are being careful, there are caveats even here. That is, technically the selection events have to be independent, and that will often not be the case. I think that this is another issue between biologists and physicists, however. That is, that in theoretical physics there is this concept of an exact solution. I seriously doubt that any theoretical biologist believes that we could develop a model that gave an exact solution in a living system. It is simply too complicated. Thus, as long as different episodes of selection, and thus temporal components of fitness, are not too highly correlated the assumption of independence will not hurt the ears of biologists too badly.


Unless you are really sensitive, a small amount of non-independence among selection episodes should not hurt your ears. (http://factsaboutbirds.blogspot.com.br/2010/08/desert-animals-list.html)

So, in sum, is life time reproductive success “fitness”? The answer is clearly no, since multigenerational processes can also enter into the equation. Instead, we need to think of it as a temporal fitness component. Am I apologetic about frequently referring to life time reproductive success as fitness, even though I know it is technically incorrect? No, I am not. Referring to it as something else is cumbersome, and honestly, in nearly every experimental system I am aware of, it is the major component of true fitness. It is basically a convenient shorthand and something that is usually pretty close to the truth.


In “truth” as in horseshoes sometimes close is good enough.  (http://lrossentertainment.wordpress.com/tag/outdoor-games-wedding-ideas/ photo credit, Sam Beebe, Ecotrust)

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  1. Bjørn:

    We never went anywhere with the fundamental theorem. He gave an example where it won’t work. His example was a moving front where selection was one direction in one area and the opposite in another area. Basically because the two processes are unrelated, (selection on one hand, a moving front on the other), trying to describe them with a single parameter (variance in fitness) is doomed to failure. I pointed out that within the confines of Fisher’s assumptions it was a mathematical truism, and that biologists (at the time I could not remember who) had called it the “not so fundamental theorem”.

    He basically wanted to demonstrate that the fundamental theorem did not always hold. Interestingly, I suspect most biologists would not be surprised by that result, but would be hard pressed to tell you why it wouldn’t hold. In any case, it never got further than a late night discussion over beer.

  2. I have made the same observations of physicists vs. biologists (indeed, education-wise I am both myself).

    The difference arise, I think, as you allude to that the kinds of systems that the two fields work on are very different in complexity. Physical systems are mostly way, way simpler than biological systems, so math can be more precise. And when math is applied with more rigor, more rigorous definitions are required.

    But in biology we work with many concepts that we cannot agree to one universal definition. Examples are species, complexity, modularity, evolution, evolvability, life, genes. And that is just fine. Clearly biologists have learned a lot about biology even if we can’t come up with definitions that always work.

    Plug: http://pleiotropy.fieldofscience.com/2014/04/pragmatic-definitions-in-biology.html

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