And now for something completely different.

Up until this point I have been writing my own thoughts about my own little world. Given that Allen, Nowak and Wilson recently published a sure to be controversial paper on inclusive fitness (Allen, Nowak and Wilson 2013 Limitations of inclusive fitness. PNAS early edition), and given the role I played in their thinking (i.e., none at all), I figured I should weigh in on their paper. So, on with the show.

The main point of the paper is that fitness components are not additive. That is, that you cannot make a clean partitioning between the effects of a behavior on the actors direct effects on themselves, and their indirect effects on others. They quote Hamilton’s original definition in support of this. They are of course correct; however, here they might have done well to read Williams:

“No matter how functionally dependent a gene may be, and no matter how complicated its interactions with other genes and environmental factors, it must always be true that a given gene substitution will have an arithmetic mean effect on fitness in any population.” (G.C.Williams, Adaptation and Natural Selection).

The point is that at any given moment it must be true that you can divide anything, including fitness, into components by whatever criteria you choose. The other point is that I have used that quote for years as a straw man, and I simply cannot believe that I just used it in a positive setting! What they are really complaining about is whether or not that partitioning is meaningful. Their point is thus incorrect in that yes, you can partition fitness into direct and inclusive components, but it is correct that in a non-additive system that partitioning will be good for the moment, and will qualitatively change every time the conditions change.

Their second point is that this applies both to Hamilton’s original formulation of inclusive fitness and to the neighbor modulated, or direct, fitness approach. They make the point that the direct fitness approach is a regression method, and regression is not a causal analysis, that in fact, it is little more than a glorified correlation:

As we all know correlation is not causation. The way regression is supposed to be used is to find the best prediction of Y given a known X. This is the classic problem that I discussed as recently as last week. Yes, we should all be using path analysis, yes it is a lot of work and, as often as not, we don’t use path analysis. Nevertheless, there has been a lot of darn good work on selection has used a regression approach, so I, at least, hesitate to dismiss correlational approaches out right.

There is another important point here that strikes close to home. That is, contextual analysis not only is a regression approach, but as I have shown elsewhere (Goodnight, 2013. Evolution 67: 1539-1548) contextual analysis uses the SAME regression equation used in the direct fitness approach. So, why do I like contextual analysis and not like the direct fitness approach? It turns out that there is a difference between the two approaches, and the difference is exactly the problem that Allen et al. are complaining about. When using contextual analysis a tangent is calculated for the fitness surface at the point that the population currently occupies. This tangent is used to calculate the strength of selection acting on the population at the current moment. This calculation is frequently used to project the future potential response to selection, but the this is an extension, not a basic part of the model. In contrast, the direct fitness approach establishes the equation at the current state of the population, and then the equation is solved for the conditions under which the slope (dW/dX) equals zero. This, then is the problem that Allen et al. identified. Using the kin selection approach we extrapolate from the current conditions to identify the optimal conditions that the population is presumably moving towards. This extrapolation works fine in a linear system, but such extrapolations are notoriously problematical in complex non-linear systems.

So, as far as this point goes, Allen et al. and I are on the same page. Kin selection has a serious problem because it is an optimality approach that uses extrapolation of the current conditions in a non-linear complex system to predict the outcome of evolution. We actually saw the same thing happen with optimal foraging theory. Twenty years ago it was a hot topic. Now days it basically doesn’t exist. When I ask people about it the general answer seems to be that it only works in overly simplistic situations, and at most can provide a qualitative guide to the real world, which is acknowledged to be a complex system.

There is actually a fairly confusing ambiguity in the paper over this topic. The real problem with kin selection stems from it being based in optimality theory, and thus requires simplistic assumptions so that it is possible to extrapolate from current to future conditions. In my mind this would bring all optimality approaches into question. Nevertheless in the discussion they bring in game theory, which is a variant on optimality theory, as one of the saviors of sociobiology. It seems to me that if kin selection is suspect, then game theory ought to be just as suspect. Perhaps I am wrong, and perhaps one of my readers can explain it to me.

It is the last part where Allen et al and I part ways. In their last section (common-sense approaches to evolutionary theory) they state: “The target of selection is not the individual, but the allele or the genomic ensemble that affects behavior.” This just floored me. They have just explained to us that biological systems are complex, and yet somehow they fail to understand that genetic systems are complex? Kin selection can be useful for developing an intuitive or qualitative grasp of social evolution, but for many reasons, including those given by Allen et al. it fails when it is applied to the real world. Similarly, purely genetic models can be useful for developing intuitive and qualitative understandings of evolution, but for many of the same reasons they fail when applied to the real world. Selection acts on the phenotype, not genes, and that is a fact. Even in rare situations where we see selection acting on the sequence of a gene, it is in fact acting on the genes phenotype, not on the gene as a purveyor of information.

Like New Zealand runner Nikki Hamblin, Allen, Nowak and Wilson ran a good race, but ultimately fell short. (http://www.stuff.co.nz/sport/other-sports/5522807/Hamblin-protest-fails-after-world-champs-fall)
I agree that inclusive fitness can be a useful heuristic. My “beef” is with those who say that inclusive fitness is the ultimate explanation for all evolved social behavior. These claims are based on using linear regression, not to generate testable hypotheses as Wade suggests, but to write equations that are “always true”. My goal in this paper was to point out that the results obtained this way are not meaningful, unless there are modeling assumptions or additional empirical observations to make meaning from them.

Ben;

Thanks for all of your input. I am trying to cover a fair amount of territory in this blog, and often step outside my comfort zone, and my knowledge of game theory models is fairly limited.

It is clear that we mostly agree on the analysis of kin selection. It is unfortunate that the controversy has Balkanized the various “factions”. The correlational approaches of neighborhood modulated fitness is a good example. Multiple regression is fine as long as you (1) don’t extrapolate far beyond your data (i.e., the current conditions), and (2) you follow Wade and Kalisz’s suggestion of treating it as an hypothesis that should be further examined using manipulative methods.

I really do think that kin selection has value in the same way that optimal foraging theory has value. It is a nice heuristic that can be used in simple models to develop an intuition on what to expect from the real world. It is sad that we are forced into arguing against this approach, when instead we should be arguing that it is a good, if somewhat unsatisfying, first step.

One further thing: Game theory is not an optimality theory. While early game theory focused on evolutionarily stable states, the focus in recent decades is much more on dynamics and stochastics.

Hi Charles,

Thank you for your analysis of our paper, and I’m glad we agree on many points.

With regard to the “target of selection”, it is of course inarguable that selection acts on phenotypes. Our point here is that the focus of analysis in evolutionary theory should be on whether a given genetic modification can establish itself in a population. Genotype-phenotype mappings (of arbitrary complexity) can be part of this analysis. Perhaps we caused confusion by using the word “target”, and if so, I apologize for that.

Mike;

Thanks for the kind words, and good to see you reading my blog!

Also thanks for bringing up your 1990 paper. It actually brings to mind the pair of papers on Impatiens:

Stevens, Goodnight and Kalisz 1995. American Naturalist 145: 513-526

Kelly 1996. American Naturalist 147: 899-918

One interpretation of these papers is that Stevens et al. used contextual analysis to identify that multilevel selection appeared to be acting in Impatiens. Kelly then did a much more detailed causal study that, among other things, confirmed that the correlational study of Stevens et al. was indeed causal.

I hope I am not offending John or misrepresenting his work, which is an excellent study.

Bassel:

Williams is dead, so we cannot know his reasoning. My interpretation of his reasoning is this: If you have an infinitely large population then for any locus you will be able to divide the population into three groups based on the genotype at that locus. This works even if there are multiple alleles e.g., A/A, A/other, other/other. You can then do a regression of fitness on the number of A alleles (2, 1 or 0 A alleles), and from that assign a fitness value (y-hat) to each genotype, and calculate the average effect of that allele on fitness.

This works fine as long as you have random mating, random interactions, and the population is indeed infinite. In this case each regression will be independent, and they can be done one at a time. If the population violates these assumptions then you need to do a multiple regression, and that is an Np hard problem.

The main problem, which I alluded to in the post, is that when the system is non-linear the regression changes as gene frequencies change. My point is that Williams is correct, the regression can in principle be done; however, it is so context dependent that it is essentially meaningless.

To your last question, no, I strongly suspect that Williams would allow a gene to have an arithmetic mean effect of zero. I am quite sure he would allow neutrality.

Charles, how does Williams know that : “it must always be true that a given gene substitution will have an arithmetic mean effect on fitness in any population”?

Doesn’t imply that neutral mutation can’t be fixed by drift?

I am confused.

Very nice analysis.

Wade and Kalisz (1990)drew an experimental road map for going from correlation to causation, urging that the gradients from phenotypic selection analyses be treated as ‘hypotheses’. These hypotheses can be tested using various experimental means for identifying agents of selection and varying their intensity.

Mike