In their section ‘Regression Method Does Not Yield Causal Explanations’, they describe 3 traits: A) a ‘hanger-on’ trait leads its bearers to seek out and interact with individuals of high fitness – they conclude the regression predicts this is mutualistic; B) a jealous trait that seeks out high-fitness partners and attack them with the aim of reducing their fitness — they conclude the regression predicts this is altruism; C) a nurse trait that will seek out low-fitness individuals and make costly attempts to improve their fitness — they conclude the regression predicts this is spite.

However, they seem to have forgotten that relatedness is negative in each of their examples. Thus they got the direct and indirect fitness effects wrong. Re-interpreting the data in light of this error, we see that the regression predicts: A) selfishness, since indirect fitness is negative and direct fitness is positive; B) is a type of unclassified social trait that should never be favoured by selection since both indirect and direct fitness are negative; C) altruism, since indirect fitness is positive, but direct fitness is negative.

Notice that these predictions match up much better with an intuitive causal interpretation of the behaviours. The hanger on seems like a pretty selfish trait, not a mutualistic one. The jealous trait seems logically like it shouldn’t exist in nature, not that it is altruistic. The nurse trait seems cooperative, indeed altruistic, not spiteful.

I agree with the general point that these causal interpretations result from correlation and therefore may not correspond to actual causal relations. Indeed, this is evident from scenario A) where Allen et al say that the hanger on trait actually has no effect on the fitness of the actor or the recipient. Thus even the reinterpreted ‘selfish’ nature of this trait is wrong. In a lot of science, however, it is true that we are often left to try to untangle correlation from causation with incomplete data. This is the basis for virtually all studies in epidemiology, for instance. Moreover, I’m not sure that the regression approach is assumption free. In performing the regression on genetic data, we *assume* that genes have a causal effect on traits, and we *assume* that the patterns we see are not statistical artifacts. If these assumptions are false then our predictions will also clearly be false.

]]>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.

]]>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.

]]>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.

]]>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.

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

I am confused.

]]>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

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