Joined: June 2009
[I posted this on TW, and Dr. GH asked me to repost it here. It mostly addresses the genetic model used in MA, rather than the implementation.]
John Sanford wrote me several weeks ago, replying to my previous comments on his model of evolution. I have just replied to his email. Since I do not have permission to quote his words, I tried to make my mail stand on its own as much as possible; if context is not clear, please ask me for clarification. (Or reply to praise my limpid prose style, or to tell me I'm a nitwit, or whatever. I.e. the usual.)
Here is my reply:
Viewed from a high level, populations crash in your model because of several features in the model. First, it has a high rate of very slightly deleterious mutations, ones that have too weak an effect to be weeded out by selection. Second, the accumulation of these mutations reduces the absolute fitness of the entire population. Third, beneficial mutations (and in particular compensating mutations) are rare enough (and remain rare enough even as the fitness declines) and of weak enough effect that they do not counteract the deleterious mutations. As far as I can tell, any model of evolution that has these features will lead to eventual extinction -- the details of the simulation shouldn't matter at this level. (Indeed, Kondrashov pointed out this general problem in 1995; I wouldn't be surprised if others have made the same point earlier.)
So there is no question that if these premises of the model are correct, organisms with modest population sizes (including all mammals, for example) are doomed, and Darwinian evolution fails as an explanation for the diversity of life. If one wishes to conclude that evolution does fail, however, it is necessary to show that all of the premises are true -- not merely that they are possible, but they reflect the real processes occurring in natural populations. From my perspective, that means you need to provide empirical evidence to support each of them, and I don't think you have done so.
Turning specifcially to issue of soft selection: it matters here becuase it severs the connection between relative fitness and absolute population fitness. The essence of soft selection is that the absolute fitness of the population does not change, regardless of the relative fitness effects of individual mutations that accumulate in the population. As Kimura put it, "Therefore, under soft selection, the average fitness of the population remains the same even if the genetic constitution of the population changes drastically. This type of selection does not apply to recessive lethals that unconditionally kill homozygotes. However, if we consider the fact that weak competitors could still survive if strong competitors are absent, soft selection may not be uncommon in nature." (p. 126, The Neutral Theory of Evolution).
(An unimportant point: my understnading from reading Wallace is that he introduced the term "soft selection" in the context of accumulating deleterious mutations (especially concerns about them raised by Jim Crow), not in connection with Haldane's dilemma or the rate of beneficial substitution. If you have a citation that provides evidence otherwise, I would be interested in seeing it. The basic model of soft selection actually goes back at least to Levene in 1953 (predating Haldane's work by a few years), when he was considering the maintenance of varied alleles in a mixed environment. So this is not a new idea, and it is (contra your suggestion) is a well-defined concept, and one that is in fact often considered in the context of deleterious mutations and genetic load. Are there any recent published discussions of genetic load that do not consider soft selection as a possibility?)
In your reply to me, you said that the default in your program is purely soft selection. I don't know what the actual default is for deciding whether fitness affects fertility (since I have not run the program), but the online user manual says that an effect on fertility is in fact the default ("The default value is ‚ÄúYes‚Äù, which means that fertility declines with fitness, especially as fitness approaches zero.") Regardless of the direct effect on fertility, the use of an additive model of fitness means that deleterious selection in your program ultimately ceases to be soft, since accumulating additive fitness always ends up or below zero, at which point the relative fitness values no longer matter. In a model of soft selection, the magnitude of the populations's fitness makes no difference at all; only the relative values of individuals have an effect. In your program, that is not the case. So in practice, your program does not seem to model long-term soft selection.
(As an aside, I'm afraid I don't understand your comments about having tested a multiplicative model of fitness. You say that in such a model, as the mean fitness falls, you see increasing numbers of individuals inherit a set of mutations that give a fitness less than or equal to zero. Under a multiplicative model, the fitness is given by f = (1-s1) * (1-s2) * (1-s3) *..., where s1, s2, s3... are the selection coefficients for the different mutations. If the various s values are less than 1.0 (as they must be if the mutations have been inherited), then f must always be greater than 0. I don't see how you can have a multiplicative model with the reported behavior. Perhaps you have a noise term that is still additive?)
The real question is whether or not soft selection is actually important and needs to be modeled. As you say, soft selection is a mental construct -- but so is hard selection. You dismiss it as a real phenonenon, but do you have any evidence to support your point here? Your populations crash because of very slightly deleterious mutations, and as far as I know, virtually nothing is known about what kind of fitness effects these mutations have. In general, there has been very little empirical work distinguishing soft from hard selection (or equivalently, quantifying the difference between absolute and relative fitness). The only recent study I know of to attempt it looked only at plant defense traits in A. thaliana (Kelley et al, Evolutionary Ecology Research, 2005, 7: 287‚Äì302), and they found soft selection effects to be more powerful than hard effects. So I do not see good empirical grounds for rejecting an important role for soft selection.
This isn't to suggest that all selection is soft, or that many mutations don't have real effects on the population fitness -- but there are good theoretical and empirical reasons to think that the net effect of many deleterious mutations is smaller when they are fixed in the population than their relative fitness would suggest. (Not that we actually know what the distribution of relative fitnesses looks like, either. You can pick a functional form for that distribution for the purpose of doing a simulation, but it based on no real experimental evidence. Are deleterious mutations really so highly weighted toward very slight effects? There are just no data available to decide.
If much selection actualy is soft, then humans (and other mammals) could have in their genome millions of deleterious mutations already, the result of hundreds of millions of years of evolution; this is the standard evolutionary model. These mutations would have accumulated as population sizes shrank slowly (relaxing selection) and functional genome sizes grew (increasing the deleterious mutation rate). Indeed, many functional parts of the genome may never have been optimized at all: the deleterious "mutations" were there from the start. The results of this process are organisms that are imperfect compared to a platonic ideal version of the species, but perfectly functional in their own right. In your response, you cite systems biology's assessment that many organisms are highly optimized to counter this possibility. I do not find this persuasive, partly because systems biologists can also cite many features that are suboptimal, but mostly because no branch of biology has the ability to quantify the overall optimization of an organism, or to detect tiny individual imperfections in fitness.
Alternatively, beneficial mutations may be more common and of larger effect than in your default model. I pointed to one recent example of a beneficial mutation with a much larger selective advantage than your model would allow (lactase persistence in human adults). In turn you suggest that such large effects occur only in response to fatal environmental conditions, but the example I gave does not fall in that class. Do you have any empirical evidence that the selective advantage is restricted to such small values?
Michael Whitlock has a nice discussion of this kind of model in a paper from 2000 ("Fixation of new alleles and the extinction of small populations: drift load, beneficial alleles, and sexual selection." (Evolution, 54(6), 2000, pp. 1855‚Äì1861.)) His model tries to answer very similar questions to yours. With the choice of parameters that he thinks is reasonable, he finds that only a few hundred individuals are needed to prevent genetic decline.
He also discusses many of the same issues that we're discussing here. For example, on the subject of soft selection he writes, "We also have insufficient information about the relationship between the effects of alleles on relative fitness in segregating populations and their effects on absolute fitness when fixed. Whitlock and Bourguet (2000) have shown that for new mutations in Drosophila melanogaster, there is a positive correlation across alleles between the effects of alleles on productivity (a combined measure of the fecundity of adults and the survivorship of offspring) and male mating success. This productivity score should reflect effects of alleles on mean fitness, but the effects of male mating success are relative. Without choice, females will eventually mate with the males available, but given a choice the males with deleterious alleles have a low probability of mating. Other studies on the so-called good-genes hypothesis have confirmed that male mating success correlates with offspring fitness (e.g., Partridge 1980; Welch et al. 1998; see Andersson 1994)."
His conclusion about his own model strikes me as equally appropriate to yours: "We should not have great confidence in the quantitative values of the predictions made in this paper. In addition to the usual concern that the theoretical model may not include enough relevant properties of the system (e.g., this model neglects dominance and interlocus interactions, the Hill-Robertson effect, the effects of changing environments), the empirical measurements of many of the most important genetic parameters range from merely controversial to nearly nonexistent."
Using this kind of model to explore what factors might be important in evolution is fine, but I think using them to draw conclusions about the viability of evolution as a theory is quite premature.