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Date: 2009/06/10 15:57:28, Link
Author: Steve Schaffner
[quote=Wesley R. Elsberry,June 10 2009,10:59][/quote]
I just got here by way of the TWeb thread (where I was commenting as sfs1). I'd be interested in helping out with an evaluation of Mendel's Accountant, although I don't know that I'll be able to run the program. I've done a fair bit of genetic modeling in the past.

I can think of several standard pop gen predictions off the top of my head that in theory should be easy to test, although there may be some practical difficulties. It's not clear that the program can run long enough to test most predictions, and it's not clear that the authors' terminology is standard enough to figure out how to construct a test.

(By the way, I recognize some names here from my t.o days. Hi.)

Date: 2009/06/11 13:02:51, Link
Author: Steve Schaffner
I may have missed something, but I haven't seen anything in the v. 1.4.1 runs that was clearly wrong, i.e. that suggested a bug in the implementation (other than the broken option for fixed selection coefficient). Which doesn't mean there aren't any bugs, but they are not obvious.

What is clear is that the default parameters for beneficial alleles are very low. Their justification for having such a low maximum beneficial effect strikes me as plausible-sounding nonsense.

It's also clear that their basic model is not one from evolutionary biology. The essential process they're modeling is the accumulation of mildly deleterious mutations, ones that have such a small functional effect that they are invisible to natural selection. This only occurs because the population starts out in a state of genetic perfection, compared to which the new mutations are deleterious. A real population would never have become that optimized, precisely because the different choices of allele are indistinguishable by NS.

For those who have the program running . . . Can it provide more output? Comparing results with theory would be much more straightforward if one could count only the number of mutations that have fixed, rather than all present in the population; it would also be useful to see the allele frequency spectrum. (And if it can't do those things, then it is of no interest as a population genetics tool.)

Date: 2009/06/11 23:09:00, Link
Author: Steve Schaffner
Quote (Zachriel @ June 11 2009,20:41)
Take a look at the distribution of beneficial mutations.

Looks right to me, given your parameters. You're getting 10 mutations/individual for 100 individuals, or 1000 mutations per generation. Of those, 1/100,000 is beneficial, so you're only getting one beneficial mutation every 100 generations. Those are the tiny blips. Once in a while one or two of them drift up to an appreciable, and the mean number of beneficial alleles per individual climbs above 1.0.

None of them fix though, which is not surprising, since they're almost all effectively neutral. Which means that you should have one fixing by chance every 20,000 generations, plus some probability from the tail at higher selection coefficient.

Date: 2009/06/12 21:56:33, Link
Author: Steve Schaffner
There may be some value in checking Mendel's Accountant, to see whether it really implements the model that it claims to, but I don't see much point in trying to cobble together a new program to simulate evolution here. That is a major research project, with many unknown parameters, i.e. a truly realistic simulation of evolution isn't possible yet.

The important questions about MA, assuming the program isn't simply fatally flawed, concern the model that it is implementing. For the default values, you don't have to run the program to know that it will produce genetic collapse of the population -- that's inevitable, given the assumptions of the model. The model assumes a large number of mildly deleterious mutations, so mild that they are unaffected by purifying selection. It also assumes purely hard selection, in which lower fitness translates directly into loss of fertility for the population, and few beneficial mutations (which are also of small effect), independent of the fitness of the population (i.e. no compensating mutations). Given those assumptions, the population will inevitably decline towards extinction, since there is no force counteracting the relentless accumulation of deleterious mutations. The model stands or falls on those assumptions; the code is a side-issue.

Date: 2009/06/13 07:01:57, Link
Author: Steve Schaffner
There is a good list of forward simulation (as opposed to coalescent) programs here. The ones I'm familiar with (apart from MA) are intended to model the behavior of sequences and mutations, not the global evolution of species.

Date: 2009/06/16 18:54:30, Link
Author: Steve Schaffner
Quote (Zachriel @ June 14 2009,08:47)
If the genome is 3e8 bases in size (or any such large number) and there is an average of one mutation per child, then we expect that ~1/3 of the children will *not* have mutations. If each mother produces 6 children, then chances are that each new generation will include many individuals
without mutations. (E.g. mice often have several litters of 4-10 pups.)

True, although that's probably not a good model for humans, who have something between 1 and 3 deleterious mutations (probably) per birth, and more likely close to the top end than the bottom of the range. That doesn't mean that the population has to collapse genetically. It just means that in the steady state, everyone is carrying a fair number of deleterious mutations, with those having the most being the least likely to reproduce.


If we use truncated selection, heritability=1, mutations=1, seed=30, all else default, this is what we see.

Note that the population survives only because of truncation selection, which is not a realistic process for such slightly deleterious mutations. In this model, each individual will have on average one new mutation with a negative selection coefficient of something like 10-6 or 10-7, but selection is nonetheless effective enough to perfectly sort the fitness of the individuals and eliminate only the least fit.


It's interesting to see how the deleterious mutations ride along with the beneficial mutations until fixation before being weeded out.

Yes. Selective sweeps in action.

Date: 2009/06/18 16:59:32, Link
Author: Steve Schaffner
Quote (Bob O'H @ June 18 2009,01:30)

My advice: keep away from heritability.  It complicates matters, and is dependent on the genetic variation in the population.  I suspect Sanford et al. don't really understand quantitative genetics: certainly Sanford makes some mistakes because of his lack of understanding in Genetic Entropy.

Modeling is easier if you simply work with the selective advantage of the genotype, rather than the selection coefficient for a partly heritable trait. Here the partly heritable trait is fitness itself, which makes my head hurt.

Indeed, but it can get arbitrarily close to 0, so it doesn't make any practical difference (unless you're working with continuous populations, when you end up with nano-foxes).

What kind of fitness are we talking about here, though? Since MA keeps the population constant, it is implicitly using relative fitness. In that case, introducing an arbitrary scaling factor into the fitness doesn't matter; it's only the ratio of fitnesses that matters. It seems to me that the model treats fitness as being relative until it get very small, at which point it is treated as absolute. But there is no simple way to determine absolute fitness from relative fitness.

This seems like a basic point, but I don't understand what the program is trying to model here.

Date: 2009/06/18 20:53:29, Link
Author: Steve Schaffner

Basically, he is applying reductions in heritability twice. The heritability function itself, and then this random procedure for selecting reproductive winners by re-ranking them before truncation and passing to the next generation. We could modify the divisor to some function(randomnum) and adjust the degree and type of randomness for picking winners {something like randomnum^N}. It's just another way of introducing random factors into the choice of winners and losers which should already have been accounted for in the heritability function.

The net result is a significant reduction in the effect of selection.

It would make more sense if it were described in terms of some other phenotype with an effect on fitness. The phenotype has a genetic component and an environmental (or random) component, i.e. has a heritability. The phenotype then confers a fitness, which is the probability of successful reproduction. The number of successful offspring is also drawn from a random distribution, which is what's being done in this bit of code (I guess treated as a binomial distribution).

As a model of selection that seems reasonable (apart from the way the noise scales), but expressing it in terms of the heritability of fitness I find hard to understand -- fitness isn't a phenotype, it's a measure of the success of a phenotype. And the whole thing is pretty convoluted, when the essence of the model could be captured simply by assigning a fitness to the genotype and then calculating the number of offspring. This is a model of evolution written by a breeder rather than by a population geneticist, I would say.

Date: 2009/06/19 13:05:28, Link
Author: Steve Schaffner
Quote (Bob O'H @ June 19 2009,12:02)
I haven't looked at the code, but if we assuming a constant population size and discrete generations, then (ignoring recombination and mutation), the way to model this is to assume that each parent has a fitness si.  The offspring are then drawn from a multinomial distribution with probability for the ith parent being


(this would reduce to a binomial distribution if there were only 2 parents).  The multinomial sampling is genetic drift.

Yes, I've written a program for that kind of model, except that I imposed selection in the differential survival of the offspring. Including options for truncation selection and a few other things, it amounted to all of 158 lines, including comments, white space and the multinomial routine.


You can treat log(si) as you would any standard trait: it's additive, so you can add the genetic and environmental effects.

I haven't thought about this before. Does adding environmental effects do anything more than reduce the effective selection coefficient?

Date: 2009/06/19 13:33:49, Link
Author: Steve Schaffner
Quote (slpage @ June 19 2009,13:09)
I am still wondering why they think that constraining the outcomes to a constant population size is biolgically realistic.

It's a feature of many population genetics models. It has the advantage of being simple. How accurate it is depends a lot on what organism you're looking at.

Of course, there's a big difference between using models to analyze how particular aspects of evolution work and trying to model the entire process well enough to say whether it can occur.

Date: 2009/06/23 19:44:21, Link
Author: Steve Schaffner
Quote (slpage @ June 23 2009,19:13)
I don't mean just allowing it to grow willy nilly - that is not realistic, either.  But if they want to claim 'most realistic' then it seems to me employing non-universal constraints negates that claim.

True, but I doubt variation in population size would have much effect on the long-term fate of the population.

I also gather that while deleterious mutations are allowed to accumulate and not reduce, that beneficials are allowed to be lost.  Is that correct?

I haven't been running the program, but I haven't seen anything obviously wrong with how they handle beneficial and deleterious mutations. In the real world, deleterious mutations of very small effect really do accumulate, and most beneficial mutations really are lost.

Date: 2009/07/09 22:15:59, Link
Author: Steve Schaffner
I'm afraid I haven't been following your program's progress in detail. What distribution of fitness effects do your mutations have?

Date: 2009/07/25 21:27:18, Link
Author: Steve Schaffner
[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:

Hi John,

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 “Yes”, 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: 287–302), 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. 1855–1861.)) 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.