Haldane's Dilemma and Selection Interference?

Haldane’s work was referenced by Kimura as support for the neutral theory of evolution, specifically the rather long time it took, about 300 generations, for a beneficial trait in a mammalian population (like cattle) to fix. The wiki entry is on Haldane’s dilemma:

Haldane's dilemma - Wikipedia

Surely one generation can “fix” all sorts of traits, just kill off every cow except a founding couple, and repeat the killing process enough through several generations, and lots of traits will fix simply by drift rather than by selection in less than 300 generations. The idea being that traits get fixed by increasing the speed of drift by having small populations for a protracted time.

Alternatively, suppose there is a single trait that resides in one male and one female, and this trait is strongly selected for (like say resistance to an epidemic). It will have comparable effects to that described in the previous paragraph by making it easier to “fix” other traits that may not have had much if any selective favorable traits at all previously. That is to say, even though these other traits were previously deleterious, they rode the train of a strongly favorable trait that suddenly emerged. I call this a selection interference scenario. I don’t know if that’s the proper term.

Alternative, simple acts of God or natural disasters could effect similar outcomes in helping to fix traits.

My guess is that Haldane modeled the population with weakish selection so that one beneficial trait wouldn’t interfere with the growth of another beneficial trait – that is to say, to limit selection interference, or maybe to sustain the population size, or both. I’m trying to understand what the dilemma is.

Assuming substitution of genes to take place slowly, one gene at a time over n generations, the fitness of the species will fall below the optimum (achieved when the substitution is complete) by a factor of about 30/ n , so long as this is small – small enough to prevent extinction. Haldane doubts that high intensities – such as in the case of the peppered moth – have occurred frequently and estimates that a value of n = 300 is a probable number of generations. This gives a selection intensity of 0.1.

Is that selection intensity the same as the s-coefficient?

regarding seleciton intensity, I, From wiki:

I = ln (s0/S)

Sal, you appear to be ignoring the highly salient–and fundamental–fact that cows and people are diploid.

That allows any recessive trait to “reside” (a bizarre word choice on your part) in a heterozygous state indefinitely.

Perhaps you should learn basic, high-school genetics first?


I’m not ignoring it.

That allows any recessive trait to “reside” (a bizarre word choice on your part) in a heterozygous state indefinitely.

Indefintely in a SMALL population?

But that’s beside the point.

Perhaps you should learn basic, high-school genetics first?

That’s a false insinuation on your part and veiled insult based on your false insinuation.

I didn’t say ALL alleles/traits would fix in one generation. That’s your false insinuation. Perhaps you could actually comment on the issue that was stated fabricate things I didn’t say.

There’s no insinuation in my question.

I didn’t say you did. I wrote that it appears that you have ignored diploidy in your rant. I stand by that.

That would be your incorrect inference. I insinuated nothing of the sort. I stand by my statement that it appears that you are ignoring diploidy.

I haven’t fabricated anything. I stand by my statement that what you wrote makes it appear that you are ignoring diploidy. Ignoring diploidy is consistent with not understanding basic, high-school genetics.

Not understanding basic genetics is common among creationists. It leads to gross underestimates of the capabilities of neutral evolution, for example.


Again, it appears that you are not familiar with another elementary genetic concept: genetic linkage. You do not need to coin a new term, you can just familiarize yourself with a sample of the thousands of papers containing the term “haplotype.”



I’m familiar with linkage. Anyway. I’m putting you on ignore, I don’t have time to deal with your false claims.

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Mr. Cordova,

Typically, in this context people address each other with first names, mine being John. I’m fine with that. A last name alone comes off as rude. If you are going to use my last name, please include the appropriate title as I did with yours above.

I have not made any false claims. I have qualified everything I have written.

If you don’t want to create the appearance of not knowing elementary genetics, you should write much more clearly and use terms that reflect your alleged understanding of the field.

But apparently not with haplotypes. :grin:


This sounds as if one is assuming that the process of a second gene substitution won’t start until the first substitution has been completed. That is, if I recall, one of the assumptions Remine made in his book. It is pretty absurd IMO.

My recommendation, @stcordova, is that you put away Remine’s book and work out the primary literature with the excellent population geneticists who participate here. That is, if they don’t mind rehashing this subject yet again, for the 10^100,000,000,000 th time.

(Hmmm… maybe that’s where you are trying to go?)


Ignoring people who know more on a topic than you do and who correct your many blunders seems to be your favorite pastime. You do however get lots of points for consistency. :slightly_smiling_face:


Evolution denialism seems to be full of such untenable assumptions. It’s as though they have no idea of the complexity of biology while at the same time claiming, “It’s so complex, it must have been designed!”

A similar one is the assumption that selection doesn’t act on existing genetic variation, as though nothing can happen until a new mutation occurs.



Thanks for your reply.

Assuming substitution of genes to take place slowly, one gene at a time over n generations …

That was from the WIKI entry describing Haldane’s Dilemma.

My recommendation, @stcordova, is that you put away Remine’s book and work out the primary literature with the excellent population geneticists who participate here. That is, if they don’t mind rehashing this subject yet again, for the 10^100,000,000,000 th time.

This discussion has nothing directly to do with defending or affirming Walter ReMine’s book. Where I was headed was the question of why selection intensity has to be so low?

Relative fitness is a quantity called w, variously described as 1+s or 1-s, where s is the selection coefficient. Unfortunately there is no universal convention…

W is absolute Darwinian fitness in simple models, and is the number of offspring born to each parent that are viable for reproduction. W can be described in terms of an individual with a trait, an allele, whatever. If we define some reference W for a reference allele, we can the define w_i for the other alleles as:

\LARGE w_i \equiv \frac{W_i}{W_{ref}}

which implies
w_{ref}=\frac{W_ref}{W_ref} = 1

the s-coefficient can be defined, using Allen Orr’s convention of using the most fit allele as the reference:

s_i \equiv w_{ref} - w_i

This convention by Orr isn’t universal, however…

Unfortunately, there is some problem translating fitness of alleles with fitness of genotypes and even worse for fitness phenotypes, etc. etc., but suffice to say this could get very complicated fast…

All that said, why did Haldane suggest low selection intensities in terms of relative fitness? If maintenance of the population size is the concern, one only need scale up the Absolute fitness numbers, right?

It seems more reasonable to say that strong selection intensities allow otherwise beneficial traits to be drifted out of the population before appearing in a single individual.

For example, it may be desirable for an individual to be fast and smart. One individual may have the fast trait and another the smart trait. If there is strong selection for the fast trait that wipes out all the individuals who are smart but don’t have the fast trait, the “beneficial” trait of being smart is selected out of the population. Whereas in a weak selection environment, all these beneficial traits have a shot at maybe getting incorporated into one eugenically ideal individual.

My understanding was that Haldane was merely observing cattle breeders trying to get the ultimate breed with all the desirable traits into one, and they couldn’t apply strong selection even when trying to do this intelligently. That is to say, killing off the all cattle missing favorable trait A but possessing favorable trait B won’t eventually result in an individual with both trait A and B somewhere down the line. This would actually be disastrous from a breeders perspective.

This is the problem of selection interference.

Kimura solved this dilemna by discovering neutral drift.

I think that wasn’t exactly the problem Haldane was trying to solve, but it was related.

“What problem was Haldane trying to solve?”


He states:

In this paper I shall try to make quantitative the fairly obvious statement that natural selection cannot occur with great intensity for a number of characters at once unless they happen to be controlled by the same gene.

So he was quantifying what was already obvious!

It is well known that breeders find difficulty in selecting simultaneously for all the qualities desired in a stock of animals or plants. This is partly due to the fact that it may be impossible to secure the desired phenotype with the genes available. But , in addition, especially in slowly breeding animals such as cattle, one cannot cull even half the females even though only one in a hundred of them combines the various qualities desired.

The situation with respect to natural selection is comparable.

Kimura solved a problem, but I don’t think THE problem Haldane was interested in, which was the
problem that breeders faced via intelligent selectoin but which was amplified in the case of natural selection. That selection intensity has to be reduced to get favorable traits to fix, not that the selection has to go to neutral. Kimura solved a related, but different problem, and he drew on Haldane’s work to solve that problem.

As an aside, I believe this is pic of Haldane. I want a suit just like that, and a cigar to go with it.

Happy New year!


I believe @Joe_Felsenstein has had thoughts on Haldane’s Dilemma.


Oh boy, have I had thoughts! In 1971, back when attention was being paid to the Cost of Natural Selection because it was thought that it was evidence for many gene substitutions being neutral, I wrote a paper, which I still think is the best-thought-out consideration of the meaning of that Cost. The paper,
whose abstract you will find here is
Felsenstein, J. 1971. On the biological significance of the cost of gene substitution. The American Naturalist 105, no. 941 (Jan. - Feb.): 1-11.
The paper is not free, but the abstract will give you a taste of the conclusions. In the next comment I will try to summarize some of my conclusions.
Unfortunately the literature on this Cost died out soon after, as it was concluded that the Cost (real or not) was not strong evidence for or against neutrality. So there was little followup, for the next 48 years.


Some conclusions. One can have an environmental change that reduces fitness, with or without there being an allele that, when it rises to frequency 1, compensates for that reduction of fitness. Or one can have an environmental change that increases fitness, or one can have a beneficial mutation that rises to frequency 1, not triggered by any environmental change. Haldane’s 1949 Cost of Natural Selection applied to the second case (environmental deterioration compensated by a substitution that it sets in motion). My 1971 reworking of Haldane’s argument assumes such an environmental deterioration every k generations. One can work out how large a reproductive excess there has to be (at low population density) to allow a population to survive this, if each substitution starts at an initial gene frequency p0. The result is close to Haldane’s. There is no assumption that one substitution finishes before the next starts, contrary to Wikipedia.


The Cost is that, if the environmental deteriorations come too often, or the initial frequency of the compensating alleles is too low, the population is gradually driven to extinction. The creationist Walter Remine has put forward an argument for a “cost” that is not a problem for survival of the population, but instead if too high it is inconsistent with our assumptions about what is changing the gene frequencies. Remine does not understand that this cost is different from Haldane’s. He also gets the history wrong in that he assumes that the attention paid to Haldane’s work in the 1960s was a desperate attempt to rescue evolutionary theory, rather than because it was thought that it had some bearing on arguments for or against neutral substitution. Remine’s cost is close to another “cost” put forward by James F. Crow and by Warren Ewens.


Finally, for a beneficial mutation that is not triggered by an environmental deterioration, there is no cost, because it raises the reproductive excess (the excess above 1 of the fitness when the population density is low). And all this has nothing to do with Muller’s Ratchet, because the theory of the Cost of Natural Selection uses the deterministic mathematics which assumes a big population and no genetic drift.


Oh, and there are many photos online showing Haldane in his later years. I got to see him in 1963, the year before he died, when he came to Madison, Wisconsin and gave a lecture. He didn’t look much like the photo posted here. It was taken in 1914, and shows him with some friends. One is Lewis Gielgud, the actor John Gielgud’s brother. In between them is Aldous Huxley, a longtime friend of Haldane’s.
Another photo I found online is at CreationWiki, where they identify as JBS Haldane a photo of his father, the important respiratory physiologist JS Haldane.


Many many thoughts :slight_smile: . Thank you for educating us @Joe_Felsenstein.

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