Haldane's dilemma

Haldane's dilemma, also known as the waiting time problem,[1] is a limit on the speed of beneficial evolution, calculated by J.

Before the invention of DNA sequencing technologies, it was not known how much polymorphism DNA harbored, although alloenzymes (variant forms of an enzyme which differ structurally but not functionally from other alloenzymes coded for by different alleles at the same locus) were beginning to make it clear that substantial polymorphism existed.

This was puzzling because the amount of polymorphism known to exist seemed to exceed the theoretical limits that Haldane calculated, that is, the limits imposed if polymorphisms present in the population generally influence an organism's fitness.

Motoo Kimura's landmark paper on neutral theory in 1968[2] built on Haldane's work to suggest that most molecular evolution is neutral, resolving the dilemma.

Although neutral evolution remains the consensus theory among modern biologists,[3] and thus Kimura's resolution of Haldane's dilemma is widely regarded as correct, some biologists argue that adaptive evolution explains a large fraction of substitutions in protein coding sequence,[4] and they propose alternative solutions to Haldane's dilemma.

In the introduction to The Cost of Natural Selection Haldane writes that it is difficult for breeders to simultaneously select all the desired qualities, partly because the required genes may not be found together in the stock; but, he writes,[5] 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.

Haldane states that this same problem arises with respect to natural selection.

And, as Haldane writes[5] [i]n 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 genes.

Haldane mentions the peppered moth, Biston betularia, whose variation in pigmentation is determined by several alleles at a single gene.

Against the originally pale lichens the darker moths were easier for birds to pick out, but in areas, where pollution has darkened the lichens, the cc moths had become rare.

Haldane mentions that in a single day the frequency of cc moths might be halved.

Another potential problem is that if "ten other independently inherited characters had been subject to selection of the same intensity as that for colour, only

One or more genes are rare because their appearance by mutation is balanced by natural selection.

A sudden change occurs in the environment, for example, pollution by smoke, a change of climate, the introduction of a new food source, predator, or pathogen, and above all migration to a new habitat.

It will be shown later that the general conclusions are not affected if the change is slow.

The problem statement is therefore that the alleles in question are not particularly beneficial under the previous circumstances; but a change in environment favors these genes by natural selection.

Note that Haldane's model as stated here allows for more than one gene to move towards fixation at a time; but each such will add to the cost of substitution.

[5] This is done by multiplying and dividing it by dq so that it is in integral form substituting q=1-p, the cost (given by the total number of deaths, 'D', required to make a substitution) is given by Assuming λ < 1, this gives where the last approximation assumes

[5] 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.

Haldane then continues:[5] The number of loci in a vertebrate species has been estimated at about 40,000.

It may take a good deal more, for if an allele a1 is replaced by a10, the population may pass through stages where the commonest genotype is a1a1, a2a2, a3a3, and so on, successively, the various alleles in turn giving maximal fitness in the existing environment and the residual environment.

[5]The number 300 of generations is a conservative estimate for a slowly evolving species not at the brink of extinction by Haldane's calculation.

Van Valen writes:[8] Haldane (1957 [= The Cost of Natural Selection]) drew attention to the fact that in the process of the evolutionary substitution of one allele for another, at any intensity of selection and no matter how slight the importance of the locus, a substantial number of individuals would usually be lost because they did not already possess the new allele.

Kimura (1960, 1961) has referred to this loss as the substitutional (or evolutional) load, but because it necessarily involves either a completely new mutation or (more usually) previous change in the environment or the genome, I like to think of it as a dilemma for the population: for most organisms, rapid turnover in a few genes precludes rapid turnover in the others.

Therefore, if it is necessary for the population to fix more than one gene, it may not have reproductive capacity to counter the deaths.

A. Sved[9] showed that a threshold model of selection, where individuals with a phenotype less than the threshold die and individuals with a phenotype above the threshold are all equally fit, allows for a greater substitution rate than Haldane's model (though no obvious upper limit was found, though tentative paths to calculate one were examined e.g. the death rate).

Additionally, the effects of density-dependent processes, epistasis, and soft selective sweeps on the maximum rate of substitution have been examined.

This parameter is generally called alpha (hence DFE-alpha), and appears to be large in some species, although almost all approaches suggest that the human-chimp divergence was primarily neutral.

However, if divergence between Drosophila species was as adaptive as the alpha parameter suggests, then it would exceed Haldane's limit.