Crimea State Medical University, Simferopol

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The Cost Of Natural Selection

The Cost Of Natural
Selection

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In the introduction to The Cost of Natural Selection Haldane writes

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, 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.
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That is, the problem for the cattle breeder is that keeping

That is, the problem for the cattle breeder is that keeping

only the specimens with the desired qualities will lower the reproductive capability too much to keep a useful breeding stock.
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Haldane states that this same problem arises with respect to natural

Haldane states that this same problem arises with respect to natural

selection. Characters that are positively correlated at one time may be negatively correlated at a later time, so simultaneous optimization of more than one character is a problem also in nature. And, as Haldane writes 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 genes.
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Haldane proceeds to define the intensity of selection regarding "juvenile survival"

Haldane proceeds to define the intensity of selection regarding "juvenile survival" (that is,

survival to reproductive age) as  I=ln(So/S) where So is the proportion of those with the optimal genotype (or genotypes) that survive to reproduce, and S is the proportion of the entire population that similarly so survive.

Selection Intensity

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The proportion for the entire population that die without reproducing is

The proportion for the entire population that die without reproducing is

thus 1-S, and this would have been 1- So if all genotypes had survived as well as the optimal. Hence So-S is the proportion of "genetic" deaths due to selection. As Haldane mentions, if  So approx S, then I approx So-S.
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Origin of the term "Haldane's dilemma" Apparently the first use of

Origin of the term "Haldane's dilemma"

Apparently the first use of the

term "Haldane's dilemma" was by
Palaeontologist Leigh Van Valen in his 1963 paper "Haldane's Dilemma,
Evolutionary Rates, and Heterosis".
Van Valen writes :
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.
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Kimura (1960, 1961) has referred to this loss as the substitutional

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. A corollary of this is that, if an environmental change occurs that necessitates the rather rapid replacement of several genes if a population is to survive, the population becomes extinct.
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The Cost Haldane writes, I shall investigate the following case mathematically.

The Cost

Haldane writes,
I shall investigate the following case mathematically. A
population is

in equilibrium under selection and mutation.
One or more genes are rare because their appearance by
mutation is balanced by natural selection.
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A sudden change occurs in the environment, for example, pollution by

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 species is less adapted to the new environment, and its reproductive capacity is lowered. It is gradually improved as a result of natural selection. But meanwhile, a number of deaths, or their equivalents in lowered fertility, have occurred.
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The selective death that must occur for a gene to be

The selective death that must occur for a gene to be

substituted was called the cost of selection by the biologist J.B.S. Haldane. The higher the intensity of natural selection, the higher the amount of selective death (or infertility) there must be. A population cannot tolerate an indefinitely large amount of selective death: if selection is too strong it will drive the population extinct. The cost of selection places an upper limit on the rate of evolution: Suppose there are two alleles in a population, A and A' with fitnesses 1 and (1-s) and frequencies p and q (=1-p) respectively.
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In any generation, of the q A' -bearers, s will die

In any generation, of the q A' -bearers, s will die

without reproducing and (1-s) will survive likeA -bearers. A proportion, sq, of the population dies without reproducing because of selection at this locus. We can now define a ratio of the proportion of individuals in the population that survive to the proportion that die: sq die, and p+q(1-s) = 1-sq survive. The ratio in one generation is sq/(1-sq). The ratio is the same every generation until A' is eliminated. As selection operates each generation, more and more selective death accumulates.
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We can now define the total cost of natural selection as:

We can now define the total cost of natural selection as: C

= S [sq /(1 - sq)] (The summation is over all the generations it takes to fix the A gene.) If a population is to maintain itself, the individuals that survive have to produce sufficient extra offspring to make up for those that die before reproduction. Because of this there will be an upper limit to the possible cost of natural selection. If the ratio was 0.999/0.001, each survivor would have to leave 1000 surviving offspring, which would be much more difficult. The upper limit suggested by Haldane for a diploid population was one gene substitution per 300 generations. Haldane’s cost of selection was used to argue that the rates of molecular evolution are too fast to be explained by natural selection.
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J.B.S. Haldane 1892-1964 Haldane was born in Oxford to John Scott

J.B.S. Haldane
1892-1964

Haldane was born in Oxford to John
Scott Haldane, a physiologist, scientist, a philosopher and a Liberal,

and Louisa Kathleen Trotter, a Conservative. His younger sister, Naomi Mitchison, became a writer, and his uncle was Viscount Haldane and his aunt the author Elizabeth Haldane.