Selection coefficient

Coefficient of Selection

A large and randomly mating population possesses high degree of variability at all times and the number of genetic recombinations on which natural selection operates is virtually unlimited. In existing environmental conditions such a population is well adapted but new phenotypes keep appearing from the new genetic combinations, some of which have advantage over the others in survival and reproduction and some are quickly eliminated by negative selection.

When the environment changes, new recombinations are made from the endless possibilities possessed by a large and heterozygous population to produce individuals that can adapt to new conditions. Then the selection force acts on the changing gene frequencies in a changing environment. Coefficient of Selection is a measure of the intensity of this selection force acting against the disadvantageous genotypes in a heterozygous population.

Selection against recessives

A vast majority of mutations are harmful in nature and when they are recessive they can express only under homozygous conditions and rapidly selected out. In such situations dominants are favoured by natural selection over the recessive mutants. So for every one offspring produced by dominants there is only 1-s offspring produced by the recessives. This is called Coefficient of Selection against the recessives and is depicted by the letter s, which is a positive number and fluctuates between 0 and 1. For lethal recessives the value of s is one (s=1) and for less damaging characters the value is proportionally lesser. The value of s will be zero for those characters which are neither advantageous nor disadvantageous, i.e. they are neutral.

Frequency of recessive gene is denoted by q while that of dominant gene by P. Formula to find out frequency of recessive gene after any number of generations is as follows:

qn =   qo___

1+ nqo

(where qois the initial frequency of recessive gene and qn is the frequency after n generations).

Advantageous mutations increase the fitness of an individual while the disadvantageous ones reduce it. Fitness is the extent to which an individual passes its genes to the future generations. Relative fitness is the ratio of offspring produced by dominants and recessives in a population from generation to generation. This is also called survival value or adaptive value.

If s = selection coefficient and if recessives are at a disadvantage than the dominants then the fitness in the next generation will be— 1: (1-s).

The following table shows relative fitness and frequencies of genes.






Initial ratio of  frequency





Relative fitness





Ratio after selection



q2 (1-s)

1- sq2

P = frequency of dominant gene; q = frequency of recessive gene; s = selection coefficient; P + q is always 1.0.

Frequency of the recessive gene in the present generation (qo) will be—

qo= Pq + q2

and the frequency in the next generation (q1) will be—

q1 = _Pq + q2 (1- s)

1 – sq2

The value of q gradually decreases because of the selection operating against recessive homozygote (aa) individuals and it will decrease rapidly if selection is intense. But when the value of q becomes very small, the rate of decrease will slow down.

Sometimes intense selection against recessives leads to their rapid elimination, as in the case of mutations that confer lethality or sterility to individuals. The value of q will then decrease rapidly and will stabilize at a very low level. Generally the coefficient of selection against recessives is small and therefore the rate of change in their gene frequencies remains slow. In that case sq2 will be so small in comparison with unity that 1-sq2 can be considered as one. 

Selection favouring dominant gene

If large number of individuals carrying dominant gene survive compared to the recessives, positive selection is said to be favouring dominant gene. Haldane calculated that the proportionate rate of increase of such a gene in a large and randomly mating population would be extremely slow but in a small population the increase can be rapid.

For example, it would take 11739 generations to increase the proportion of this gene from 0.000,001 to 0.000,002 with the above mentioned selection pressure. That means it is extremely difficult for a gene having mild selection pressure to establish itself if it is not aided by other factors, and the process in the case of a favourable recessive genes, although similar, is extremely slow. However, in a changing environment, under strong selection pressure a rapid change in gene frequencies can result. For example, plants and animals colonised land by a rapid burst of evolution during Silurian-Devonian period.

Gametic selection

When survival and fertilizing capacities of gametes are different, one type of gametes can have advantage over the others during fertilization, which is a segregational differential. If fitness of allele a is less than that of allele A, then relative fitness of gamete A and a will be 1: (1-s). If frequency of dominant allele is P then the frequency of recessive allele will be q (1-s).

P+q(1-s) = 1

P+q-sq = 1

1-sq = 1 (since P+q = 1)

In the next generation, the amount of change will be—

Delta q = q1– q2

= q (1-s)  _ qo


= -sq (1-q)


The value of delta q being negative suggests that the frequency of gene a will reduce in each generation.

Selection favouring heterozygotes (=Heterosis)

The adaptive value of heterozygotes is generally superior to that of homozygotes. The phenomenon is known as heterosis. Gene frequencies in a large and randomly mating population are determined by the selection coefficient against the homozygotes. If s1 is the selection coefficient against the dominant gene and s2 against the recessive gene and if s1 and s2 are constant, the equilibrium will be a stable one. But if s1 and s2 are disturbed by any reason, then the equilibrium will return back to the same level gradually.

There will be no change in gene frequencies if s1P = s2q.

It is presumed that all types of heterozygotes are similar in fitness while homozygotes are inferior. But sometimes heterozygotes may have variability in fitness among themselves and may be competing to survive. The condition in which different alleles are maintained in stable equilibrium in one type of environment is called balanced polymorphism, which is of great significance in evolution, as it provides reserves from which a population can draw should the conditions change.  

However, if selection is against heterozygotes, the consequences will be entirely different. For instance, detrimental recessives are harboured in heterozygous state and frequency of heterozygote carriers is always higher than the homozygous recessives, which express themselves from time to time but get selected out. Examples of deleterious recessives in man are: Alkaptonuria, which occurs in one out of a million persons but the gene is carried by1/500 heterozygotes. Similarly, sickle cell anaemia occurs in 1/500 individuals but the frequency of heterozygotes is 1 in 10. Cystic fibrosis incidence is very low, one in 1000 individuals but heterozygote carriers occur at one in every 16 persons. Similarly, only one in 25,000 persons suffers from phenylketonuria but one in every 80 individuals is a carrier.