3 Changes of Gene Frequency
There are two sorts of process through which changes of gene frequency, and consequently of genotype frequencies, are brought about:
- systematic processes, which tend to change the gene frequency in a manner predictable both in amount and in direction
- migration
- mutation
- selection
- dispersive process, which arises in small populations from the effects of sampling, and is predictable in amount but not in direction.
3.1 Migration
A large population consists of a proportion m of new immigrants in each generation, let the frequency of a certain gene(allele) be \(q_m\) ammong the immigrants and \(q_0\) among the natives. The frequency of the gene in the mixed population \(q_1\), will be:
\[q_1 = mq_m + (1-m)q_0 = m(q_m-q_0)+q_0\]
the change of gene frequency, \(\Delta q\),
\[\Delta q = q_1 - q_0 = m(q_m - q_0)\]
It shows the rate of change of gene frequency in a population subject ot immigration depends, as much be obvious, on the immigration rate and on the difference of gene frequency between immigrants and natives.
3.2 Mutation
3.2.1 Non-recurrent mutation
Consider first a mutational event that gives rise to just one representative of the mutated gene or chromosome in the whole population. This sort of mutation is of very little importance as a cause of change of gene frequency, because the product of a unique mutation has only a very small chance of surviving in a large population.
3.2.2 Recurrent mutation
Suppose gene A1 has a frequency u per generation to A2 and gene A2 has a frequncy v to v1. Then the change of gene frequncy in one generation:
\[\Delta q = up_0 - vq_0\]
where \(p_0\) and \(p_1\) are the initial frequncies of A1 and A2 alleles.
The point of equilibrium is when \(\Delta q = 0\)
About the effect of mutation on gene frequncy:
- Mutation rates are generally very low (\(10^-5\) or \(10^-6\) for most organisms), mutation alone can produce very slow changes of gene frequncy. on an evolutionary time-scale they might be important.
- Some research shows that reverse mutation (from mutant to wild type) is usually much less frequent than forward mutation.
3.3 Selection
The contribution of offspring to the next generation is call fitness of the individual, or sometimes the adaptive value, or selective value. If the differences of fitness are in any way associated with the presence or absence of a particular gene in the individual's genotype, then selection operates on that gene.
selective elimination may operate either through reduced viability (生存能力) or through reduced fertility (繁殖能力), in the widest sense, including mating ability, or through both.
The strength of the selection is expressed as the coefficient of selection, s, which is the proportionate reduction in the gametic contribution of a particular genotype compared with a standard genotype, usually the most favoured.
The contribution of the favoured genotype is taken to be 1, and the contribution of the genotype selected against is then 1-s. This expresses the fitnees of one genotype realtive to the other. Fitness, defined in this way as the proportionate contribution of offspring, should strictly speaking be called relative fitness.
The fitness of a genotype depends on the environmental circumstances in which the individual lives, and also on the genotype with respect to genes at other loci.
Table Degrees of dominance with respect to fitness (adapted from Fig. 2.1)
| degrees of domiance | \(A_1A_1\) | \(A_1A_2\) | \(A_2A_2\) |
|---|---|---|---|
| No dominance | 1 | \(1-\frac{1}{2}s\) | 1-s |
| Partial dominance | 1 | 1-hs | 1-s |
| Complete dominance | 1 | 1 | 1-s |
| Overdominance | 1-\(s_1\) | 1 | 1-\(s_2\) |
3.3.1 Change of gene frequency under selection
Consider the case of complete dominance with selection acting against the recessive homozygote.
Table 2.1 Selection against a recessive gene.
| \(A_1A_1\) | \(A_1A_2\) | \(A_2A_2\) | Total | |
|---|---|---|---|---|
| Initial frequencies | \(p^2\) | 2pq | \(q^2\) | 1 |
| Coefficient of selection | 0 | 0 | s | |
| Fitness | 1 | 1 | 1-s | |
| Gametic contribution | \(p^2\) | 2pq | \(q^2(1-s)\) | \(1-sq^2\) |