Another process that may bring about change in the allelic frequencies is the influx of genes from other populations, commonly called migration or gene flow. One of the assumptions of the Hardy-Weinberg law is that migration does not take place, but many natural populations do experience migration from other populations. The overall effect of migration is twofold: (1) it prevents genetic divergence between populations and (2) it increases genetic variation within populations.

The effect of migration on allelic frequencies Let us consider the effects of migration by looking at a simple, unidirectional model of migration between two populations that differ in the frequency of an allele a. Say the frequency of this allele in population I is qI and in population II is qII (< Figure 23.10a and b). In each generation, a representative sample of the individuals in population I migrates to population II (< Figure 23.10c) and reproduces, adding its genes to population II's gene pool. Migration is only from population I to population II (is unidirectional), and all the conditions of the Hardy-Weinberg law apply, except the absence of migration.

After migration, population II consists of two types of individuals (< Figure 23.10d). Some are migrants; they make up proportion m of population II, and they carry genes from population I; so the frequency of allele a in the migrants is qI. The other individuals in population II are the original residents. If the migrants make up proportion m of population II, then the residents make up 1 — m; because the residents originated in population II, the frequency of allele a in this group is qII. After migration, the frequency of allele a in the merged population II (qij) is:

Therefore, change due to mutation in a single generation is extremely small and, as the frequency of p drops as a result of mutation, the amount of change will become even smaller (< Figure 23.9). The effect of typical mutation rates on Hardy-Weinberg equilibrium is negligible, and many generations are required for a population to reach muta-tional equilibrium. Nevertheless, if mutation is the only force acting on a population for long periods of time, mutation rates will determine allelic frequencies.

where qI(m) is the contribution to q made by the copies of allele a in the migrants and qn(1 — m) is the contribution to q made by copies of allele a in the residents. The change in the allelic frequency due to migration (Aq) will be equal to the new frequency of allele a (qI'I) minus the original frequency of the allele (qII):

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