Which one of the following factors will not affect the Hardy-Weinberg equilibrium?

The correct option is Constant gene pool.

The Hardy-Weinberg equilibrium is a fundamental principle in population genetics which states that the allele and genotype frequencies in a population will remain constant from generation to generation in the absence of other evolutionary influences.

The equilibrium is mathematically represented by the equation:

$p^2+2pq+q^2=1$

where $p$ and $q$ represent the frequency of the dominant and recessive alleles, respectively. For this equilibrium to hold true, several assumptions must be met, including random mating, a large population size, no mutation, no natural selection, and no gene flow (migration).

Let's evaluate the factors mentioned in the options:
1. Genetic recombination: The crossing over and independent assortment during meiosis produce new combinations of alleles, which can alter genotype frequencies and affect the equilibrium.
2. Genetic drift: This refers to random fluctuations in allele frequencies in small populations due to chance events, which directly disrupts the equilibrium.
3. Gene migration: Also known as gene flow, this involves the movement of alleles into or out of a population due to immigration or emigration, which changes the allele frequencies and disrupts the equilibrium.
4. Constant gene pool: A constant gene pool means that the collection of genes and their alleles within the population does not change. Since the gene pool remains stable and unchanging, it does not disrupt the allele frequencies, and therefore, it will not affect the Hardy-Weinberg equilibrium.