The Hardy-Weinberg equilibrium is a principle that predicts how gene frequencies in a population's gene pool will remain constant over time, assuming certain conditions are met. These conditions include no mutation, random mating, no gene flow, infinite population size, and no selection. If any of these conditions are violated, then the Hardy-Weinberg equilibrium can be disrupted.

Option A: Genetic recombination

Genetic recombination refers to the process by which genetic material is rearranged or exchanged between different chromosomes or between different regions within the same chromosome. It can introduce new gene combinations into a population but does not itself change allele frequencies unless it is associated with differential survival or reproduction. Thus, genetic recombination alone does not disrupt Hardy-Weinberg equilibrium.

Option B: Genetic drift

Genetic drift is a stochastic effect that occurs due to the random sampling of alleles when gametes are formed, and it can greatly influence the allele frequencies in small populations. It can cause random changes in allele frequencies over time, thereby affecting the Hardy-Weinberg equilibrium.

Option C: Gene migration

Gene migration or gene flow involves the transfer of alleles from one population to another. When individuals move between populations, they can introduce new alleles to the gene pool, or change the relative frequencies of existing alleles, both of which disturb the Hardy-Weinberg equilibrium.

Option D: Constant gene pool

A constant gene pool implies no change in allele frequencies over time, which is in line with the Hardy-Weinberg principle. Therefore, by definition, this factor does not affect or disrupt the Hardy-Weinberg equilibrium.

Based on these explanations, Option D: Constant gene pool is the factor that will not affect the Hardy-Weinberg equilibrium as it represents the ideal condition where allele frequencies remain consistent, which is central to the Hardy-Weinberg principle.