A genetically stable population of squirrel has occupied the deserts of Arizona for several years. The gene pool of this squirrel population will most likely continue to remain stable if

the population size is reduced
the number of mutations is increased
frequent migrations occur
random mating occurs

random mating occurs

The gene pool of a squirrel population will most likely continue to remain stable if random mating occurs. Random mating ensures that individuals in the population have an equal chance to breed with any other individual, which helps prevent any one allele from becoming predominant or disappearing from the population. This promotes genetic diversity and helps maintain stability in the gene pool.

Reducing the population size can actually lead to a decrease in genetic diversity, as genetic drift becomes more significant in smaller populations. Genetic drift is the random change in allele frequencies due to chance events, and it can cause the loss of certain alleles or fixation of others, potentially reducing the genetic variation in the population.

Increasing the number of mutations, although it can introduce new genetic variation, may also disrupt the stability of the gene pool. Mutations are random changes in the genetic material, and while some mutations may be beneficial, many are neutral or harmful. The accumulation of harmful mutations can lead to decreased fitness and potential population decline.

Frequent migrations can introduce new alleles into the population, increasing genetic variation. While this can be beneficial for overall genetic health, it may also disrupt the stability of the gene pool if individuals with different genetic backgrounds frequently interbreed. Over time, frequent migrations can lead to the mixing of populations and potentially reduce the distinctiveness of the original gene pool.

In conclusion, random mating is the most likely factor to maintain a genetically stable population of squirrels in the desert of Arizona, as it promotes genetic diversity and prevents the loss or fixation of specific alleles.