Final answer:
If the frequency of the dominant allele in a mouse population is x, then the frequency of the recessive allele is (1 - x). This concept is part of population genetics, which investigates the relationships between allele frequencies and resulting phenotypes. An example in mice involves individual coat colors influenced by dominant and recessive alleles at multiple loci, including an epistatic relationship between the genes responsible for agouti coat color and pigment production.
Step-by-step explanation:
If there are two alleles of a gene controlling coat color in a population of mice, and the frequency of the dominant allele is some frequency (x), then it must be true that the frequency of the recessive allele is represented by the variable (1 - x) to complete the allele frequency equation, where the sum of the frequencies of both alleles equals 1 (p + q = 1). This is due to the fact that allelic frequencies must add up to 100% of the gene pool for a given locus.
An example illustrating the relationship between alleles and phenotypes can be seen in the phenotypic ratio of coat colors in mice, which involves epistasis. In mice, the agouti coat color (A) is dominant over solid colors (a), and a separate gene (C) influences pigment production. The recessive c allele does not produce pigment, leading to an albino phenotype regardless of the A gene's alleles. For instance, any mice carrying the cc genotype will be albino.
When considering population genetics, the mathematical model that represents different alleles includes variables p and q. Here, 'p' is typically used to represent the frequency of the dominant allele, and 'q' the frequency of the recessive allele. These allele frequencies can help predict the frequencies of resulting genotypes. For instance, if 'p' represents the dominant allele frequency and 'q' represents the recessive allele frequency for a hypothetical allele, the frequency of the homozygous dominant genotype would be p², the heterozygous genotype 2pq, and the homozygous recessive genotype q².
Understanding the interaction between different alleles and how they contribute to the genetic structure of a population allows scientists to predict the distribution of phenotypes.