Final answer:
Mutation-selection balance is a state where new mutations in a population are balanced by natural selection. In the case of phenylketonuria (PKU), this balance involves the recessive allele associated with the condition. Understanding this balance requires knowledge of genetic probabilities, the use of Punnett squares, and the Hardy-Weinberg principle.
Step-by-step explanation:
The concept of mutation-selection balance refers to the balance in a population where the rate of new deleterious mutations is balanced by the rate at which these are eliminated by natural selection. When a population has a genetic disorder, such as phenylketonuria (PKU), caused by a recessive allele, the allele can persist in the population due to individuals who are carriers but do not express the condition (heterozygotes). PKU manifests in individuals with two copies of the recessive allele and can lead to cognitive deficits and other health issues if left untreated. Carriers may pass on the allele to their offspring without realizing it, as they do not show symptoms of PKU.
Using a Punnett square to analyze genetic probabilities, if two carriers of an allele associated with PKU (heterozygotes) have children, there's a 25% chance that their child will express the PKU phenotype. This probability is derived from the possible combinations of their alleles: 25% chance of two recessive alleles (resulting in PKU), 50% chance of one dominant and one recessive allele (carrier), and 25% chance of two dominant alleles (not a carrier).
Going further, the Hardy-Weinberg principle provides a mathematical baseline for studying allele frequencies in a non-evolving population. Deviations from expected values under this principle suggest that evolutionary forces, like mutation or selection, are acting on the population. Therefore, a population in mutation-selection balance for the PKU allele would be experiencing new mutations introducing the PKU allele at a rate that equals the rate of its removal by natural selection, ideally maintaining a constant allele frequency over time.