If 4 percent of a population in equilibrium expresses a recessive trait, what is the probability that the offspring of two individuals who do not express the trait will express it?

Verified step by step guidance

1. Identify that the problem is based on Hardy-Weinberg equilibrium, which is used to calculate allele frequencies in a population.
2. Recognize that the recessive trait is expressed by individuals with the homozygous recessive genotype (q^2). Given that 4% of the population expresses the recessive trait, set q^2 = 0.04.
3. Calculate q by taking the square root of q^2: q = \sqrt{0.04}.
4. Determine the frequency of the dominant allele (p) using the equation p + q = 1.
5. Calculate the probability that two heterozygous individuals (carriers) will have an offspring expressing the recessive trait, which is given by the probability of both parents being heterozygous (2pq) and the probability of their offspring being homozygous recessive (1/4).

Key Concepts

Hardy-Weinberg Equilibrium

The Hardy-Weinberg Equilibrium is a principle that describes the genetic variation in a population that is not evolving. It provides a mathematical model to predict allele frequencies and genotype frequencies in a population under certain conditions, such as no mutation, migration, or selection. This concept is essential for understanding how traits are distributed in a population and serves as a baseline for studying genetic changes.

Recessive Trait

A recessive trait is a phenotype that only manifests when an individual has two copies of the recessive allele. In the context of genetics, if a trait is recessive, it can be masked by a dominant allele. Understanding how recessive traits are inherited is crucial for predicting the likelihood of offspring expressing these traits, especially when considering the genotypes of the parents.

Punnett Square

A Punnett Square is a diagram used to predict the genotypes of offspring from a cross between two individuals. It allows for the visualization of how alleles combine during reproduction, helping to determine the probability of inheriting specific traits. In this scenario, using a Punnett Square can clarify the likelihood that offspring of two non-expressing individuals will express a recessive trait, given the allele frequencies in the population.