Question

In a population that meets the Hardy-Weinberg equilibrium assumptions, $81\mathrm{\%}$ of the individuals are homozygous for a recessive allele. What percentage of the individuals would be expected to be heterozygous for this locus in the next generation?

Short answer

Answer: 18%

Step-by-step solution

Understand Hardy-Weinberg equilibrium equation

The Hardy-Weinberg equilibrium equation is given by the formula: $p^2+2pq+q^2=1$, where p is the frequency of the dominant allele, q is the frequency of the recessive allele, $p^2$ represents the frequency of homozygous dominant individuals, $2pq$ represents the frequency of heterozygous individuals, and $q^2$ represents the frequency of homozygous recessive individuals in a population.

Calculate frequency of homozygous recessive individuals

We are given that $81\mathrm{\%}$ of the population are homozygous recessive individuals. To get the frequency, we need to convert this percentage into a decimal. So, $q^2=0.81$.

Calculate frequency of recessive allele

To find the frequency of the recessive allele (q), take the square root of the frequency of homozygous recessive individuals: $q=\sqrt{q^2}=\sqrt{0.81}=0.9$.

Calculate frequency of dominant allele

Since there are only two types of alleles for a locus in the Hardy-Weinberg equilibrium, we can calculate the frequency of the dominant allele (p) using the formula: $p=1-q$. So, $p=1-0.9=0.1$.

Calculate frequency of heterozygous individuals

Now, we can use the Hardy-Weinberg equilibrium equation to find the frequency of heterozygous individuals (2pq): $2pq=2\times 0.1\times 0.9=0.18$.

Convert frequency into percentage

Finally, to express the frequency of heterozygous individuals as a percentage, multiply the frequency by 100: $0.18\times 100=18\mathrm{\%}$. So, we would expect $18\mathrm{\%}$ of the individuals in the next generation to be heterozygous for this locus.

Key concepts

Homozygous Recessive Individuals

Homozygous recessive individuals are key to understanding genetic variations in a population. These are individuals who carry two copies of the same recessive allele for a specific gene. When considering the Hardy-Weinberg equilibrium, which serves as a model for genetic distribution in a population, homozygous recessive individuals are represented by the term $q^2$ in the equation. This model assumes no evolution is occurring—that is, the frequencies of alleles (gene variants) do not change over time.

In practical terms, if 81% of a population are homozygous recessive, this tells us the frequency of this genetic trait within that group. It's quite straightforward to evaluate the presence of this trait in future generations by using the Hardy-Weinberg equation, which in turn helps predict genetic diversity and potential for genetic diseases linked to recessive alleles.

Allele Frequency

Allele frequency is the cornerstone of population genetics. It measures how common a particular allele—or version of a gene—is in a population. Two frequencies are at play: one for the dominant allele (represented by $p$) and one for the recessive allele ($q$). These frequencies are crucial because they determine the genetic variability and potential evolutionary changes in a group of organisms.

The Hardy-Weinberg equation, $p^2+2pq+q^2=1$, hinges on the fact that the sum of these probabilities (p and q) is 1, or 100 percent. When the allele frequencies are known, as in our exercise where $q$ was calculated to be 0.9, scientists can gauge the genetic makeup of the next generation—helping to predict prevalence of diseases, response to selection pressures, or even how a population might adapt to environmental changes.

Heterozygous Individuals

Heterozygous individuals possess two different alleles for a given gene, one from each parent. In terms of the Hardy-Weinberg equilibrium, these individuals are significant because their genetic makeup includes both dominant and recessive alleles, represented by $2pq$ in the formula. This heterozygosity is essential for maintaining genetic diversity within a population, contributing to the ability of a species to adapt and survive in changing environments.

Knowing the percentage of heterozygous individuals, like the 18% calculated in the exercise, provides insight into the genetic structure of a population. This balance between homozygosity and heterozygosity shapes the overall genetic health and resilience against potential threats, such as diseases or changes in habitat.