Hardy–Weinberg Principle Explains Genetic Stability in Populations
The Hardy–Weinberg principle
The Hardy–Weinberg principle is a mathematical model that predicts how allele and genotype frequencies remain constant in a population—unless evolutionary forces act upon it.
- This principle is foundational for understanding genetic stability and changes in populations.
Using the Hardy–Weinberg Equation
- The equation is expressed as:
$$p^2 + 2pq + q^2 = 1$$
- Where:
- $p$ = frequency of the dominant allele.
- $q$ = frequency of the recessive allele.
- $p^2$ = frequency of homozygous dominant individuals.
- $q^2$ = frequency of homozygous recessive individuals.
- $2pq$ = frequency of heterozygous individuals.
When using the Hardy–Weinberg equation, always start by calculating $q^2$ if you know the frequency of a recessive phenotype. This makes it easier to find $q$ and $p$.
How to Calculate Allele Frequencies
- Identify the frequency of homozygous recessive individuals ($q^2$).
- Take the square root of $q^2$ to find $q$ (recessive allele frequency).
- Use $p + q = 1$ to calculate $p$ (dominant allele frequency).
- Albinism is caused by a recessive allele.
- In North America, 1 in 20,000 individuals has albinism ($q^2$ = $0.00005$):
$$q$ = $\sqrt{0.00005}$ = $0.007$$
$$p = 1 - 0.007 = 0.993$$
Frequencies:
$$p^2 = (0.993)^2 = 0.986 \quad \text{(homozygous dominant)}$$
$$q^2 = 0.00005 \quad \text{(homozygous recessive)}$$
$$2pq = 2(0.993)(0.007) = 0.0139 \quad \text{(heterozygous/carriers)}$$
Applications of the Hardy–Weinberg Equation
1. Estimating Carrier Frequencies for Recessive Disorders
ExampleTay–Sachs Disease
- In a Mediterranean population, the frequency of affected individuals ($q^2$) is 0.0003:
$$q = \sqrt{0.0003} = 0.017$$
$$p = 1 - 0.017 = 0.983$$
Frequencies:
$$p^2 = (0.983)^2 = 0.966 \quad \text{(homozygous dominant)}$$
$$q^2 = 0.0003 \quad \text{(homozygous recessive)}$$
$$2pq = 2(0.983)(0.017) = 0.033 \quad \text{(heterozygous/carriers)}$$
2. Detecting Evolutionary Changes
Deviations from Hardy–Weinberg predictions indicate evolutionary forces like selection, drift, or gene flow are acting on the population.
3. Monitoring Genetic Diversity in Conservation
Conservation biologists use the equation to track genetic diversity in endangered populations, ensuring sufficient variation for adaptation.
Hardy–Weinberg as a Tool for Genetics
- The Hardy–Weinberg principle provides a framework for predicting genetic stability.
- It helps estimate allele frequencies, identify carriers of recessive diseases, and detect evolutionary changes.
- Populations rarely meet all Hardy–Weinberg assumptions, highlighting the dynamic nature of genetic variation.
- What are the five conditions of Hardy–Weinberg equilibrium?
- How can you use the Hardy–Weinberg equation to determine if a population is evolving?
- Why is a large population size important for maintaining genetic equilibrium?
- How does the Hardy–Weinberg principle illustrate the relationship between mathematical models and biological reality?
- What are the limitations of applying this model to real-world populations?
