Use the Hardy–Weinberg principle to calculate allele and genotype frequencies in populations and state the conditions when this principle can be applied (the two equations for the Hardy–Weinberg principle will be provided, as shown in the Mathematical requirements)

SouravNovember 1, 2024

Answer

The Hardy-Weinberg principle provides a mathematical framework for understanding allele and genotype frequencies in populations that are not evolving. This principle can be applied under specific conditions and is represented by two key equations.

Hardy-Weinberg Equations

1. Allele Frequencies:
   • p+q=1
   • Here, $p$ represents the frequency of the dominant allele, and $q$ represents the frequency of the recessive allele.
2. Genotype Frequencies:
   • p2+2pq+q2=1
   • In this equation:
     • p2 is the frequency of homozygous dominant individuals (AA),
     • 2pq is the frequency of heterozygous individuals (Aa),
     • q2 is the frequency of homozygous recessive individuals (aa).

Conditions for Application

The Hardy-Weinberg principle can be applied under the following conditions:

1. No Mutations: There are no changes to alleles due to mutations.
2. Random Mating: Individuals mate randomly without preference for specific genotypes.
3. No Gene Flow: There is no immigration or emigration affecting allele frequencies.
4. Large Population Size: The population is sufficiently large to minimize the effects of genetic drift.
5. No Natural Selection: All alleles confer equal fitness, meaning no selective advantage for any genotype.

If any of these conditions are violated, the population may evolve, and allele frequencies may change over time.

Calculating Allele and Genotype Frequencies

To illustrate how to calculate allele and genotype frequencies using the Hardy-Weinberg principle, consider an example with a population of 100 pea plants where 16 are homozygous recessive (yy):

1. Calculate q2:
   • The frequency of the homozygous recessive genotype (yy) is given by:
     q2=16/100=0.16
2. Calculate $q$:
   • To find the frequency of the recessive allele (y):
     q=q2=0.16=0.4q=q2​=0.16​=0.4
3. Calculate p:
   • Using the equation $p+q=1$:
     $p=1-q=1-0.4=0.6$
4. Calculate Genotype Frequencies:
   • Now, use $p$ and $q$ to find genotype frequencies:
     • Frequency of homozygous dominant (YY):
       p2=(0.6)2=0.36p2=(0.6)2=0.36
     • Frequency of heterozygous (Yy):
       $2pq=2(0.6)(0.4)=0.48$
     • Frequency of homozygous recessive (yy):
       q2=(0.4)2=0.16q2=(0.4)2=0.16
5. Summary of Frequencies:
   • Homozygous dominant (YY): 36%
   • Heterozygous (Yy): 48%
   • Homozygous recessive (yy): 16%

References

1. Biology LibreTexts. (n.d.). Hardy-Weinberg Principle of Equilibrium. Retrieved from https://bio.libretexts.org/Bookshelves/Introductory_and_General_Biology/General_Biology_(Boundless)/19:_The_Evolution_of_Populations/19.01:_Population_Evolution/19.1C:_Hardy-Weinberg_Principle_of_Equilibrium
2. Khan Academy. (n.d.). Hardy-Weinberg equilibrium: Mechanisms of evolution. Retrieved from https://www.khanacademy.org/science/ap-biology/natural-selection/hardy-weinberg-equilibrium/a/hardy-weinberg-mechanisms-of-evolution
3. Nature Education Scitable. (n.d.). The Hardy-Weinberg Principle. Retrieved from https://www.nature.com/scitable/knowledge/library/the-hardy-weinberg-principle-13235724
4. Germanna Community College. (2012). Hardy-Weinberg Equilibrium [PDF]. Retrieved from https://germanna.edu/sites/default/files/2022-03/Hardy%20Weinberg%20Equilibrium.pdf