Hardy-Weinberg Equilibrium

BIOL 101: Hardy-Weinberg Equilibrium Study Notes

Introduction

• Topics discussed include the conditions necessary for non-evolution, the concepts of evolution in relation to allele frequency, and Hardy-Weinberg calculations.

• Important terms include:

  • Hardy-Weinberg Equilibrium: A model that describes a non-evolving population.

Key Ideas

Hardy-Weinberg Model Overview

• The Hardy-Weinberg model represents a theoretical framework for understanding genetic variation in a population that is not evolving.

• This model can be viewed as a baseline from which evolutionary changes can be measured.

Historical Figures

• Godfrey Hardy: An English mathematician known for his work in population genetics.

• Wilhelm Weinberg: A German obstetrician who independently derived the same conclusions as Hardy.

• Both Hardy and Weinberg contributed to the foundation of the Hardy-Weinberg equilibrium model.

Conditions for Non-Evolution

Five Conditions for Hardy-Weinberg Equilibrium

To maintain a non-evolving population, the following five conditions must be met:

1. Mutations: Must be absent (no new genetic variations).

2. Population Size: Must be large (effectively infinite) to avoid genetic drift.

3. Immigration/Emigration: Must be none (no gene flow).

4. Mating: Must occur randomly (no preferences).

5. Reproductive Success: Must be equal (no natural selection favoring one genotype over another).

Table of Conditions

Genetic Variation and Evolution

• The Hardy-Weinberg model describes an idealized state against which genetic variations in nature can be measured. It allows for the detection of evolutionary changes by indicating deviations from the equilibrium state.

• This means by defining what non-evolution looks like, we can identify evolution in action in natural populations.

Hardy-Weinberg Calculations

Population Example: Butterflies

• Population Data: Total number of butterflies = 1000

  • 490 AA (dark-blue wings)

  • 420 Aa (medium-blue wings)

  • 90 aa (white wings)

Genotype Frequencies

• Calculate the genotype frequencies using the following formulas:

  • Dark blue (AA): \frac{490}{1000} = 0.49

  • Medium blue (Aa): \frac{420}{1000} = 0.42

  • White (aa): \frac{90}{1000} = 0.09

Allele Frequencies

• Total alleles in the population = 2000 (since each butterfly has 2 alleles)

• Frequency of allele A:

  • A = \frac{(490 \text{ AA}) \times 2 + (420 \text{ Aa})}{2000} = \frac{1400}{2000} = 0.7

• Frequency of allele a:

  • a = \frac{(90 \text{ aa}) + (420 \text{ Aa})}{2000} = \frac{600}{2000} = 0.3

Predicting Next Generation Genotype Frequencies

• If the population remains in Hardy-Weinberg equilibrium,

  • The frequencies in the next generation will remain:

  • AA (0.49)

  • Aa (0.42)

  • aa (0.09)

Evolutionary Conditions

Conditions Leading to Evolution

If evolution were to occur, the following conditions would be present:

Hardy-Weinberg Equations

• Allele Frequencies: p + q = 1

  • Where p is the frequency of the dominant allele (A), and q is the frequency of the recessive allele (a).

• Genotype Frequencies: p^2 + 2pq + q^2 = 1

  • Where

  • p^2 = frequency of homozygous dominant (AA)

  • 2pq = frequency of heterozygous (Aa)

  • q^2 = frequency of homozygous recessive (aa)

Examples and Applications

Blue-footed Boobies Case Study

• Example given where frequency of recessive allele (w) is 0.4:

  • Frequency of non-webbed feet = 1 - q^2 ext{(for recessive trait)}

  • If q = 0.4 then p = 1 - 0.4 = 0.6.

Case Study for Cystic Fibrosis

• 4% of individuals are homozygous recessive (aa), hence:

  • q^2 = 0.04
    ightarrow q = 0.2
    ightarrow p = 0.8

  • Calculate heterozygote frequency: 2pq = 2(0.8)(0.2) = 0.32 ext{ (approx. 1 in 3)}

Conclusion

• The Hardy-Weinberg equilibrium provides a crucial framework for understanding allele and genotype frequencies in non-evolving populations. Through its application, one can gain insights into the evolutionary pressures acting on real populations.