Chapter 23: Evolutionary Processes and the Hardy-Weinberg Principle

Chapter 23: Evolutionary Processes

Introduction to Evolutionary Processes

Evolution is defined as a change in allele frequencies within a population over time. This process is driven by four main mechanisms, each with distinct consequences for genetic variation and fitness.

• Natural Selection: Increases the frequency of alleles that enhance reproductive success in a specific environment.

• Genetic Drift: Causes random changes in allele frequencies, especially in small populations.

• Gene Flow: Occurs when individuals migrate between populations, introducing or removing alleles.

• Mutation: Continuously introduces new alleles into the gene pool, modifying allele frequencies.

Any change in allele frequency constitutes evolution. Populations can evolve through any of these processes, even in the absence of natural selection.

23.1 Null Hypothesis: The Hardy-Weinberg Principle

Learning Objectives

• Describe the gene pool concept

• Calculate allele and genotype frequencies

• Understand the Hardy-Weinberg Equilibrium (HWE) concept

• Describe the five assumptions of Hardy-Weinberg

• Use Hardy-Weinberg to test for evidence of evolution

The Hardy-Weinberg Principle

Developed by G.H. Hardy and Wilhelm Weinberg in 1908, the Hardy-Weinberg Principle provides a mathematical model to study allele and genotype frequencies in a population under ideal conditions. It serves as the null hypothesis for evolutionary studies, predicting what happens when all individuals mate randomly and no evolutionary forces act on the population.

The Gene Pool Concept

The gene pool is the sum of all copies of all alleles at all loci in a population. It is the source of genetic variation that produces the phenotypic traits on which natural selection can act. Measures of genetic variation estimate the composition of the gene pool.

Hardy-Weinberg Principle: Mathematical Model

• Consider a gene with two alleles: A and a.

• Let p represent the frequency of allele A, and q represent the frequency of allele a.

• Because there are only two alleles, their frequencies sum to 1: $p + q = 1$

• Three possible genotypes: AA, Aa, and aa.

• The Hardy-Weinberg equation predicts genotype frequencies: $p^2 + 2pq + q^2 = 1$

  • Frequency of AA: $p^2$

  • Frequency of Aa: $2pq$

  • Frequency of aa: $q^2$

Estimating and Calculating Allele Frequencies

• Allele frequency formula: $p = \frac{\text{number of copies of the allele in the population}}{\text{sum of alleles in the population}}$

• For two alleles (A and a): $p = \frac{2N_{AA} + N_{Aa}}{2N}$ $q = \frac{2N_{aa} + N_{Aa}}{2N}$

• Where $N_{AA}$, $N_{Aa}$, and $N_{aa}$ are the numbers of individuals with each genotype, and $N$ is the total number of individuals.

Example Calculation

• Population 1 (mostly homozygotes): $N_{AA} = 90$, $N_{Aa} = 40$, $N_{aa} = 70$, $N = 200$ $p = \frac{180 + 40}{400} = 0.55$ $q = \frac{140 + 40}{400} = 0.45$ Genotype frequencies: AA: $90/200 = 0.45$ Aa: $40/200 = 0.20$ aa: $70/200 = 0.35$

• Population 2 (mostly heterozygotes): $N_{AA} = 45$, $N_{Aa} = 130$, $N_{aa} = 25$, $N = 200$ $p = \frac{90 + 130}{400} = 0.55$ $q = \frac{50 + 130}{400} = 0.45$ Genotype frequencies: AA: $45/200 = 0.225$ Aa: $130/200 = 0.65$ aa: $25/200 = 0.125$

Monomorphic and Polymorphic Loci

• If only one allele exists at a locus, its frequency is 1 (monomorphic locus; allele is fixed).

• If more than one allele exists, the locus is polymorphic.

Hardy-Weinberg Equilibrium (HWE)

If allele and genotype frequencies remain constant from generation to generation, the population is in Hardy-Weinberg Equilibrium. This occurs only if certain assumptions are met.

• After one generation of random mating, genotype frequencies are: AA: $p^2$ Aa: $2pq$ aa: $q^2$

Assumptions of the Hardy-Weinberg Model

• Random mating: No mate choice; gametes combine randomly.

• No natural selection: All individuals contribute equally to the gene pool.

• No genetic drift: No random changes in allele frequencies (large population size).

• No gene flow: No migration of individuals into or out of the population.

• No mutation: No new alleles introduced into the gene pool.

Violation of any assumption results in evolution.

Establishing Hardy-Weinberg Equilibrium

Even if a population does not initially fit Hardy-Weinberg proportions, a single generation of random mating will restore equilibrium genotype frequencies, provided the assumptions are met.

• Example: Initial genotype frequencies AA: 45%, Aa: 20%, aa: 35% After one generation: AA: 30.25%, Aa: 49.50%, aa: 20.25%

Genotypic Probabilities

• Probability of two A alleles: $p \times p = p^2$

• Probability of two a alleles: $q \times q = q^2$

• Probability of heterozygote (Aa): $p \times q + q \times p = 2pq$

Utility of the Hardy-Weinberg Model

Although no natural population meets all Hardy-Weinberg assumptions, the model is useful for:

• Predicting genotype frequencies from allele frequencies

• Identifying evolutionary mechanisms when observed frequencies deviate from predictions

Case Study: Testing for Hardy-Weinberg Equilibrium in Butterfly Populations

Background

• Two populations of endangered butterflies are studied for the Pgi gene (phosphoglucose isomerase), which affects flight metabolism.

• The gene has two alleles: A and C.

• If the gene is under selection, the population should NOT be in HWE for this gene.

Steps to Test for Hardy-Weinberg Equilibrium

1. Estimate genotype frequencies: Divide the number of individuals with each genotype by the total sample size.

2. Calculate observed allele frequencies: Frequency of A = frequency of AA + 0.5 × frequency of AC.

3. Calculate expected genotype frequencies: Use observed allele frequencies and the Hardy-Weinberg equation.

4. Statistically compare observed and expected values: Typically using a chi-square test.

Example Table: Observed & Expected Genotypes

Population	Data Type	AA	AC	CC	Allele Frequency (A)	Allele Frequency (C)
Population 1	Observed	0.249	0.498	0.253	0.498	0.502
Population 1	Expected	0.247	0.500	0.253	0.497	0.503
Population 2	Observed	0.369	0.208	0.423	0.473	0.527
Population 2	Expected	0.223	0.499	0.278	0.473	0.527

Interpreting Results

• If observed and expected genotype frequencies are similar, the population is likely in HWE (no evolution at that locus).

• If they differ significantly, the population is not in HWE (evolution is occurring at that locus).

• Statistical tests (e.g., chi-square) are required to confirm deviations from HWE.

Summary Table: Hardy-Weinberg Principle

Assumption	Effect if Violated
Random mating	Non-random mating alters genotype frequencies
No natural selection	Selection changes allele frequencies
No genetic drift	Random changes in allele frequencies (especially in small populations)
No gene flow	Migration introduces or removes alleles
No mutation	New alleles introduced, changing frequencies

Key Equation:

$p^2 + 2pq + q^2 = 1$

Where $p$ and $q$ are the frequencies of two alleles at a locus.

Example Application: Testing for Hardy-Weinberg Equilibrium in natural populations helps identify whether evolutionary processes are acting on a gene. If observed genotype frequencies deviate from expected values, one or more assumptions of the Hardy-Weinberg model are being violated, indicating evolution is occurring.

Additional info: The Hardy-Weinberg model is foundational in population genetics and is used as a baseline to detect evolutionary change. It is also applied in medical genetics, conservation biology, and evolutionary biology to understand genetic structure and dynamics of populations.