Chapter 20 part 1

Population Genetics and Evolution

Introduction to Population Genetics and Evolution

Population genetics studies the distribution and change of allele frequencies under the influence of evolutionary processes. Evolution is defined as the change in genetic variation (e.g., allele frequencies) in a population over time.

• Evolution is not the improvement of species toward an optimum, adaptation toward an ideal form, or changes that an individual organism experiences.

• Key evolutionary forces include random mating, genetic drift, natural selection, migration, and mutation.

Evolutionary Genetics

Evolutionary genetics focuses on how genetic variation is inherited and changes over time within populations.

• Allele frequency: The proportion of a specific allele among all alleles at a genetic locus in a population.

• Genotype frequency: The proportion of a specific genotype among all individuals in a population.

• Calculating allele frequencies from genotype frequencies and vice versa is fundamental for understanding population structure.

• Hardy-Weinberg equilibrium provides a mathematical model for predicting genotype frequencies from allele frequencies under ideal conditions.

Random Mating and Hardy-Weinberg Equilibrium

Random mating is a key assumption of Hardy-Weinberg equilibrium. It does not change allele frequencies but allows prediction of genotype frequencies.

• If p is the frequency of allele G and q is the frequency of allele g, then:

$p + q = 1$

• Genotype frequencies: $GG = p^2$, $Gg = 2pq$, $gg = q^2$

• Random mating maintains allele frequencies but changes genotype frequencies to Hardy-Weinberg proportions.

Example Table: Hardy-Weinberg Genotype Frequencies

Genotype	Expected Frequency
GG	$p^2$
Gg	$2pq$
gg	$q^2$

Conditions for Hardy-Weinberg Equilibrium

• Individuals select mates at random

• Population size is infinite

• No natural selection

• No migration into population

• No mutation introducing new alleles

When these conditions are met, genotype frequencies can be predicted from allele frequencies.

Calculating Allele and Genotype Frequencies

Allele and Genotype Frequencies in Human Populations

Genotype and allele frequencies can be calculated from observed counts in a population. If the population is in Hardy-Weinberg equilibrium, expected frequencies can be compared to observed frequencies using the chi-square test.

Example Table: Genotype and Allele Frequencies

Genotype	Observed Count	Observed Frequency	Expected Frequency
MM	342	0.332	0.331
MN	500	0.486	0.489
NN	187	0.182	0.180

• Allele frequencies: $F(M) = p = \frac{2(342) + 500}{2 \times 1029} = 0.575$; $F(N) = q = \frac{2(187) + 500}{2 \times 1029} = 0.425$

• Genotype frequencies sum to 1: $p^2 + 2pq + q^2 = 1$

Estimating Allele Frequencies with Complete Dominance

When a trait shows complete dominance, allele frequencies can be estimated assuming Hardy-Weinberg equilibrium.

• For a recessive disease allele frequency $q = \sqrt{1/2000} = 0.022$

• Carrier frequency: $2pq = 2(0.022)(0.978) = 0.0437$

• Homozygous wild-type frequency: $p^2 = (0.978)^2 = 0.9558$

Extending Hardy-Weinberg Calculations to Multiple Alleles

For loci with more than two alleles, the sum of allele frequencies equals 1.

• Example: Blood type alleles A, B, O with frequencies $p$, $q$, $r$

$p + q + r = 1$

Example Table: Blood Type Genotype Frequencies

Genotype	Expected Frequency
AA	$p^2$
Ai	$2pr$
BB	$q^2$
Bi	$2qr$
AB	$2pq$
ii	$r^2$

Hardy-Weinberg Equilibrium for X-linked Genes

Reaching equilibrium for X-linked genes takes longer due to differences in allele transmission between males and females.

• Allele frequencies fluctuate more in early generations before stabilizing.

Non-Random Mating

Types of Non-Random Mating

Non-random mating alters genotype frequencies but not allele frequencies. Two main types are inbreeding and assortative mating.

• Inbreeding: Mating between relatives increases the frequency of homozygotes.

• Assortative mating: Mating based on similarity (positive) or difference (negative) in traits.

Example Table: Inbreeding and Genotype Frequencies

Generation	A1A1	A1A2	A2A2
1	0.250	0.500	0.250
2	0.375	0.250	0.375
3	0.437	0.125	0.437
4	0.468	0.063	0.468

• Inbreeding coefficient ($F$): Probability that two alleles are identical by descent.

• For first cousins: $F = (\frac{1}{8})^2 = \frac{1}{64}$ for a specific allele; $F = 4(\frac{1}{8})^2 = \frac{1}{16}$ for any allele.

Assortative Mating

• Positive assortative mating: Increases homozygosity for specific traits.

• Negative assortative mating: Increases heterozygosity for specific traits.

Genetic Drift in Finite Populations

Genetic Drift

Genetic drift is the random fluctuation of allele frequencies due to chance events in finite populations.

• More pronounced in small populations.

• Can lead to fixation (frequency = 1) or loss (frequency = 0) of alleles.

Example Table: Effect of Population Size on Genetic Drift

Population Size	Allele Frequency Fluctuation
10	High
100	Low

Founder Events and Bottlenecks

• Founder event: A small group establishes a new population, leading to non-representative sampling of alleles (e.g., Ellis-van Creveld syndrome in isolated populations).

• Population bottleneck: A sharp reduction in population size reduces genetic variation and changes allele frequencies (e.g., kinked tail in cheetahs).

Summary: Population genetics provides the mathematical and conceptual framework for understanding how evolutionary forces shape genetic variation in populations. Key concepts include Hardy-Weinberg equilibrium, allele and genotype frequency calculations, the effects of non-random mating, and the impact of genetic drift, founder events, and bottlenecks.