Population Genetics: Principles, Calculations, and Evolutionary Forces

Population Genetics

Introduction to Genetic Variation

Population genetics is the study of genetic variation within populations and the evolutionary forces that shape this variation. All organisms exhibit genetic variation, which can be observed in traits such as human physical diversity or the spotting patterns of Asian lady beetles.

• Genetic variation refers to differences in DNA sequences among individuals in a population.

• Variation is essential for evolution and adaptation.

• Examples: Human height, skin color, and beetle spot patterns.

25.1 Genotypic and Allelic Frequencies

Describing the Gene Pool

Population genetics quantifies genetic variation using genotypic and allelic frequencies, which describe the composition of a population's gene pool.

• Genotypic frequency: The proportion of individuals with a specific genotype in a population.

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

• Formulas:

  • Genotypic frequency: $f(AA) = \frac{\# \text{AA individuals}}{N}$, where $N$ is the total number of individuals.

  • Allelic frequency: $\text{frequency of allele} = \frac{\text{copies of the allele}}{\text{total copies of all alleles at the locus}}$

• For loci with multiple alleles or X-linked loci, calculations are adjusted accordingly.

• Example: In a population of 100 frogs (64 GG, 32 Gg, 4 gg), the frequency of allele g is $\frac{(2 \times 4) + 32}{(2 \times 64) + (2 \times 32) + (2 \times 4)} = \frac{40}{200} = 0.2$.

25.2 The Hardy-Weinberg Law

Effect of Reproduction on Genotypic and Allelic Frequencies

The Hardy-Weinberg law provides a mathematical model for understanding how allele and genotype frequencies behave in an ideal population.

• Assumptions: Large population, random mating, no mutation, migration, or natural selection.

• Predictions:

  • Allelic frequencies remain constant from generation to generation.

  • Genotypic frequencies stabilize after one generation of random mating.

• Genotype proportions: $p^2$ (homozygous dominant), $2pq$ (heterozygous), $q^2$ (homozygous recessive).

• Equation: $p + q = 1$ and $p^2 + 2pq + q^2 = 1$

• Example: If $p = 0.8$ and $q = 0.2$, then $p^2 = 0.64$, $2pq = 0.32$, $q^2 = 0.04$.

Implications of Hardy-Weinberg Equilibrium

• Genotype frequencies are determined by allele frequencies.

• When one allele is much more common, most individuals are homozygotes.

• Heterozygote frequency is highest when $p = q = 0.5$.

Concept Checks and Applications

• Tay-Sachs Disease: Autosomal recessive disorder. If disease frequency is $1/3600$, the proportion of heterozygous carriers can be calculated using Hardy-Weinberg principles.

• Cat Color Example: In a population of 100 cats, 19 are all white. If in Hardy-Weinberg equilibrium, the frequency of the all-white allele is 0.10.

25.3 Nonrandom Mating

Effects on Genotypic Frequencies

Nonrandom mating alters genotypic frequencies but does not necessarily change allelic frequencies.

• Positive assortative mating: Like individuals mate more frequently.

• Negative assortative mating: Unlike individuals mate more frequently.

• Inbreeding: Mating between relatives increases homozygosity.

• Outcrossing: Mating between unrelated individuals increases heterozygosity.

• Inbreeding coefficient (F): Measures the probability that two alleles are identical by descent.

• Inbreeding depression: Reduced fitness due to increased homozygosity of deleterious alleles.

TABLE: Generational Increase in Homozygotes (Self-Fertilization, $p = q = 0.5$)

Generation	Genotypic Frequencies: AA	Genotypic Frequencies: Aa	Genotypic Frequencies: aa
1	1/4	1/2	1/4
2	1/4 + 1/8 = 3/8	1/4	1/4 + 1/8 = 3/8
3	3/8 + 1/16 = 7/16	1/8	3/8 + 1/16 = 7/16
4	7/16 + 1/32 = 15/32	1/16	7/16 + 1/32 = 15/32
n	(1 - (1/2)n)/2	(1/2)n	(1 - (1/2)n)/2
∞	1/2	0	1/2

TABLE: Effects of Inbreeding on Japanese Children

Genetic Relationship of Parents	F	Mortality of Children (through 12 years of age)
Unrelated	0	0.082
Second cousins	0.016 (1/64)	0.108
First cousins	0.0625 (1/16)	0.114

• Inbreeding increases the percentage of homozygous individuals in a population.

• Inbreeding often has deleterious effects on crops, such as reduced yield in corn as inbreeding coefficient increases.

25.4 Evolutionary Forces Affecting Allelic Frequencies

Mutation

Mutation introduces new alleles into a population and can change allelic frequencies over time.

• Forward mutation: Changes a wild-type allele to a mutant allele.

• Reverse mutation: Changes a mutant allele back to wild-type.

• Recurrent mutation leads to a stable equilibrium of allele frequencies.

Migration (Gene Flow)

Migration is the movement of individuals (and their genes) between populations, altering allelic frequencies.

• The amount of change depends on the difference in allele frequency and the extent of migration.

• Formula for unidirectional migration: $q' = (1 - m)q_1 + m q_2$, where $m$ is the proportion of migrants, $q_1$ is the allele frequency in the resident population, and $q_2$ in the migrant population.

Genetic Drift

Genetic drift refers to random changes in allele frequencies due to chance events, especially in small populations.

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

• The rate of drift is inversely related to population size.

• Founder effect: Small group establishes a new population, often with reduced genetic variation.

• Bottleneck effect: Population size is drastically reduced, leading to loss of genetic diversity.

• Example: Northern elephant seals experienced a bottleneck, resulting in low genetic variation.

• Example: The Old Order Amish population shows high frequency of Ellis-van Creveld syndrome due to founder effect.

Natural Selection

Natural selection is the differential survival and reproduction of individuals due to differences in phenotype.

• Fitness: The reproductive success of a genotype.

• Selection coefficient (s): Measures the strength of selection against a genotype.

• Types of selection:

  • Directional selection: Favors one extreme phenotype.

  • Overdominance: Heterozygotes have higher fitness than either homozygote.

  • Underdominance: Heterozygotes have lower fitness than either homozygote.

• Natural selection produces adaptations, such as polar bears' traits for Arctic survival.

TABLE: Effects of Evolutionary Forces on Genetic Variation

Evolutionary Force	Effect Within Populations	Effect Between Populations
Mutation	Increases genetic variation	Increases divergence
Migration	Increases genetic variation	Decreases divergence
Genetic Drift	Decreases genetic variation	Increases divergence
Natural Selection	Can increase or decrease variation	Can increase or decrease divergence

Additional info: The study notes include expanded definitions, formulas, and examples for clarity and completeness, as well as reconstructed tables for generational changes in genotype frequencies and effects of inbreeding.