Population Genetics Notes

Chapter 18: Population Genetics

18.1 Detecting Genetic Variation

• Population genetics reveals geographic structure and likely origins of plant and animal species based on levels of genetic variation within and among populations.
• It forms the foundation for studying evolutionary change in populations.
• Applications include DNA forensics, paternity testing, and human disease mapping, all based on probabilities of individuals possessing a particular genotype relative to others in a population.
• These applications rely on associations of specific molecular variants with disease states.

Revised Definitions for Population Genetics

• Locus: A designated location on a chromosome; can be a single nucleotide or a stretch of many nucleotides.
• Allele: A site at which DNA sequence differs among or between genomes; can be coding or non-coding.
• Most nucleotide changes do not affect phenotype.

Variation Among Homologous DNA Sequences

• Single Nucleotide Polymorphisms (SNPs): Detected by sequencing, PCR, and microarrays.
  • Common SNPs have a frequency of ≥ 5%, while rare SNPs have a frequency of < 5%.
  • SNPs can be in coding or non-coding regions (ncSNP).
  • If in a coding region, they can be synonymous, nonsynonymous, or nonsense.
• Microsatellites: Repeats of short 2-6 bp motifs.
  • Different microsatellite alleles have different physical lengths (e.g., [AG]3 and [AG]5).

Haplotypes

• Haplotype: A unique combination of alleles at multiple loci on the same chromosome or chromosome region.
• Example: A prevalent Y-chromosome haplotype among Asian men may trace back to Genghis Khan.
• Haplotype networks illustrate human Y chromosome variation and geographical distribution.

Gene Pool Characterization

• The gene pool can be characterized by genotype and allele frequencies.
• Genotype frequencies: What are the frequencies of AA, Aa, and aa?
• Allele frequencies: What are the frequencies of A and a?

Calculating Genotypic Frequencies

• Example: In a population of 16 individuals: 5 AA, 8 Aa, 3 aa.
• Frequency of AA (fAA) = 5/16 = 0.3125
• Frequency of Aa (fAa) = 8/16 = 0.5
• Frequency of aa (faa) = 3/16 = 0.1875

Calculating Allele Frequencies

Method 1: From Population Sample

• In 16 diploid individuals, there are 32 alleles.
• Homozygotes carry two copies of the same allele.
  • AA individuals carry two A alleles.
  • aa individuals carry two a alleles.
• Heterozygotes carry one copy of each allele.
  • Aa individuals carry one A and one a allele.
• Formula:
  • $f_A (p) = {2(number of AA) + number of Aa} / {total number of alleles}$
  • $f_a (q) = {2(number of aa) + number of Aa} / {total number of alleles}$
• Example:
  • $p = {2(5) + 8} / {32} = 0.5625$
  • $q = {2(3) + 8} / {32} = 0.4375$
• Note: Allele and genotypic frequencies sum to 1.
  • $p + q = 1$
  • $f<em>{AA} + f</em>{Aa} + f_{aa} = 1$

Method 2: From Genotypic Frequencies

• Formula:
  • $p = f<em>{AA} + (0.5 * f</em>{Aa})$
  • $q = f<em>{aa} + (0.5 * f</em>{Aa})$
• Example:
  • $p = 0.3125 + (0.5 * 0.5) = 0.5625$
  • $q = 0.1875 + (0.5 * 0.5) = 0.4375$

Hardy-Weinberg Equilibrium (HWE)

• In a randomly mating, sexually reproducing population, allele and genotype frequencies remain unchanged from one generation to the next.
• Constant frequencies form the equilibrium distribution, also known as Hardy-Weinberg Equilibrium (HWE).
• Genotype frequencies in terms of p and q:
  • AA: $p^2$
  • Aa: $2pq$
  • aa: $q^2$
• Where:
  • p is the frequency of the A allele
  • q is the frequency of the a allele
• HWE is only true for a population if several assumptions are met.
• Effect of sexual reproduction on variation.

Predicting Frequencies in the Next Generation

• Given specific genotype and/or allele frequencies in generation t, can we predict these frequencies in generation t + 1?
• Assumptions:
  • $f_{AA} = 0.25, p = 0.5$
  • $f_{Aa} = 0.50, q = 0.5$
  • $f_{aa} = 0.25$
• Gametes are produced in proportion to the relative abundances of A and a alleles in generation t. Assume random mating.
• Formulas for next generation (t+1):
  • $f'_{AA} = (p * p) = p^2$
  • $f'_{Aa} = (p * q) + (q * p) = 2pq$
  • $f'_{aa} = (q * q) = q^2$
• Example:
  • $f'_{AA} = (0.5)^2 = 0.25$
  • $f'_{Aa} = 2(0.5)(0.5) = 0.5$
  • $f'_{aa} = (0.5)^2 = 0.25$
• If the frequencies remain the same from generation t to t+1, the population is in Hardy-Weinberg Equilibrium.

Hardy-Weinberg Equilibrium Explained

• Describes a special relationship between allele frequencies and genotype frequencies.
  • $p^2$ = frequency of AA homozygotes
  • $2pq$ = frequency of Aa heterozygotes
  • $q^2$ = frequency of aa homozygotes
• Requires that several assumptions are met.

Applying HWE: Example Calculation

• Consider a population: 90 AA, 420 Aa, 490 aa (Total = 1000)
• Calculate genotype frequencies:
  • $f_{AA} = 90/1000 = 0.09$
  • $f_{Aa} = 420/1000 = 0.42$
  • $f_{aa} = 490/1000 = 0.49$
• Assuming Hardy-Weinberg equilibrium:
  • $p = {sqrt(f_{AA})} = {sqrt(0.09)} = 0.3$
  • $q = {sqrt(f_{aa})} = {sqrt(0.49)} = 0.7$

Assumptions of Hardy-Weinberg Equilibrium

• Under assumptions of Hardy-Weinberg equilibrium, allele and genotypic frequencies remain constant across generations.
• Assumptions:
  • Mating is random
  • No natural selection
  • No subpopulation structure
  • Population is large (no genetic drift)
  • No mutation
  • No gene flow (i.e., no migration)

Hardy-Weinberg Equilibrium and Rare Alleles

• Most copies of rare alleles are found in heterozygous condition.
• Example:
  • If $q = 0.001$, then
  • $f_{aa} = q^2 = (0.001)^2 = 0.000001$
  • $f_{Aa} = 2pq = 2 * (0.999) * (0.001) = 0.001998$
  • Rare alleles are more likely to be found in heterozygous form.

Departures from Hardy-Weinberg Equilibrium

• Departures from HWE indicate that the required assumptions are NOT met and thus evolutionary forces are acting on a population.
• Example: For p = 0.4 and q = 0.6
  • In HWE:
    • $f_{AA} = p^2 = 0.16$
    • $f_{Aa} = 2pq = 0.48$
    • $f_{aa} = q^2 = 0.36$
  • Not in HWE:
    • $f_{AA} = 0.28$
    • $f_{Aa} = 0.24$
    • $f_{aa} = 0.48$
• Allele frequencies can always be calculated from genotype frequencies, but the HWE relationship does not hold if assumptions of HWE are violated.

Non-Random Mating

• Non-random mating is a violation of HWE assumptions.
  1. Assortative mating: Based on phenotypic resemblance.
     • Positive assortative mating: like mates with like; increases homozygosity.
     • Negative assortative mating: like mates with unlike; increases heterozygosity.
  2. Isolation by distance: Mate only with neighbors.
     • Leads to population structure: allele frequencies vary across the landscape.
  3. Inbreeding: Related individuals mate more often than would occur by chance.
     • Increases homozygosity.
     • Enforced outbreeding also possible: related individuals mate less often than would occur by chance.

Isolation by Distance: Example

• Allele frequency may vary along a gradient.
• Example data from Kansas City, Hutchinson, and Elkhart showing varying allele frequencies and HWE status.

Inbreeding

• Inbreeding increases homozygosity and increases the possibility that an individual will possess alleles that are identical by descent.
• Identical by descent (IBD): Probability that 2 alleles are derived from the same SINGLE allele that exists (existed) in an earlier generation.
• Probability of alleles being IBD is measured by the inbreeding coefficient (F).

Calculating Inbreeding Coefficient (F)

• Identify 'inbreeding loops'
• Formula: $F = (1/2)^n$, where n is the number of individuals in the loop (loop doesn’t include individual for whom F is calculated).
• Examples:
  • Half-sib mating: $F = (1/2)^3 = 1/8$
  • Brother-sister mating: $F = (1/2)^3 + (1/2)^3 = 1/4$
  • Parent-offspring mating: $F = (1/2)^2 = 1/4$
  • First-cousin mating: $F = (1/2)^5 + (1/2)^5 = 1/16$

Inbreeding and Recessive Diseases

• Inbreeding drastically increases the probability that offspring will inherit recessive diseases (that rare alleles will be found in homozygous condition).
• Modified genotype frequencies to account for inbreeding:
  • $f_{AA} = p^2 + pqF$
  • $f_{Aa} = 2pq – 2pqF$
  • $f_{aa} = q^2 + pqF$
• Example: If q = 0.01 and F = 0.25
  • $f_{aa} = (0.01)^2 + (0.99)(0.01)(0.25) = 0.002575$

Genetic Drift

• Genetic drift = random fluctuation in allele frequencies due to ‘chance’ events.
• Effect is inversely proportional to population size
  • Genetic drift has weaker effects in larger populations
  • Genetic drift has stronger effects in smaller populations
• Can result in loss or fixation of alleles
• Similar to effects of inbreeding
  • Increases homozygosity, decreases heterozygosity

Founder Effect

• The founder effect: genetic drift arising from sampling of a larger population during the ‘founding’ of a new population.
• Genetic diversity reduced in human populations that have experienced founder events.

Genetic Drift and Neutral Theory

• Probability of fixation of an allele is equal to its starting frequency.
• Initial frequency of new mutation is $1/2N$, where N is population size.
• Probability of loss is thus $1 – (1/2N)$; most mutations are lost!
• Substitution rate (k) = $2Nμ * 1/2N = μ$
  • Where μ is the mutation rate.
• Substitution rate serves as a molecular clock if μ is constant over time.
• Alleles that become fixed are called substitutions.

Natural Selection

• Natural selection: differential rates of survival and reproduction among different genotypes.
• Fitness:
  • Consequence of relationship between phenotype and environment.
  • Same genotype may have different fitness in different environments.
  • Absolute fitness (W): Number of offspring produced per individual or genotype.
  • Relative fitness (w): Fitness of an individual or genotype relative to the individual or genotype with the highest fitness; typically bounded by 0 and 1.

How Selection Alters Allele Frequencies

• Differential survival of genotypes (e.g., a/a is lethal).
• Corrected frequencies are calculated by dividing viable genotype frequencies by the sum of those frequencies.
• Instead of being lethal, genotype a/a might have reduced fitness relative to genotypes A/A and A/a.
• We can assign a relative fitness value (w) to each genotype:
  • w = 0, lowest fitness
  • w = 1, highest fitness
• After selection, allele frequencies change.

Selection on Dominant Versus Recessive Allele

• Selection can act differently on dominant versus recessive alleles, influencing how quickly allele frequencies change.

Forms of Selection

1. Directional Selection:

• Moves an allele frequency in one direction until it’s fixed or lost.
  • A. Positive selection: Brings a new, favorable allele to a higher frequency.
    • Selective sweep: when a favorable allele reaches fixation in a population.
  • B. Purifying selection: Removes deleterious mutations from the population and prevents degradation of existing adaptive traits.

2. Balancing Selection:

• If the heterozygous genotype has higher fitness than either homozygote, both (or multiple) alleles are maintained in the population.
• Produces increased genetic variation in and around the site of selection.