Population Genetics and Gene Flow Notes

Population Genetics: Allele Frequencies

• BI2131 Animal Diversity and Adaptation
• Pablo Orozco-terWengel

Core Topics

• Population genetic variation
• Genetic variation
• Hardy-Weinberg Principles
• F-statistics and their derivatives
• Spatial considerations: models and approaches
• Gene-flow and divergence

Genetic Variation

• Various measures of allelic variability
• Heterozygosity
• Phenotypic similarity (allele sharing)

Allelic Diversity

• $N_{all}$: Number of alleles per locus (mean)
• Sensitive to sample size
• Can be a very sensitive indicator of genetic drift

Allele Frequency

• Calculated as the proportion of all allelic observations.
• In a diploid population, the formula is: $x/2N$, where N is the number of individuals in the sample
• Allele frequencies can change rapidly under drift.

Heterozygosity (H)

• A statistically robust estimate of genetic diversity
• Observed Heterozygosity ($H_o$): proportion of heterozygous individuals in a population/sample
• Expected Heterozygosity ($H_E$): expected value under Hardy-Weinberg Equilibrium (HWE); estimated from allelic frequencies!
  • $H_E$ is the value compared between populations (little bias)

Population Structure and Hardy-Weinberg Equilibrium (HWE)

• Hardy-Weinberg principle is a fundamental concept.

Hardy-Weinberg Revision

• Consider a single locus with two alleles {A, a} with frequencies p and q, respectively.

• Summed frequencies in zygotes:
  • AA: $P' = p^2$
  • Aa: $Q' = pq + qp = 2pq$
  • aa: $R' = q^2$
• These are the expected values assuming random mating.

Deviations from HWE

• Consistent deviation across loci suggests a demographic explanation (e.g., non-random mating).
  • Example: Inbreeding (mating between relatives) leads to an excess of homozygotes.
• Consistent deviation at a particular locus across populations suggests a genetic explanation (e.g., natural selection).
  • Example: natural selection favoring an allele

F Statistics

• Sewall Wright’s (1921) index of allele fixation.

• Quantifies the reduction in heterozygosity (H) compared to what is expected under HWE at any demographic level with respect to any other.

• Summarizes genetic variance within a population, i.e., how genetic variation is partitioned between demographic levels.

• Uses the symbol F followed by subscripts: $F<em>{IS}$, $F</em>{ST}$, $F_{IT}$

• $F_{IS}$: Correlation among genes (individuals) within a subpopulation; a measure of inbreeding. Range = -1, 0, +1.

• $F_{ST}$: Correlation among genes (individuals) within a subpopulation compared with the entire sample; a measure of subpopulation structure or genetic differentiation. Range = 0, 1.

• $F_{IT}$: Correlation among genes (individuals) within the whole sample; a measure of ‘random’ genetic similarity. Range = -1, 0, +1.

F Statistics Context

Spatial Models of Population Structure

1. Discrete subpopulations: island and stepping-stone models.
2. Isolation-by-distance (IBD): continuous populations.

Island Model (Wright)

• All subdivisions can exchange migrants.
• Distance does not affect gene flow.

Stepping-Stone (Kimura) Model

• Dispersal is more likely between adjacent subpopulations.
• Distance does matter.

Isolation-by-Distance (Wright)

• Series of overlapping neighborhoods.
• Distance matters, as does dispersal ability.
• Space/Geography

Model Predictions

• Models make different predictions about the shape of the relationship between genetic and geographic distance.

Quantifying Gene Flow

• Direct methods:
  • Ecological & genetic data.
  • Focus on individual movements over the short term.
  • Limited scope.
• Indirect methods:
  • Genetic data.
  • Focus on gene movements over the longer term.
  • Based on assumptions.

Indirect Methods

• Indirect methods relate genetic subdivision & gene flow.
• Example: for an island model:
  • $F_{ST} = 1 / (1 + 4Nm)$
  • Where:
    • N = Population size
    • m = Proportion of the population that migrates

Determining Significance

• Determining significance of genetic subdivision & geographic distance etc

Mantel Tests

• Examine the association between two matrices, usually:
  1. Pairwise genetic distances
  2. Pairwise geographic distances

Implementation of Mantel Tests

• Mantel tests find by permutation (simulation) how many times the observed result arises by chance in the same data.
• If the frequency is low, the observed result can be accepted with confidence.

Example

Genetic divergence and units for conservation in the Komodo dragon Varanus komodoensis

• The study investigates nuclear genetic variation in Komodo dragons per population for all loci combined.
• A = mean number of alleles
• $H_o$ = mean observed heterozygosity
• $H_E$ = mean expected heterozygosity

Key Findings Highlighted

• Island size correlates with genetic diversity
• $F_{ST}$ correlates with island proximity
• Nm estimates
  • Nm BETWEEN Komodo and the rest is ~0.1
  • Nm BETWEEN Rinca and Flores >1