Population genetics

Population Genetics Notes

Hardy-Weinberg Equilibrium

• Definition: A principle that states gene frequencies remain stable in a population under certain assumptions.

• Assumptions for Hardy-Weinberg Equilibrium:

  • 1. Mating is random: The selection of mates is not influenced by their genotypes.

  • 2. No selection: All genotypes have equal chances of survival and reproduction.

  • 3. No mutation: Allele frequencies remain unchanged as there are no new alleles introduced.

  • 4. No migration: The population is closed, meaning there is no influx or outflow of individuals.

  • 5. Large population: The population is sufficiently large to minimize random sampling errors (no genetic drift).

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

  • $p$ = frequency of the dominant allele

  • $q$ = frequency of the recessive allele

  • $p^2$ = frequency of homozygous dominant individuals

  • $2pq$ = frequency of heterozygous individuals

  • $q^2$ = frequency of homozygous recessive individuals

Genetic Drift

• Definition: A process where allele frequencies change in small populations due to random chance.

• Implications: Over generations, populations may become increasingly different or diverge in allele frequencies due to drift.

  • Chance of allele disappearance: Small populations are particularly vulnerable to the random loss of alleles from the gene pool.

• Example:

  • Polydactyly in Maritime cats: A trait that is more common due to genetic drift in a small population of cats.

• Additional Example:

  • Rabbit population:

  • Changes in allele frequencies ($p$ and $q$) with each generation.

  • In the third generation, for instance, a specific allele (e.g., the b allele) may be lost due to random chance, leading to the absence of white rabbits in future generations.

Effect of Population Size on Genetic Drift

• Observation: Smaller populations experience more significant changes in allele frequencies due to genetic drift.

• Graphical Representation:

  • Demonstrates the relationship between population size and the degree of drift.

Founder Effect

• Definition: A phenomenon that occurs when a small founding population leads to changes in gene frequency due to chance.

• Example:

  • Severe combined immunodeficiency (SCID) in Arabian horses:

  • An autosomal recessive disease represented as (cc).

  • In England:

    • Frequency: $q^2 = 0.01$ (1% of Arabians have the disease) thus $q = 0.1$.

  • In Australia, two stallions imported from England (both carriers, Cc) resulted in a higher frequency of affected foals:

    • 17/204 = 8.3 ext{%} of foals affected.

Breed Introduction

• Definition: The process of introducing a breed to a new area, leading to possible changes in gene frequencies.

• Characteristics:

  • Often involves a relatively small founding population.

  • Gene frequency in the new area may significantly differ from the original population.

• Examples:

  • Holsteins introduced to Kenya.

  • Llamas to California.

  • Rare dog breeds brought to Canada.

Population Bottleneck

• Definition: A significant reduction in population size for one or more generations, leading to altered allele frequencies and loss of genetic diversity.

• Examples:

  • North American Bison: Historical reductions in population size.

  • White Park cattle: Endangered after WWII with only 4 herds remaining in the 1960s.

  • Cheetahs: Other endangered species undergoing population bottlenecks.

• Consequences:

  • Show ring practices and artificial insemination (AI) often promote the use of a limited number of sires, further reducing genetic diversity.

  • For example, 20 years ago, one Saler bull was present in over 70% of pedigrees.

Gene Flow

• Definition: The recurrent exchange of new alleles between subpopulations through migration.

• Two Extremes:

  • Panmictic Population:

  • Free exchange of breeding individuals without geographic barriers.

  • Genetic Isolates:

  • Subpopulations breed solely within themselves, referred to as a “closed” herd.

Cline

• Definition: The phenotypic gradient across geographical regions influenced by gene flow.

• Characteristics:

  • Gene flow is greatest between adjacent populations.

• Comparison of Zebras:

  • Exhibit varied phenotypes depending on geographical overlap (e.g., Grevy's vs. Grant's zebra).

Migration

• Definition: Change in gene frequencies due to the transfer of genetic material between populations.

• Migratory Patterns:

  • In the wild, migrations may occur due to natural movements (e.g., crossing rivers).

  • In domestic animals, migration often occurs through the buying or selling of animals (e.g., acquiring new stock for a herd).

• Gene Flow Dependent Factors:

  • Rate of immigration.

  • Differences in gene frequencies between populational generations.

• Mathematical Representation of Migration:

  • New allele frequency given by:

  • $q_{new} = q(1 - M) + Q(M)$

    • where:

    • $q$ = island recessive allele frequency

    • $Q$ = mainland recessive allele frequency

    • $M$ = proportion of immigrants in the island population.

Examples of Migration Effects

• Pig Company Case Study:

  • A closed herd buys in Berkshire boars to establish a colored crossbred boar line.

  • Initial allele frequencies:

  • Yorkshire (white) $q = 0$ (all dominant)

  • Berkshire (black) $Q = 0.8$ (allele frequency).

  • After one generation:

  • $q_{new} = 0(0.5) + 0.8(0.5) = 0.4$ (40% of the new generation is expected to express the recessive trait).

• Impact Over Multiple Generations:

  • For continued gene flow effects, the formula becomes:

  • $q_t = (1 - M)^t(q - Q) + Q$

    • where:

    • $t$ = number of generations.

Example for Livestock Selection

• Loan Example:

  • Goal: Buy more red cattle with a loan for improved profitability.

  • Current herd: 80 cows (only 9% red).

  • Buying new heifers (20, with 64% red) will modify the herd's genetics over 3 generations (considering generation intervals).

• Mathematical Calculation Results:

  • Following the formula, $qt$ should yield approximately 30% of calves being red after three generations.

  • Changing the scenario to buying new bulls (3 from the herd) will yield 55% red calves, indicating a quicker genetic improvement and success.

• Regulatory Considerations:

  • Regulatory Impact on Migration:

  • Import and export regulations can inhibit migration.

  • Examples include:

    • Canada’s restrictions due to disease (e.g., foot and mouth disease).

    • Australia's demands for genetic assessments (karyotyping).

Summary of Migration Effectiveness

• The success of gene flow is influenced by:

  • Rate of migration and the difference in allele frequencies.

  • Decision-making on whether to acquire more individuals or genetically superior stock is vital for optimizing outcomes.

  • As proximity to a genetic goal increases, the achievable genetic changes tend to diminish.