HWE

Hardy-Weinberg Equilibrium

• Gene frequencies remain stable under certain conditions.

  • Assumptions for Hardy-Weinberg Equilibrium:

  1. Random Mating: Individuals pair by chance.

  2. No Selection:

     • Fitness and selection coefficient (s) contribute to allele frequencies.

  3. No Mutation:

     • Mutations introduce new alleles, and thus affect gene frequencies.

  4. No Migration:

     • The population is closed to outside gene flow.

     • Examples include differentiation between mainland and island populations.

  5. Large Population:

     • Minimizes genetic drift effects.

Mutation

• Defined by the rate $= \text{mutation rate}$.

  • New mutations occur per cell division.

  • Mutation rates are generally low:

  • Example: $1.1 \times 10^{-8}$ in humans.

  • New mutations contribute to genetic diversity but do not significantly alter frequencies in large populations.

Genetic Drift

• Occurs when small subpopulations diverge genetically over generations.

• Characteristics of Genetic Drift:

  • Small populations are more susceptible to changes due to random chance leading to drift.

  • Allele frequencies can drastically shift over generations.

  • E.g. an allele may completely disappear from a gene pool due to random chance.

Population Size and Its Effects

• Example of a cattle herd increments:

  • In 2023, a ranch buys 30 cows and 1 bull.

  • Calving in 2024 results in 14 heifers, all half-sisters.

  • In 2025, the herd size grows to approximately 60 females, all closely related.

  • Implications:

  • Despite a numerical equivalence, they represent a reduced genetic variety compared to 60 unrelated females.

Effective Population Size (Ne)

• A population must maintain a size that can:

  • Prevent inbreeding.

  • Preserve genetic variation for selection (to avoid fixation).

• Formula:
  $ext{Ne} = \frac{4 \times \text{sire} \times \text{dams}}{\text{sire} + \text{dams}}$

• Alternatively, in broader context: $\text{Ne} = \frac{4 \times N<em>m \times N</em>f}{N<em>m + N</em>f}$

  • Where:

  • $N_m$ = number of males,

  • $N_f$ = number of females.

Calculation of Effective Population Size

• Example Calculation:

  • Given a ranch with 300 adult cattle (10 bulls and 290 cows):
    $\text{Ne} = \frac{4(10)(290)}{10 + 290} = 38.7$

  • If every sire and dam ratio is equal:
    $\text{Ne} = \frac{4(150)(150)}{150 + 150} = 300$

Gene Fixation and Inbreeding Depression

• Probability that a gene becomes fixed:
  $P = \frac{1}{2Ne}$

• For the aforementioned population of 10 bulls and 290 cows:
  $P = \frac{1}{2(38.7)} = 0.013$

• Estimates suggest a Ne of 50 is necessary to avoid inbreeding depression.

  • Example: Endangered species such as the Sage Grouse.

Heritability

• Goal of Breeders:

  • Alter phenotype to enhance environmental adaptability.

  • Change the genotype of breeding stock.

  • Evaluate which of the two approaches yields a greater impact.

Effects on Phenotype

• Two kinds of effects:

  1. Additive Effects:

  • Sum of traits from alleles influences the phenotype.

  1. Non-Additive Effects:

  • Includes dominance deviations and epistatic interactions.

• Expressed Phenotype Equation: $\text{Phenotype} = \text{Genotype} + \text{Environment}$

  • Factors influencing phenotype include feeding, housing, health, and stress.

  • The objective is to select breeds based on genotype, not just phenotype.

Polygenic Inheritance

• Defined by multiple genes influencing a single trait.

• Characteristics:

  • When more than three genes affect a trait, it is termed polygenic.

• Examples include:

  • Coat color in cattle

  • Head shape in horses

  • Litter size in cats

  • Egg production in chickens.

Interactive Effects

• Interaction among two or more loci affecting a trait.

• Example:

  • Coat color in cattle is influenced by multiple genes.

  • E locus (Extension, gene: MC1R):

    • Black (ED) > wildtype (E+) > red (e).

  • D locus (Diluter, gene: PMEL17):

    • DD = dark, Dd = medium, dd = dilute.

• Combined interaction results in color variation based on genotype.

Epistasis

• Definition: The action of one gene masks the effect of another gene's phenotype.

  • Epistatic Gene: The gene that masks.

  • Hypostatic Gene: The gene being masked.

• Example with albinism:

  • Gene TYR: Responsible for albinism, prevents coat and eye pigmentation.

  • Hypostatics' (e.g. MC1R) effects cannot be exhibited without the influence of the epistatic gene TYR.

Additive Effects

• The sum of alleles from multiple genes determines the phenotype.

• Example concerning milk yield:

  • Genotype Representation:

  • LLLlll = average yield of ~1800 liters.

  • LLLLLL = ~2200 liters.

  • llllll = ~1400 liters.

  • The presence of more L alleles correlates with higher yield but is also affected by nutrition, age, and health conditions.

  • Result: Slow genetic progress in improving yield.

Examples of Additive Effects in Different Traits

• Example of dog height:

  • Genotype HHHHHH corresponds to taller dogs (~66 cm).

  • Genotype hhhhh corresponds to shorter dogs (~60 cm).

  • Each H allele contributes approximately 1 cm to the height measurement, but also influenced by environmental factors.

Gene Interaction in Phenotypic Expression

• Genes can interact, resulting in distinctive phenotypes.

• Example of Dwarfism in Dogs:

  • Interaction between genotypes HHHhhh and either AA or Aa leads to moderate height, while with aa, it results in dwarfism.

• Illustrates how genetic combinations can lead to various physical forms in species such as Basset Hounds.