Variation Selection

Concept of Heterozygous Advantage

• Can only be applied when gene frequencies remain constant from birth to adulthood.

• Different genotypes exhibit differing survival rates.

Example of Heterozygous Advantage in Sickle-Cell Anaemia

• Sickle cell anaemia is a genetic blood disorder caused by a mutation in the hemoglobin gene (mutant aa compared to the healthy AA gene).

• This mutation involves a DNA change from TT to GTG, which leads to altered protein structures and affects red blood cell health.

• The condition is notably prevalent in equatorial regions, particularly in Africa.

Statistical Analysis in Sickle Cell Anaemia

Mutation

• Concept of Mutation

  • Defined as the random change of nucleotides (or amino acids) in the genetic material.

• Types of Mutations

  • Forward Mutation: Conversion of allele A to allele a at a rate of u.

  • Backward Mutation: Conversion of allele a back to allele A at a rate of v.

• Equilibrium Frequencies

  • The equilibrium frequencies of p and q due to mutation can be expressed mathematically by mutation rates.

Example Calculation of Mutation Rates

Mutation and Selection Dynamics

• Interactions between Mutation and Selection

  • New mutations prevent deleterious alleles from being completely eliminated within populations.

  • Mutation rates for recessive diseases generally is $u = 1 \times 10^{-5}$ or 1 in 100,000

  • This equation is for non lethal, but deleterious alleles, where s is the selection coefficient ( 1 - w )

    

  • In a case whereby the mutation is lethal, the equation used would be

    

Example equation for mutation selection

Violation to Hardy-Weinberg: Non-Random Mating

• Concept of Inbreeding

  • Defined as mating between organisms that are more closely related than the average relationship within a population.

  • Increases frequency of homozygous genotypes and may lead to deleterious recessive alleles surfacing.

• Inbreeding Coefficient (F)

  • Represents the probability that two alleles are identical by descent.

  • Higher F indicates a stronger degree of inbreeding.

Calculating Inbreeding Coefficients from Pedigrees

• Step 1: Identify Loops in Pedigree

  • A loop must connect from an individual (X) through one parent to a common ancestor and back without reusing individuals.

  • Count the steps involved in each identified loop.

• Step 2: Contributing Each Loop to F

  • Calculate the contribution of each loop to the inbreeding coefficient

• Example of inbreeding calculation

Inbreeding and genotype frequencies

• Outbred Hardy-Weinberg Frequencies

  • Homozygous dominant = $p^2$

  • Heterozygous = $2pq$

  • Homozygous recessive = $q^2$

• Inbred Hardy-Weinberg Frequencies

  • Homozygous dominant: $p^2 + pqF$

  • Heterozygous: $2pq - 2pqF$

  • Homozygous recessive: $q^2 + pqF$

Example in Autosomal Recessive Disease

• If a disease occurs in 1 in 40,000 individuals, calculate the expected impact on individual X in the pedigree.

• Step 1: Identify Loops Again with noted contributions.

• Step 2: calculate loop contributions

• Step 3: sum the loop contributions