AGB 121: Principles of Animal Genetics and Population Genetics (2+1)

AVERAGE EFFECT

• Parents pass on their genes and not their genotypes to the next generation.
• Thus genotypic value cannot be transmitted from parents to offspring.
• A new measure of value is therefore needed which will refer to genes.
• The new measure is the average effect .

The average effect of a gene is the mean deviation from the population mean of individuals which received that allele from one parent, with the other allele received from the other parent having come at random from the population

• The average effect of a gene depends on the gene frequency. The average effect is therefore a property of the population as well as of the gene.
• Consider a locus with two alleles A₁ and A₂ at frequencies p and q respectively.
  • Let us first take the average effect of the gene A₁ , for which we shall use the symbol µ₁.
  • If A₁ gametes unite at random with gametes from the population
    • A₁ A₁ genotype produced frequency = p of and
    • A₁ A₂ genotype produced frequency = q
    • The genotypic value of A₁ A₁ = +a and that of A₁ A₂ = d
    • The mean of these = pa + qd (taking of the proportions in which they occur)
  • Average effect of the A₁ gene (µ₁) = pa + qd - M
    • µ₁ = pa + qd - { a ( p - q )+ 2pqd }
    • µ₁ = q [ a + d ( q - p )]
  • Similary for the A₂ gene
    • µ₂ = -p [ a + d ( q - p )]
  • Now consider the average effect of the gene substitution. This is the difference which would be caused by changing one allele in an average individual into the other allele, so that µ = p ( a - d ) + q ( d + a ) = a + d ( q - p )
    • The relation of µ to µ ₁ and µ₂ can be seen as
      • µ₁ - µ₂ = a + d ( q - p ) = µ
  • Therefore µ₁ = q µ ; µ₂ = -p µ