chapter3 Change of gene frequency in small populations- The idealized population.ppt

Chapter 3
Change of gene frequency in small populations
- The idealized population
Random drift
Random change of gene frequency from generation to generations
Occurring in small populations
Arising from the random sampling of gametes
Random drift
When a large population is divided into several small sub-populations, and they are isolated from each other, then along with the random drift in the sub-populations, the following will happen:
Differentiation between sub-populations
Uniformity within sub-populations
Increased homozygosity
Idealized population
Divide a large population of Hardy-Weinberg equilibrium (base population) into a large number of sub-populations (lines) , each with size N and meets the following conditions:
No migration between lines, no selection and mutation within each lines
No overlap of generations
Same number of breeding individuals in all lines and all generations
Same number of breeding males and females
Random mating (including self-fertilization) within each line
Idealized population
Base population
N
N
N
N
N
N
N
N
N
N
2N
2N
2N
2N
2N
2N
2N
2N
2N
2N
Generation
0
1
2
Gametes
Breeding individuals
Gametes
Breeding individuals
Change of gene frequencies(variance of gene frequency)
Consider a single locus with two alleles A1 and A2
The frequency of A2 in the base population is q0
In generation one, the 2N genes in each line are a random sample of genes in the base population.
The frequency of A2 in generation one follows binomial distribution
Change of frequency in the ith line:
Expectation of frequencies:
Variance of frequencies:
Change of gene frequencies(variance)
Generation t:
All lines are fixed. A1 will be fixed in the proportion p0 of lines, and A2 in the remaining proportion q0 of lines.
Changes of genotype frequencies
If N is large enough, then
The genotypic frequencies in the population as a whole
Inbreeding
Mating of individuals that are related to each other by ancestry
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