Genes in Populations

Hardy Weinburg Principle

use allele frequency in a population to predict the genotype frequency in their offspring

assumptions:

(1) all genotypes can be accurately identified; the frequency of the phenotype is the same as the frequency of the genotype
(2) there are no mutations
(3) mating is completely random and does not cross generations
(4) there is no selection with respect to genotype
(5) there is an infinitely large population

p and q represent the frequency of two alleles in a population

p² = frequency of individuals with AA genotype

2pq = frequency of individuals with Aa genotype

q² = frequency of individuals with aa genotype

p + q = 1

p²+ 2pq + q² = 1

0.36 + 0.48 + 0.16 = 1

HW applications:

if you know the frequency of a recessive phenotype you can calculate frequency of the recessive allele and the frequency of heterozygotes Þ q² = # of affected homozygotes; p = 1 - q

this information is used to counsel couples who may be at risk

(i.e. no family history of disease Þ use general population risk of being carrier)

example: sickle cell disease

p = 1 - q = 19/20 ~ 1

carrier frequency = 2pq = 1/10

example: cystic fibrosis

p = 1 - q = 49/50 ~ 1

carrier frequency = 2pq = 1/25

Deviations from HW

Mutation: mutation rate is approximately 1/million in the human population

Selection: mutations that effect reproductive fitness can change allele frequency

certain alleles can either increase or decrease reproductive fitness Þ heterozygote advantage

i.e. in sickle cell disease, carriers are more resistant to malaria

explains carrier frequency much greater than predicted by HW

genetic drift: large variations in allele frequency occurring by chance (more likely in smaller populations)

Non-random mating, small pop. size, population migration

consanguinity: mating within the family

inbreeding coefficient (F): rate of homozygous recessives getting both alleles from a common ancestor

1/2000 for the general population

1/4^(x+1) where x = order of relatedness (1^st cousin x=1 Þ F = 1/16; 2^nd cousin x=2 Þ F = 1/64)

if the frequency of an allele in a population is 1/1000; the chance of 1^st cousin couples both carrying the mutant

allele is 1/1000 x 1/16 = 1/16000

founder effect: population is small due to a migration Þ genetic drift, inbreeding

genetic bottleneck: drastic reductions in populations (i.e. plague, relocation of American Indians)

what can cause allele frequency to increase in a population?