Population Genetics - Hardy Weinberg Equilibrium

1. Population Genetics- Hardy Weinberg Equilibrium Newcastle February 14th 2008

2. Hardy-Weinberg Equilibrium Describes a state in a large randomly breeding population where the gene frequencies and genotype ratios remain constant from one generation to the next Named after the GH Hardy and Wilhelm Weinberg

3. Hardy-Weinberg equilibrium • Allele N; normal dominant allele • Allele n; defective recessive allele • Homozygous nn individuals – have disease state so severe that prevents reproduction • Could be assumed that the n allele would disappear from the population • does not occur because of the equilibrium that develops within the population • Example – hamsters with black coat dominant allele (B - 80%) and grey coat recessive allele (b - 20% ); random mating of alleles Thus 0.5(0.16+0.16)+0.04=0.20 of allele population will be the ‘b’ allele which is the same as in first generation

4. Hardy-Weinberg equilibrium • Is a means of maintaining the reservoir of variability • Enables gene pool to change if future generations require • Indicates that no evolutionary forces are in effect in the population

5. Evolutionary forces affecting Hardy-Weinberg equilibrium • Most natural populations do exhibit changing allele and genotype frequencies over the generations • Known to be due to a number of factors which may be operating and allow evolution to occur • Natural selection • Population size • Mating patterns • Mutation

6. Natural selection • Individuals with certain genes may be more likely or less likely to survive and reproduce • - often considered as way of describing Darwin’s criteria of survival (fitness) • -can be due to a differential mortality or differential fecundity Peppered moth - industrial vs country locations

7. Natural selection • Sickle cell anaemia • Heterozygote advantage in carriers of trait (resistance to malaria) • Cystic fibrosis • increased fertility • decreased fertility

8. Population effects Large populations are ideal to maintain equilibrium Population effects that alter equilibrium: 1. Genetic drift – random process and not adaptive

9. Population effects 2. Bottleneck effect – population vastly reduced eg due to hurricane or other catastrophe Unrelated to phenotype who lives and thus contributes to future generations

10. Population effects 3. Founder effect - often seen when small number of individuals (some with rare genotype) colonise new geographical area and reproduce in relative isolation

11. Population effects 4. Migration/Gene flow - occurs when isolated populations with distinct gene pools mix and exchange alleles eg Mass emigration in previous years

12. Mating patterns • Random mating is ideal to maintain equilibrium but this tends to be species dependent • Assortative mating • Within assortative mating, same alleles may be randomly mixed • eg blood type, whilst others are not eg height, intelligence

13. Mating patterns • Consanguinity – serves to increase homozygosity (reduces variability in gene pool) • Sexual selection – female animals frequently chose among many possible fathers for their offspring; selecting father with best genes or best resource provider

14. Mutation • Serves to increase the types of alleles (increases variability in gene pool) • Probably only plays a minor role in evolution as rates are so low; although gene • duplication may have contributed significantly Shuffled with rest of gene pool and creates new reservoir for evolution to act upon

15. Using Hardy-Weinberg in the study of human disease • Derivation of equation Only 2 alleles in a population A=dominant allele (p) a=recessive allele (q) And therefore p+q=1 And in diploidy (p+q)2=1 =nt p2+2pq+q2 =1 If allele A is represented by p then AA individuals will be p2 If allele a is represented by q then aa individuals will be q2 And heterozygotes will be 2pq

16. Hardy Weinberg equation • Generalisations and extensions • For three alleles (p+q+r)2 =1 =nt p2+q2+r2+2pq+2pr+2qr=1 • For polyploidy (p+q)n =1, where n = ploidy (eg tetraploidy, n=4)

17. Use in carrier frequency determination • If we know the frequency of affected individuals in recessive disease we can determine the carrier frequency • Using p+q=1 and p2+2pq+r2 =1 Eg in disease Allabamosis (A- normal allele; a-mutant recessive allele) Say affected individuals account for 4% population (aa homozygous recessive) then q2=0.04; q=0.2 and knowing that p+0.2=1 then p=0.8 Predicted genotype frequencies >>>>> p2+2pq+q2 =1 0.64+(2 x 0.8 x 0.2)+0.04=1 0.64+0.32+0.04=1 Thus AA individuals will represent 64% population Carrier Aaindividuals will represent 32% population And aa individuals represent 4% population If the population is equilibrium!!!!!!

18. SummaryHardy Weinberg Equilibrium • Describes a state in a large randomly breeding population where the gene frequencies and genotype ratios remain constant from one generation to the next • Is a means of maintaining the reservoir of variability • Indicates that no evolutionary forces are in effect in the population • However most populations are evolving due to number of number of factors • Natural selection • Population size • Mating patterns • Mutation • Can be used to predict carrier frequencies and determine if evolutionary forces are at work on a given locus in a given population