Richard Barber Richard.Barber@bwhct.nhs.uk 17 th January Population Genetics

1. What is Hardy-Weinberg equilibrium and what factors can distort this equilibrium? How can we use this to calculate carrier frequencies of recessive diseases if we know the proportion of people who are affected? Richard Barber Richard.Barber@bwhct.nhs.uk 17th January Population Genetics

2. What is Hardy-Weinberg equilibrium ? • The Hardy-Weinberg model, describes and predicts genotype and allele frequencies in a non-evolving population. • The model has five basic assumptions • 1) the population is large • 2) there is no gene flow between populations • 3) new mutations are negligible • 4) individuals are mating randomly • 5) natural selection is not operating on the population. • Given these assumptions, a population's genotype and allele frequencies will remain unchanged over successive generations, and the population is said to be in Hardy-Weinberg equilibrium.

3. Imagine a Founder Population 30 individuals - genotype ‘AA’ 70 individuals - genotype ‘aa’  Allele frequencies:  A = 0.3, a = 0.7 Genotype frequencies: AA = 0.3                                  Aa = 0.0                                  aa = 0.7 After a period of breeding, the numbers of heterozygotes will increase, and the homozygotes decrease. After many generations, the numbers of individuals with these genotypes will stabilise. This will be at H-WE. 

4. 2 Allele System At Equilibrium Allele:   Aa Frequency:  pq p + q = 1  Genotype:   AAAaaa Frequency:  p2 2pqq2 p2 + 2pq + q2 = 1

5. Curves showing the proportions of homozygotes A/A (blue line), homozygotes a/a (orange line), and heterozygotes A/a (green line) in populations of different allelic frequencies if the populations are in H-WE

6. Generalization for polyploidy • The H-W principle may also be generalized to polyploid systems, for organisms that have more than two copies of each chromosome. Consider again only two alleles. The diploid case is the binomial expansion of: • (p + q)2 • and therefore the polyploid case is the binomial expansion of: • (p + q)c • where c is the ploidy, for example with tetraploid (c = 4): • Expected genotype frequencies for tetraploidy • AAAA p4 • AAAa 4p3q • AAaa 6p2q2 • Aaaa 4pq3 • aaaa q4

7. The Population is Large • When individuals in a population reproduce, they do not necessarily reproduce their alleles in the exact proportions in which they have them. • When gametes are made through meiosis, each contains one of the two alleles for each trait, and which of those alleles gets passed on to the offspring depends on which gamete, by chance, goes into forming the offspring. • Sometimes some alleles are passed on more than would be expected, other times less than would be expected. The allele frequency will fluctuate at random from generation to generation. • This sampling effect is more pronounced in small populations. • Random genetic drift.

8. Gene Migration • Many species are made up of local populations whose members tend to breed within the group. Each local population can develop a gene pool distinct from that of local populations. • However, members of one population may breed with occasional immigrants from an adjacent population of the same species. • This can introduce new alleles or alter existing allele frequencies.

9. Random Mating • If individuals are choosy in their selection of mates the allele frequencies may become altered. • Humans tend not to mate at random, preferring phenotypes like themselves (eg height and skin colour). • Assortative mating. • Consanguinity is based on choosing a partner based on relatedness not phenotype. • Both mechanisms lead to an increase in homozygosity above the level expected by H-WE. Inbreeding leads to homozygosity by descent. • The probability of homozygosity by descent is called the inbreeding coefficient (F)

11. Natural Selection • If individuals having certain alleles are better able to produce mature offspring than those without them, the frequency of those alleles will increase. • While directional selection eventually leads to the loss of all alleles except the favoured one, some forms of selection, such as balancing selection, lead to equilibrium without loss of alleles

12. New Mutations • The frequency of alleles in a population will not remain in equilibrium if there are new mutations. • Mutation will have a very subtle effect on allele frequencies. Mutation rates are of the order 10−4 to 10−8, and the change in allele frequency will be, at most, the same order. • Recurrent mutation will maintain alleles in the population, even if there is strong selection against them.

13. The Uses of H-WE • The H-W model enables us to compare a population's actual genetic structure over time with the genetic structure we would expect if the population were in H-WE (i.e., not evolving). • If genotype frequencies differ from those we would expect under equilibrium, we can assume that one or more of the model's assumptions are being violated, and attempt to determine which one(s). • For clinical genetics its main use is in autosomal recessive diseases to estimate gene frequencies and carrier frequencies

14. Congenital Adrenal Hyperplasia is an autosomal recessive disease with an incidence of 1 in 10,000. • A CAH affected man and his wife with no family history wish to know the risk that their current pregnancy is affected by CAH • The incidence of CAH (1 in 10,000) = q2 • Thus q = √ 1/10,000 = 1/100 • Then as p + q = 1 the frequency of the normal alleles must be = 99/100 • 2pq = 2 x 99/100 x 1/100 = 0.0198 ~ 1/50 • So our affected man’s wife is at 1 in 50 risk of being a CAH carrier • Overall the risk to the current pregnancy is 1 in 100

15. X-Linked Disorder • Red-green colour blindness affects 1/12 men. • So q = 1/12, p = 11/12 • Female carrier frequency = 2pq • = 2 x 1/12 x 11/12 = 22/144 = ~1/6.5 • Females with colour blindness • = q2 = (1/12)2 = 1/144

16. Multiple Alleles • p2 + 2pq + 2pr + q2 + 2qr + r2 =1

17. ABO blood groups has dominant, co-dominant and recessive phenotypes • Let A = p, B = q, O = r • p2 + 2pq + 2pr + q2 + 2qr + r2 = 1 • AA + AB + AO + BB + BO + OO = 1 • Phenotype A AA + AO p2 + 2pr • Phenotype AB AB 2pq • Phenotype B BB + BO q2 + 2qr • Phenotype O OO r2 • Phenotypes A + O = p2 + 2pr + r2 = (p + r)2 • Phenotypes B + O = q2 + 2qr + r2 = (q + r)2 • √(A + O) = (p + r) = 1 - q • √(B + O) = (q + r) = 1 - p

18. Other Uses • Can also calculate mutation rates where selection is acting against a mutation. • Mutation has to replace the mutations lost to selection • s is the co-efficient of selection, chance of reproductive failure due to selection • fittest s = 0 • lethal s = 1 • m = sq2 (AR), m = sq(AD), m = sq/3 (XR) • This can be used to test for heterozygote advantage • CF and cholera or tuberculosis

19. Useful Websites • http://science.nhmccd.edu/biol/hwe.html • http://courses.bio.psu.edu/fall2005/biol110/hardy_weinbergII_answers.pdf • http://www.ngrl.org.uk/Manchester/Downloads/Training%20&%20Education/Risk%20Calculation%20Questions2006.pdf • Some worked through questions with answers • http://www.evotutor.org/EvoGen/EG1A.html • An animated version oh H-WE