Hardy Weinberg Principle

Transcription

1 Hardy Weinberg Principle Population genetics study of properties of genes in populations Hardy Weinberg original proportions of genotypes in a population will remain constant from generation to generation Sexual reproduction (meiosis and fertilization) alone will not change allelic (genotypic) proportions. 1

2 Hardy Weinberg Principle Necessary assumptions Allelic frequencies would remain constant if population size is very large random mating no mutation no gene input from external sources no selection occurring 2

3 FREQUENCY OF ALLELES IN THE POPULATIONS FREQUENCY OF ALLELES IN GAMETES A a A AA Aa a Aa aa 3

4 FREQUENCY OF ALLELES IN THE POPULATIONS FREQUENCY OF ALLELES IN GAMETES A 0,9 a 0,1 A 0,9 AA 0,81 Aa 0,09 a 0,1 Aa 0,09 aa 0,01 4

5 FREQUENCY OF ALLELES IN THE POPULATIONS FREQUENCY OF ALLELES IN GAMETES A a 0,9 0,1 p q A AA Aa 0,9 0,81 0,09 p p 2 pq a Aa aa 0,1 0,09 0,01 q pq q 2 5

6 FREQUENCY OF ALLELES IN THE POPULATIONS FREQUENCY OF ALLELES IN GAMETES A a 0,9 0,1 p q A AA Aa 0,9 0,81 0,09 p p 2 pq a Aa aa 0,1 0,09 0,01 q pq q 2 AA 0,81 p 2 2Aa 0,18 2pq aa 0,01 q 2 6

7 Hardy Weinberg Equilibrium Population of cats n= white and 84 black bb = white B_ = black Can we figure out the allelic frequencies of individuals BB and Bb? 7

8 Hardy Weinberg Principle Calculate genotype frequencies with a binomial expansion (p+q) 2 = p 2 + 2pq + q 2 p2 = individuals homozygous for first allele 2pq = individuals heterozygous for alleles q2 = individuals homozygous for second allele 8

9 Hardy Weinberg Principle p 2 + 2pq + q 2 and p+q = 1 (always two alleles) 16 cats white = 16bb then (q 2 = 0.16) This we know we can see and count!!!!! If p + q = 1 then we can calculate p from q 2 square root of q 2 = q.16 q=0.4 p + q = 1 then p=1 q p =.6 ( = 1) p 2 =.36 All we need now are those that are heterozygous (2pq) (2 x.6 x.4)= = 1 9

10 Hardy Weinberg Equilibrium 10

11 Five Agents of Evolutionary Change 1 Mutation Mutation rates are generally so low they have little effect on Hardy Weinberg proportions of common alleles. ultimate source of genetic variation 11

12 Severe Autosomal Recessive disease 12

13 2 Gene flow movement of alleles from one population to another tend to homogenize allele frequencies 13

14 Migrations 14 14

15 Five Agents of Evolutionary Change 3 Nonrandom mating assortative mating phenotypically similar individuals mate Causes frequencies of particular genotypes to differ from those predicted by Hardy Weinberg. 15

16 Five Agents of Evolutionary Change 4 Genetic drift statistical accidents. Random fluctuations in the frequency of the appearance of a gene in a small isolated population, presumably owing to chance rather than natural selection. Frequencies of particular alleles may change by chance alone. important in small populations founder effect few individuals found new population (small allelic pool) bottleneck effect drastic reduction in population, and gene pool size 16

17 Genetic Drift Bottleneck Effect 17

18 5 Five Agents of Evolutionary Change Selection Only agent that produces adaptive evolutionary change artificial breeders exert selection natural nature exerts selection variation must exist among individuals variation must result in differences in numbers of viable offspring produced variation must be genetically inherited natural selection is a process, and evolution is an outcome 18

19 Five Agents of Evolutionary Change Selection pressures: avoiding predators matching climatic condition pesticide resistance 19

20 Natural Selection Biston Betularia 1848 Rare black animals

21 Severe Autosomal Recessive disease 21

22 Next generation Severe Autosomal Recessive disease A a A a AA Aa aa 1 lethal /200 20/ /198 18/ AA.91 x Aa 2 x.91 x aa.09 x

23 Heterozygote Advantage Heterozygote advantage will favor heterozygotes, and maintain both alleles instead of removing less successful alleles from a population. 23

24 Measuring Fitness Fitness is defined by evolutionary biologists as the number of surviving offspring left in the next generation. relative measure Selection favors phenotypes with the greatest fitness. 24

25 Selection and H-W population analysis Natural selection is caused by differential fitness Fitness (w) is a measure of a genotype s success at contributing to the next generation Survival or viability (v) Reproduction or fecundity (f) Fitness w = (v)(f) 25

26 Single locus, 2 alleles Alleles A 1 A 2 Genotype A 1 A 1 A 1 A 2 A 2 A 2 Frequency p 2 2pq q 2 Absolute fitness* w 11 w 12 w 22 Mean fitness w = p 2 w pq w 12 + q 2 w 22 of population *calculated directly from survival and viability data 26

27 Result if w 11 < w 12 > w 22 Heterozygous advantage (overdominance) 27

28 Heterozygous Advantage w 11 =0.60 w 12 =1.00 w 22 =0.60 Intense selection without change in allele frequency! 28

29 Heterozygote Advantage in man Sickle cell anemia Homozygotes exhibit severe anemia, have abnormal blood cells, and usually die before reproductive age. Heterozygotes are less susceptible to malaria. 29

30 The Plasmodium life cycle 30

31 Sickle Cell and Malaria 31

32 32

33 Deleterious recessive alleles may, in some cases, provide a small benefit to heterozygotes Phenylketonuria (PKU) autosomal recessive Heterozygous advantage in PKU seems to operate via protection against mycotoxins produced by Aspergillus and Penicillium that infest stored foods. Mild, wet climate of Ireland and W Scotland encourages mold growth; these areas have suffered repeated famines during which moldy food were eaten. Heterozygous (PKU) women have lower spontaneous abortion rate. Solution? Test early. Treat w/ low-protein diet. 33

34 Classic PKU is caused by a complete or near-complete Deficiency of phenylalanine hydroxylase activity; without dietary restriction of phenylalanine, most Children with PKU develop profound and irreversible intellectual disability. PAH deficiency can be diagnosed by newborn screening in virtually 100% of cases based on detection of hyperphenylalaninemia using the Guthrie assay on a blood spot obtained from a heel prick. 34

35 PKU Diet >> No mental retardation - aa will reproduce 1/ incidence of the disease Aa 1/50 in the population aa x AA >>>> Aa 100% Expected phenotype >>> normal, but 35

36 Aa x AA >>> Aa the Maternal PKU Collaborative Study reports that even at maternal plasma Phe concentrations of µmol/l, 6% of infants are born with microcephaly and 4% with postnatal growth retardation. If maternal plasma Phe concentrations are greater than 900 µmol/l, the risk is 85% for microcephaly, 51% for postnatal growth retardation, and 26% for intrauterine growth retardation. The risk for these abnormalities is both dose and time dependent. 36

37 The abnormalities that result from exposure of a fetus to high maternal plasma Phe concentration are the result of 'maternal HPA/PKU'. The likelihood that the fetus will have congenital heart disease, Intrauterine and postnatal growth retardation, microcephaly, and intellectual disability depends upon the severity of the maternal HPA and the effectiveness of the mother's dietary management. 37

38 Population PAH Deficiency in Live Births Carrier Rate Citation Turks 1/2,600 1/26 Ozalp et al [1986] Irish 1/4,500 1/33 Northern European heritage, East Asian 1/10,000 1/50 Japanese 1/143,000 1/200 Finnish, Ashkenazi Jewish 1/200,000 1/225 DiLella et al [1986] Scriver & Kaufman [2001] Aoki & Wada [1988] Scriver & Kaufman [2001] African ~1/100,000? Anecdotal 38

39 Cystic fibrosis, (CF), AR disease, affects lungs, sweat glands and digestive system. It is caused by the malfunction of the CFTR protein, which controls intermembrane transport of chloride ions, which is vital to maintaining equilibrium of water in the body. The malfunctioning protein causes viscous mucus to form in the lungs and intestinal tract. In the past children born with CF had a life expectancy of only a few years, now increased to adulthood. However, even in these individuals, male and female, CF typically causes sterility. It is the most common genetic disease among people of European descent. Approximately 1/25 persons of European descent is a carrier, and 1 in 2500 to 3000 children born is affected by cystic fibrosis. 39

40 In CF carriers, survivorship is influenced in relation to diseases involving loss of body fluid, typically due to diarrhea. The most common of them is cholera, patients often die of dehydration due to intestinal water losses. In a mouse model of CF the heterozygote (carrier) mouse had less secretory diarrhea than normal, non-carrier mice. Thus resistance to cholera explained the selective advantage to being a carrier for CF and why the carrier state was so frequent. A second theory is that CF mutation provides resistance to tuberculosis, which was responsible for 20% of all European deaths between 1600 and 1900, so even partial protection against the disease could account for the current high gene frequency. 40

41 Aa frequency Risk for affected children Incidence of disease 1/30 1/30 x 1/30 x 1/4 1/3,600 1/50 1/50 x 1/50 x 1/4 1/10,000 1/100 1/100 x 1/100 x 1/4 1/40,000 If I know the incidence of the disease, I can calculate easily the number of Aa in the population 41

42 I I:1 I:2 II II:1 II:2 II:3 II:3 1/10,000 II:2 1 x 1/50 x 1/4 1/200 affected 199/200 unaffected II:3 1/10,000 II:2 status not known 2/3 x 1/50 x1/4 1/300 affected 299/300 unaffected 42