2 Population GeneticsMendelian genetics predicts the outcome of specific matings between individualsWhat about the genetics of an entire population?Population = all individuals of one species living in a given areaPopulation genetics works with the entire gene poolor all the alleles present in the whole population
3 How will alleles change in the population? Among a population of 2000 people:720 have blue eyes (recessive)1280 have brown eyes (dominant)DNA testing reveals:320 are homozygous for Brown Eyes(BB)960 are heterozygous for Brown Eyes (Bb)
4 Allele frequency f(B)= 960 + 320 + 320/ 4000 = 0.4 Allele frequency is the fraction:no. of a particular alleleno. of all alleles in populationFor these 2000 people, there are 4000 alleles in the gene pool:720 bb960 Bb320 BBhow many B alleles?how many b alleles?f(B)= / 4000 = 0.4F(b) = /4000 = 0.6
5 What happens in the next generation? In all the matings for this generation, what is the chance that an egg with the B allele will be fertilized by a sperm with the b allele and create a person with Bb genotype?Recall:40% of all eggs will carry B60% of all sperm will carry bRecall the Rule of Multiplication:(prob. of event a) (prob of event b)= probability of both events happening0.4 x 0.6 = 0.2424% of offspring Bb*Assuming no difference between sexesand no mating preferences!
6 What happens in the next generation? In all the matings for this generation:0.4 x 0.4 = 16% BB0.4 x 0.6 x 2 = 48% BbBb and bB(rule of addition)0.6 x 0.6 = 36% bb40%60%BbBBBbbb
7 What happens in the next generation? In all the matings for this generation:if 4000 offspring are born:0.4 x 0.4 = 16% BB BB0.4 x 0.6 x 2 = 48% Bb Bb0.6 x 0.6 = 36% bb bb2560 Brown1440 Blue
8 What happens in the next generation? New allele frequencies:If 4000 offspring640 BB1920 Bb1440 bb3200 B allele/8000 = 0.44800 b allele/8000 = 0.6After 5 generations:64,000 offspring10,240 BB30,720 Bb23,040 bb51,200 brown alleles / 128,000 = 0.476,800 blue alleles / 128,000 = 0.6
9 After 5 generations (or any number): Allele frequencies do not change!Recessive alleles are maintained in the population*If some specific assumptions are made
10 Hardy-Weinberg equilibrium Godfrey Hardy (mathematician) and Wilhelm Weinberg (physician) (early 1900s):Given some assumptions, allele frequencies won’t change:The population is largeMating is randomNo migration in or outNo mutationNo selection (no allele is advantageous)How often in nature are ALL of these assumptions met?Rarely, if ever. This is an “ideal” state.
11 Does Hardy-Weinberg work? In large populations, the Hardy-Weinberg equations predict results quite well for many traitsIf a population is not in equilibrium:Allele frequencies are changingEvolution is occurring!
12 Hardy-Weinberg equations Allele frequency:Let p = frequency of the dominant alleleLet q = frequency of the recessive alleleThen, p + q = 1Genotype frequency:p2 = frequency of homozygous dominant genotypeq2 = frequency of homozygous recessive genotype2pq = frequency of heterozygous genotypep2 + 2pq + q2 = 1
13 4 Steps to solving H-W Problems set recessives = q2Take square root of q21-q = pPlug into expanded equationExample: 16% of the cat population is white:q2= 0.16square root = 0.4= p p = 0.6(.6) (.4) = 1so, 36% of population is TT48% of population is Tt
14 Another Example:Fraggles are mythical, mouselike creatures that live beneath flower gardens.Of the 100 fraggles in a population, 75 have green hair (FF or Ff) and 25 have grey hair (ff).Assuming genetic equilibrium:What are the gene frequencies of F and f?What are the genotypic frequencies?
15 Answer to Fraggle Problems: Gene frequencies:q2= .25, so:q= .5p= .5Genotypic frequenciesFF = .25Ff = .5f f = .25
16 Application of H-W principle Sickle cell anemiainherit a mutation in gene coding for hemoglobinoxygen-carrying blood proteinrecessive allele = snormal allele = Slow oxygen levels causes RBC to sicklebreakdown of RBCclogging small blood vesselsdamage to organsoften lethal
17 Sickle cell frequency High frequency of heterozygotes 1 in 5 in Central Africans = Ssunusual for allele with severe detrimental effects in homozygotes1 in 100 =ssusually die before reproductive ageWhy is the s allele maintained at such high levels in African populations?Suggests some selective advantage of being heterozygous…
18 MalariaSingle-celled eukaryote parasite (Plasmodium) spends part of its life cycle in red blood cells123
19 Heterozygote Advantage In tropical Africa, where malaria is common:homozygous dominant (normal)die or reduced reproduction from malaria: SShomozygous recessivedie or reduced reproduction from sickle cell anemia: ssheterozygote carriers are relatively free of both: Sssurvive & reproduce more, more common in populationHypothesis:In malaria-infected cells, the O2 level is lowered enough to cause sickling which kills the cell & destroys the parasite.Frequency of sickle cell allele & distribution of malaria
20 Sickle Cell Example:If 9% of an African population is born with a severe form of sickle-cell anemia (ss), what percentage of the population will be more resistant to malaria?f(ss)= .09 = q2q= .3P= .72pq= .42so 42% of the population is resistant to malaria.
21 Using Hardy-WeinbergCystic Fibrosis: 1 in 1700 US Caucasian newborns have cystic fibrosis. Use an F for the normal allele and f for recessive:What percent of the above population have cystic fibrosis?What percent are healthy, non carriers?What percent are carriers of cyctic fibrosis?In a population of 1700 people, how many would you expect to be homozygous normal?In a population of 1700 people, how many would you expect to be heterozygous?= q2q= .024p= .976P2= .95242pq= .04681700 x .9524= 16191700 x .0468= 80