Population GeneticsPowerPoint PresentationSlide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12KNOW THIS.Slide 14Slide 15Population GeneticsI. Estimating allele frequenciesA. Calculating relative frequencies of each genotype within a population:P = relative frequency of A1A1 genotype# of A1A1 individuals/total # of individuals in popH = relative frequency of A1A2 genotype# of A1A2 individuals/total # of individuals in popQ = relative frequency of A2A2 genotype# of A2A2 individuals/total # of individuals in popRelative frequency of the A1 allele:p = P + 1/2HRelative frequency of the A2 allele:q = Q + 1/2HThese are relative frequencies so p + q = 1.0Example: In a sample of 1000 individuals from a population, the following number of individuals of each genotype were observed.Genotype N A1A1240A1A2 400A2A2 360What are the relative frequencies of the A1 and A2 alleles in this population?Population GeneticsII. Hardy-Weinberg Equilibrium (HWE)A. When no forces of evolution influence allele frequencies at a single gene locus1. Consequences: -locus is said to be in genetic equilibrium-allele frequencies will predict genotype frequencies-genotype frequencies will remain the SAME from generation to generation -HWE is a property of a GENE, not of an individual or a population2. Assumptions of Hardy-Weinberg Equilibrium1) large population size (N > 1000) -- insures no effects of genetic drift2) no external forces act to alter genotype frequencies -- no natural selection, no mutation, no migration3) random mating with respect to genotypes -- no assortative mating, sexual selection, or inbreeding3. Are these assumptions ever met?-selectively neutral loci -- genes whose phenotypes have no positive or negative effectsExample: blood cell surface antigens like LM - LN or A, B, O blood groupsC. Properties of the Hardy-Weinberg Principle1. If a locus is in HWE, one can use the following formula to predict genotype frequencies from the allele frequencies: (p + q)2 = p2 + 2pq + q2 = 1.0Where p = relative frequency of A1 alleleq = relative frequency of A2 allelep2 = relative frequency of A1A1 genotype2pq = relative frequency of A1A2 genotypeq2 = relative frequency of A2A2 genotypeD. Implications of HWE for a gene locus1. Genotype frequencies will remain CONSTANT from one generation to the next2. Allelic variation is NOT LOST between successive generations-rare alleles do not go extinct if locus is in HWESuppose A2 is rare: q = 0.01 and p = 0.99Thus most of the A2 alleles are found in heterozygotes and will be maintained as long as the locus remains in HWE3. How fast can a locus reach HWE in a population?-ONE generation of random mating will restore a locus to HWE 4. Single locus with multiple alleles can also be in HWE (won’t have problems like this)3 alleles = (p + q + r)2= p2 + 2pq + r2 + 2pr + 2rq + q2 = 1.05. Sex-linked loci can also be in HWEFemales: p2=P, 2pq=H, q2=Q Males: p=P, q=QE. Using Hardy-Weinberg Equilibrium as a test for evolution1. HWE predicts that allele frequencies will remain the same across generations2. Evolution is a change in allele frequencies across generations3. Thus deviations of OBSERVED genotype frequencies from EXPECTED HWE genotype frequencies = EVOLUTION at that locus4. Example:Genotype N Relative freq.P=A1A1 240 0.24H=A1A2 400 0.40Q=A2A2 360 0.36A1 = p = 0.44 A2 = q = 0.56Is this locus in HWE?p2 = (0.44)2 = 0.192pq = 2(0.44)(0.56) = 0.49q2 = (0.56)2 = 0.32What we really want to know--Do observed genotype frequencies = expected genotype frequenciesISP = p20.24 = 0.19H = 2pq 0.40 = 0.49Q = q20.36 = 0.32No, more homozygotes and fewer heterozygotes than HWE predicts--some type of evolution is occurring at this locusKNOW THIS. Can use Chi-Square to test if this difference is significantConvert frequencies back to # of individuals:HWE expected Observedp2 = 0.19 x 1000 = 190 P = 2402pq = 0.49 x 1000 = 490 H = 400q2 = 0.32 x 1000 = 320 Q = 360Now set up X2; df = k - r where k = # of phenotypes and r = # of alleles 3 - 2 = 1 df5. Importance of Hardy-Weinberg Principle to population genetics-provides a starting point to test for evolution within populations-if locus is not in HWE, then evolution must be acting on the locus-next step is to figure out which force of evolution is causing the deviation from HWEDeafness is a recessive trait found in dalmatians. Within the U.S. population, the frequency of deaf dalmatians is 3%. Assuming that the deafness locus is in Hardy-Weinberg equilibrium, what proportion of carriers of this trait are found in the U.S.