Lecture 9b: Applications of the Hardy-Weinberg Theorem

Transcription

1 Lecture 9b: Applications of the Hardy-Weinberg Theorem For a two-allele locus: Let p = the frequency of one allele in the population (usually the dominant) Let q = the frequency of the recessive allele Notice that: p + q = 1 p = 1 q q = 1 p Genotypes should occur in the population according to: p 2 = proportion of population that is homozygous for the dominant allele (e.g., RR) 2pq = proportion of population that is heterozygous (e.g., Rr) q 2 = proportion of population that is homozygous for the recessive allele (e.g., rr) Given either p or q, one can solve for the rest of the above What would q be if p = 0.6? What would 2pq be if p = 0.5? Given the frequency of either homozygous genotype, the rest of the can be solved What would q be if p 2 = 0.49? The Hardy-Weinberg is used to predict genotype frequencies in a population. Predicted genotype frequencies are compared with actual frequencies. used for traits in simple dominant-recessive systems must know frequency of recessive homozygotes "The Hardy-Weinberg is based on Mendelian genetics. It is derived from a simple Punnett square in which p is the frequency of the dominant allele and q is the frequency of the recessive allele." 1

2 Hardy-Weinberg theorem Counting Alleles assume 2 alleles = B, b frequency of dominant allele (B) = p frequency of recessive allele (b) = q frequencies must add to 1 (100%), so: p + q = 1 Hardy-Weinberg theorem Counting Individuals frequency of homozygous dominant: p x p = p 2 frequency of homozygous recessive: q x q = q 2 frequency of heterozygotes: (p x q) + (q x p) = 2pq frequencies of all individuals must add to 1 (100%), so: H-W formulas..again.!!!! Alleles: p + q = 1 B b Individuals: Using Hardy-Weinberg population: 100 cats 84 black, 16 white How many of each genotype? p 2 =.36 2pq=.48 q 2 =.16 q 2 (): 16/100 =.16 q (b):.16 = 0.4 p (B): = 0.6 What Must assume are the genotype population frequencies? is in H-W equilibrium! You need to be able to work with the Hardy- Weinberg. For example, if 9 of 100 individuals in a population suffer from a homozygous recessive disorder can you calculate the frequency of the disease-causing allele? Can you calculate how many heterozygotes are in the population?. The terms in the represent the frequencies of individual genotypes. [A genotype is possessed by an individual organism so there are two alleles present in each case.] P and q are allele frequencies. Allele frequencies are estimates of how common alleles are in the whole population. It is vital that you understand the difference between allele and genotye frequencies. 2

3 9 of 100 (frequency = 0.09) of individuals are homozygous for the recessive allele. What term in the H-W is that equal to? It s q 2. If q 2 = 0.09, what s q? Get square root of q 2, which is 0.3, which is the frequency of the allele a. If q=0.3 then p=0.7. Now plug p and q into to calculate frequencies of other genotypes. p 2 = (0.7)(0.7) = frequency of AA 2pq = 2 (0.3)(0.7) = 0.42 frequency of Aa. To calculate the actual number of heterozygotes simply multiply 0.42 by the population size = (0.42)(100) = 42. Example If only 6% of the population displays pale eyes (recessive gene e). What is the frequency of genotype Ee in this population? q 2 = > q = 0.24 p + q = 1 ---> p = 0.76 Ee = 2pq = 2(0.76)(0.24) = 0.36 Hardy-Weinberg Problem sets Lets get our calculators!!! Problem 1 What genetic factors must be occurring for a Hardy-Weinberg equilibrium to exist? 3

4 Problem 2 In a population of 1000 penguins, there are two different foot colour phenotypes namely yellow (dominant) and blue (recessive). If 12 penguins have blue feet, find the following. a. The frequency of both alleles. b. The frequencies of the three possible genotypes. Problem 3 Cystic fibrosis is a genetic disorder in homozygous recessives that causes death during the teenage years. If 4 in 10,000 newborn babies have the disease, what are the expected frequencies of the three genotypes in newborns, assuming the population is at Hardy-Weinberg equilibrium? Problem 4 The allele y occurs with a frequency of 0.8 in a population of clams. Give the frequency of genotypes YY, Yy, and yy Problem 5 16% of a human population is unable to taste the chemical PTC. These non-tasters are recessive for the tasting gene. a. What percentage of individuals in the population are tasters..? b. What is the frequency of the dominant and recessive alleles..? c. What percentage of the population are heterozygous for the trait Problem 6. The delta-32 mutation is a recessive gene that gives humans protection from HIV infection. The allele frequency in a town in Sweden is 20% a. What percentage of the population have 2 copies of the gene and are therefore immune to HIV..? b. What percentage of the population are less susceptible to the disease since they are heterozygous..? Question 7 Two percent of humans on the planet have red hair (a recessive trait). a. What percentage of humans are heterozygous for this trait b. Twelve percent of people in Zimbabwe have red hair. What percentage of this population is homozygous for non-red hair 4

5 Question 8 A population of zebras is in Hardy- Weinberg equilibrium. A researcher counts 16% of organisms that are homozygous recessive for a particular trait. What percentage are homozygous dominant? Question 9 In USA, the total human population is 300million of this American population have a recessive trait called cystic fibrosis. How many americans are carriers?? And the BIG ONE..Problem 10 In the year 2374, humans have finally developed the technology necessary for time travels. You are a scientist interested in the population genetics of extinct animals. Taking advantage of this technological advance, you decide to go to the past 8 million years to conduct a field work in Venezuela to study a population of Phoberomys pattersoni, the world s largest extinct rodent weighing approximately 700 kg and looking vaguely like a giant guinea pig. The coat color of this rodent varies between tan (dominant) and brown (recessive). Assume the population is in Hardy-Weinberg equilibrium. You observe 336 tan Phoberomys and 64 brown Phoberomys during your study. Answer questions on the following slide.. Problem 10: Questions a) What is the frequency of the homozygous recessive genotype? b) What is the allelic frequency of the dominant (tan) allele in the population? c) Of the animals you observed, how many were heterozygous? d) You make another trip to Venezuela and this time you observe 650 animals. How many of the 650 animals would you expect to be tan, assuming the population is still in Hardy-Weinberg equilibrium? e) How many of these tan animals are homozygous for the dominant allele? Problem 10: Questions cont f. How many of these 650 animals would you expect to be brown, assuming the population is still in H-W equilibrium..? g. As you observe the animals, you count 200 brown Phoberomys and 450 tan. Conduct a chi-square test to determine if your observations are significantly different from what you expected. h. What does your result in (g) mean in terms of the genetic composition of this population of Phoberomys Any Questions..????? Any Pane Questions?? Varikuvharwa here..?? Kikikikikikikikikiki..!!!!!!! 5