7.012 Lecture Notes - Lecture 4: Esther Lederberg, Petri Dish, Replica Plating

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rosi10agarwal

4 Apr 2023

School

MIT

Department

Biology

Course

7.012

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This field was advanced by laws proposed by two people hardy and weinberg. Suppose in a population there are 2 alleles for a given gene, a and a. How often an a allele will be in the egg (in female) = p. How often an a allele will be in the egg = q a q. A p there are only 2 alleles for gene so aa p2. If you know allele frequencies, you can calculate genotype frequencies: At hardy-weinberg equilibrium: (p+q)2 = 1 (cid:198) p2 + 2pq + q2 = 1 q2. This is the equilibrium distribution called the hardy-weinberg. Frequency of individuals in a population with cystic fibrosis is 1/2000. Assuming equilibrium, allele frequencies (and therefore genotype frequencies) do not change over time. Allele frequencies tend to stay constant in populations. Let a = normal or wild type allele and a = cystic fibrosis (disease) allele q2 (affected individuals) = 1/2000 so q =

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Hardy-Weinberg Equilibrium Problems

p is the frequency of the dominant allele in the population

q is the frequency of the recessive allele in the population

p2 is the frequency of the homozygous dominant genotype

q2 is the frequency of the homozygous recessive genotype

2pq is the frequency of the heterozygous genotype

p + q = 1

p2 + 2pq + q2 = 1 Find q2 ï q ï p ï p2 ï 2pq

A rare disorder of cystic fibrosis (characterized by abnormal transport ofchloride and sodium across an epithelium, leading to thick, viscous secretions) occurs every 1 in 3,300 births. To express this trait one must be homozygous recessive (ff).

The cystic fibrosis allele is represented by f. The normal allele is F. Suppose both parents have alleles Ff. The possible combinations of alleles in the children are FF, Ff, Ff and ff. The alleles ff will cause the disease. So, although the parents do not have cystic fibrosis, they can produce children with the disease. The parents are called 'carriers' of the disease

What is the frequency of the population that carries the trait? (Ff)

For the data set below, determine whether the genotypefrequencies represent a population in Hardy-WeinbergEquilibrium.(The significant digits allow you to assume you canhave an exactly representative sample of 1000 individuals. Thecritical value at probability 0.05 with (only) one degree offreedom is 3.84.) You will use a Chi-squared test and answer thequestions below.

Genotype: AA Aa aa

Frequency: 0.312 0.335 0.353

a. Let p = frequency of the "A" allele and q = the frequency ofthe "a" allele. Within a perfectly representative sample of 1000individuals, how many "A" alleles would there be?

b. Therefore, what is the value of p?

c. After finding the actual values of p and q, what are theexpected values of individuals with the genotypes AA, Aa andaa?

d. What is your Chi-squared value? e. Is this population inHardy-Weinberg equilibrium?

cyanbat514

1 A) Cystic Fibrosis is an autosomal recessive disease, 1 out of every 2500 individuals of Caucasian descent in the US have cystic fibrosis. What frequency of cystic fibrosis carriers would you expect in the Caucasian population of the US under Hardy Weinberg Equilibrium? Show your work. (1 pt)

1 B) You know that penguin tuxedo color is a classic Mendelian single-gene trait, the allele for black and white tux coloring (T) is dominant over gray and white tux coloring (t). In a population of penguins, there are 400 black and white tuxedoed penguins and 200 gray and white tuxedoed penguins.

(i) Which observed genotypic or allelic frequencies can be calculated from this scenario without assuming Hardy Weinberg Equilibrium? (1.5 pt)

(ii) In one to two sentences, explain why differences may arise between observed and expected genotype frequencies. (1 pt)

1 C) You are studying inheritance of external keratin features in a dinosaur. Analysis has found that the presence of feathers is due to codominance between the AS (scales) and AH (horns) alleles. In one generation of a population you find 78 scaled dinosaurs, 76 feathered dinosaurs, and 64 horned dinosaurs.

(i) What are the observed allele frequencies of AS and AH ? Use p for the frequency of AS and q for the frequency of AH . Show your work. (1.5 pt)

(ii) What are the observed genotypic frequencies? Show your work. (1 pt)

(iii) Given the allelic frequencies calculated above, what are the expected number of scaled, feathered, and horned dinosaurs in a population of the same size (218) under Hardy Weinberg Equilibrium? Show your work. (1.5 pt)

(iv) Use a chi-square test to examine whether the gene you are studying is under Hardy Weinberg Equilibrium in this population. Show your work. Do you accept or reject the null hypothesis? (2 pts)

7.012 Lecture Notes - Lecture 4: Esther Lederberg, Petri Dish, Replica Plating

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