CHI-SQUARE EXERCISE – PROBLEM 1

 

In Drosophila:

 

A = normal wing                     B = brown body color

a = vestigial wing                    b = ebony color

 

A pair of parental flies, AaBb x AaBb, are allowed to breed.  Their offspring are allowed to interbreed with each other for many generations.  You sample 80 flies from a population of 500 and find the following:

 

Normal wing, brown color:     49

Normal wing, ebony color:     15

Vestigial wing, brown color:   9

Vestigial wing, ebony color:   7

Total sample:                           80

 

In your sample of 80 you find 39 males and 41 females.

 

Do the following calculations and show your work on the Hand-In:

 

  1. Calculate chi-square for the distribution of body color and wing type.
  2. What are your degrees of freedom?
  3. What percentage of the time do you expect this deviation due to chance?

 

Extra (not required on hand-in):

  1. Calculate chi-square for distribution of males and females.
  2. What are your degrees of freedom?
  3. What percentage of the time would you expect this deviation due to chance?

CHI-SQUARE EXERCISE – PROBLEM 2

 

In sweet peas, purple flowers (A) are dominant to white (a).  However, a second gene codes for an enzyme involved in pigment production; at least one copy of the dominant allele for this gene (B) must be present for purple flowers to be possible.  In other words, bb plants have white flowers even if they are AA or Aa.

 

Two purple-flowered plants that are AaBb are crossed: AaBb x AaBb.  Their offspring are used to establish a population.  After a number of generations for that population, you randomly sample 100 plants and count:

 

            Purple-flowered plants:           58

            White-flowered plants:           42

 

Do the following calculations and show your work on the Hand-In:

 

  1. Calculate chi-square for distribution of flower color.
  2. What are your degrees of freedom?
  3. What percentage of the time would you expect this deviation due to chance?

CHI-SQUARE EXERCISE – PROBLEM 3

 

In parakeets, feather color is determined by two genes:

 

A = yellow pigment produced            B = blue melanin produced

a = no yellow pigment produced        b = no blue melanin produced

 

A bird that makes both yellow pigment and blue melanin is green (A_B_).  A bird that makes no yellow pigment and no blue melanin is white (aabb).

 

Two doubly heterozygous birds are mated: AaBb x AaBb

 

They produce many offspring that are used to establish a population.  After a number of generations you have a flock of 75 birds in your large aviary.  You randomly sample 20 birds and count the following:

 

Yellow parakeets        4

Blue parakeets             4

Green parakeets          12

White parakeets          0

 

In your sample you find 8 males and 12 females.

 

Do the following calculations and show your work on the Hand-In:

 

  1. Calculate chi-square for the distribution of feather color.
  2. What are your degrees of freedom?
  3. What percentage of the time do you expect this deviation due to chance?

 

Extra (not required on hand-in):

  1. Calculate chi-square for distribution of males and females.
  2. What are your degrees of freedom?
  3. What percentage of the time would you expect this deviation due to chance?

 


CHI-SQUARE EXERCISE – PROBLEM 4 (extra)

 

In Drosophila, eye color is an X-linked trait, and females are XX while males are XY.  The alleles for eye color are:

 

XR = red eyes (dominant)

Xr = white eyes (recessive)

Y = no allele (Y chromosome)

 

Your TA gives you a male fly and a female fly as gifts, and you decide to start a colony:

 

Parents                        XRXr  x  Xr Y

 

You allow the offspring of these parents to interbreed, and continue interbreeding for several generations.  Soon your population reaches over 1000 flies.  You take a random sample of 100 flies and observe:

 

            30 red-eyed females

            28 red-eyed males

            22 white-eyed females

            20 white-eyed males

 

Do the following:

 

  1. Calculate chi-square value for your results (combined calculation for both eye color and sex).
  2. What are your degrees of freedom?
  3. What percentage of the time would you expect this deviation due to chance?

CHI-SQUARE EXERCISE – PROBLEM 5 (extra)

 

In Drosophila:

 

N = normal wing; frequency of allele N = p

n = vestigial wing; frequency of allele n = q

 

You have a population of 200 flies and you divide them into 2 equal groups such that in these beginning populations p = 0.5 and q = 0.5:

 

GROUP 1:      50 normal-winged (25 male, 25 female)

                        50 vestigial-winged (25 male, 25 female)

 

GROUP 2:      50 normal-winged (25 male, 25 female)

                        50 vestigial-winged (25 male, 25 female)

 

Group 1 flies are allowed to remain in a cage and interbreed for many generations.

 

Group 2 flies are kept in a cage that has a fan constantly blowing into it.  These flies are allowed to interbreed for many generations.

 

After the population in each cage is over 1000, you randomly sample 100 flies from each cage and find:

            Group 1:          76 normal winged                   Group 2:          8 normal-winged

                                    24 vestigial-winged                                         92 vestigial-winged

 

Do the following:

 

  1. Calculate chi-square for Group 1’s wing phenotypes.
  2. What are your degrees of freedom?
  3. What percentage of the time would you expect this deviation due to chance?
  4. Calculate chi-square for Group 2’s wing phenotypes.
  5. What are your degrees of freedom?
  6. What percentage of the time would you expect this deviation due to chance?
  7. How did environment affect wing type?