Question

Imagine that you attempted to recreate Mendel's work with garden peas. You began by crossing true breeding violet-flowered, tall plants with white-flowered dwarf plants. After self-crossing the F1 generation, you obtain the following phenotypes in the F2 generation:
80 tall, violet flowers
36 tall, white flowers
39 dwarf, violet flowers
5 dwarf, white flowers

a. How many tall plants with violet flowers were expected?
b.How many tall plants with white flowers were expected?
c. How many dwarf plants with violet flowers were expected?
d. How many dwarf plants with white flowers were expected?

Use a chi-square analysis to test the hypothesis that the F2 data for stem length (tall:dwarf) is consistent with Mendel's law of segregation. Calculate the chi square value.

Use a chi-square analysis to test the hypothesis that the F2 data for stem length (tall:dwarf) and flower color (violet:white) is consistent with Mendel's law of independent assortment. Calculate the chi square value.

Answer 1

Answer:

(a) 90

(b) 30

(c) 30

(d) 10

F2 data for stem length (tall:dwarf) is consistent with Mendel's law of segregation.

F2 data for stem length (tall:dwarf) and flower color (violet:white) is consistent with Mendel's law of independent assortment

Explanation:

The F2 phenotypes are supposed to be in 9:3:3:1 according to Mendelian law. The total number of F2 progeny is: 80 + 36 + 39 + 5 = 160

(a) Hence, the expected number of tall, violet plants will be:

            9/16 x 160 = 90

(b) Expected number of tall, white plants will be:

            3/16 x 160 = 30

(c) Expected number of dwarf, violet plants will be:

            3/16 x 160 = 30

(d) Expected number of dwarf, white plants will be:

            1/16 x 160 = 10.

Total number of tall F2 plants = 80 + 36 = 116

Total number of dwarf F2 plants = 39 + 5 = 44

Expected ratio of tall:dwarf plants according to Mendel = 3:1

Expected number of tall plants = 3/4 x 160 = 120

Expected number of dwarf plants = 1/4 x 160 = 40

Chi square $X^2$

= $\frac{(observed frequency - expected frequency)^2}{expected frequency}$

$X^2$ for tall = $\frac{(116 - 120)^2}{120}$

                                    = 0.1333

$X^2$ for dwarf = $\frac{(44 - 40)^2}{40}$

                                      = 0.40

Total $X^2$ = 0.1333 + 0.4

                                    0.5333

Degree of freedom = n - 1

                                   2 - 1 = 1

Tabulated $X^2$ (α = 0.05) = 3.841

Since the tabulated $X^2$ is more than the calculated $X^2$, the hypothesis that the F2 data for stem length (tall:dwarf) is consistent with Mendel's law of segregation is accepted.

                                       Observed    Expected    $X^2$

tall, violet flowers                  80          90         $\frac{(80-90)^2}{90} = 1.11$

tall, white flowers                36            30          $\frac{(36-30)^2}{30} = 1.2$

dwarf, violet flowers             39           30         $\frac{(39-30)^2}{30} = 2.7$

dwarf, white flowers            5              10         $\frac{(5-10)^2}{10} = 2.5$

       Total                             160           160                       7.51

Degree of freedom = 4 - 1 = 3

Tabulated $X^2$ (α = 0.05) = 7.815

The tabulated $X^2$ value is more than the calculated $X^2$ value. Hence, F2 data for stem length (tall:dwarf) and flower color (violet:white) is consistent with Mendel's law of independent assortment.