Download Genetics and the Chi-squared test

Genetics and the Chi-squared test
1
Pollen from a pure-bred tomato plant with white flowers and yellow fruit was transferred to
the stigmas of a pure-bred plant with yellow flowers and red fruit. All the F1 generation had
yellow flowers and red fruit.
(a)
Explain why all the F1 plants had yellow flowers and red fruit.
……………………………………………………………………………………………………
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……………………………………………………………………………………………………
……………………………………………………………………………………………………
(b)
In a test cross, pollen from the F, generation was transferred to pure-bred plants with
white flowers and yellow fruit. The ratio of phenotypes expected among the offspring of
a dihybrid test cross such as this is 1:1:1:1.
Seeds from the test cross were collected and grown, giving plants with the following
phenotypes:
yellow flowers and red fruit
87
yellow flowers and yellow fruit
13
white flowers and red fruit
17
white flowers and yellow fruit
83
200
A chi-squared (2 ) test can be carried out to check whether the numbers of each
phenotype of offspring resulting from the test cross are in agreement with a 1:1:1:1 ratio.
Part of the calculation is shown in Table 1.
Table 1
phenotypes
observed
number (O)
expected ratio
expected
number (E)
O–E
(O – E)2
(O – E)2 / E
 (O-E)2 / E = 2
yellow flowers
red fruit
87
1
50
37
1369
27.38
yellow flowers
yellow fruit
13
1
50
white flowers
red fruit
17
1
50
white flowers
yellow fruit
83
1
50
33
1089
21.78
[3]
(i) Complete the shaded boxes in Table 1.1 to calculate 2 for these results.
[3]
(ii) State the number of degrees of freedom applicable to these results.
……………………………………………………………………………………………….
[1]
(iii) Use the calculated value of2 and the table of probabilities provided in Table 2 to
find the probability of the results of the test cross departing significantly by chance
from the expected ratio.
probability (p) ………………………………………………………………………………
[1]
Table 2
degrees of
freedom
1
2
3
4
probability, p
0.10
2.71
4.61
6.25
7.78
0.05
3.84
5.99
7.82
9.49
0.02
5.41
7.82
9.84
11.67
0.01
6.64
9.21
11.35
13.28
0.001
10.83
13.82
16.27
18.47
(iv) State what statistical conclusion may be drawn from the probability found in (b)(iii)
about the difference between expected and actual results.
……………………………………………………………………………………………
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(c)
Most tomato plants have leaves with cut margins, but some varieties have leaves that
are broad and entire – like the leaves of potato plants. A pair of alleles controls this
feature: the dominant allele, C, for cut and the recessive allele, c, for potato.
A pair of alleles also controls the colour of stems of tomato plants: the dominant allele,
P, for purple and the recessive, p, for green.
A student crossed plants that were heterozygous for both conditions. The student found
four different phenotypes amongst the offspring. One in sixteen of the offspring had
potato-shaped leaves and green stems.
Complete the genetic diagram below to explain the results of this cross.
[2]
F1
genotypes
………………………………….. …………………………………..
F1
………………………………….. …………………………………..
phenotypes
F1 gametes
………………………………….. …………………………………..
F2
…………………………………………………………………………
genotypes
and
…………………………………………………………………………
phenotypes
…………………………………………………………………………
F2 ratio
…………………………………………………………………………
[5]
[Total: 15]
(c) Explain the discrepancy between the expected and the actual results of the test cross.
[5]
[Total:
15]