Concept explainers
For Mendel’s data for the experiment in Figure 2.8, conduct a chi square analysis to determine if the data agree with Mendel’s law of independent assortment.
To review:
Chi-square analysis for determining Mendel’s law of independent assortment.
Introduction:
Mendel’s law of independent assortment states that when crossing takes place between individuals, the alleles get sorted into different gametes independently. Chi-square test is the test which is used to determine the difference between the observed value and the expected value. It either accepts or rejects the hypothesis proposed from the test.
Explanation of Solution
In Mendel’s analysis of two-factor crosses, he crossed two true-breeding pea plants that possess two different characters. One of the strains is round, yellow seeds (RRYY) which is dominant and the other strain is wrinkled, green seeds (rryy) which is a recessive genotype. The data obtained in Mendel’s experiment is given below as:
Parental cross | F1 generation | F2 generation |
Round, yellow X wrinkled green seeds | All round, yellow | 315round, yellow seeds |
108 round, green seeds | ||
101 wrinkled, yellow seeds | ||
32 wrinkled, green seeds |
In the data, a total of 556 (315+108+101+32) offspring were obtained in the F2 generation. The observed data is consistent with 9:3:3:1 ratio. The cross between the F2 offspring is shown below.
Parents: RrYy and RrYy
Gametes:
Parent 1: RY, Ry, Ry, and Ry
Parent 2: RY, Ry, Ry, and Ry
Cross using Punnett square:
Gametes | RY | Ry | rY | ry |
RY | RRYY | RRYy | RrYY | RrYy |
Ry | RRyY | RRyy | RrYy | Rryy |
rY | RrYY | RrYy | rrYY | rrYy |
Ry | RrYy | Rryy | rrYy | rryy |
The number of offspring with different phenotypes is calculated below using the probability formula,
Thus, by using this formula, the expected number of offspring with different phenotypes is calculated below:
For round pod and yellow seed,
For yellow pod and wrinkled seed,
For green pod and round seed,
For green pod and wrinkled seed,
Hence, 313 (round, yellow), 104 (wrinkled yellow), 104(round, green), and 35 (wrinkled, green) offspring are expected in each phenotype.
By using the chi-square test, the observed value and the expected value are taken in the formula which is represented as:
Hence, thechi-square value of the observed and the expected data is 0.5.
We get a value of 0.51. Degree of freedom is n-1, where n= 3 with four categories of observations.
The P value is checked in the chi-square table for the value of 0.5.If the P-value lies within the range of 0.80 and 0.95, it indicates the deviation between expected results and observed results. The value is between 80% and 95%. Thus, the hypothesis that the data agrees with Mendel’s law of independent assortment is accepted.
Therefore, it can be concluded that chi-square analysis ranges between 0.8 and 0.9%, so there is only a slight deviation between the compared values. Thus, chi-square analysis confirms that the null hypothesis and the results are in favor of the law of independent assortment.
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Chapter 2 Solutions
Genetics: Analysis and Principles
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