# Mendel crossed pea plants that produced round seeds with those that produced wrinkled seeds and self-fertilized the progeny. In the F2, he observed 5474 round seeds and 1850 wrinkled seeds. Using the letters W and w for the seed texture alleles, diagram Mendel’s crosses, showing the genotypes of the plants in each generation. Are the results consistent with the Principle of Segregation?

Mendel crossed pea plants that produced round seeds with those that produced wrinkled seeds and self-fertilized the progeny. In the F2, he observed 5474 round seeds and 1850 wrinkled seeds. Using the letters W and w for the seed texture alleles, diagram Mendel’s crosses, showing the genotypes of the plants in each generation. Are the results consistent with the Principle of Segregation?

## Answer

To determine if Mendel’s results are consistent with the Principle of Segregation, we need to follow Mendel’s crosses step-by-step and analyze the genotype ratios in the F2 generation.

### Mendel’s Crosses

**Parental Generation (P):**- Round seeds (RR or Rr) × Wrinkled seeds (rr)
- In Mendel’s experiments, round seeds were dominant, and wrinkled seeds were recessive. Thus, we can assume the round-seeded plant is homozygous dominant (RR), and the wrinkled-seeded plant is homozygous recessive (rr).

**F1 Generation:**- The cross: RR × rr
- All F1 offspring will have the genotype Rr (heterozygous) and will exhibit the dominant round seed phenotype.
- Genotype of F1: Rr × Rr

**F2 Generation:**- Self-fertilization of F1 plants (Rr × Rr):
- To determine the F2 genotypes and phenotypes, we use a Punnett square:

**R****r****R**RR Rr **r**Rr rr **Genotypes:**- RR: 1/4
- Rr: 1/2
- rr: 1/4

**Phenotypes:**- Round seeds (RR or Rr): 3/4
- Wrinkled seeds (rr): 1/4

**Phenotype Ratios in F2:**- According to Mendel’s results:
- Round seeds: 5474
- Wrinkled seeds: 1850

- Total seeds in F2 = 5474 + 1850 = 7324
- Expected ratio of round to wrinkled seeds = 3:1
- Expected number of round seeds = $43 ×7324≈5493$
- Expected number of wrinkled seeds = $41 ×7324≈1831$

- According to Mendel’s results:

### Chi-Square Test

To check the consistency with the Principle of Segregation, we use the chi-square test to compare the observed numbers with the expected numbers:

**Observed Values:**- Round seeds: 5474
- Wrinkled seeds: 1850

**Expected Values:**- Round seeds: 5493
- Wrinkled seeds: 1831

**Chi-Square Calculation:**

\text{Chi-Square Calculation:}

\chi^2 = \frac{(O - E)^2}{E}

\text{For round seeds:}

\frac{(5474 - 5493)^2}{5493} \approx \frac{(-19)^2}{5493} \approx 0.0007 \text{For wrinkled seeds:} \frac{(1850 - 1831)^2}{1831} \approx \frac{19^2}{1831} \approx 0.198

\text{Total } \chi^2 \text{ value:}

\chi^2 \approx 0.0007 + 0.198 \approx 0.199

\text{Degrees of freedom} = \text{Number of categories} - 1 = 2 - 1 = 1

\text{Using chi-square tables, for 1 degree of freedom, the critical value at a 0.05 significance level is 3.841.}

\text{Since } \chi^2 \approx 0.199 \text{ is less than 3.841, we fail to reject the null hypothesis.}