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?

Question

Sourav Pan · 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 = 34×7324≈5493frac{3}{4} times 7324 approx 549343​×7324≈5493
 	Expected number of wrinkled seeds = 14×7324≈1831frac{1}{4} times 7324 approx 183141​×7324≈1831



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:

 

[latex] text{Chi-Square Calculation:} [/latex]

 

[latex] chi^2 = frac{(O - E)^2}{E} [/latex]

 

[latex] text{For round seeds:} [/latex]

 

[latex] frac{(5474 - 5493)^2}{5493} approx frac{(-19)^2}{5493} approx 0.0007 [/latex]

[latex] text{For wrinkled seeds:} [/latex]

[latex] frac{(1850 - 1831)^2}{1831} approx frac{19^2}{1831} approx 0.198 [/latex]

 

[latex] text{Total } chi^2 text{ value:} [/latex]

 

[latex] chi^2 approx 0.0007 + 0.198 approx 0.199 [/latex]

 

[latex] text{Degrees of freedom} = text{Number of categories} - 1 = 2 - 1 = 1 [/latex]

 

[latex] text{Using chi-square tables, for 1 degree of freedom, the critical value at a 0.05 significance level is 3.841.} [/latex]

 

[latex] text{Since } chi^2 approx 0.199 text{ is less than 3.841, we fail to reject the null hypothesis.} [/latex]

Mendel’s Crosses

Chi-Square Test

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