Question

German abbot Gregor Mendel published his famous pea results in 1866, to what can be described as a general shrug. Fast forward 35 year when two scientists, Hugo de Vries and Carl Correns, independently arrived to the same conclusions and rediscovered his work. This would catch the general attention and eventually redefined the fields of genetics, evolutionary biology, and population genetics.

In 1904, William Bateson, Edith Saunders, and Reginald Punnett (of the Punnett square fame) published odd results: when selfing pea plants investigating pollen shape and flower color, the F2 generation deviated dramatically from the Mendelian 9:3:3:1 ratio expected of the F2 generation looking at 2 traits:

Phenotype	Observed	Expected
Purple, long	1528	1199
Purple, round	106	400
Red, long	117	400
Red, round	381	133
Total	2132	2132

Discuss how and why those numbers deviate from Mendelian expectations (i.e is there any pattern of divergence in the data ?; what might be causing this divergence?) Why are these surprising or not surprising? Note that purple flowers and long pollen are the dominant phenotypes, while red flowers and round pollen are recessive.

Answer 1

Null Hypothesis: 1:1:1:1

Alternative Hypothesis: 9:3:3:1

Calculation:-

Phenotype	Observed(O)	Expected(E)	(O-E)	(O-E)2	(O-E)2/E	?2
Purple, long	1528	1199	329	108241	90.276	969.024
Purple, round	106	400	-294	86436	216.090
Red, long	117	400	-283	80089	200.222
Red, round	381	133	248	61504	462.436
Total	2132	2132

Degrees of freedom: 4-1 = 3

Critical value: The table value of chi-square for 3df at 0.05 is 7.82.

As calculated value of Chi-square for 3 df 969.024< critical value 7.82, so null hypothesis re rejected, i.e there is significant difference between the observed and expected result. So, here alternative hypothesis is accepted.

These are not surprising.