MathBench > Probability

Linked Genes and Recombination
Advanced Punnett

Yoda's Ears

  Vulcans Yodites
122 104
21 8
20 20
37 18

"Maybe we should send the Yodite data over to the Jedi to figure out," suggested Kirk while stifling a yawn and reaching for some technologically advanced potato chips.

"Naw, we can do it here. It'll be easy."

"Uh huh. So basically we have to go through the whole thing again, starting with making sure each of the genes is playing by the rules separately?"

"Yup. Let's see, we should get a 3:1 ratio for ear shape (112 vs. 38) and for psionic powers (124 vs. 26)"

"Hold on," interrupted Kirk, "I may not be a doctor, but I am a ship captain, and that means I'm good at one thing anyway."

"What, impressing 23rd century girls?"

Yoda"No, Bones, strategy. If we want to get out of this fake conference room anytime soon, we need to show that at least one of the genes is NOT playing by the rules. And the most likely candidate is the gene for psionic powers. 124 vs. 26 really is not very close to a 3 to 1 ratio. Attack the weak spot."

"OK, fine," grimaced Bones. "Here's a chi-square table:"


observed ("o") expected ("e") (o-e) (o-e)2 (o-e)2/e
Total 150 150    

chi-square table

"Fascinating," declared Kirk in his best Vulcan manner, again. "What does it mean?"

"Well, the chi-square calc is higher than the chi-square crit for 1 degree of freedom, so the null hypothesis that the gene assorts randomly must be rejected. Oh, heck, I'm a doctor, not a statistician.... It means that not nearly as many psionic Yodites were produced as there should have been. Almost like they were dying out before they got counted, or something."

"You mean like being psychic was too great a stress on the infants?"

"Maybe, but who knows? There could be a lot of different explanations."

"So does that mean we get to stop? We can't keep going with our tests?"

"Yup. That's the end of the line. Since the psionic gene doesn't assort randomly, we can't make any prediction about the ratio for the dihybrid cross. And therefore we don't have any way to test whether the genes are linked or not linked. Not until someone does more research into these missing psychic Yodites. And don't be looking at me like that. It was in a galaxy far away and long ago."