MathBench > Probability

More Mice with Fangs: Intermediate Punnett Squares

Really big Punnett Squares

In fact we could use Punnett Squares to determine what happens when there are more than 2 genes. For example, in a five-way cross, mom and dad each have 5 traits by which their egg or sperm can differ. Along the top you would need to list each possibility. If you called the gene pairs Aa, Bb, Cc, Dd, Ee, then the first entry along the top of the Punnett Square could be ABCDE, followed by ABCDe, then ABCdE, then ABcDE, etc.

How many rows and columns would there be in a 5-way cross?

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I think I have the answer: 32 columns and 32 rows in the Punnett Square, and over 900 offspring genotypes.

Yuck. If you needed to work with the number of genotypes in the question above, I would suggest using the rules of logic (AND and OR) we have already discussed - and not a Punnett Square! But luckily you don't need to do that now.

Just for the really curious, here is the tri-hybrid cross AaBbCc x AaBbCc. I'm not going to fill in the kids, but you would know how to do it, right?

  ABC ABc AbC aBC Abc aBc abC abc
ABC                
ABc                
AbC                
aBC                
Abc                
aBc                
abC                
abc                

Fun, huh? One thing you can notice from this table is that there is only ONE way to get the all-recessive phenotype -- the very last square. So the proportion of triple-recessives from a dihybrid cross is approximately 1/64. The other things to notice about the table would take some time to work out... And of course, not all triple crosses are tri-hybrid crosses.

The next and final page is a review, and after that you can proceed to the quiz.