So far we’ve been talking about simple ratios, but how can we mathematically figure out the probability or the percentage that an organism will inherit a trait?
Consider a cross between YyRr and YyRr. Using a Punnett square, we can deduce that for colour, ½ the offspring will be Yy, ¼ yy, and ¼ YY. The same probabilites apply for shape: ½ Rr, ¼ rr, and ¼ RR. (Remember Y=yellow, y=green, R=round, r=wrinkled.) But how do we then figure out how many will be round and yellow, or green and wrinkled?
The rules of probability, of course.
We can determine the probabilities of the genotypes by just multiplying the traits we want to know about together. For example, what’s the probability of the pea ending up yellow and wrinkled? Well, we know that ¾ of our offspring will be yellow, and ¼ will be wrinkled. ¾ x ¼ = 0.1875. So about 18.75% of our offspring will be both yellow and wrinkled. (If you don’t like fractions, just use 0.75x0.25.)
What about green and wrinkled? ¼ x ¼ = 0.0625. So 6.25% will be green and wrinkled. We can do the same for the others:
Yellow and round: ¾ x ¾ = 0.5625 = 56.25%
Green and round: ¼ x ¾ = 0.1275 = 18.75%
Adding all of these up gets you 100%, of course. It also gives us our ratio that we’ve talked about—9:3:3:1.
Further resources: Probability in Genetics: Multiplication and Addition Rules video