Calculating Punnet Squares Quickly ``` Name: Justine Status: student Grade: 9-12 Location: CO Country: USA Date: Spring 2013 ``` Question: I am on Science Olympiad (A national science tournament for high school and middle school teams). I am on a high school team and am currently working on a genetics event. For this event we have to be able to solve multiple trait punnet squares. Mostly the tests just have dihybrid crosses, but I have seen some questions on a 5 or more trait cross! (i.e.: AaBbCCDdEe x aaBbccDdee) Obviously a 5 x 5 trait square would have 1,024 boxes.... And would take much too long to write out. (We only have 1 hour) My question is: Is there anyway to calculate a punnett square with 5 or more traits quickly? We are allowed to have a calculator, maybe it is possible to multiply the frequencies of the different alleles Replies: Hi Justine, Thanks for the question. Punnet squares get unwieldy for more than two genes. You won't get a question which tells you to list all possible genotypes and their frequencies in which you have to use a Punnet square. You will be expected to find the frequency of a particular genotype in the progeny. For instance, in the cross AaBbCCDdEe x aaBbccDdee, find the frequency (or probability) of the genotype aaBbCcddEe. Just treat them as a bunch on singlegene Punnet squares: The probability of the offspring having the genotype aa: P(aa) = 1/2*1 = 1/2 The probability of the offspring having the genotype Bb: P(Bb) = 1/2 The probability of the offspring having the genotype Cc: P(Cc) = 1*1 = 1 The probability of the offspring having the genotype dd: P(dd) = 1/2*1/2 = 1/4 The probability of the offspring having the genotype Ee: P(Ee) = 1/2*1 = 1/2 So the probability of the aaBbCcddEe genotype is P(aaBbCcddEe) = 1/2*1/2*1*1/4*1/2 = 1/32 I hope this helps. Please let me know if you have more questions. Thanks Jeff Click here to return to the Mathematics Archives

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