I am currently doing some research into distributions and probabilities with Mendellian genetics. I came across this problem that I cannot seem to wrap my head around.

Given that the population has two characteristics, they are color and texture. Supposed two dihybrids reproduce (AaBb x AaBb) and if the dominant form of the color gene is contributed, then the dominant form of the texture gene is three times as likely to be contributed as the recessive form. If the recessive color gene is contributed then the dominant and recessive genes for texture are equally likely.

From this the geneotypic distribution has to be calculated.

I know the solution is:

[9/64   6/64   1/64   3/16   1/4   1/16   1/16   2/16   1/16]

 AABB   AABb   AAbb   AaBB   AaBb  Aabb   aaBB   aaBb   aabb

When I performed the punnett square I got the distribution of:

 [1/16   2/16   1/16   2/16   4/16   2/16   1/16   2/16   1/16]

 AABB   AABb   AAbb   AaBB   AaBb  Aabb   aaBB   aaBb   aabb

and did not know where to go from there.

My question is how did they incorporate the "times as likely" condition into the solution.

  • $\begingroup$ What are these traits exactly ? just colors ? From the data it seems that homozygosity is not preferred $\endgroup$ – WYSIWYG Mar 5 '14 at 4:54

You are... done. You fully answered the question; if I were you, I might just put it in ratio format instead of probability, just to be safe.

The three times thing is a bit weird, but I have seen it before. First, let's look at the phenotypic ratio of the progeny: 9:3:3:1 for Dominant Both:Dominant A Recessive B:Recessive A Dominant B: Recessive Both.

Let's find out how many dominant and recessive there are for each trait. For the dominant A trait, you add up the 9 and 3, because they are the only two types of dominant phenotypes, and find that 12 different organisms of the 16 possible are dominant for Trait A, so the probability of getting trait A is 3/4 or 75%. This means that 4 of the 16 orgamisms are recessive for Trait A, so the probability of being recessive for Trait A is 4/16, or 25%. Therefore, the ratio of Dominant Organism probability:Recessive organism probability is 75% to 25%, or 3:1. This means that it is 3 times as likely to get the dominant trait than the recessive trait. Make sense?

  • $\begingroup$ Hi, I understand what you are telling me there but what I really wanted to know is how to move from the punnett square distribution I got ( [1/16 ... 1/16] ) to the distribution that was stated in the solution ( [1/64 ... 1/16] ). $\endgroup$ – user2958395 Mar 6 '14 at 0:59

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