Basic Genetics

Biology Level 2

The above picture shows punnet square for mono hybrid cross, involving the trait : colour of pea pod.

If we draw a punnet square for an $n$ -hybrid cross ( A cross between two organisms, where $n$ traits are considered ), how many unit squares does it contain ?

If the answer is of the form $a^{bn}$ for positive integers $a,b > 1$ , enter $(a+b)$ .

The answer is 4.

1 solution

Nihar Mahajan
Feb 29, 2016

For mono-hybrid cross , as shown in the figure in the question , it will have $y,y$ in row and $Y,y$ in column , giving us $2\times 2=4=2^2=2^{2(1)}$ unit squares. Now , for dihybrid cross suppose $RR,YY$ are two dominant pairs of gametes and $rr,yy$ are recessive. Then we will have $ry,Ry,rY,Ry$ in row as well as in column , giving us $4\times 4=16=2^4=2^{2(2)}$ unit squares, by seeking the same logic and pattern we conclude that for n-hybrid cross , there will $2^{2n}$ unit squares. Hence $a+b=2+2=\boxed{4}$ .

Moderator note:

Good explanation of the initial cases of this hybrid cross. Arguably, you should do the $n = 3$ case, in order to show the pattern.

Can you give any combinatorial proof, instead of relying just on pattern ?

Venkata Karthik Bandaru - 5 years, 3 months ago

If n traits are there the side of the punnet square will be 2^n because for every trait there will be two outcomes, just like when we toss a coin n times there are two outcomes H and T the total number of possibilities are 2^n. The number of unit squares is area of the square which will be 2^2n.

Kushagra Sahni - 5 years, 3 months ago

Yup, that's good reasoning. Note that the 2 possibilities you are referring to is the allele pair.