In beavers the production of musk oil is controlled by a polygenetic trait found
ID: 34047 • Letter: I
Question
In beavers the production of musk oil is controlled by a polygenetic trait found on 5 pairs of alleles hat are independently assorted the musk levels produce ordors that fall in the following patterns
Number of Dark Traits
(Capital Letters) Odor Level
10 Torture Devise
9 Oh my god!
8 Wow
7 Stinky
6 Strong
5 Musky
4 Unpleasant
3 Smelly
2 Mild
1 Frogant
0 None
What are the chances of having an offspring with a strong odor level when crossing a musky female (AABbCcDdee) with an unpleasant male (aaBbCcDdEe)
Explanation / Answer
To get an offspring with a STRONG odor level = (AABbCcDdee) X (aaBbCcDdEe)
If the genotype of the offspring has 6 dark allele (6 Capital Letter) then only strong odor offspring will be produced.
The above cross also be shown with the bionomial expansion (A+B)10 where the letter A = number of capital letters and the letter B = number of small case letters. Each term in the expression represents the number of offspring with a specific skin color phenotype based on the number of capital letters in the genotype.
So,
A10+10A9B+45A8B2+120A7B3+210A6B4+252A5B5+210A4B6+120A3B7+45A2B8+10AB9+B10
Thus 210 offsprings have 6 capital letters( dark traits) , thus 210 offspring is produced with a strong odor level when crossing a musky female (AABbCcDdee) with an unpleasant male (aaBbCcDdEe).
(A+B)n=A10+10A9B+45A8B2+120A7B3+210A6B4+252A5B5+210A4B6+120A3B7+45A2B8+10AB9+B10
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