Suppose a particular species of fly has two pairs of traits: X paired with x and Y paired with y, with X and Y
the dominant alleles. Suppose a fly with genotype XxYY mates with a fly with genotype Xxyy.
1. Write the two polynomials associated with the genotype of each of the flies above. Multiply each
polynomial out separately, so that you have two terms for each polynomial.
(X+x)(Y+Y)=2XY+2xY (X+x)(y+y)=2Xy+2xy
2. Multiply the two polynomials together to get the polynomial associated with the set of offspring of
this mating. (This polynomial will have three terms.) What percentage of each of these three
genotypes will appear in the new generation?
2Xy 2xy
2XY 4XXYy 4XxYy
2xY 4XxYy 4xxYy
4XXYy + 8XxYy + 4xxYy
Divide coefficients by 4+8+4=16
25% XXYy, 50% 8XxYy, 25% xxYy
3. Suppose now that the phenotype X will survive to reproductive age at a 4-to-1 rate, the phenotype x
will survive to reproductive age at a 3-to-1 rate, the phenotype Y will survive to reproductive age at
a 2-to-1 rate, and the phenotype y will survive to reproductive age at a 5-to-1 rate. What
percentage of each genotype will survive to reproductive age in the next generation?
genotypes 4XXYy + 8XxYy + 4xxYy
phenotypes X Y X Y x Y
multipliers 4 2 4 2 3 2
4×4×2 8×4×2 4×3× 2
32 + 64 + 24 = 120
32/120=27% XXYy, 64/120=53% 8XxYy, 24/120=20% xxYy
Note: You can clear fractions in several ways, but if you did it right you should all have gotten populations
fractions of 4/15, 8/15, and 3/15, or some form of these three fractions.
Quiz #2
Solutions