25. (14 points) The following pathway produces pigments in butterfly wings, a di

Question

25. (14 points) The following pathway produces pigments in butterfly wings, a diploid organism The 6 genes for these enzymes are all on different chromosomes. Show your work. Orange Red 4 White Yell 2&3 Blue Enzyme #1 converts a white precursor to a yellow pigment. Both functional enzymes #2 and #3 are required to convert yellow to blue pigment, and enzyme #4 converts yellow to orange pigment. Either #5 or #6 can convert orange pigment into red pigment, wild-type butterflies have functional copies of all 6 enzymes, make both red and blue pigments, and so have a purple color. Butterflies that make blue pigment plus orange pigment (but not red) are brown. You cross a true-breeding brown butterfly to a true-breeding yellow butterfly to make Fl progeny The genotype of the true-breeding yellow is (1+1+2-2-3-3-4-4-5+5+6+6+). You then cross F1 siblings to make F2 progeny. Fraction of F2 generation of each color: White: 0 Yellow:-- Orange: 21/1024 Red: 315/1024 Blue 7/64 -7/16 15/16 9/64 9/16 Purp 405/1024 Brown 27/1024 9/16315/16 9/16*1/16

Explanation / Answer

Given is the genotype of true breeding yellow butterfly, which is (1+1+2-2-3-3-4-4-5+5+6+6+). This produces gametes which are all (1+2-3-4-5+6+).

The genotype of a true breeding brown butterfly is (1+1+2+2+3+3+4+4+5-5-6-6-). Hence it produces gamets of the genotye (1+2+3+4+5-6-).

The genotype of the F1 progeny is (1+1+2+2-3+3-4+4-5+5-6+6-) and therefore 2^5 = 32 different types of gametes can be produced.

Therefore in the F2 progeny there can be 32 * 32 = 1024 different genotypes.

As all gametes have homozygoes copies of gene 1, no white butterflies can be obtained. Hence white = 0.

Presence of blue or purple pigment in the wings of a butterfly is a type complementary gene interaction, as atleast one dominant allele of both genes 2 and 3 are necessary for the blue phenotype. For a complementary gene interaction, the phenotypic ratio is 9:7 i.e. 9 butterflies out of 16 have the blue wings while the rest have other coloured wings.

Similarly, the presence of red wings in butterflies is a duplicate gene interaction. In such interaction presence of a dominant allele from either of the two genes i.e. 5 and 6 is required for the phenotype. In such cases, the phenotypic ratio is 15: 1, which means 15 out of 16 butterflies carry a dominat allele of either 5 or 6 and hence have red wings.

Butterflies with yellow wings are formed when gene 4 is recessive. We know that 7/16 are butterflies wings with colors other than blue or purple. Of these only 1/4 of them carry a recessive gene 4 which results in yellow color. Therefore total yellow butterflies are 7/16 * 1/4= 7/64

Orange pigmented wings are produced when recessive copies of both genes 5 and 6 are present which by the duplicate gene ratio is 1/16. We know that 7/16 butterflies have colors other than blue. onle 3/4 of them have the chance of having red or orange color (as presence of recessive genes of either 2 or 3 results in orange or red).

Therefore red pigment is present in 7/16 * 3/4 * 15/16 = 315/ 1024

and orange pigment is present in 7/16 * 3/4 * 1/16 = 21/1024

We know that blue or purple pigmented butterflies are 9/16 (ratio from complementary gene interaction). Only when both genes 2 and 3 are dominant and 4 is recessive, blue is obtained which is 1/4.

Therefore blue butterflies are obtained 9/16 * 1/4 = 9/64 times.

Purple blutterflies are obtained when both blue and red pigments are pruduced. We know 9/16 have both purple and blue pigments and 3/4 have orange pigment.

If red color is produced then butterflies have purple pigment and this happens 15/16 times (ratio from duplicate gene interaction)

therefore purple butterflies are 9/16 * 3/4 * 15 /16 = 405 /1024

and

brown butterflies are 9/16 *3/4 * 1/16 = 27/1024.

Hopefully this gives a clarity on how the ratios are obtained.

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