Treehoppers have either purple, or green, or white skin.
Other geneticists have determined that:
(1) whenever one white treehopper is mated with another white treehopper all the progeny are white.
(2) whenever two pure bred purple treehoppers are mated all their progeny are purple.
(3) whenever two pure bred green treehoppers are mated all their progeny are green.
(4) whenever a pure bred green treehopper is mated with a pure bred purple treehopper all their
progeny are purple.
The information provided above is not sufficient to allow you to explain completely the inheritance of skin color in the treehopper. Therefore you mate a pure bred purple treehopper with a pure bred white treehopper. All the F1 progeny are purple. You then inbreed the individuals in the F1 generation to obtain an F2 generation. The F2 progeny appear with the following phenotypes:

P: purple X white
F1: purple
F2: 9000 purple 3000 green 4000 white out of 16000 total.

a. Based on this data, how many genetic loci control skin color in the treehopper and why is there this amount of genetic loci?
b. Define symbols and assign genotypes to the original purple and white parents in this cross.
Symbols =

Purple parent:
White parent:
a. Based on the data, there are likely two genetic loci that control skin color in the treehopper. This can be inferred from the F2 phenotypic ratio of 9000 purple: 3000 green: 4000 white out of a total of 16000 individuals.
To understand why there are likely two genetic loci, we can consider the possible genetic combinations that can produce the observed phenotypic ratios. Since the F1 generation resulted in all purple progeny, we can conclude that the purple trait is dominant over the white trait. Therefore, the purple parent must be heterozygous for the skin color genes (we'll assign it the genotype "Pp").
In the F2 generation, the phenotypic ratio of 9000 purple: 3000 green: 4000 white suggests a 9:3:4 Mendelian ratio. This ratio is consistent with a dihybrid cross involving two genetic loci. In this case, we can assume that the purple trait is dominant over both the green and white traits, and the white trait is recessive to both purple and green.
Therefore, we can conclude that there are two genetic loci controlling skin color in the treehopper, with two alleles at each locus: one for purple (P) and one for green (G). The white trait is likely controlled by a combination of recessive alleles at both loci.
b. Symbols:
Purple parent: PP (pure bred dominant for purple)
White parent: ww (pure bred recessive for white)