When crossing two pink-flowered plants both heterozygous for necessary transcription factor genes (AaBb), a dihybrid cross gives a phenotypic ratio of 9:3:3:1. The 9 represents pink flowers while 3:3:1 are different non-pink colorations.
The question asks about the expected phenotypic ratios when crossing two pink-flowered plants that are both heterozygous for genes encoding transcription factors related to flower color. This is a scenario involving a dihybrid cross with both genes being necessary for a pink phenotype, which is a situation of independent assortment and incomplete dominance.
If each plant is heterozygous for both genes (AaBb x AaBb), we use a Punnett square to calculate the phenotypic ratio. Since both genes are required for pink color, only offspring with at least one dominant allele from each gene (A-B-) will be pink. For each gene independently, the ratio of dominant to recessive phenotypes will be 3:1, as Mendelian genetics predicts.
By applying the product rule to both independent 3:1 ratios, we get a combined phenotypic ratio for the dihybrid cross. The phenotype ratio would be 9:3:3:1, with 9/16 having both dominant alleles (pink flowers), 3/16 having one dominant allele for the first gene and two recessive for the second (not pink), 3/16 the opposite, and 1/16 having all recessive alleles (not pink). It's important to note that plant coloration might not follow these ratios precisely if there are other genetic or environmental factors involved.