Final answer:
This genetics problem suggests a two-gene inheritance pattern, necessary for purple flowers. White and red can be observed as the result of different combinations or lack of these genes, which align with neither gene being completely dominant over the other when alone, thus requiring both for purple pigment expression.
Step-by-step explanation:
Genetics is a fundamental topic in Biology that explains the inheritance patterns of traits in organisms, as demonstrated by Gregor Mendel's experiments. In the scenario where a pure-breeding red flower plant is crossed with a pure-breeding white flower plant, resulting in all white flowers in the F1 generation, it suggests an inheritance pattern where color is determined by two genes.
When the F1 plants are intercrossed, the F2 generation shows a phenotypic ratio that is unlike typical Mendelian single-gene ratios, indicating more complex interactions. Specifically, the results suggest that two genes are involved in determining the flower color and that a dominant allele of two different genes is necessary for purple flowers, as seen by the presence of purple flowers in the F2 generation. Consequently, the correct answer is that "A dominant allele of two genes is necessary for purple flowers."
Mendel's work laid the foundation for modern genetics, demonstrating patterns of inheritance through controlled experiments with pea plants, where traits like flower color did not blend but were passed on as distinct units of inheritance, now known as genes.