Final answer:
The genetic hypothesis explaining a 9:3:3:1 ratio in an F1 dihybrid cross is Mendelian inheritance, involving independent assortment and dominance.
Step-by-step explanation:
The genetic hypothesis that explains the inheritance of two characters in a F1 dihybrid cross resulting in a 9:3:3:1 phenotypic ratio is Mendelian inheritance involving independent assortment and dominance.
In this cross, two characteristics are inherited where each gene has two alleles including a dominant and a recessive allele. The 9:3:3:1 ratio indicates that the genes assort independently and the alleles for each gene follow the dominant and recessive pattern.
For instance, in pea plants, if one gene represents seed texture with alleles for round (dominant) or wrinkled (recessive), and another gene represents seed color with alleles for yellow (dominant) or green (recessive). When F1 offspring are heterozygous for both traits, the F2 generation will show the typical dihybrid 9:3:3:1 ratio.
This results from applying the product rule to the separate monohybrid 3:1 ratios of each trait, producing a combined expected proportion of round and yellow offspring as (3/4) × (3/4) = 9/16, reflecting the patterns of inheritance first described by Gregor Mendel.