Final answer:
The inheritance pattern seen in the cross between true-breeding black and white hamsters, resulting in F1 offspring with a 9:3:4 ratio of black, tan, and white hamsters, is indicative of Recessive Epistasis.
Step-by-step explanation:
In the case of the cross between true-breeding black and white hamsters, the F1 generation displays a phenotypic distribution that is not consistent with simple Complete Dominance. Instead, the presence of 175 black, 58 tan, and 82 white hamsters suggests a more complex inheritance pattern. This pattern does not fit with Recessive Lethality because we see tan individuals, nor does it align with Reciprocal Recessive Epistasis since we would typically expect a more straightforward phenotypic ratio.
The observed 9:3:4 ratio is characteristic of Recessive Epistasis, where one gene can mask the expression of another gene. In this scenario, it is likely that a second gene is influencing the fur color where individuals with two copies of the recessive allele at this second gene are tan, regardless of the alleles they possess for the initial gene that determines black or white color.