Final answer:
The MC1R gene is essential for determining hair pigment in rock pocket mice, which is highlighted by the study of coat color genetics in these mice.
Step-by-step explanation:
The importance of the gene responsible for hair pigment in rock pocket mice was revealed through the study of the mice's coat color genetics. The gene MC1R (Melanocortin 1 receptor) is significant in determining hair pigment. In the context of mouse genetics, as shown in the provided figures, while the agouti (A) gene impacts the pattern of the coat color, a separate gene (C) controls the actual production of pigment. When the C gene carries the recessive c allele, the resulting mouse is albino, showcasing an example of epistasis where one gene's expression is dependent on another gene.
Therefore, the correct answer to the question about which gene is important for determining hair pigment in rock pocket mice is MC1R, which is responsible for producing the melanin pigment that gives the fur its color.