Final answer:
The pedigree provided indicates that individuals with brown eyes but with light-eyed offspring must be carriers of the recessive allele associated with eye color.
Step-by-step explanation:
The pedigree analysis for an eye color gene shows the inheritance pattern within a family where a loss-of-function, recessive allele leads to lighter eye color, and a functional allele causes brown eyes. Since brown is dominant over the lighter color, individuals with brown eyes can still be carriers of the recessive allele.
Carriers must have one copy of the non-melanin-producing allele and one copy of the melanin-producing allele. Carriers can be identified if they have light-eyed offspring, which indicates they have passed on the recessive allele.
Considering light-colored eyes are dominant over brown eyes, any parent of a child with light-colored eyes who themselves have brown eyes must be a carrier of the recessive allele.