Weekly Problem: Guinea Pig Fur Color Genetics

The Problem

In a laboratory study, scientists are breeding guinea pigs to understand the genetics of fur color. They observe an interesting pattern:

When two black guinea pigs mate, about 3/4 of their offspring are black, while 1/4 are white.
When two white guinea pigs mate, ALL of their offspring are white.
When a black guinea pig mates with a white guinea pig, approximately 1/2 of the offspring are black and 1/2 are white.

This pattern has confused the researchers, because it doesn’t seem to follow the simple dominant/recessive genetic inheritance rules they expected. Your challenge: Can you develop a genetic model that explains these breeding results? What’s happening with these guinea pig genes? This is inspired by a famous example discussed by Judea Pearl in “The Book of Why,” highlighting how we can reason about causality and genetic inheritance.

The Observed Breeding Patterns

Researchers conducting controlled breeding experiments with guinea pigs have documented the following consistent patterns: