Chapter 20, Problem 38P

Achromatopsia is a rare autosomal recessive form of complete color blindness that affects about $1$ in $20,000$ people in most populations. People with this disorder see only in black and white and have extreme sensitivity to light and poor visual acuity. On Pingelap Island, one of a cluster of coral atoll islands in the Federated States of Micronesia, approximately $10$ percent of the $3000$ indigenous Pingelapese inhabitants have achromatopsia.

Achromatopsia was first recorded on Pingelap in the $\text{mid-1800s}$, about four generations after a typhoon devastated Pingelap and reduced the island population to about $20$ people. All Pingelapese with achromatopsia trace their ancestry to one male who was one of the $20$ typhoon survivors. Provide a genetic explanation for the origin of achromatopsia on Pingelap, and explain the most likely evolutionary model for the high frequency there of achromatopsia.