Tay–Sachs disease is an autosomal recessive neurological disorder that is fatal in infancy. Despite its invariably lethal effect, Tay–Sachs disease occurs at very high frequency in some Central and Eastern European (Ashkenazi) Jewish populations. In certain Ashkenazi populations, 1 in 750 infants has Tay–Sachs disease. Population biologists believe the high frequency is a consequence of genetic bottlenecks caused by pogroms (genocide) that have reduced the population multiple times in the past several hundred years. Assuming mating occurs at random in this population, what is the probability a couple are both carriers of Tay–Sachs disease?

Key Concepts

Autosomal Recessive Inheritance

Tay–Sachs disease is inherited in an autosomal recessive manner, meaning that an individual must inherit two copies of the mutated gene (one from each parent) to express the disease. Carriers, who have one normal and one mutated gene, do not show symptoms but can pass the mutated gene to their offspring. Understanding this inheritance pattern is crucial for calculating carrier probabilities in a population.

Hardy-Weinberg Principle

The Hardy-Weinberg principle provides a mathematical framework for understanding genetic variation in a population at equilibrium. It states that allele and genotype frequencies will remain constant from generation to generation in the absence of evolutionary influences. This principle is essential for estimating the frequency of carriers in a population, as it allows for the calculation of expected genotype frequencies based on known allele frequencies.

Genetic Bottleneck

A genetic bottleneck occurs when a population's size is significantly reduced for at least one generation, leading to a loss of genetic diversity. In the context of Tay–Sachs disease, historical events such as pogroms have caused such bottlenecks in Ashkenazi Jewish populations, resulting in a higher frequency of certain genetic traits, including the Tay–Sachs allele. This concept helps explain the elevated carrier rates observed in these populations.