Scenario #1
Easter Island is a small island in the southern Pacific Ocean. It lies approximately 3,500 kilometers east of Chile and is considered one of the most remote islands. It is also a volcanic island. In 2025, Easter Island had a population of 16,000. However, many of the island’s residents were killed during a series of volcanic eruptions that occurred in the year 2065.

Of the original population, only 200 people survived. It is now 100 years later, and the population of Easter Island has reached 800. Of the current population, 328 people are homozygous recessive for Marfan syndrome, which is autosomal (mm genotype). Marfan syndrome is a genetic disorder that affects the connective tissue. Symptoms of Marfan syndrome include increased height, thinness, flexible joints, heart complications, and long arms, legs, fingers, and toes.

q2 –

q –

p –

p2 –

2pq –

p = 0.36

q = 0.64

p² = 0.13

2pq = 0.46

q² = 0.41

Explanation:

We need to use the Hardy-Weinberg equations:

p + q = 1

p² + 2pq + q² = 1

p: the frequency of the dominant allele

q: the frequency of the recessive allele

p²: the frequency of homozygous dominant

2pq: the frequency of heterozygous

q²: the frequency of homozygous recessive

Here, we know that 328/800 people are homozygous recessive, which means that q² = 328/800 = 0.41.

Then, q = √0.41 = 0.64, and p = 1 - q = 1 - 0.64 = 0.36.

Now, we have p² = (0.36)² = 0.1296 ≈ 0.13 and 2pq = 2 * 0.36 * 0.64 = 0.4608 ≈ 0.46.

The answers are:

p = 0.36

q = 0.64

p² = 0.13

2pq = 0.46

q² = 0.41

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