A form of dwarfism known as Ellis–van Creveld syndrome was first discovered in the late 1930s, when Richard Ellis and Simon van Creveld shared a train compartment on the way to a pediatrics meeting. In the course of conversation, they discovered that they each had a patient with this syndrome. They published a description of the syndrome in 1940. Affected individuals have a short-limbed form of dwarfism and often have defects of the lips and teeth, and polydactyly (extra fingers). The largest pedigree for the condition was reported in an Old Order Amish population in eastern Pennsylvania by Victor McKusick and his colleagues (1964). In that community, about 5 per 1000 births are affected, and in the population of 8000, the observed frequency is 2 per 1000. All affected individuals have unaffected parents, and all affected cases can trace their ancestry to Samuel King and his wife, who arrived in the area in 1774. It is known that neither King nor his wife was affected with the disorder. There are no cases of the disorder in other Amish communities, such as those in Ohio or Indiana.
From the information provided, derive the most likely mode of inheritance of this disorder. Using the Hardy–Weinberg law, calculate the frequency of the mutant allele in the population and the frequency of heterozygotes, assuming Hardy–Weinberg conditions.

Verified step by step guidance

1. Step 1: Determine the mode of inheritance based on the pedigree information. Since all affected individuals have unaffected parents and the disorder appears in about 5 per 1000 births, this suggests a recessive inheritance pattern. In autosomal recessive disorders, affected individuals are homozygous for the mutant allele, while parents are typically heterozygous carriers without symptoms.
2. Step 2: Define the allele frequencies using Hardy–Weinberg notation. Let \(q\) represent the frequency of the mutant allele and \(p\) represent the frequency of the normal allele. Since there are only two alleles, \(p + q = 1\).
3. Step 3: Use the frequency of affected individuals to find \(q\). The frequency of affected individuals corresponds to the homozygous recessive genotype, which is \(q^2\). Given that the frequency of affected individuals is 5 per 1000 births, express this as \(q^2 = \frac{5}{1000}\).
4. Step 4: Calculate the frequency of heterozygotes (carriers). The heterozygous genotype frequency is given by \$2pq\(. Since \)p = 1 - q\(, substitute this into the expression to get \)2q(1 - q)$.
5. Step 5: Summarize the results. You now have expressions for the mutant allele frequency \(q\), the normal allele frequency \(p\), and the heterozygote frequency \$2pq$. These can be used to understand the genetic structure of the population under Hardy–Weinberg equilibrium.

Key Concepts

Autosomal Recessive Inheritance

Autosomal recessive disorders require two copies of a mutant allele for the phenotype to be expressed. Affected individuals often have unaffected parents who are carriers (heterozygotes). The disorder appears in offspring when both parents pass on the mutant allele, explaining why the syndrome appears in certain populations with a common ancestor.

Hardy–Weinberg Equilibrium

The Hardy–Weinberg law predicts genotype frequencies in a population under ideal conditions (no mutation, migration, selection, or genetic drift). It relates allele frequencies (p and q) to genotype frequencies (p², 2pq, q²), allowing calculation of carrier and affected individual frequencies from observed disease prevalence.

Founder Effect and Population Genetics

The founder effect occurs when a small group establishes a new population, carrying limited genetic variation. This can increase the frequency of rare alleles, as seen in the Amish community descended from Samuel King. Understanding this helps explain the high incidence of Ellis–van Creveld syndrome in this isolated population.