One of the first Mendelian traits identified in humans was a dominant condition known as brachydactyly. This gene causes an abnormal shortening of the fingers or toes (or both). At the time, some researchers thought that the dominant trait would spread until 75 percent of the population would be affected (because the phenotypic ratio of dominant to recessive is 3 : 1). Show that the reasoning was incorrect.

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Understand that the 3:1 phenotypic ratio (dominant : recessive) applies to the offspring of heterozygous parents in a controlled Mendelian cross, not directly to the overall population frequency.

Define the frequency of the dominant allele as $p$ and the recessive allele as $q$, where $p + q = 1$ in the population under Hardy-Weinberg equilibrium.

Recall that the frequency of individuals showing the dominant phenotype is given by $p^2 + 2pq$, since both homozygous dominant ($p^2$) and heterozygous (\$2pq$) genotypes express the dominant trait.

Note that the frequency of the recessive phenotype is $q^2$, representing homozygous recessive individuals.

Use the relationship $p + q = 1$ and the expression for dominant phenotype frequency $p^2 + 2pq = 1 - q^2$ to show that the maximum proportion of affected individuals cannot simply be 75%, because this depends on allele frequencies in the population, not just Mendelian ratios from a single cross.

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Mendelian Inheritance and Phenotypic Ratios

Mendelian inheritance describes how traits are passed from parents to offspring through dominant and recessive alleles. A 3:1 phenotypic ratio typically appears in a monohybrid cross of heterozygotes, meaning 75% of offspring show the dominant trait in that specific generation, not the entire population over time.

Allele Frequency vs. Phenotypic Ratio

Phenotypic ratios describe the proportion of traits in offspring from specific crosses, while allele frequencies represent how common an allele is in a population. The 3:1 ratio applies to offspring genotypes, not to the overall population frequency, which is influenced by factors like mating patterns and selection.

Population Genetics and Hardy-Weinberg Equilibrium

Population genetics studies allele frequencies in populations over time. Hardy-Weinberg equilibrium predicts stable allele frequencies without evolutionary forces. A dominant trait does not necessarily increase to 75% prevalence because allele frequencies depend on genotype proportions and fitness, not just dominance.