# 4.4: Studying Evolution in Action

- Page ID
- 191500

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### The Hardy-Weinberg Equilibrium

### Interpreting Evolutionary Change: Nonra **ndom Mating **

### Defining a Species

### Micro- to Macroevolution

## Special Topic: Calculating the Hardy-Weinberg Equilibrium

\[1 – p = q \nonumber\]

and

\[1 – q = p. \nonumber\]

\[p^2+ 2pq + q^2 =1 \label{Hardy-Weinberg formula}\]

- \(p^2\) represents the frequency of the homozygous dominant genotype;
- \(2pq\) represents the frequency of the heterozygous genotype; and
- \(q^2\) represents the frequency of the homozygous recessive genotype.

Let’s imagine we have a population of ladybeetles that carries two alleles: a dominant allele that produces red ladybeetles and a recessive allele that produces orange ladybeetles. Since red is dominant, we’ll use \(R\) to represent the red allele, and *r *to represent the orange allele. Our population has ten beetles, and seven are red and three are orange (Figure 4.24). Let’s calculate the number of genotypes and alleles in this population.

###### Solution

\[rr = 0.3 \nonumber\]

therefore,

\[r = \sqrt{0.3} = 0.5477 \nonumber\]

and

\[R = 1 – 0.5477 = 0.4523 \nonumber\]

Using the Hardy-Weinberg formula (Equation \ref{Hardy-Weinberg formula}):

\[\begin{align*} 1 &=0.4523^2 + 2 (0.4523)(0.5477) +0.5477^2 \\[4pt] &= 0.20 + 0.50 + 0.30 \end{align*}\]

Thus, the genotype breakdown is:

- 20% \(RR\)
- 50% \(Rr\), and
- 30% \(rr\)

That is 2 red homozygotes, 5 red heterozygotes, and 3 orange homozygotes.