Scientists are studying several populations of finches on neighboring islands in the South Pacific. Previous genetic analysis has shown that a single gene controls tail-feather length in the finch populations and that the allele for long tail feathers (\(L\)) is dominant to the allele for short tail feathers (\(l\)). On two separate islands, the scientists recorded the number of finches with long tail feathers and the number of finches with short tail feathers. The results are shown in the table below.

If the two finch populations are each in Hardy-Weinberg equilibrium and are isolated from each other, then which of the following graphs correctly displays the relative genotype frequencies?

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The homozygous recessive (\(ll\)) frequency is \(q^2\), where

$$ p^2+2pq+q^2=1 $$

We can calculate the frequency for both islands:

Only one graph reflects these values for \(ll\).

We could also obtain the corresponding \(p^2\) and \(2pq\) values for further verification. Here is the work for island 1:

$$ q^2=0.27 \hskip{2em} q=.52 $$ $$ p + q = 1 $$ $$ p + 0.52 = 1 $$ $$ p = 0.48 \hskip{2em} p^2=0.23 $$ $$ 2pq = 2(0.52)(0.48) = 0.50 $$