The distributions of beak size in a bird population at two different times, \(t=0\) and \(t=t_1\), are shown below. At \(t=0\) beak sizes form a single narrow peak centred around 5 mm. By \(t=t_1\) the distribution has split into two separate peaks, one smaller and one larger than 5 mm, with very few birds still having a beak size close to 5 mm.
In going from time \(t=0\) to \(t=t_1\), the variance of the distribution in beak size in the population has _________.
Show Hint
Variance measures how spread out the values are from the mean; compare how far the bulk of the birds sit from 5 mm at each time point.
Step 1: Recall what variance measures.
Variance measures how spread out a set of values is around the mean. A tall, narrow peak means low variance, since most values sit close to the mean. A wide or split distribution means high variance, since values are spread far from the mean.
Step 2: Look at the distribution at \(t=0\).
At \(t=0\), almost all the birds have a beak size close to \(5\) mm, forming one narrow, tall peak. Very few birds have beak sizes near \(0\) or near \(10\) mm. This is a low variance distribution.
Step 3: Look at the distribution at \(t=t_1\).
At \(t=t_1\), the single peak has split into two peaks, one centred below \(5\) mm and one centred above \(5\) mm, and almost no birds are left with a beak size close to \(5\) mm itself. Now a large share of birds sit far from the old mean of \(5\) mm, on either side.
Step 4: Compare the spread.
Even though the mean beak size may still be near \(5\) mm, since the two new peaks look roughly symmetric around it, individual birds are, on average, much farther from that mean than they were at \(t=0\). This is the classic signature of disruptive selection, where selection favours both extremes of a trait and works against the middle, splitting one population into two phenotypic groups and pushing the variance up.
Step 5: Rule out the other options.
The distribution clearly did not shrink or stay the same, since the birds spread out into two distant clusters rather than staying bunched near \(5\) mm. It also did not reduce to zero, since there is still plenty of variation, in fact more than before, just arranged into two groups instead of one.
Step 6: Final answer.
The spread of beak sizes around the mean grew larger from \(t=0\) to \(t=t_1\).
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