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: Picture the two snapshots.
At $t=0$ nearly every bird has almost the same beak size, so the population looks like one tight cluster on the beak size axis. At $t=t_1$ that cluster has broken into two separate clusters sitting apart from each other, with a gap in the middle where the old average used to be.
Step 2: Connect this to variance directly.
Variance adds up the squared distance of every bird's beak size from the population mean. When birds are packed close to the mean, those squared distances are small, and variance is small. When birds move away from the mean into two separated groups, those squared distances grow, and variance grows with them.
Step 3: Notice this is disruptive selection.
A single peak breaking into two peaks, with the middle emptying out, is the textbook signature of disruptive selection: individuals with average trait values do worse than individuals with extreme trait values, so the extremes become more common over time and the middle becomes rarer.
Step 4: See why the other choices fail.
"Decreased" or "stayed the same" would only make sense if the population had become more uniform or unchanged, but the figure shows the opposite, a single group turning into two separated groups. "Reduced to zero" would mean every bird ended up with the exact same beak size, which is not what the two peaked curve at $t=t_1$ shows.
Step 5: Conclude.
Since birds are now, on average, farther from the mean than before, the variance has grown.
\[ \boxed{\text{Increased}} \]
