How might an extended period of drought influence the ground finch?

A drought would most likely cause there to be a scarcity of food for the ground finch, because the plants/seeds that it feeds on would be dying at a higher rate without water. The resulting scarcity of food would be a selective pressure against the finches, meaning only the finches that had certain adaptations would survive the drought and be able to reproduce.

For instance, maybe the drought kills most of the plants that have small seeds and doesn't kill as many plants with large seeds. In this case, the ground finches that have larger beaks would be more well adapted to eat the available food and survive the drought. They would then reproduce at a higher rate than finches with smaller beaks, and therefore they would pass on their genes to the next generation.  As generations passed the large-beak ground finches would be more common in the population and the small-beak finches would become less common.