A fourteen-year study of finches on the Galapagos islands concluded that there is a definite relationship between climate and the population size of finch species that thrive at various times.
Conclusion (in question stem)
Climatic variations cause a major difference in survival rates of small and large finches.
Evidence
During droughts, large finches survive better because their large bills can crack the large, hard seeds that smaller finches can't access. In rainy years, large finches survive worse because the moisture fosters plants that produce small seeds, and large finches must consume enormous numbers of small seeds to meet their energy demands — too many to eat fast enough.
Evaluate
The general storyline here is that droughts favor the survival rates of large finches (because of large, hard seeds) whereas rainy years favor the survival rates of small finches (because of small seeds).
It's established that the small finches can't survive on the large seeds (because they can't crack them open) and the large finches can't survive on the small seeds (because you they just can't eat them fast enough to satisfy their huge energy demands).
Goal
The only thing that seems to be missing is the unstated idea that during droughts, the small finches can't find enough of their small seeds to survive. And that during rainy seasons, the large finches can't find enough of their large seeds to survive.