The likely explanation is that population 1 had traits which were more favorable to its survival than population 2's in the new conditions. It wouldn't have to do with food competition, but the traits they already have that may or may not be conducive to their survival in the new conditions.
Explanation:
Let me explain. Say a drought occurred on an island. Population 2 relied on eating bugs that lived in the green grasses. Population 1 relied on eating cactus fruit, which is drought-resistant. Say that because of the drought, population 2 started to decrease since there were less bugs to eat because the grasses dried up. Population 1 is unaffected because the bugs they eat were still in abundance.
This all has to do with the concept of natural selection. Species with traits that are good for their environment will likely do well unless a change in conditions occurs which makes their traits no longer favorable.
