The population of rabbits on the volcanic island in big portion will dye out, some as a direct consequence from the volcanic eruption, and some because of the lack of food resources. Because the food will be much more scarce, the rabbits will become much smaller, thus needing less food, and also the reproduction process will be much slower and delayed, and as the island recovers from the eruption, the small remaining population of rabbits will start adapting on the new food sources. Once the rabbits are adapted to the new food resources their population will start rising again.