The species most likely to adapt and evolve to changes in the environment instead of going extinct is an insect species with a high reproduction rate and a significant mutation rate.
Insects that reproduce quickly can generate numerous offspring, increasing the chance of some individuals possessing traits that may help them survive in the new environmental conditions. Additionally, a significant mutation rate allows for greater genetic diversity, providing more opportunities for beneficial adaptations to arise in response to the drastically changed conditions on the island (e.g., lower temperatures and reduced sunlight).
In contrast, the other species (the large mammals and the birds) either have low reproduction rates, specific food needs, or specific habitat requirements that make it more difficult for them to adapt to rapid environmental changes.