Avolcanic island in the middle of the pacific ocean explodes, and all life is removed from the island. however, decades later, the island has a covering of plant life, and some animals have appeared. this is an example of

secondary succession

Explanation:

In the described scenario we have a destruction of an ecosystem because of natural causes, volcano in this case. All that has left after the volcanic eruption has been barren land. After this has happened life started colonizing the volcanic island again, in a process known as primary succession. In the primary succession it is the organisms that have the lowest of requirements for survival that will inhabit the island. Over time, as they die, they will provide biomass for the ground, thus soil will start to form. Once there's soil formed a process called secondary succession will start. In this process the island will start to be inhabited by some plants and smaller animals. These plants and animals will contribute to further enhancing the living conditions on the island, and the island will gradually be getting larger plants and larger animals, thus a new ecosystem will be formed on the place of the old one.