When a volcano erupts under the ocean and creates a new island, the process that occurs is known as primary succession.
Primary succession happens in environments that are newly formed or disturbed where no soil exists, such as after a volcanic eruption. In this case, the lava cools to form solid land, and from that barren landscape, life begins to develop. Initially, the bare rock is colonized by organisms like lichens and mosses that can withstand harsh conditions and help to create soil by breaking down the rock and adding organic material as they die. Over time, this leads to the establishment of more complex communities including grasses, shrubs, and eventually trees.
Thus, the correct answer is a) primary succession.