Final answer:
When the immigration rate of species to an island equals the extinction rate, the number of species on the island remains constant, reflecting a balance in the dynamic processes of immigration and extinction.
Step-by-step explanation:
When the immigration rate of species to an island equals the extinction rate of species already present, the number of species on the island is constant. This concept is based on the theory of island biogeography, developed by Robert H. MacArthur and Edward O. Wilson, which describes how the number of species on an island represents a balance between the processes of immigration and extinction. As immigration adds species and extinction removes them, an equilibrium is reached when these two rates are equal. This balance can be disturbed if either the immigration rate increases or the extinction rate decreases, leading to a change in the number of species present.