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In island ecology, the theory based on the emigration and immigration rate of species on habitat and oceanic islands is called the island equilibrium model.

In biogeography, the term island represents the subcontinental land area separated by natural or artificial means.

Thus, the species colonize from the mainland to the island.

Therefore, the given statement is false.

The several physical characteristics of the island are smaller landmass and a variety of water like ocean, river, and mountains that encloses the island.

Thus, the smaller island will not support many species.

Therefore, the given statement is false.

The roles of the island in an ecosystem are the defense against natural events, soil formation, and the formation of geophysical diversity.

Thus, the species richness will be higher on the larger island; the large island supports many species and is close to the mainland for their colonization on the island.

Therefore, the given statement is true.

Various problems related to the island ecosystem are waste disposal, soil loss, fisheries, domestic waste, and water shortage.

Thus, species richness is not found on the small island.

Therefore, the given statement is false.