Island biogeography preicts that a single large area would have higher biodiversity than sevral small areas, the statement is true.
Island theory of biogeography explains differences in species diversity based on island size (eg, large islands tend to have more species of a given category than small islands). This means that the number of species found on an island will be determined by the area of the island.
Larger islands tend to have more species than smaller islands because there is indeed a greater diversity of habitats and, therefore, more available resources. In its simplest theoretical formspecies from the source area disperse to an island at a certain rate (immigration curve), depending on the size of the island and the distance from the source area.
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