Final answer:
The theory of island biogeography actually states that smaller islands have a higher rate of extinction due to factors like lower immigration rates, less diversity of habitats, and smaller populations.
Step-by-step explanation:
The statement "The theory of island biogeography predicts that the extinction rate is greater on large islands than on small islands." is false. According to the theory of island biogeography, developed by Robert H. MacArthur and Edward O. Wilson, smaller islands actually have a higher probability of extinction compared to larger ones. This is due to several factors: Smaller islands have lower immigration rates for new species, are less geographically diverse which means fewer niches for speciation, and support smaller populations which increase the likelihood of extinction. Larger islands generally have more diverse habitats and larger populations, which can support a greater number of species and reduce the risk of extinction.