I do not think the regional species richness on the mainland will affect how many species are predicted to be found on an island based on the equilibrium theory of island biogeography. The theory focuses on predicting the amount of species present for, as an example, a large island close or far to the mainland; it focuses on the relationship between species and a particular area. Regional species richness relates to the amount of species found in a region, combining all the residing communities in that region. Regional species richness does not take extinction or immigration rates into account, like the equilibrium theory does.
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