Proportional mixture of two rarefaction/extrapolation curves to forecast biodiversity changes under landscape transformation.

Progressive habitat transformation causes global changes in landscape biodiversity patterns, but can be hard to quantify. Rarefaction/extrapolation approaches can quantify within-habitat biodiversity, but may not be useful for cases in which one habitat type is progressively transformed into another habitat type. To quantify biodiversity patterns in such transformed landscapes, we use Hill numbers to analyse individual-based species abundance data or replicated, sample-based incidence data. Given biodiversity data from two distinct habitat types, when a specified proportion of original habitat is transformed, our approach utilises a proportional mixture of two within-habitat rarefaction/extrapolation curves to analytically predict biodiversity changes, with bootstrap confidence intervals to assess sampling uncertainty. We also derive analytic formulas for assessing species composition (i.e. the numbers of shared and unique species) for any mixture of the two habitat types. Our analytical and numerical analyses revealed that species unique to each habitat type are the most important determinants of landscape biodiversity patterns.