From species-area relationships to biodiversity risk assessment

Biodiversity is commonly summarized by macroecological mean patterns, most prominently the species-area relationship (SAR) linking habitat area to expected species richness. Yet conservation, policy, and economic decisions increasingly require risk metrics: probabilities of rare but consequential biodiversity shortfalls, including local collapse. Such tail risks are central in finance and insurance but remain difficult to quantify in ecology because the data needed to estimate full richness distributions are rarely available at decision scales. Here we provide a mechanistic route from species-area relationships to biodiversity risk metrics. We show that when regional species abundances are w