Island biogeography through the lens of multiscale metapopulation dynamics: insights into species-area relationships

While island biogeography focuses on species richness equilibrium driven by immigration and extinction, and metapopulation theory examines single-species dynamics across fragmented habitats, their interplay remains poorly understood. In particular, the species-area relationship remains a subject of ongoing debate, yet there are limited theoretical foundations to explain it. To address this, we developed a multiscale stochastic metapopulation model to investigate diversity patterns on islands, bridging the gap between island biogeography and metapopulation theory. Our model integrates regional colonization from a mainland with local colonization-extinction processes within islands at the single-species level, then extends this to multiple, independent species. By analyzing the stationary properties of this model, we generate novel predictions of Species Area Relationship (SAR) based on local extinction rates, within-island colonization rates, and mainland immigration rates. We demonstrate how the interplay of these parameters influences the relationship, predicting patterns that can resemble either the power-law of Arrhenius or the semi-logarithmic relationship of Gleason, depending on the relative importance of mainland immigration versus within-island dynamics, and on the nature of the species abundance distribution in the mainland. This unified framework offers new insights into the mechanisms driving species richness and distribution across spatial scales, providing a more holistic understanding of biodiversity patterns in fragmented landscapes.