A unified framework for species spatial patterns: Linking the occupancy area curve, Taylor's Law, the neighborhood density function and two‐plot species turnover

The description of spatial patterns in species distributions is central to research throughout ecology. In this manuscript, we demonstrate that five of the most widely used species‐level spatial patterns are not only related, but can in fact be quantitatively derived from each other under minimal assumptions: the occupancy area curve, Taylor's Law, the neighborhood density function, a two‐plot variant of Taylor's Law and two‐plot single‐species turnover. We present an overarching mathematical framework and derivations for several theoretical example cases, along with a simulation study and empirical analysis that applies the framework to data from the Barro Colorado Island tropical forest plot. We discuss how knowledge of this mathematical relationship can support the testing of ecological theory, suggest efficient field sampling schemes, highlight the relative importance of plot area and abundance in driving turnover patterns and lay the groundwork for future unified theories of community‐level spatial metrics and multi‐patch spatial patterns.