Natural communities inhabit a world of great complexity in time and space. The physical environment has many spatial complexities in its topography, hydrology and soils. And it changes over time: organisms experience varying weather and climatic changes on many scales interacting in a variety of ways with spatial environmental variation. Various processes, not just the physical environment, but also interactions between organisms, cause their densities to vary greatly in space and time too. It has often been hypothesized that these different kinds of variation have important roles in diversity maintenance. But what are those roles? Development of mathematical models with such complexities is not easy, and so it is perhaps not surprising that much mathematical theory, even if it addresses density variation in time or space, rarely includes variation in the physical environment. The theory coming from this lab is different. We have embraced environmental complexity, and gathered the mathematical tools necessary to study it. The result is a comprehensive multiscaled theory of diversity maintenance that includes the standard equilibrium theory as a special case. This work has led to the recognition of several new species coexistence mechanisms including the storage effect, nonlinear competitive variance, and fitness-density covariance.
