An ecological framework linking scales across space and time based on self-thinning.

Scaling up from measurements made at small spatial and short temporal scales is a central challenge in the ecological and related sciences, where predictions at larger scales and over long time periods are required. It involves two quite distinct aspects: a formulation of a theoretical framework for calculating space-time averages, and an acquisition of data to support that framework. In this paper, we address the theoretical part of the question, and although our primary motivation was an understanding of carbon accounting our formulation is more general. To that end, we adopt a dynamical systems approach, and incorporate a new dynamical formulation of self-thinning. We show how to calculate rates of change for total (and average) plant dry mass, volume, and carbon, in terms of the properties of the individual plants. The results emphasize how local scale statistics (such as, variation in the size of individuals) lead to nonlinear variation at larger scales. Further, we describe how regular and stochastic disturbance can be readily incorporated into this framework. It is shown that stochastic disturbance at patch-scales, results in (to first approximation) regular disturbance at ecosystem scales, and hence can be formulated as such. We conclude that a dynamical formulation of self-thinning can be used as a generic framework for scaling ecological processes in space and time.