Abstract:  Our research addresses the issue of how ecological processes occurring at different temporal and spatial scales interact and result in ecosystem level patterns, and how those patterns feed back to affect the lower levels. This is the one of the most fundamental questions in theoretical biology and also the central questions in sustainability. The general approach is to consider populations and communities as complex adaptive systems, which result from self-organization on multiple levels. The mathematics include three major components: 1) the use of individual-based models for simulating complex-adaptive systems and interactions on multiple scales, 2) the development of different scaling methods that approximate individual-based processes, and 3) the investigation of various inverse problems to connect models with empirical data. In this presentation we show how this research framework applies to forest ecology. We have developed a new spatial individual-based forest model that includes crown plasticity. Its structure allows us to derive an accurate approximation for the individual-based model that predicts mean densities and size structures using the same parameter values and functional forms, and, also, is analytically tractable. The approximation is represented by a system of Von Foerster partial differential equations coupled with an integral equation that we call the Perfect Plasticity Approximation (PPA). We have derived a series of analytical results including equilibrium abundances for trees of different crown shapes, stability conditions, and transient behaviors, such as the constant yield law and self-thinning exponents, and two species coexistence conditions. Finally, we will briefly review other projects where we employ this research framework such as scaling of nutrient cycles in aquatic ecosystems, self-organization in social systems and disease modeling.