I want to use mathematical models to understand how diversity is organized, constrained, and controlled in biological systems. My models are constructed using fractal and asymmetric branching networks along with ordinary, partial, and stochastic differential equations. I analyze these models using asymptotic methods, optimization theory, dynamical systems methods, and numerical methods. I test the predictions of these models by performing statistical analyses on large empirical data sets obtained by my collaborators or compiled from the literature. I would contribute to the department by using and teaching a variety of mathematical methods and by bringing to the department my diverse experience constructing quantitative models from conceptual ideas, a suite methods for analyzing large empirical and comparative data sets, and a fresh perspective on many scientific and other applied problems.