savageAssistant Professor, Department of Biomathematics and Department of Ecology and Evolutionary Biology

Tools and Techniques: allometric scaling theory; evolutionary theory; network theory; asymptotics; stochastic processes; models of fractal and asymmetric branching networks; diffusion-reaction equations; optimization



Interests: vascular networks; cancer; sleep times; organization and constraint of diversity

Personal Statement:
Biological systems display extraordinary diversity in form and function. By understanding this diversity, we can discover mechanisms that provide critical new insights into biomedical problems. My overall research goal is to combine novel mathematical models with newly collected or analyzed empirical data to understand how biological systems are organized, constrained, and controlled across multiple levels of organization. This approach often relies on an evolutionary understanding of the factors that drive biological systems. These evolutionary factors are often revealed through comparative analyses of organisms and species. In this way, I have found new results and published papers in diverse areas such as tumor growth, animal and plant vascular networks, sleep times, cell size, and even the effects of global warming on ecosystems.

For example, vascular networks exhibit remarkably consistent patterns in their branching architecture. Over the past decade, several models have focused on the structure of vascular networks to explain the allometric scaling of metabolic rate with body size. Intense debate has surrounded existing models and the accuracy of their predictions. To test theory more directly, I worked with a Masters student to construct software for extracting large volumes of high quality data on the geometry of branching architecture from medically relevant, radiographic images, in collaboration with clinical radiologists. Similarly detailed data are being collected for plants in collaboration with the Enquist and Sperry labs. To develop a model that can be reconciled with new empirical results emerging from these data analyses, I have begun to perform detailed calculations of fluid resistance and flow in vascular systems. I am also working to devise analytical and numerical methods for networks composed of asymmetric branching—when one vessel branches into two or more daughter vessels that have different radii, lengths, and flow rate. These new models are essential to investigate the selective and developmental forces that mold vascular networks, and thus far, results reveal intriguing developmental and environmental influences.