Cluster 9
Mathematical Modeling of Biological Systems
Introduction
This cluster will introduce students to a wide variety of mathematical models used in biology. Students will learn how to construct mathematical models and use mathematical techniques to analyze these models in order to gain insight to biological phenomena. No prior experience in mathematical modeling or the biological topics covered is necessary, but a strong interest in both mathematics and biology is
essential.
Core Courses (4 Weeks)
Dynamics of Biological Systems: Patterns in Time and Space
Most biological systems are dynamic, producing fascinating patterns in both time and space. Examples include outbreaks of epidemics, the development of spots on a leopard, the synchronization of flashing fireflies, and pathological rhythms in the heart. Identifying the mechanisms that underlie the “spatio-temporal” dynamics of biological systems can not only lead to better understanding of natural phenomena but also help us to design more effective interventions when necessary. Mathematical modeling plays a fundamental role in identifying these mechanisms. In this course, students will use computer simulation and mathematical analysis to explore the dynamics in models of a variety of biological processes and to gain insight into the mechanisms that produce complex temporal and spatial patterns.
Networks and Games in Biology
Biological systems often involve many interacting components that form complex networks. These networks occur at all biological scales ranging from genes to ecosystems. Network theory provides a collection of mathematical and computational methods to understand the structure and function of these networks. When networks consist of interacting individuals, individuals within these networks may play different strategies to increase their reproductive success. Strategies exhibiting greater reproductive success are more likely to spread through the population. Evolutionary game theory examines the long-term outcomes of these interactions and has provided important insights into the evolution of cooperation, social learning, animal conflicts, and language. In this course, students will learn the fundamentals of network theory and evolutionary game theory. Computational methods will be applied to biological data sets to examine the structure and function of ecological or metabolic networks, and will be used to identify how the structure of social networks facilitate or inhibit the evolution of cooperation.
Morphmetry and Allometry: Relationships of shape and Size in Biological Organisms
Allometry, also referred to as biological scaling, is the study of the relationship between body size and the properties of an organism. For example, as the body size of mammals increases, brains get bigger and life spans increase. Morphometrics is the quantitative analysis of the size and shape of organisms. Allometry and morphometrics can be used to address important questions in physiology, developmental biology, evolution and ecology. In this course, students will learn the basic concepts of allometry and morphometrics, and discuss examples that include modeling the shape and size of the mammalian brain (a research project being carried out at the Center for Neuroscience at UC Davis). As a hands-on example, students will compare the geometry of the eggs of various birds. Students will collect data and perform statistical analysis to compare the shapes of the eggs and look for underlying scaling laws.
Modified 2012-01-13T20:00:00Z