Thisisthefourthvolumeintheseries“TutorialsinMathematicalBiosciences. ” These lectures are based on material which was presented in tutorials or developed by visitors and postdoctoral fellows of the Mathematical B- sciences Institute (MBI), at The Ohio State University. The aim of this series is to introduce graduate students and researchers with just a little ba- ground in either mathematics or biology to mathematical modeling of biol- ical processes. The ?rst volume was devoted to mathematical neuroscience, which was the focus of the MBI program 2002–2003. The second volume dealt with mathematical modeling of calcium dynamics in signal transduction, the focus of the MBI program in the winter of 2004. The third volume dealt with topics of cell cycle, tumor growth, and cancer therapy; these topics featured in several workshops held at the MBI in the fall of 2003. The present volume deals with a variety of topics of evolution and ecology, which were considered in the MBI during the year 2005–2006. These topics include phylogenetics; evolution of genes through migration–selection; ecological modeling; and e- lutionofdispersalandpopulationdynamics. Documentationofthe2005–2006 activities, including streaming videos of the workshops, can be found on the Web site: http://mbi. osu. edu. Phylogenetics is the study of the evolutionary relations of genes and - ganisms. Phylogenetic trees are represented by graphs in which the leaves represent observed biological entities. In constructing such graphs, one tries to trace the evolution of species, traits, or diseases. The ?rst two chapters of this volume deal with phylogenetics.
The book offers an easy introduction to fast growing research areas in evolution of species, population genetics, ecological models, and population dynamics. The first two chapters review the concept and methodologies of phylogenetic trees; computational schemes and illustrations are given, including applications such as tracing the origin of SARS and influenza. The third chapter introduces the reader to ecological models, including predator-prey models. This chapter includes and introduction to reaction-diffusion equations, which are used to analyze the ecological models. The next chapter reviews a broad range of ongoing research in population dynamics, including evolution of dispersal models; it also features interesting mathematical theorems and lists open problems. The final chapter deals with gene frequencies under the action of migration and selection. The book is addressed to readers at the level of grad students and researchers. A background in PDEs is provided.
