Probabilistic Models of Population Evolution Scaling Limits, Genealo
This expository book presents the mathematical description of evolutionary models of populations subject to interactions (e.g. competition) within the population. The author includes both models of finite populations, and limiting models as the
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Étienne Pardoux
Probabilistic Models of Population Evolution Scaling Limits, Genealogies and Interactions
Mathematical Biosciences Institute Lecture Series The Mathematical Biosciences Institute (MBI) fosters innovation in the application of mathematical, statistical and computational methods in the resolution of significant problems in the biosciences, and encourages the development of new areas in the mathematical sciences motivated by important questions in the biosciences. To accomplish this mission, MBI holds many week-long research workshops each year, trains postdoctoral fellows, and sponsors a variety of educational programs. The MBI lecture series are readable up to date introductions into exciting research areas that are inspired by annual programs at the MBI. The purpose is to provide curricular materials that illustrate the applications of the mathematical sciences to the life sciences. The collections are organized as independent volumes, each one suitable for use as a module in standard graduate courses in the mathematical sciences and written in a style accessible to researchers, professionals, and graduate students in the mathematical and biological sciences. The MBI lectures can also serve as an introduction for researchers to recent and emerging subject areas in the mathematical biosciences. Marty Golubitsky, Michael Reed Mathematical Biosciences institute
More information about this series at http://www.springer.com/series/13083
Mathematical Biosciences Institute Lecture Series Volume 1: Stochastics in Biological Systems Stochasticity is fundamental to biological systems. While in many situations the system can be viewed as a large number of similar agents interacting in a homogeneously mixing environment so the dynamics are captured well by ordinary differential equations or other deterministic models. In many more situations, the system can be driven by a small number of agents or strongly influenced by an environment fluctuating in space or time. Stochastic fluctuations are critical in the initial stages of an epidemic; a small number of molecules may determine the direction of cellular processes; changing climate may alter the balance among competing populations. Spatial models may be required when agents are distributed in space and interactions between agents form a network. Systems evolve to become more robust or co-evolve in response to competitive or hostpathogen interactions. Consequently, models must allow agents to change and interact in complex ways. Stochasticity increases the complexity of models in some ways, but may smooth and simplify in others.
Volume 1 provides a series of lectures by internationally well-known authors based on the year on Stochastics in biological systems which took place at the MBI in 2011–2012. Michael Reed, Richard Durrett Editors
Mathematical Biosciences Institute Lecture Series Volume 1: Stochastics in Biological Systems Stochastic Population and Epidemic Models Linda S. Allen Stochastic Analysis of Biochemical Systems David Anderson; Thomas G.
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