Models And Methods For Biological Evolution
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Models and Methods for Biological Evolution
Biological evolution is the phenomenon concerning how species are born, are transformed or disappear over time. Its study relies on sophisticated methods that involve both mathematical modeling of the biological processes at play and the design of efficient algorithms to fit these models to genetic and morphological data. Models and Methods for Biological Evolution outlines the main methods to study evolution and provides a broad overview illustrating the variety of formal approaches used, notably including combinatorial optimization, stochastic models and statistical inference techniques. Some of the most relevant applications of these methods are detailed, concerning, for example, the study of migratory events of ancient human populations or the progression of epidemics. This book should thus be of interest to applied mathematicians interested in central problems in biology, and to biologists eager to get a deeper understanding of widely used techniques of evolutionary data analysis.
A Biologist's Guide to Mathematical Modeling in Ecology and Evolution
Author: Sarah P. Otto
language: en
Publisher: Princeton University Press
Release Date: 2011-09-19
Thirty years ago, biologists could get by with a rudimentary grasp of mathematics and modeling. Not so today. In seeking to answer fundamental questions about how biological systems function and change over time, the modern biologist is as likely to rely on sophisticated mathematical and computer-based models as traditional fieldwork. In this book, Sarah Otto and Troy Day provide biology students with the tools necessary to both interpret models and to build their own. The book starts at an elementary level of mathematical modeling, assuming that the reader has had high school mathematics and first-year calculus. Otto and Day then gradually build in depth and complexity, from classic models in ecology and evolution to more intricate class-structured and probabilistic models. The authors provide primers with instructive exercises to introduce readers to the more advanced subjects of linear algebra and probability theory. Through examples, they describe how models have been used to understand such topics as the spread of HIV, chaos, the age structure of a country, speciation, and extinction. Ecologists and evolutionary biologists today need enough mathematical training to be able to assess the power and limits of biological models and to develop theories and models themselves. This innovative book will be an indispensable guide to the world of mathematical models for the next generation of biologists. A how-to guide for developing new mathematical models in biology Provides step-by-step recipes for constructing and analyzing models Interesting biological applications Explores classical models in ecology and evolution Questions at the end of every chapter Primers cover important mathematical topics Exercises with answers Appendixes summarize useful rules Labs and advanced material available
Methods and Models in Mathematical Biology
This book developed from classes in mathematical biology taught by the authors over several years at the Technische Universität München. The main themes are modeling principles, mathematical principles for the analysis of these models and model-based analysis of data. The key topics of modern biomathematics are covered: ecology, epidemiology, biochemistry, regulatory networks, neuronal networks and population genetics. A variety of mathematical methods are introduced, ranging from ordinary and partial differential equations to stochastic graph theory and branching processes. A special emphasis is placed on the interplay between stochastic and deterministic models.