Tutorials_In_Mathematical_Biosciences_IV__Evolution_and_Ecology_-_Avner_Friedman.pdf

Lecture Notes in Mathematics

1922

Editors:

J.-M. Morel, Cachan

F. Takens, Groningen

B. Teissier, Paris

Editors Mathematical Biosciences Subseries:

P.K. Maini, Oxford

Avner Friedman (Ed.)

Tutorials in

Mathematical Biosciences IV

Evolution and Ecology

With Contributions by:

C. Cosner ¢ D. Janies ¢ L.S. Kubatko

Y. Lou ¢ T. Nagylaki

ABC

Editor

Avner Friedman

Mathematical Biosciences Institute

Ohio State University

231 West 18 th Avenue

Columbus, OH 43210-1292

USA

e-mail: afriedman@math.ohio-state.edu

afriedman@mbi.ohio-state.edu

Library of Congress Control Number: 2007933684

Mathematics Subject Classiﬁcation ( 2000): 35J20 , 35J60 , 35K55 , 35K57 , 62P10 , 62P12 ,

92B99 , 92D10 , 92D15 , 92D25 , 92D40

ISSN print edition: 0075-8434

ISSN electronic edition: 1617-9692

ISBN 978-3-540-74328-6 Springer Berlin Heidelberg New York

DOI 10.1007 / 978-3-540-74331-6

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is

concerned, speciﬁcally the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting,

reproduction on microﬁlm or in any other way, and storage in data banks. Duplication of this publication

or parts thereof is permitted only under the provisions of the German Copyright Law of September 9 ,

1965 , in its current version, and permission for use must always be obtained from Springer. Violations are

liable for prosecution under the German Copyright Law.

Springer is a part of Springer Science+Business Media

springer.com

° Springer-Verlag Berlin Heidelberg 2008

The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply,

even in the absence of a speciﬁc statement, that such names are exempt from the relevant protective laws

and regulations and therefore free for general use.

Typesetting by the author and SPi using a Springer L A T E X macro package

Cover design: design & production GmbH, Heidelberg

Printed on acid-free paper

41 /SPi

5 4 3 2 1 0

SPIN: 12109630

Preface

This is the fourth volume in the series “Tutorials in Mathematical Biosciences.”

These lectures are based on material which was presented in tutorials or

developed by visitors and postdoctoral fellows of the Mathematical Bio-

sciences Institute (MBI), at The Ohio State University. The aim of this series

is to introduce graduate students and researchers with just a little back-

ground in either mathematics or biology to mathematical modeling of biolog-

ical processes. The ﬁrst 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 evo-

lution of dispersal and population dynamics. Documentation of the 2005–2006

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 or-

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 ﬁrst two chapters of

this volume deal with phylogenetics. Chapter 1 is a general survey on estima-

tion of phylogenetic trees with emphasis on likelihood methods. Chapter 2 is

concerned with computational methods of very large trees, exploring other

optimality methods, with application to the study of the evolution of SARS

and inﬂuenza.

The next three chapters deal with population genetics and population

dynamics. Chapter 3 introduces reaction–diﬀusion equations as a mathemat-

ical framework to study ecological models. It then addresses the following

ecological questions: what is the minimal patch size necessary to support a

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika: