A Short History of Mathematical Population Dynamics
As Eugene Wigner stressed, mathematics has proven unreasonably effective in the physical sciences and their technological applications. The role of mathematics in the biological, medical and social sciences has been much more modest but has recen
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Nicolas Bacaër
A Short History of Mathematical Population Dynamics
Nicolas Bacaër IRD (Institut de Recherche pour le Développement) Bondy France [email protected]
Whilst we have made considerable efforts to contact all holders of copyright material contained in this book, we have failed to locate some of them. Should holders wish to contact the Publisher, we will make every effort to come to some arrangement with them ISBN 978-0-85729-114-1 e-ISBN 978-0-85729-115-8 DOI 10.1007/978-0-85729-115-8 Springer London Dordrecht Heidelberg New York British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Mathematics Subject Classification (2010): 00A09, 01A05, 92D10, 92D25, 92D30, 92D40 © Springer-Verlag London Limited 2011 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of 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 laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Cover design: deblik Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To Aili, Nina and Sophie
Preface
Population dynamics is the area of science which tries to explain in a simple mechanistic way the time variations of the size and composition of biological populations, such as those of humans, animals, plants or microorganisms. It is related to, but still quite distinct from, the more descriptive area of population statistics. One common point is that they make extensive use of mathematical language. Population dynamics is at the intersection of various fields: mathematics, social sciences (demography), biology (population genetics and ecology) and medicine (epidemiology). As a result it is not often presented as a whole, despite the similarities between the problems met in various applications. A notable exception in French is the book Mathematical Population Theories1 by Alain Hillion. But it presents the subject from the point of view of the mathematician, distinguishing various types of model: discrete-time models (t = 0, 1, 2...) and continuous-time models (t is a real number), deterministic models (future states are known exactly if the present state is known exactly) and stochastic models (where probabil
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