Ecological Orbits: How Planets Move and Populations Grow LEV GINZBURG MARK COLYVAN OXFORD UNIVERSITY PRESS Ecological Orbits This page intentionally left blank Ecological Orbits How Planets Move and Populations Grow LEV GINZBURG MARK COLYVAN 1 2004 1 Oxford New York Auckland Bangkok Buenos Aires Cape Town Chennai Dar es Salaam Delhi Hong Kong Istanbul Karachi Kolkata Kuala Lumpur Madrid Melbourne Mexico City Mumbai Nairobi S ˜ ao Paulo Shanghai Taipei Tokyo Toronto Text Copyright © 2004 by Applied Biomathematics Artwork by Amy Dunham © 2002 Applied Biomathematics Published by Oxford University Press, Inc., 198 Madison Avenue, New York, New York 10016 www.oup.com Oxford is a registered trademark of Oxford University Press All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Oxford University Press. Library of Congress Cataloging-in-Publication Data Ginzburg, Lev R. Ecological orbits: how planets move and populations grow / Lev Ginzburg, Mark Colyvan. p. cm. Includes bibliographical references (p. ). ISBN 0-19-516816-X 1. Population biology. 2. Ecology. I. Colyvan, Mark. II. Title. QH352.G55 2003 577.8'8—dc21 2003048690 135798642 Printed in the United States of America on acid-free recycled paper To Tatyana (1946–2000) Difficulty in imagining how theory can adequately describe nature is not a proof that theory cannot. —Robert MacArthur (1930–1972) Neruda: Le metafore? . . . Quando parli di una cosa, la paragonono ad un’ altra. . . . Postino: É semplice! Perchè questo nome é cosí complicato? [Neruda: Metaphors? . . . It’s when you speak of one thing, com- paring it to another. . . . Postino: That’s simple! Why do they use such a complicated name?] —Dialogue between the characters Pablo Neruda and the postman in the movie Il Postino (1995) Preface The main focus of this book is the presentation of the “inertial” view of population growth. This view provides a rather simple model for complex population dynamics, and is achieved at the level of the single species, without invoking species interactions. An important part of our account is the maternal effect. Invest- ment of mothers in the quality of their daughters makes the rate of reproduction of the current generation depend not only on the current environment but also on the environment experienced by the preceding generation. The inertial view is a significant departure from traditional ecological theory, which has been developing within the Lotka– Volterra framework for close to a century. One way to see this departure is to focus attention away from the growth rate as the sole variable responding to the environment, and toward “ac- celeration,” or the rate of change of the growth rate between consecutive generations. More precisely, our suggestion is that population growth is a second-order dynamic process at the single-species level, and the second-order character is not nec- essarily the result of species interactions. If the inertial view of population growth proves correct, a great deal of current theory on population growth will need to be rethought and revised. As will become clear, our inspiration for looking at ecology in the way we do comes from similar moves in physics—in par- ticular, the move from Aristotelian to Newtonian physics. So let us say a few words in defense of our apparent “physics envy.” Many biologists and ecologists find deference to physics, as the viii Preface Alfred James Lotka (1880–1986) science to which all other sciences must aspire, somewhat dis- tasteful. Those who find this deference to physics unreasonable are generally concerned by the inappropriateness of the meth- ods of physics to other branches of science. They suggest that biology, for example, would be better served if biologists did biology instead of trying to mimic the methods and successes of physics. We agree that the methods of the various sciences are quite different and that, in general, the methods of physics are of little use to biologists. But this does not mean that the various branches of science cannot take inspiration from one another. Preface ix Vito Volterra (1860–1940) The inspiration here is metaphorical, not mechanical. We see an abstract connection between a certain innovation in the devel- opment of physics around the time of Galileo and an analogous way to approach population growth. We are not suggesting any mechanistic similarities between the ways in which populations grow and the ways planets move. At the same time, we are not trading in mere metaphors. Although the inspiration for looking at ecology in the way we do comes from metaphorical connec- tions with physics, these connections can, and will, be spelled out via the mathematics employed in the respective theories we present. [...]... is dedicated to Tatyana and her well-intentioned advice Contents 1 On Earth as It Is in the Heavens 3 1.1 1.2 How Populations Grow 1.3 Metaphors and the Language of Science 1.4 2 How Planets Move 4 Inertial Population Growth Does Ecology Have Laws? 6 9 11 2.1 Ecological Allometries 2.2 Kepler’s Laws 2.3 What Is a Law of Nature? 2.4 3 8 12 Laws in Ecology 21 26 30 Equilibrium and Accelerated Death 34... intentionally left blank Ecological Orbits This page intentionally left blank One On Earth as It Is in the Heavens Populations grow and decline; planets roll relentlessly around the sun On the face of it, planets and populations have nothing to do with one another Indeed, they are studied by completely different branches of science Planets are studied by a branch of physics—astronomy; populations of living... refer to ecological causal mechanisms and must be tested by ecological methods, against ecological data 1.4 Inertial Population Growth According to our view, populations are inertial That is, populations tend to grow according to the Malthusian law (i.e., exponentially), and the effect of an external force, such as a change in environment, is to produce an “acceleration”—a rate of change 10 Ecological. .. ecology And these two disciplines have little in common Any suggestion that one theory describes both planetary motion and population growth is surely misguided There are some similarities between planets and populations, however For a start, the laws of nature are meant to hold everywhere in the universe We expect planets in far-off galaxies to be governed by the same natural laws as our own Earth And. .. lived on a planet like Venus, for instance, with constant, thick cloud cover 1.2 How Populations Grow Now let’s consider the ways populations grow Populations whose abundances are cyclic are a minority, but these minority cases, we believe, tell us something about the general theory of population growth In this way, cycling populations in ecology are very much like planetary orbits for physics Suppose... ecology and describes exponential or Malthusian growth, after Thomas Malthus (1766– 1834) It describes the default situation for populations how they behave in the absence of any disturbing factors The important question remains, however, of how external “forces” act on this background state Do environmental forces affect the per capita growth rate directly, or do they affect the rate of change of this growth... natural laws as our own Earth And we expect theories of population growth to hold for whatever strange creatures inhabit those far-off planets, just as these theories hold for rabbits, bacteria, and humans here on Earth Second, both planets and populations are capable of periodic behavior Planets trace out elliptical orbits around the sun and (more or less) repeat these orbits, taking (more or less) the... that populations literally grow in the same way that bodies move Indeed, that doesn’t even make sense What we propose is that an understanding of why certain developments in physics were so successful will help us to make analogous moves in the advancement of population ecology We use planetary orbits as a central and important metaphor to guide us in thinking about such matters Our ultimate aim, however,... Mikkelson, Kim Sterelny, and Bill Wimsatt We are also indebted to Carol Booth for her help with the index, to Amy Dunham for her artwork, to Elizabeth Milliman for data analysis and editorial assistance, to Herb Mummers for editorial and technical assistance, to Edward Beltrami and Patrícia Maragliano for translating and transcribing the dialogue from Il Postino, and to John Damuth and Justin Roman for... of precision and has been found to hold for animals as small as shrews and up to Does Ecology Have Laws? 13 Figure 2.1 Kleiber allometry between body size and metabolism (from Brown and West, 2000, p 6, modified from Hemmingsen, 1960) Displayed in three functional groups: unicellular organisms, poikilotherms (cold-blooded vertebrates and invertebrates), and homeotherms (warm-blooded birds and mammals) . Ecological Orbits: How Planets Move and Populations Grow LEV GINZBURG MARK COLYVAN OXFORD UNIVERSITY PRESS Ecological Orbits This. intentionally left blank Ecological Orbits How Planets Move and Populations Grow LEV GINZBURG MARK COLYVAN 1 2004 1 Oxford New York Auckland Bangkok Buenos Aires