1、Use R!Series Editors:Robert GentlemanKurt HornikGiovanni ParmigianiFor other titles published in this series, go toM. Henry H. StevensA Primer of Ecology with RM. Henry H. Stevens Department of Botany Miami University Oxford, OH 45056, USA ISBN 978-0-387-89881-0DOI 10.1007/978-0-38

2、7-89882-7e-ISBN 978-0-387-89882-7Springer Dordrecht Heidelberg London New YorkLibrary of Congress Control Number: 2009927709© Springer Science+Business Media, LLC 2009. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Scienc

3、e+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now

4、known or hereafter developed is forbidden.The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.Printed on acid-pape

5、rSpringer is part of Springer Science+Business Media ()To my perfect parents, Martin and Ann, to my loving wife, Julyan,and to my wonderfully precocious kids, Tessa and Jack.PrefaceGoals and audienceIn spite of the presumptuous title, my goals for this book are modest. I wrote it as the manual I wis

6、h I had in graduate school, and a primer for our graduate course in Population and Commu Miami University1Ecology atIt is my hope thaters can enjoy the ecological content and ignore theR code, if they care to. Toward this end, I tried to make the code easy to ignore, by either putting boxes around i

7、t, or simply concentrating code in some sectionsand keeit out of other sections.It is also my hope that ecologists interested in learning R will have a rich yetgentle introduction to this amazing programlanguage. Toward that end, Ihave included some useful functions in an R package called primer. Li

8、ke nearly all R packages, it is available through the R projects repositories, the CRAN mirrors. See the Appendix for an introduction to the R language.I have a hard time learning something on my own, unless I can do somethingwith the material. Learning ecology is no different, and I find that mysan

9、d I learn theory best when we write down formulae, manipulate them, and explore consequences of rearrangement. This typically starts with copying down,verbatim, an expression in a book or paper. Therefore, I encourageers totake pencil to paper, and fingers to keyboard, and copy expressions they see

10、in this book. After that, make sure that what I have done is correct by trying some of the same rearrangements and manipulations I have done. In addition, try things that arent in the book have fun.A pedagogical suggestionFor centuries, musicians and composers have learned their craft in part bycopy

11、ing by hand the works of others. Physical embodiment of the musical notes1 Miami University is located in the Miami River valley in Oxford, Ohio, USA; the region is home to the Myaamia tribe that dwelled here prior to European occupa- tion.VIIIPrefaceand their sequences helped them learn composition

12、. I have it on great authority that most theoreticians (and other mathematicians) do the same thing they start by copying down mathematical expressions. This physical process helps get the content under their skin and through their skull. I encourage you to do the same. Whether otherwise indicated o

13、r not, let the first assigned problem at the end of each chapter be to copy down, with a pencil and paper, the mathematical expression presented in that chapter. In my own self-guided learning, I have often taken this simple activity for granted and have discounted its value tomy own detriment. I am

14、 not surprised how oftens also take thiivityfor granted, and similarly suffer the consequences. Seeing the logic of something is not always enough sometimes we have to actually recreate the logic for ourselves.Comparison to other textsIt may be useful to compare this book to others of a similar ilk.

15、 This book bearsst similarities to two other wonderful primers: Gotellis A Primer ofitsEcology, and Roughgardens Primer of Theoretical Ecology. I am more familiar with these books than any other introductory texts, and I am greatly indebted to these authors for their contributions to my education an

16、d the discipline as a whole.My book, geared toward graduates, includes movanced materialthan Gotellis primer, but most of the ecological topics are similar. I attempt to start in the same place (e.g., “What is geometric growth?”), but I develop many of the ideas much further. Unlike Gotelli, I do no

17、t cover life tables at all,but rather, I devote an entire chapter to demographic matrix ms. I include achapter on commustructure and diversity, including multivariate distances,species-abundance distributions, species-area relations, and island biogeography, as well as diversity partitioning. My boo

18、k also includes code to implement most of the ideas, whereas Gotellis primer does not.This book also differs from Roughgardens primer, in that I use the OpenSource R programlanguage, rather than®, and I do not coverphysiology or evolution. My philosphical approach is similar, however, as I tend

19、 to “talk” to the er, and we fall down the rabbit hole together2.Aside from Gotelli and Roughgardens books, this book bears similarity in content to several other wonderful introductions to mathematical ecology or biology. I could have cited repeatedly (and in some places did so) the following: Elln

20、er and Guckenheimer (2006), Gurney and Nisbet (1998), Kingsland (1985), MacArthur (1972), Magurran (2004), May (2001), Morin (1999), Otto and Day (2006), and Vandermeer and Goldberg (2007). Still others exist, but I have not yet had the good fortune to dig too deeply into them.AcknowledgementsI am i

21、ndebted to Scott Meiners and his colleagues for their generous sharing of data, metadata, and statistical summaries from the Buell-Small Succession2 Froms Adventures in Wonderland (1865), L. Carroll (C. L. Dodgson).PrefaceIX), a 50+ year study of secondary succes-Study (sion (supported in part by NS

22、F grant DEB-0424605) in the North American temperate deciduous forest biome. I would like to thank Stephen Ellner for Rosss Bombay plague death data and for R code and insight over the past few years. I am also indebted to Tom Crist and his colleagues for sharing some of their moth data (work suppor

23、ted by The Nature Conservancy Ecosystem Research Program, and NSF DEB-0235369).I am grateful for terosity of early reviewers anders, each of whomhas contributed much to the quality of this work: Jeremy Ash, Tom Crist, David Gorchov, Raphael Herrera-Herrera, Thomas Petzoldt, James Vonesh, aswell as s

24、everal anonymous reviewers, and thes of our Population andCommuEcology class. I am also grateful for the many conversations ands shared with four wonderful mathematicians and theoreticians: Jayanth Banavar, Ben Bolker, Stephen Ellner, Amit Shukla, and Steve Wright I never have a conversation with th

25、ese people without learning something. I have beenparticularly fortunate to have team-taught Population and CommuEcologyat Miami University with two wonderful scientists and educators, Davd Gorchovand Thomas Crist. Only with this experience, of workingly with thesecolleagues, have I been able to att

26、empt this book. It should go without saying, but I will emphasize, that the mistakes in this book are mine, and there would be many more but for the sharp eyes and insightful minds of many other people.I am also deeply indebted to the R Core Development Team for creating,maintaining and pushing forw

27、ard the R programlanguage and environment173. Like the air I breathe, I cannot imagine my (professional) life without it. I would especially like to thank Friedrich Leisch for the development of Sweave,which makes literate programeasy 106. Because I rely on Aquamacs,ESS, LATEX, and a host of other O

28、pen Source programs, I am deeply grateful to those who create and distribute these amazing tools.A few other R packages bear special mention. First, Ben Bolkers text 13and packages for ming ecological data (bbmle and emdbook) are broadlyapplicable. Second, Thomas Petzoldts and Karsten Rinkes simecol

29、 packageprovides a general computational architecture for ecological ms, and im-plements many wonderful examples 158. Much of what is done in this primer (especially in chapters 1, 36, 8) can be done with simecol, and sometimes done better. Third, Robin Hankins untb package is an excellent resource

30、for exploring ecological neutral theory (chapter 10) 69. Last, I relied heavily on the deSolve 190 and vegan packages 151.Last, and most importantly, I would like to thank those to whom this book is dedicated, whose love and senses of humor make it all worthwhile.Martin Henry Hoffman StevensOxford,

31、OH, USA, EarthFebruary, 2009ContentsPart I Single Species Populations1Simple Density-independent Growth . . . . . . . . . . . . . . . . . . . . . . . .345578101013141617181920212123242627313A Very Specific Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .A Simple

32、 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Exploring Population Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...4Projecting population into the future . . . . . . . . . . . . . . . . .Effects of initial population size

33、 . . . . . . . . . . . . . . . . . . . . . .Effects of different per capita growth rates . . . . . . . . . . . . .Average growth rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.4Continuous Exponential Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . ..21.4.3

34、1.4.4Motivating continuous exponential growth . . . . . . . . . . . . .Deriving the time derivative . . . . . . . . . . . . . . . . . . . . . . . . .Doubling (and tripling) time . . . . . . . . . . . . . . . . . . . . . . . . .Relating and r . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35、. . . . . .1.51.6Comments on Simple Density-independent Growth Ms . . . .M ...6ing with Data: Simulated Dynamics . . . . . . . . . . . . . . . . . . .Data-based approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Looking at and collecting the data . . . .

36、. . . . . . . . . . . . . . . .One simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Multiple simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Many simulations, with a function . . . . . . . . . . . . . . . . . . . .Analyzing results . . .

37、. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.7Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2Density-independen

38、t Demography . . . . . . . . . . . . . . . . . . . . . . . . . .2.1 A Hypothetical Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33343636373..4The population projection matrix . . . . . . . . . . . . . . . . . . . .A brief primer on matrices . . . . . .

39、 . . . . . . . . . . . . . . . . . . . .Population projection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Population growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .XIIContents2.2Analyzing the Projection Matrix . . . . . . . . . . . . . . . . . . . . . . .

40、. . . .404142444546484949505152545556595...6Eigenanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Finite rate of increase . . . . . . . . . . . . . . . . . . . . . . . . . . .Stable stage distribution . . . . . . . . . . . . . . . . . . .

41、 . . . . . . . . .Reproductive value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Sensitivity and elasticity More demographic m. . . . . . . . . . . . . . . . . . . . . . . . . . . .s . . . . . . . . . . . . . . . . . . . . .s with Data . . . . . . . . . . . . . . . . .2.3Confron

42、ting Demographic M...62.3.7An Example: Chamaedorea palm demography . . . . . . . . . .Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Preliminary data management . . . . . . . . . . . . . . . . . . . . . . .Estimating projection m

43、atrix . . . . . . . . . . . . . . . . . . . . . . . .Eigenanalyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Bootstrapa demographic matrix . . . . . . . . . . . . . . . . .The demographic analysis . . . . . . . . . . . . . . . . . . . . . . . . . . .2.4Summary . . .

44、. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3Density-dependent Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61626264

45、66686975767979858689923.1Discrete Density-dependent Growth . . . . . . . . . . . . . . . . . . . . . . . . ...43.1.5Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Relations between growth rates and density . . . . . . . . . . . .Effect of i

46、nitial population size on growth dynamics. . . . .Effects of . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Effects of rd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.2Continuous Density Dependent Growth . . . . . . . . . . . . . . .

47、. . . . . ...4Generalizing and resimplifying the logistic m Equilibria of the continuous logistic growth m. . . . . . . . . . . .Dynamics around the equilibria stability . . . . . . . . . . . .Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48、Other Forms of Density-dependence . . . . . . . . . . . . . . . . . . . . . . . .um Sustained Yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Fitting Ms to Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.5.1The role of resources in alteri

49、ng population interactions within a simple food web . . . . . . . . . . . . . . . . . . . . . . . . . . . .Initial data exploration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .A time-implicit approach . . . . . . . . . . . . . . . . . . . . . . . . . . . .A time-explicit approach . . .

50、 . . . . . . . . . . . . . . . . . . . . . . . . .92939510110710.Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4P

51、opulations in Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1111121141171171Source-sink Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Two Types of Metapopulations. . . . . . . . . . . . . . . . . . . . . . . . . . .

52、. .Related Ms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.3.1 The classic Levins m. . . . . . . . . . . . . . . . . . . . . . . . . . . .4.3.2 Propagule rain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .ContentsXIII4.3.3 The rescue

53、 effect and the core-satellite m. . . . . . . . . .120123125128132134.7Parallels with Logistic Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Habitat Destruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Core-Satellite Simulations . . . . .

54、 . . . . . . . . . . . . . . . . . . . . . . . . . . . .Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Part II Two-species Interacti

55、ons5LotkaVolterra Interspecific Competition . . . . . . . . . . . . . . . . . . .1351361361371391401411431461461481491501511551571585.1Discrete and Continuous Time Ms . . . . . . . . . . . . . . . . . . . . . .5.1.1 Discrete time m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.1.2

56、Effects of . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.1.3 Continuous time m. . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.2Equilbria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.2.1 Isoclines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.2.2 Finding equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Dynamics at the Equilibria . . . . . . .