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Towards a Unifying Theory of Vegetation Dynamics

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Towards a Unifying Theory of Vegetation Dynamics TOWARDS A UNIFYING THEORY OF VEGETATION DYNAMICS by Madhur Anand Department of Plant Sciences [Environmental Science] Subrnitted in partial filfillrnent of the requirements for the degree of Doctor of Philosophy Faculty of Graduate Studies The University of Western Ontario London, Ontario May 1997 National Libraiy Bibliothèque nationale !*m of Canada du Canada Acquisitions and Acquisitions et Bibliographie SeMces senrices bibliographiques 395 Wellington Street 395, rue Wellington OttawaON K1AON4 Ottawa ON KIA ON4 Canada Carlada The author has granted a non- L'auteur a accorde une licence non exclusive licence allowing the exclusive permettant à la National Library of Canada to Bibliothèque nationale du Canada de reproduce, loan, distribute or sell reproduire, prêter, distribuer ou copies of this thesis in microform, vendre des copies de cette thèse sous paper or electronic formats. la forme de microfiche/film, de reproduction sur papier ou sur format électronique. The author retains ownership of the L'auteur conserve la propriété du copyright in ths thesis. Neither the droit d'auteur qui protège cette thèse. thesis nor substantid extracts fiom it Ni la thèse ni des extraits substantiels may be printed or otherwise de celle-ci ne doivent être imprimés reproduced without the author's ou autrement reproduits sans son permission. autorisation. ABSTRACT The thesis to be argued is that vegetation dynamics is a unified, complex chaotic process, hierarchically unfolding over spatio-temporal scales, where determinism and randomness convolute, shifting in dominance through sequential phases. Conventional theory, known as the Clements-Gleason controversy, views determinism and randomness as mutually exclusive phenornena. My goal is to prove conventional theory wrong. 1 use the language of dynarnical systems theory to conceptualize vegetation dynamics as an analytical space-time trajectory. The phase space coordinates are derived from cornpositional data. Two case studies are presented. The first short-term dynamics in an Atlantic heathland recovering from fire and grazing. Dynamics is obsewed to be transient, beginning with linear determinism and then collapsing into a chaotic nonlinear phase. The stationary Markov chain serves as an excellent reference set for detecting determinisrn, and the model fits the observed process quite well. However, this simple linear model cannot account for the phase transition defining the natural process. Interestingly, simulation experiments on the stationary Markov chah with various levels of random perturbation recover the obsewed two-phase structure surprisingly well. The simulated process is deterministically chaotic, possessing a positive Lyapunov exponent and high fractal dimension. This verifies that passage between dominant deterrninism and dominant randornness is a distinctly possible event and suggests that the heathland process is highly complex and unpredictable in the long-tem. The second case study of long-term postglacial vegetation dynarnics revealed a surprising repetition of the pattern seen in the heathland. The two-phase complex chaotic structure re-emerged, revealing the hierarchical nature of vegetation dynamics. Against better intuition, apparently random effects can enhance the appearance of determinism through a synergistic accumulation of small feedback effects. Determinism is thus not always dominant, but rather appears as an underlying wave which may at times be overwhelmed by randomness. The fact that determinism and randomness are not easily teased apart suggests that both Clements' and Gleason's views are necessary. "Chaos" provides the basis for a unified theory of vegetation dynamics. Classical theones are reconciled and in fact reside as special cases. keywords: chaos, coding, complexity, determinism, diversity, entropy, information theory, modelling, succession 1 thank my supervisor, Dr. L. Orloci, for his unfailing guidance, wisdom and inspiration, which were fundamental in defining the path which brought me here. 1 am eminently grateful to hirn for providing me with an open and fertile acadernic environment, which included access to facilities, opportunities to travel to conferences, participation in scientific research at an international level and, most importantly, a passion towards science and life in general. 1 thank the members of rny advisory cornmittee for much guidance and expert advice. Specifically 1 thank the late Dr. R. C. Jancey for instructive and clarifying discussions. I am most grateful to Dr. M. A. Maun for sage advice and contagious enthusiasm toward my research. 1 consider myself extremely lucky to have crossed paths with Dr. A. L. Szilird who provided invaluable insight and a truly fresh perspective to me on the subject. 1 thank the institutional and panel members of the Natural Science and Engineering Research Council of Canada for scholarships and the Chair and members of the Department of Plant Sciences at the University of Western Ontario for the quality intellectual and collegiate environment. Colleagues, fnends, and fellow graduate students. Dr. R. C. Bailey, Dr. J. Bowles, L. Coklin, Dr. G. Gray, Dr. R. H. Green, X. S. He, Dr. A. Heinicke, Dr. L. Kari, T. Kavanaugh, M. Kennedy, Dr. M. A. Lachance, L. R. Little, Dr. R. Martin, A. Raake, S. Tavares, Dr. C. G. Trick, A. Tsang, Dr. D. Urban, Dr. D. B. Walden: thank you for your confidence in me. To my family, I give rny love and warmest thanks for the encouragement, high hopes, and unconditional faith which kept me looking forward and up to new vistas. TABLE OF CONTENTS Page . CERTIFICATE OF EXAMINATION............................................. il .*. AB STRACT.................................................................................. iii ACKNO WLEDGMENTS............................................................... vi TABLE OF CONTENTS. .............................................................. vii LIST OF TABLES ........................................................................ xii ... LIST OF FIGURES ....................................................................... x~ii LIST OF APPENDICES ................................................................ xv Chapter 1. ABOUT PERTINENT CONCEPTS IN GENERAL ......... 4 1 .1 Introduction. .................................................................. 4 1.2 Pattern, process and mechanism: the distinction ................ 6 1.3 The scale paradigm......................................................... 9 1.3.1 Definition ........................................................... 9 1.3.2 Views of the medium........................................... 11 1.4 Unsolved problems in the pattern, process, mechanism complex ..................................................... 15 1.4.1 Uniqueness ......................................................... 19 1.4.2 Stability .............................................................. 22 In terlude.. ..................................................................................... 24 vii Chapter 2 . THE MEDIUM ............................................................ 25 2.1 Characteristics of the vegetation system............................. 25 3.1.1 Definitions .......................................................... 25 2.1.2 Scale.................................................................. 26 2.1.3 Views: Reductionist or Holistic, Static or Dynamic .......................................... 28 2.2 Pattern analysis in vegetation ............................................ 32 2.3 Process in the vegetatioa system ..................................... 38 2.4 Mechanisms in the vegetation system................................. 42 2.5 Summary ....................................................................... 45 In terlude ....................................................................................... 46 Chapter 3 . HOW COMPLEX IS COMPLEX? .................................. 47 3.1 The vegetation system is complex ..................................... 47 3.2 Kolmogorov complexi ty .................................................. 48 3.2.1 Entropy ........... ..... ............................................ 49 3.2.2 Coding .............................................................. 51 3.2.3 To ta1 complexity ................................................. 56 3.3 Test cases and results ....................................................... 57 3.4 Complexity and hierarchy ................................................ 67 3.4.1 Models of partitioning ......................................... 70 3.4.2 A worked example.............................................. 72 3.4.3 Conclusions from hierarchical ... partitioning ................................................... 78 3.5 Discussion ...................................................................... 79 Interlude ....................................................................................... 84 ... Vlll Chapter 4 . CONTROVERSY OF HISTORIC PROPORTIONS AND CALLS FOR ITS RESOLUTION..................... 85 4.1 Foundation. edifice. superstructure ................................... 85 4.2 Clements-Gleason ............................................................ 88 4.3 Classics examined anew ................................................... 89 Interlude ....................................................................................... 92 Chap ter 5 . MODELLING DETERMINISM .................................... 93 5.1 The role of models ........................................................
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