Multi-scale trajectory analysis: powerful conceptual tool for understanding ecological change

Abstract

The model at the basis of trajectory analysis is conceptually simple. When applied to time series vegetation data, the projectile becomes a surrogate for vegetation state, the trajectory for the evolving vegetation process, and the properties of the trajectory for the true process characteristics. Notwithstanding its simplicity, the model is well-defined under natural circumstances and easily adapted to serial vegetation data, irrespective of source. As a major advantage, compared to other models that isolate the elementary processes and probe vegetation dynamics for informative regularities on the elementary level, the trajectory model allows us to probe for regularities on the level of the highest process integrity. Theories and a data analytical methodology developed around the trajectory model are outlined, including many numerical examples. A rich list of key references and volumes of supplementary information supplied in the Web Only Appendices rounds out the presentation.

Key words： attractor migration; determinism; fractal dimension; parallelism; periodicity; phase structure

Acknowledgements

The paper’s contents evolved at activities in four sites: the Department of Ecology, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil; Department of Biology, Laurentian University, Sudbury, Canada; Department of Botany, The University of Hawaii at Manoa, Honolulu; and the Department of Biology, The University of Western Ontario, London, Ontario. I express gratitude to Professors Valério De Patta Pillar, Madhur Anand, Dieter Mueller-Dombois, and Guillermo Goldstine for facilities and facilitation. My deepest expressions of gratitude are due to Forest Eng. Márta Mihály for advice and sustained, unfailing support. Some tables and figures were adopted from earlier versions published in Community Ecology with permission.

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