Chaos, Cycles and Spatiotemporal Dynamics in Plant Ecology

Abstract

1 We review the problems concerned with describing ecological variability and explain why nonlinear systems theory and chaos may be of relevance for understanding pattern and change in ecosystems. 2 The basic concepts of chaos are considered briefly, where possible in the context of plant ecology. We outline the period doubling route to chaos and associated concepts of bifurcation, universality, sensitivity to initial conditions, dimensionality, attractors and Lyapunov exponents. 3 Examples are selected from the literature to illustrate how nonlinear models and time series analysis have already contributed to research in plant ecology. 4 Key methods used to detect the presence of chaos in ecological time series, including determination of the 'return map,' the Lyapunov exponent, the technique of nonlinear prediction and the method of surrogate data, are surveyed. We discuss how small sample-size, as typically acquired in field-studies, can act as a formidable limitation in such approaches. 5 Models of plant communities, which emphasize the importance of spatiotemporal dynamics, are outlined. The concept of deterministic chaos is shown to be useful in this setting also.

Plant coexistence depends on ecosystem nutrient cycles: Extension of the resource-ratio theory

“…This observation should be seriously considered in the current debate about oscillatory phenomena in plant communities (35)(36)(37) and their consequences for plant diversity (38). Indeed, preliminary extensions of our model have illustrated that oscillations may promote coexistence of more than two species on two limiting nutrients (T.D., unpublished results).…”

Forests as complex adaptive systems: implications for forest management and modelling

“…comPlexIty, forests and forest management As our understanding of chaos theory and complexity science increases and with the advent of powerful computers, ecological systems including forests have become increasingly understood and viewed as complex adaptive systems (LevIn, 1998(LevIn, , 2005Cadenasso et al, 2006;Solé and BascomPte, 2006). A forest can therefore be classified as complex and adaptive as it displays the following properties: (1) it is composed of many parts (e.g., trees, insects, soil) and processes (e.g., nutrient cycling, seed dispersal, tree mortality, decay), (2) these parts and processes interact with each other and with the external environment over multiple spatial and temporal scales (e.g., competition, dispersal, disturbance), (3) these interactions give rise to heterogeneous structures and nonlinear relationships (e.g., above and belowground species mixtures and relationship between growth and light), (4) these structures and relationships are neither completely random nor entirely deterministic, but instead represent a combination of randomness and order (e.g., precisely predicting the development of even single species stands is impossible), (5) they contain both negative and positive feedback mechanisms, stabilising or destabilising the system, depending on conditions (e.g., N-fixation, rainfall interception, density-dependent mortality), (6) the system is open to the outside world, exchanging energy, materials, and/or information (e.g., nutrient, water cycling, albedo), (7) it is sensi- tive to the initial conditions following a major disturbance and subsequent perturbations (e.g., rodent population that feeds on the seedbank), and (8) it contains many adaptive components and subsystems nested within each other, giving rise to emergent properties (e.g., carbohydrates that form into trees).…”

Sistemas complexos: novas formas de ver a Botânica

“…Uma vez que a própria vida e os mais variados sistemas vivos (células, organismos, comunidades) são sistemas dinâmicos não lineares, freqüentemente apresentando dinâmica caótica, determinadas diferenças ambientais poderiam levar à evolução de ecossistemas específicos, em um tempo relativamente curto. A importância de dinâmicas caóticas para a organização espaço-temporal de uma comunidade vegetal tem sido reconhecida (Hastings et al 1993, Stone & Ezrati 1996, Anand 1997. Da mesma forma, alguns autores (Shishkin 1992, Amzallag 1999) têm sugerido que a formação de ecótipos estáveis pode ser alcançada em poucas gerações com base em processos epigenéticos.…”