Endogenous Fractal Dynamics at Alpine Treeline Ecotones

Abstract

Many of the hypotheses proposed to explain ecotones are based on an individualistic paradigm and are essentially static. While they include local feedbacks, they ignore the interactions between pattern and process across scales. These feedbacks in ecotones are nonlinear in nature and complicate the relations of pattern and process in vegetation, which, combined with observed fractal patterns, suggests a complexity science approach to investigate ecotone dynamics. A cellular automaton of alpine treeline, including nonlinear, local, positive, and negative feedbacks in tree establishment and mortality, as reported in field studies, is used as a model system. Fourier analysis of simulated alpine treelines shows fractal patterns across the treeline landscapes, which are created by patch development. The temporal evolution of the spatial pattern is also fractal. Landscape scale linear correlations between spatial pattern and the rate of advance of trees into tundra arise from localized nonlinear interactions. A tree-patch-landscape scale explanation of pattern-process interaction is proposed in which the endogenous feedbacks determine the spatial and temporal fractal properties of the ecotone. The simulated treeline advance exhibits self-organized complexity and may indicate a potential strategy for monitoring change.

Transition from Connected to Fragmented Vegetation across an Environmental Gradient: Scaling Laws in Ecotone Geometry

“…At that point, the forest becomes fragmented. Farther uphill, the sizes of fragments decrease and the forest vegetation vanishes; see the map in Zeng and Malanson (2006). Apart from alpine tree lines, the same general pattern has also been documented at the edges of a gallery forest (map in Loehle et al 1996) and of piñon-juniper woodlands (map in Milne et al 1996).…”

“…The emergence of a sharp boundary is usually explained by positive feedback caused by a cooperative interaction between members of the community (Loehle et al 1996;Milne et al 1996;Wilson et al 1996;Keitt et al 2001;Li 2002;Zeng and Malanson 2006;Solé 2007). It is reasonable to assume that positive feedback would sharpen the boundary.…”

Emergence of Distinct Spatial Patterns in Cellular Automata with Inertia: A Phase Transition-Like Behavior

“…(ii) Ecotones' boundary extensions and shapes usually are driven by climate conditions and species competition [26][27][28]63]. Such boundaries may or may not arise depending on the strength and interplay of these factors (say, quantified by a parameter λ).…”

Geomorphological limits to self-organization of alpine forest-tundra ecotone vegetation

“…We use a modified version of the cellular automaton (CA) simulation created by Zeng and Malanson (2006) as a starting point. To incorporate geomorphology as an exogenous template on which the ecological dynamics play out, we alter the underlying surface that determines the probability of a cell changing from tundra to tree or vice versa, termed 'site-quality' from the perspective of a tree.…”

“…Zeng and Malanson (2006) assumed a bell-shaped positive feedback to the probability of conversion of tundra to tree that peaked when half of the neighboring cells is occupied by trees. This form captured the effects of positive feedback but with those reduced by an abundance of trees where they were cancelled out by the negative feedbacks.…”