There, the probability that a site will be occupied by a certain vegetation type changes continuously through space, without correlations between the states of different sites. The simplest case is the gradient random map (GRM). This phenomenon is studied here with gradient percolation models.
An abrupt change from the connected to the fragmented state occurs even along a smooth gradient. A decrease in density inevitably leads to fragmentation. Moving along a gradient, the density of a particular vegetation type (e.g., forest) decreases. Our main objective is to model the effect of smooth changes in environmental conditions. In this article, we study the geometry of this transition zone with spatially explicit numerical simulations. Several studies have emphasized that natural boundaries are not straight lines but gradual (“soft” Forman 1995), with a transition zone (ecotone) of considerable spatial extent. 1996) and of piñon‐juniper woodlands (map in Milne et al. 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. Farther uphill, the sizes of fragments decrease and the forest vegetation vanishes see the map in Zeng and Malanson ( 2006). At that point, the forest becomes fragmented. The average gap size typically increases toward the edge, where small gaps become large enough to coalesce. Inside the forest zone, a relatively high cover of forest is interspersed with gaps of various sizes. Observing the vegetation along a gradient, for example, from lower to higher altitudes across an alpine tree line, often reveals a complex pattern of patches.
Detecting boundary shifts has been suggested for biomonitoring climate change (Kimball and Weihrauch 2000 but see Zeng and Malanson 2006 and references therein).īecause the geometries of most natural vegetation boundaries are complicated, it is not self‐evident what to measure, that is, which feature of a boundary could be sufficiently general to enable comparisons between years and/or geographic regions. Interest in this topic increased further after reports of significant shifts in vegetation boundaries (e.g., tree lines) due to recent climate changes (Allen and Breshears 1998 Danby and Hik 2007). The distribution of vegetation across environmental gradients has received considerable attention since the beginnings of vegetation science, for example, in gradient analysis (Whittaker and Niering 1965). This offers a new tool for detecting a shift of the boundary due to a climate change. We propose to use the hull edge to define the boundary of a vegetation type unambiguously. To demonstrate that the model is applicable to real data, a hull edge of fractal dimension 7/4 is shown on a satellite image of a piñon‐juniper woodland on a hillside. The result is the same for different spatial models, suggesting that there are universal laws in ecotone geometry. The boundary of connected vegetation delineated by a particular step length is termed the “ hull edge.” We found that for every step length and for every gradient, the hull edge is a fractal with dimension 7/4. Connectivity is characterized from the perspective of various species that use this vegetation type for habitat and differ in dispersal or migration range, that is, “step length” across the landscape. A static (gradient percolation) model is compared to dynamic (gradient contact process) models. We use spatially explicit simulations to study the transition from connected to fragmented vegetation. A change in the environmental conditions across space-for example, altitude or latitude-can cause significant changes in the density of a vegetation type and, consequently, in spatial connectivity.
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