Critical thresholds in species' responses to landscape structure

Ecology, Dec, 1995 by Kimberly A. With, Thomas O. Crist

INTRODUCTION

Small changes in the spatial patterning of resources can produce abrupt, sometimes dramatic ecological responses; such transition ranges are deemed critical thresholds (Turner and Gardner 1991). Critical thresholds occur particularly where the phenomenon of interest exhibits a nonlinear relationship with spatial scale, owing to shifts in the underlying process(es) at different scales or because new constraints govern the process at different scales (O'Neill et al. 1986, Kotliar and Wiens 1990). Landscapes may exhibit critical thresholds in connectivity, often with serious ecological consequences (Gardner et al. 1987, Krummel et al. 1987, O'Neill et al. 1988b). A familiar example of this is habitat fragmentation. As the landscape becomes dissected into smaller and smaller parcels, landscape connectivity - the spatial contagion of habitat - may abruptly become disrupted. But at what point does habitat fragmentation disrupt landscape connectivity? Percolation theory (Orbach 1986, Stauffer and Aharony 1991) has recently been used as a neutral model to predict where these critical thresholds occur and thus how landscape structure might affect ecological processes (e.g., Gardner et al. 1987, 1989, 1992, O'Neill et al. 1988b). A neutral landscape map is produced from a random distribution of habitat(s) and is used as a null model to explore how ecological processes operate in heterogeneous environments in the absence of specific landscape patterns. Neutral landscapes thus serve as a baseline for statistical comparisons with patterns on real landscapes (Gardner et al. 1987, Gardner and O'Neill 1991).

To illustrate, consider a landscape to be a two-dimensional grid in which the grid cells are classified according to the landscape element of interest (e.g., habitat type). Percolation theory predicts that a random distribution of a single cell type that comprises at least 0.5928 of the landscape has a very high probability of spanning the map (Gardner et al. 1987). As the critical threshold ([p.sub.c]) is reached, isolated patches of habitat become connected to form one continuous cluster. Each habitat cell of the percolating cluster is joined with a neighboring habitat cell along at least one horizontal or vertical edge [ILLUSTRATION FOR FIGURE 1 OMITTED]. Any organism capable of using the habitat should be able to traverse or "percolate" across this landscape, because it has a high degree of connectivity. Below this critical threshold ([p.sub.c] [less than] 0.5928), suitable habitat occurs as smaller, isolated patches. The landscape becomes disconnected when the "backbone" of the percolating cluster is broken by removing critical habitat cells along the spine and separating the cluster into two separate habitat patches. This results in the abrupt transition characteristic of percolating networks [ILLUSTRATION FOR FIGURE 2 OMITTED]. The disruption in landscape connectivity may limit movement of organisms, resulting in disjunct populations. Small changes in the composition of the landscape near the critical threshold are thus likely to have discernable effects on the distribution and persistence of populations (Turner and Gardner 1991).

The spatial mosaic of a landscape determines how a foraging animal responds to the distribution of resources (e.g., Senft et al. 1987). Spatial heterogeneity also influences the dispersal and distribution of animals across a landscape (Turchin 1991, Johnson et al. 1992), which in turn may have important consequences for the stability and persistence of populations (Wiens 1976, den Boer 1981, Fahrig and Merriam 1985, Kareiva 1990, Gilpin and Hanski 1991). Understanding how landscape structure affects the distribution of species may afford new insights into the organization of communities or species' responses to habitat fragmentation (e.g., Pearson et al., in press).

Our objective in this paper is to identify the critical threshold at which populations become disjunct as a function of increasing habitat fragmentation. The critical threshold is defined as the proportion of the landscape at which populations shift from random to clumped distributions. Toward this end, we assessed how species' dispersal capabilities and degree of habitat specialization interact with landscape structure to affect patterns of distribution. We suggest that the critical threshold is not an inherent property of a landscape, but emerges from the interplay of species' interactions with landscape structure. While habitat fragmentation refers to the connectivity of habitat types within a landscape, connectivity ultimately depends upon a species' ability to move across the landscape (O'Neill et al. 1988b, Pearson et al., in press). Species differ in the scales at which they interact with the environment (Morse et al. 1985, Swihart et al. 1988, Milne et al. 1992, With 1994). Even a scarce resource that has a patchy distribution is not necessarily fragmented if a species is able to operate at a broad enough spatial scale to use the resource effectively. Increasing habitat fragmentation may thus have little effect on species distributions until some critical level of connectivity is disrupted. It is not clear a priori where the critical threshold lies for species with different dispersal capabilities or habitat preferences (e.g., Plotnick and Gardner 1993). We provide an empirical example (grasshopper distributions in a shortgrass prairie) to illustrate how percolation theory can be applied to predict patterns of distribution for different species across a landscape.