Detection of critical densities associated with pinon-juniper woodland ecotones

The interfaces between pifion-juniper canopies and grasslands in the southwestern USA present an opportunity to use the modern theory of spatial phase transitions as a formal characterization of ecotone structure. The theory requires an estimation of a critical value of tree cover at which the woodlands switch abruptly from a fragmented collection of small patches of trees to a network of connected canopies. Presumably, this transition is associated with critical environmental conditions that regulate the ecologies of trees vs. grasses. We developed and tested a new method to estimate the critical cover value of woodlands on complex terrain. The method was based on multiscale assessments of the associations between local tree coverage and two types of patch edge. Tests on artificial gradient percolation maps revealed an interaction between the type of edge used (''hull edge,'' which is based on only the orthogonal connections between canopy-occupied cells, vs. ''accessible edge,'' which is based on both orthogonal and diagonal connections beween canopy-occupied cells) and the neighborhood rule used to define a cluster (von Neumann 5-cell or Moore 9-cell). When applied to digitized, geographically referenced aerial photographs, the method indicated that areas less than or equal to 6.6 ha exhibited the theoretical critical value of 59.3% cover predicted for square lattices and the 5-cell neighborhood. Construction of both edge types on a given map can reveal locations of steep environmental gradients that may be buffered against modest climate fluctuations. The edges can be used in the calibration of independent variables to predict tree cover. The agreement between the expected and observed critical densities will motivate extensions of phase transition theory to studies of ecotones in real landscapes.