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Many ecosystems can be viewed as lying within a continuum between grassland and forest, where ground coverage by woody plants (trees and shrubs) ranges from non-existent to complete. Patterns of energy, water, and biogeochemistry are often heterogeneous between canopy patches beneath woody plants and the intercanopy patches that separate them. Notably, connectivity between patch types is produced by processes such as shading, root uptake of resources, and redistribution of runoff. Patch-scale connectivity is hypothesized to influence trends in energy, water, and biogeochemistry as a function of woody plant canopy coverage. When connectivity is strong, the mean for an ecosystem property is expected to change in a more curvilinear than linear fashion along the continuum. Associated variance is expected to be greatest not midway along the continuum, as might be expected, but rather at a site with substantially less than 50% canopy coverage. These hypotheses collectively provide a framework for future research and are directly applicable to numerous, seemingly disparate environmental issues associated with encroachment, xerification (desertification), deforestation, die-off, fire, and restoration.