Surface metrics for landscape ecology: a comparison of landscape models across ecoregions and scales

The patch-mosaic model is lauded for its conceptual simplicity and ease with which conventional landscape metrics can be computed from categorical maps, yet many argue it is inconsistent with ecological theory. Gradient surface models (GSMs) are an alternative for representing landscapes, but adoption of surface metrics for analyzing spatial patterns in GSMs is hindered by several factors including a lack of meaningful interpretations. We investigate the performance and applicability of surface metrics across a range of ecoregions and scales to strengthen theoretical foundations for their adoption in landscape ecology. We examine metric clustering across scales and ecoregions, test correlations with patch-based metrics, and provide ecological interpretations for a variety of surface metrics with respect to forest cover to support the basis for selecting surface metrics for ecological analyses. We identify several factors complicating the interpretation of surface metrics from a landscape perspective. First, not all surface metrics are appropriate for landscape analyses. Second, true analogs between surface metrics and patch-based, landscape metrics are rare. Researchers should focus instead on how surface measures can uniquely measure spatial patterns. Lastly, scale dependencies exist for surface metrics, but relationships between metrics do not appear to change considerably with scale. Incorporating gradient surfaces into landscape ecological analyses is challenging, and many surface metrics may not have patch analogs or be ecologically relevant. For this reason, surface metrics should be considered in terms of the set of pattern elements they represent that can then be linked to landscape characteristics.