Variable choice

Many specific abiotic variables have been suggested for defining facets. These variables can generally be classified as topographic, edaphic, or climatic (Kirkpatrick and Brown 1994, Faith and Walker 1996, Wessels et al. 1999, Anderson and Ferree 2010, Beier and Brost 2010). We examined the role of variable choice in land-facet classification and subsequent prioritization by comparing the distribution of facets and priority regions that were designated with topographic variables only, with the addition of edaphic variables, or with the addition of geologic type (Table 1). We obtained 30-m resolution topographic data, elevation and slope, from the National Elevation Dataset (Gesch 2009). We used five continuous soil variables: organic matter, bulk density, depth to bedrock, depth to the root restrictive layer, and accumulated water content from the STATSGO database available at a scale of 1:250,000. For direct comparison with geology, we created a categorical soil variable by clustering the variability of these five soil properties into nine categories. We used geologic data from the United States Geologic Survey (Hunting et al. 1961, Jennings et al. 1977, Bond et al. 1978, Stewart and Carlson 1978, Hintz et al. 1980, Green et al. 1994, Raines and Johnson 1995, Richard et al. 2000) available at a scale of 1:500,000 and classified the rock types in this data into 9 broader geologic types according to the categories defined in Anderson et al. (2010).

Resolution

To determine if the resolution of the data had an impact on facet designation and subsequent conservation prioritization, we designated land facets from raster data at two resolutions: 270 m and 1 km. We resampled topographic raster data, originally at 30-m resolution, to 270 m and 1 km using bilinear interpolation. Because of cell size, 1-km data were resampled from previously resampled 90-m rasters. Vector data (soils and geology) were converted to rasters at the two resolutions using maximum combined area for cell assignment.

Facet designation

Many approaches have been suggested for identifying unique facets in a landscape. These range from simple overlays of the spatial distributions of categorical variables to more complex and computationally intensive ordinations. We designated facets using three different approaches: a categorical overlay, a clustering algorithm, and a hybrid approach that clusters data within topographic classes. For the overlay approach, we designated facets from unique combinations of variable categories and/or variable classes for continuous data. We divided each continuous variable into classes based on ecologically meaningful divisions or into classes commonly used for that variable in the literature when possible (Table 2). For the clustering approach, we used the k-means clustering algorithm with 20 random starts and 10,000 iterations to designate land facets from continuous variables. We clustered data into every number of clusters between 3 and 199 and used the Hartigan index to identify the optimal number of clusters for which to cluster the data (Hartigan 1975). For the hybrid approach, we used a combination of the categorical overlay and clustering algorithm in a method similar to the method described by Jenness et al. (2012) for designating land facets. We first identified regions of unique topography by overlaying classes of elevation and slope as in the categorical overlay approach. Within each of these topographic classes, we then used the fuzzy c-means clustering algorithm to cluster the other variables. The optimal number of clusters within each topographic class was chosen from between 3 and 8 clusters by majority agreement between 8 different indices. (Table 1)

Data Processing

We removed all cells that were classified as open water in the national land classification dataset (Comer et al. 2003). We normalized the data for k-means and the c-means portion of the hybrid processing and tested the influence of normalizing data within an ecoregion versus normalizing data across 14 ecoregions throughout the Pacific Northwest.

Prioritization

For each facet model, we used Marxan (Ball and Possingham 2000) to prioritize regions for conservation. Marxan uses a simulated annealing algorithm to identify networks of planning units in which targeted quantities of facets are represented at a minimal cost. We aimed to represent 30% of each facet’s land area remaining after the removal of regions considered to be developed in the NLCD. A target of 30% is commonly used for ecological systems in ecoregional planning by The Nature Conservancy (TNC). We used level 6-digit hydrologic unit codes (HUCs) as planning units for Marxan prioritization. We used land-use suitability as the cost of each planning unit based on four premises that TNC identified in the Cascades Ecoregion Assessment: land is more suitable for conservation if it is 1) less fragmented, 2) larger, 3) consists of habitat areas that are closer together, and 4) publicly owned and managed. Based on these premises, the cost of each planning unit was calculated based on the combination of normalized values from 1) weighted land uses where more developed land is more costly, 2) weighted degrees of protection where private land with no legal protection is more costly, and 3) road density where higher densities of roads are more costly. The weightings were provided by TNC and were the average of weightings used in five ecoregion assessments.

We parameterized Marxan to achieve 100% of the targeted quantities of facets in 80% of the 1,000 iterations, but to fail to achieve at least one target in 20% of the iterations. This parameterization strikes a balance between a network that achieves all targets at any cost and a network that is completely determined by cost. We ran 1,000 iterations of Marxan on each set of facets.

Model Sensitivity

To determine the sensitivity of conservation prioritization to methodological decisions and data choices, we compared the spatial distributions of priority planning units and conservation networks. Specifically, we compared the number of times a planning unit was chosen in 1,000 iterations (i.e., the irreplaceability value) between facet models. A planning unit that is highly irreplaceable is prioritized in most or all 1,000 Marxan iterations; whereas a planning unit with low irreplaceability is prioritized in few iterations if at all. We also compared the similarity of best networks across facet model by comparing the degree of network overlap using the Jaccard index (Jaccard 1901). The best network is the network of planning units that achieves all targets at the lowest cost. Because best networks will likely vary in the total quantity of planning units included in a network, we also compared the degree of overlap of networks created from the top 26% of the most irreplaceable planning units.

Although spatial distribution of networks or priority planning units may vary, these differences may be inconsequential if the network created to represent the targets of one facet model incidentally represents the targets of another facet model. We evaluated the incidental representation between facet models.