Effects of cost surface uncertainty on current density estimates from circuit theory

Abstract

Background: Conservation practitioners are often interested in developing land use plans that increase landscape connectivity, which is defined as the degree to which the landscape facilitates or impedes movement among resource patches. Landscape connectivity is often estimated with a cost surface that indicates the varying costs experienced by an organism in moving across a landscape. True, or absolute costs are rarely known however, and therefore assigning costs to different landscape elements is often a challenge in creating cost surface maps. As such, we consider it important to understand the sensitivity of connectivity estimates to uncertainty in cost estimates.

Methods: We used simulated landscapes to test the sensitivity of current density estimates from circuit theory to varying relative cost values, fragmentation, and number of cost classes (i.e., thematic resolution). Current density is proportional to the probability of use during a random walk. Using Circuitscape software, we simulated electrical current between pairs of nodes to create current density maps. We then measured the correlation of the current density values across scenarios.

Results: In general, we found that cost values were highly correlated across scenarios with different cost weights (mean correlation ranged from 0.87 to 0.92). Changing the spatial configuration of landscape elements by varying the degree of fragmentation reduced correlation in current density across maps. We also found that correlations were more variable when the range of cost values in a map was high.

Discussion: The low sensitivity of current density estimates to relative cost weights suggests that the measure may be reliable for land use applications even when there is uncertainty about absolute cost values, provided that the user has the costs correctly ranked. This finding should facilitate the use of cost surfaces by conservation practitioners interested in estimating connectivity and planning linkages and corridors.

Keywords: Circuit theory; Circuitscape; Cost surface; Current density; Dispersal; Landscape connectivity; Least cost path.

Figure 1. Simulated cost surfaces with three levels of fragmentation.

Cost surfaces with 100 × 100 pixels and a 20-pixel buffer around the perimeter (140 × 140 cells total). All maps had a total ratio of 25% low cost (white), 25% medium cost (grey) and 50% high cost (black). Treatments included (A) High fragmentation (randomized), (B) Medium fragmentation and (C) Low fragmentation. Each cell was assigned a weight corresponding to its cost. For each level of fragmentation, we generated 10 maps with varying cost weights.

Figure 2. Simulated cost surfaces with varying thematic resolution (three, six and 12 categories).

Cost surfaces with 100 × 100 pixels and a 20-pixel buffer around the perimeter (140 × 140 cells total). All maps had a total ratio of 25% low cost (white), 25% medium cost (grey) and 50% high cost (black). Treatments included three levels of thematic resolution (A) three categories, (B) six categories and (C) 12 categories. Each cell was assigned a weight corresponding to its cost. For each level of thematic resolution, we generated 10 maps with varying cost weights.

Figure 3. Example current density maps for cost surfaces at three levels of fragmentation.

Examples of current density maps at a resolution of 140 × 140 cells for landscapes with different fragmentation levels (high, medium and low), different cost classes, and a 20-pixel buffer. (A), (C) and (E) had a costs of 7.5 (high), 5 and 1 (low), whereas (B), (D) and (F) had costs of 1,000, 100, 10, respectively. Highest current density is indicated by red. Node locations are indicated by areas of high current density around perimeters, especially evident in (A) and (F).

Figure 4. Example current density maps from an urban landscape.

Two examples of current density maps for an urban study area in Oakville, Ontario: (A) had costs of 1 (low), 2 and 3 (high) and (B) had costs of 1, 100 and 150. The Spearman rank correlation was 0.68, lowest of all comparisons for this landscape (mean (range) R_S = 0.85 (0.62–1.00) n = 45 comparisons).

Figure 5. Effect of the range of cost values on correlation of current density across landscapes.

Effect of the absolute value of the difference in the range of cost values in a landscape (log₁₀-transformed) on the Spearman correlation between current density estimates in pairs of landscapes: (A) high, (B) medium and (C) low fragmentation.

Figure 6. Effect of cost range on current density.

Effect of the absolute value of the difference in the range of cost values in a landscape (log₁₀-transformed) on mean and maximum current density estimates cross 10 different cost scenarios. We have shown here (A) the medium fragmentation scenarios in a simulated landscape and (B) the real, urban landscape.

Figure 7. Examples of current density maps with different thematic resolutions.

Examples of current density maps at a resolution of 140 × 140 cells for landscape depictions with different thematic resolutions (three (A, B), six (C, D), or 12 (E, F) categories), different costs, and a 20-pixel buffer. (A), (C) and (E) had costs of 1 (low), 5 and 7.5 (high), whereas (B), (D) and (F) had costs of 10, 100, 1,000, respectively. Highest current density is indicated by red. Node locations are indicated by areas of high current density around perimeters.