Ecological Archives E096-122-A2

Meryl C. Mims, Ivan C. Phillipsen, David A. Lytle, Emily E. Hartfield Kirk, and Julian D. Olden. 2015. Ecological strategies predict associations between aquatic and genetic connectivity for dryland amphibians. Ecology 96:1371–1382. http://dx.doi.org/10.1890/14-0490.1

Appendix B. Additional description of landscape resistance methods and tables describing landscape resistance values and source data, correlation coefficients between resistance/distance values, mixed-effects modeling results for major genetic clusters of canyon treefrogs and Mexican spadefoots, and results of multiple regression with distance matrices.

Landscape resistance and distance details and construction

We hypothesized relationships between genetic and structural connectivity along a gradient of species water requirements. Final hypotheses were organized into six categories. Two categories imply no correlation with landscape factors: isolated populations (high genetic differentiation between sampling locations driven primarily by low migration, genetic drift, and/or small populations) and panmixia (low genetic differentiation due to high gene flow between all sampling locations and/or large populations). The other four categories imply a specific relationship between genetic connectivity and some landscape factor. These categories are summarized in Table B1. Each category – terrestrial, aquatic, topography, and isolation-by-distance – was evaluated using one or multiple landscape resistance surfaces built with spatial data. These resistance surfaces and data are summarized in Table B1, and details for data layers and sources are included in Table B2.

Hypothesized resistances of structural connectivity between sampling locations were built using CIRCUITSCAPE (McRae 2006), a program utilizing circuit theory to simulate gene flow through a resistance surface. CIRCUITSCAPE allows for gene flow (i.e., "current") to travel across multiple pathways, reporting pairwise summations of resistance between sampling locations. To generate these pairwise data, we built raster maps of resistance (low to high) using data in Table B2. A geographic information system (ArcGIS 10.1, Environmental Systems Research Institute) was used to catalog and manipulate landscape data and generate resistance raster maps. Each resistance map was scaled for hypothesized landscape resistance to gene flow from 1 - 100 where 1 indicates low resistance and 100 indicates high resistance. The scale of resistance values was arbitrary and was designed to reflect hypothesized relationships between landscape features and genetic connectivity. We examined two additional scales of resistance (1 - 1000 and 1 - 10,000), but resistances and the relationships with genetic connectivity were highly correlated (r > 0.99). Thus only results for resistances from 1 – 100 are included in this manuscript.

To balance demand for computational resources with maintaining enough detail to realistically examine structural connectivity, all resistance maps were scaled to 60 m resolution, which involved resampling of some data layers. The spatial extent of resistance rasters ensured a buffer of at least 30 km from the edge of the raster to a given sample site. With this grain and extent, we were able to perform all CIRCUITSCAPE analyses in the pairwise source/ground modeling mode and using a cell connection scheme of eight neighbors, allowing maximum freedom of current flow. Due to the location of one Mexican spadefoot sampling site near the US-Mexico border, the 30 km buffer required use of spatial data from the US and Mexico. Data are generally more widely available and higher resolution for the US, and in some cases in our study Mexico's data are courser resolution (Table B2). However, it is unlikely that the resolution of data for Mexico would skew structural connectivity estimates between populations of any species, particularly with only one sample site very near the border.

Some landscape resistance layers had moderate to strong correlations with one another. These correlations are summarized in Table B3 and were taken into account in all analyses of genetic and structural connectivity relationships.

Mixed-effects modeling results for canyon treefrog and Mexican spadefoot genetic clusters

Mixed-effects modeling results (individual factors and couplet models) for canyon treefrog and Mexican spadefoot genetic clusters are presented in Table B4. Methods and results are presented in the main text.

Multiple regression with distance matrices (MRDM) methods and results

MRDM evaluates relationships between one or many explanatory distance matrices and a response distance matrix and uses permutation to determine statistical significance of the overall model. MRDM also informs significance of each explanatory variable in a model, and those significance values can help elucidate drivers among correlated structural connectivity hypotheses. We included one distance matrix (with the highest R²β value as calculated by mixed-effects modeling) from each structural connectivity category to build global MRDM models. For cases in which multiple variables were included in the supported model, we evaluated the variance inflation factor of each predictor variable. A variance inflation factor > 10 is considered a threshold at which collinearity of variables is problematic for interpreting model results (Kutner et al. 2004). Variance inflation factor was evaluated using the linear form of each model with the R package "car" (Fox and Weisberg 2011). Pairwise landscape resistances were then dropped according to significance (least significant dropped first) until only one resistance layer remained. We inferred strength of model fit by evaluating overall R² and the significance of explanatory variables (pairwise landscape resistances) included in the model. MRDM results are summarized in the main text of the manuscript and are presented in Table B4 of this appendix.

Literature cited

Fox, J., and S. Weisberg. 2011. An R Companion to Applied Regression, Second Edition. Thousand Oaks CA: Sage. URL: http://socserv.socsci.mcmaster.ca/jfox/Books/Companion

Kutner, M., C. Nachsheim, and J. Netter. 2004. Applied Linear Regression Models. McGraw-Hill, New York, New York, USA.

McRae, B. H. 2006. Isolation by resistance. Evolution 60:1551–1561.

Table B1. Descriptions and data used to construct resistance layers for each connectivity hypothesis (data described in Table B2, and note that data used often include different sources for Arizona and Mexico). Isolated population and panmixia hypotheses presented in text are not included here because they are not associated with effects of any particular landscape driver. Additional details available upon request from M.C. Mims.

Table B2. Data, details, resolution, and source information for spatial and environmental data used to create resistance layers (Table B1).

Table B2, continued.

Table B3. Pearson correlation coefficients between pairwise resistance/distance values for each species and their major genetic clusters, identified in Fig. 2 of the main text.

Table B4. Mixed-effects modeling results for major genetic clusters for canyon treefrogs (CT-W: canyon treefrog – west; CT-H canyon treefrog - Huachucas) and Mexican spadefoot (MS-E: Mexican spadefoot - east). Genetic clusters are identified in Figure 2 of the main text. Top R²β values for single-resistance (top) and couplet-resistance (below) models are highlighted in bold font. IP and P hypothesize no landscape effect, indicated by poor model performance across all other models. A dash indicates no support for IP or P. All R²β correlation coefficients are positive with the exception of a negative relationship with Slope in models denoted with underlined text.

Table B5. MRDM results by species. Correlation between genetic distance and landscape resistance were consistent within a species or group and are shown as positive (+) or negative (-). R² and p values generated from permutation tests are shown for the overall model, and p values for each factor are included. Best models shown in bold font, and for best models with > 2 factors, variance inflation factors (vif) are included in italicized text just below each factor in the model. *For Mexican spadefoots, the Stream-only and Euclidean-only models performed similarly. A partial mantel test was used to evaluate correlation between genetic distance and either Stream or Euclidean while controlling for the other. The partial mantel statistic was more significant for Stream (p = 0.030) than for Euclidean (p = 0.093). †vif > 10 indicates high collinearity among predictor variables. Note that for both canyon treefrog clusters, vif values suggest interpreting results with caution.

Table B5, continued.

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