Landscape Genetics Road Elevation Cover type kms 513 10 20 10 20 kms N N W E W Canopy cover cost (a) E S Olympic mts sites S Olympic mts sites Elevation High: 100 High; 302 Low: Low: 137 (b) (c) 10 20 kms N W E S Olympic mts sites Resistance High: 1.17597 Low: 0.000594961 (d) Resistance surface Figure Steps to building a resistance surface using multiple landscape features (a) Road through the study area (b) Map of canopy cover in the area; blue indicates low cost areas, red indicates high cost, and green triangles represent sampling locations (c) Map of elevation in the study area; red indicates high elevation and high cost, yellow shows intermediate cost and blue shows low cost (d) Multivariate resistance surface indicating cumulative costs from (a)–(c) Graph Theory and Network Analyses Graph theory can be applied in population and landscape genetics by treating localities or individuals as nodes and connections between them as edges as in a network (Dyer and Nason, 2004) The strength of each edge is essentially proportional to the rate of gene flow between the two nodes that it connects (as estimated by their genetic covariance), and a complete lack of an edge suggests significant population subdivision (Dyer and Nason, 2004; Dyer, 2007) Originally, this framework was applied using the software POPGRAPH, whereby genetic structure was estimated across all nodes simultaneously, and users could test for population subdivision as indicated by significant deficiencies of edges between user-defined groups of nodes (Figure 4; Dyer and Nason, 2004) An empirical study that used this approach showed that, taken together, high elevation sites were significantly genetically differentiated from low elevation sites for the long-toed salamander (Giordano et al., 2007) Network analyses have been applied in the graph– theoretic approach to model functional connectivity (Garroway et al., 2008; Murphy et al., 2010) In addition to understanding overall connectivity of nodes and substructure across an entire network, analyses can also determine the properties of a specific node Aside from the degree centrality of a node, which is an estimate of connectivity based on the number of connections it has to other nodes, other commonly evaluated properties include eigenvector centrality and betweenness (Garroway et al., 2008) Eigenvector Figure Example of a network using a graph–theoretic approach Symbols indicate different sampling localities (i.e., nodes); shape size is proportional to the amount of observed genetic structure Different shapes represent different genetic clusters, and lines between shapes (i.e., edges) represent significant genetic exchange between the two sampling localities that the lines connect centrality incorporates both direct and indirect connectivity of particular nodes, thereby weighting well-connected nodes more heavily than those that are less connected Betweenness is the number of shortest paths that a particular node