Applications of graph theory to landscape genetics.

We investigated the relationships among landscape quality, gene flow, and population genetic structure of fishers (Martes pennanti) in ON, Canada. We used graph theory as an analytical framework considering each landscape as a network node. The 34 nodes were connected by 93 edges. Network structure was characterized by a higher level of clustering than expected by chance, a short mean path length connecting all pairs of nodes, and a resiliency to the loss of highly connected nodes. This suggests that alleles can be efficiently spread through the system and that extirpations and conservative harvest are not likely to affect their spread. Two measures of node centrality were negatively related to both the proportion of immigrants in a node and node snow depth. This suggests that central nodes are producers of emigrants, contain high-quality habitat (i.e., deep snow can make locomotion energetically costly) and that fishers were migrating from high to low quality habitat. A method of community detection on networks delineated five genetic clusters of nodes suggesting cryptic population structure. Our analyses showed that network models can provide system-level insight into the process of gene flow with implications for understanding how landscape alterations might affect population fitness and evolutionary potential.