Estimating host influence on cross-species transmission
Our goal was to see if some host species were more likely to be involved in cross-species transmission of various parasite species. For each parasite species and site, we constructed undirected networks of hosts with edge connections weighted by the epidemic overlap value for each host combination, while removing host species with no connections from the network. Because some parasites produce long-lived spores capable of delaying transmission (and for others we lack the necessary natural history information), we summed the epidemic overlap values across years for each site. Since we were purely interested in potential cross-species transmission, we did not include loops as we did for the networks described above (i.e., no connections of a host species to itself). Additionally, we dropped very small networks (two or fewer host species), because our measures of host influence were not applicable.
As a proxy for the influence of each host species on cross-species transmission of different parasites, we calculated the eigenvector centrality for the host nodes in each network. Eigenvector centrality was useful because it considers the entire network and emphasizes second order connections; a given node is more central if it is connected to other nodes that themselves are more central (Bonacich 2007). If one imagines a random walk across a network, the stationary distribution of time spent at each node is proportional to the eigenvector centrality. Eigenvector centrality scores range from 0 to 1, with 1 being most central, and were calculated on weighted networks. We chose eigenvector centrality because it emphasizes connections throughout the network, which could be important in a community disease context where there might be chains of transmission across different host species (Gómez et al. 2013).