Network Metrics: Modularity
To better characterize seasonality in network structures, we used a betweenness community detection method (Newman & Girvan 2004) to create modules within each seasonal network. We evaluated the modularity of each seasonal network, using the equation:
\(Q=\frac{1}{2m}\ \sum_{i,j}{\left(A_{\text{ij}}-\frac{k_{i}\bullet k_{j}}{2m}\right)\bullet\delta_{m_{i,}m_{h}}}\),
where \(m\) are the total number of interactions in the network, \(A\)is the adjacency matrix of the network (\(A_{i,j}=1\) if there is an interaction between species \(i\) and \(j\), otherwise 0), \(k_{i}\) are the number of interactions of node \(i\), \(m_{i}\) is the module of species \(i\), and \(\delta\) is a Kronecker’s delta (\(\delta_{a,b}=1\ if\ a=b,\ \text{otherwise}\ 0\)) (Stouffer & Bascompte 2011). Higher modularity values indicated that partitions between close knit groups were more easily detectable and meaningful within the community. Network visualization and modularity detection were both implemented using the igraph package R (Csárdi & Nepusz 2006).