Table 2.

A description of the characteristics of random, small-world, and scale-free networks with possible biological interpretations in terms of landscape connectivity

Random networks: A class of networks characterized by a short characteristic path length, binomial degree distribution, and a small average clustering coefficient. Because each node is approximately equally well connected, the characteristic path length increases monotonically after random or targeted node removal. If the genetic connectivity among populations displays random graph properties, this would suggest that dispersal among populations was entirely random and unstructured and that populations are separated by short paths (direct or through intermediate populations). Extirpations of populations would steadily decrease the ease through which genes were exchanged among populations.

Small-world networks: A class of networks characterized by a short characteristic path length, binomial degree distribution, and a large mean clustering coefficient. Small-world networks are similar to random networks in that each node has approximately the same influence on the characteristic path length if removed, however the added feature of clustering might create alternate paths between nodes such that impact of node removal could be less than on random networks. If genetic connectivity has these characteristics genes can be efficiently exchanged among populations ‘locally’ and ‘globally’. Given that there will likely be increasing fitness costs of dispersal with increasing geographic distances and greater robustness to losses of populations, we might predict the small-world network characteristics to be common to well connected populations.

Scale-free networks: A class of networks characterized by a short characteristic path length and a power-law degree distribution. The average clustering coefficient can vary. Most nodes have relatively few connections while a few nodes are highly connected hubs Because most nodes are not particularly well connected, the random removal of even a high proportion of nodes tends to have little impact on the network characteristic path length. However, the targeted removal of the most connected nodes leads to a rapid increase in the characteristic path length and network fragmentation. From a biological perspective, the random removal of population nodes could be considered analogous to stochastic extirpation perhaps due to severe weather events, whereas removal of the most connected nodes might occur, for example, due to over harvest of populations in high quality habitats. In this case ‘hub’ populations would warrant considerable concern within management and conservation strategies.