Figure 2
Modularity as a function of the threshold distance. (a) The plot shows the results of over 100 random landscapes (each with 100 habitat fragments) with coordinates drawn from uniform distributions. In each case, the network with the highest modularity corresponds to the percolation distance (orange P). Since each landscape has a different percolation distance, the boxplot shows a relative increase of distance from the percolation distance P to the distance which generates a fully connected matrix F and 20 other distances equally spaced in between. Modularity is significant throughout nearly the entire range of threshold distances. The pervasiveness of the pattern shows that it is scale-invariant. Increasing threshold distance is equivalent to reducing the scale at which we look at the landscape. However, threshold distances close to the distance in which the resulting graph is a fully connected network, result in a non-significant modular pattern. (b) The plot represents the random landscape depicted in Fig. 1. For distances shorter than the percolation distance (blue-shaded area) the different components also tend to have a modular structure. Modularity increases as the size of the components increase until it peaks at around the percolation distance (orange dotted line). Grey circles represent significant values of modularity, while white circles represent non-significant values. (A zoomed-in version of the distances shorter than the percolation distance, and the size of each individual component can be found at Supplementary Fig. 2).
