Continental-scale pollution of estuaries with antibiotic resistance genes

Many networks of interest in the sciences, including a variety of social and biological networks, are found to divide naturally into communities or modules. The problem of detecting and characterizing this community structure has attracted considerable recent attention. One of the most sensitive detection methods is optimization of the quality function known as "modularity" over the possible divisions of a network, but direct application of this method using, for instance, simulated annealing is computationally costly. Here we show that the modularity can be reformulated in terms of the eigenvectors of a new characteristic matrix for the network, which we call the modularity matrix, and that this reformulation leads to a spectral algorithm for community detection that returns results of better quality than competing methods in noticeably shorter running times. We demonstrate the algorithm with applications to several network data sets.

Estuarine and coastal transformation is as old as civilization yet has dramatically accelerated over the past 150 to 300 years. Reconstructed time lines, causes, and consequences of change in 12 once diverse and productive estuaries and coastal seas worldwide show similar patterns: Human impacts have depleted >90% of formerly important species, destroyed >65% of seagrass and wetland habitat, degraded water quality, and accelerated species invasions. Twentieth-century conservation efforts achieved partial recovery of upper trophic levels but have so far failed to restore former ecosystem structure and function. Our results provide detailed historical baselines and quantitative targets for ecosystem-based management and marine conservation.