Characterization of the robustness against invasions for different topological structures.

<p>Shown are three example cases: A, a branch, B, a bifurcation, and C, a clique. Nodes indicated by a square with a C enclosed are assumed to be locked in a cooperative strategy due to their large number of connections to other cooperators (not shown).</p

Bridging ties are the origin of coordination failures.

<p>The PGP network has many more tree-like structures than the URV network. Shown is the fraction of nodes that are not in 2-components for both empirical networks. Clearly, they are much more frequent in the PGP network (panel A, left) than in the URV (panel B, right). This is in agreement with our claim that they are responsible for the observed effect, as discussed in the main text.</p

Synthetic heterogeneous networks (Barabási-Albert scale-free networks) only give rise to coordination failures when there is lack of redundant paths.

<p>Stationary density of cooperators <i>x</i>* as a function of game parameter <i>T</i>, for three instances of Barabási-Albert scale-free networks with degrees <i>k = </i>2, 4, and 8 (see legend). Redundant paths between nodes are only scarce for the case of <i>k</i> = 2, which is strictly a tree by construction. Notice also that clustering is very low in all three cases (mean value <0.01). Network size is <i>N</i> = 10⁴ nodes, network generation parameters are <i>m</i>₀ = <i>m</i> = <i>k</i>/2 <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0015210#pone.0015210-Albert1" target="_blank">[54]</a>.</p

Cooperation maps for different values of <i>S</i> and <i>T</i> show coordination failures on the PGP network.

<p>Asymptotic density of cooperators for social dilemmas on the URV (left), PGP (middle) and degree-preserving randomized PGP networks (right). Top row: Unconditional imitation rule; bottom row: replicator rule. In the upper left quadrant of each panel we have the Harmony game (0<<i>S</i>, <i>T</i><1), in the upper right quadrant the Snowdrift game (0<<i>S<1), in the bottom left the Stag Hunt game (−1<<i>S<0), and in the bottom right the Prisoner Dilemma (−1<<i>S<0</i>, <i>1). Numbers above and below each quadrant represent the average value of the cooperation level in the quadrant. Note the anomalous smooth transition in the PGP network (middle column), which indicates the existence of coordination failures. For comparison, the URV network shows a very small region where coordination is not achieved, comparable to the results of model networks. The randomized version (not shown) gives essentially the same results as the original network, indicating the absence of peculiar features in its topology.</i></i></i></p

Topological traps are obstacles to the growth of clusters of equal strategists.

<p>A simple example is a link between two nodes of different degrees, connected to all cooperators (in red) or all defectors (in blue). See main text for a discussion.</p

Effect of correlation-preserving rewirings on the evolutionary outcome, along the parameter diagonal <i>S</i> = −<i>T</i> (SH quadrant).

<p>Panel A: Stationary density of cooperators as a function of <i>T</i>, for substrates constructed by rewiring the PGP network but preserving degree correlations up to the indicated order. We observe that the smooth transition, which characterizes the coordination failure in the PGP network, disappears when degree correlations of order 3 are destroyed, indicating that the origin of this phenomenon is related to such correlations. Panel B: Influence of bottom-up rewirings. Black and green symbols correspond, respectively, to the original PGP network and a randomized version preserving degree correlations up to order 2. Symbols in other colors correspond to intermediate cases, where only nodes with the indicated degrees are rewired. We observe that the change between the extreme cases (sharp vs. smooth transitions) depends on the degree of the nodes involved in the rewiring process. Inset of Panel B: normalized cumulative distributions of number of nodes (blue circles) and number of stubs (green squares) vs node degree <i>k</i>, of the PGP network. Nodes of lower degrees are the majority, but their stubs represent a much smaller portion in the total network.</p

High-throughput tool to discriminate effects of NMs (Cu-NPs, Cu-nanowires, CuNO₃, and Cu salt aged): transcriptomics in <i>Enchytraeus crypticus</i>

<p>The current testing of nanomaterials (NMs) via standard toxicity tests does not cover many of the NMs specificities. One of the recommendations lays on understanding the mechanisms of action, as these can help predicting long-term effects and safe-by-design production. In the present study, we used the high-throughput gene expression tool, developed for <i>Enchytraeus crypticus</i> (4 × 44k Agilent microarray), to study the effects of exposure to several copper (Cu) forms. The Cu treatments included two NMs (spherical and wires) and two copper-salt treatments (CuNO₃ spiked and Cu salt field historical contamination). To relate gene expression with higher effect level, testing was done with reproduction effect concentrations (EC₂₀, EC₅₀), using 3 and 7 days as exposure periods. Results showed that time plays a major role in the transcriptomic response, most of it occurring after 3 days. Analysis of gene expression profiles showed that Cu-salt-aged and Cu-nanowires (Nwires) differed from CuNO₃ and Cu-nanoparticles (NPs). Functional analysis revealed specific mechanisms: Cu-NPs uniquely affected senescence and cuticle pattern formation, which can result from the contact of the NPs with the worms’ tegument. Cu-Nwires affected reproduction via male gamete generation and hermaphrodite genitalia development. CuNO₃ affected neurotransmission and locomotory behavior, both of which can be related with avoidance response. Cu salt-aged uniquely affected phagocytosis and reproductive system development (via different mechanisms than Cu-Nwires). For the first time for Cu (nano)materials, the adverse outcome pathways (AOPs) drafted here provide an overview for common and unique effects per material and linkage with apical effects.</p