Towards a proper assignment of systemic risk: the combined roles of network topology and shock characteristics.

The 2007-2008 financial crisis solidified the consensus among policymakers that a macro-prudential approach to regulation and supervision should be adopted. The currently preferred policy option is the regulation of capital requirements, with the main focus on combating procyclicality and on identifying the banks that have a high systemic importance, those that are "too big to fail". Here we argue that the concept of systemic risk should include the analysis of the system as a whole and we explore systematically the most important properties for policy purposes of networks topology on resistance to shocks. In a thorough study going from analytical models to empirical data, we show two sharp transitions from safe to risky regimes: 1) diversification becomes harmful with just a small fraction (~2%) of the shocks sampled from a fat tailed shock distributions and 2) when large shocks are present a critical link density exists where an effective giant cluster forms and most firms become vulnerable. This threshold depends on the network topology, especially on modularity. Firm size heterogeneity has important but diverse effects that are heavily dependent on shock characteristics. Similarly, degree heterogeneity increases vulnerability only when shocks are directed at the most connected firms. Furthermore, by studying the structure of the core of the transnational corporation network from real data, we show that its stability could be clearly increased by removing some of the links with highest centrality betweenness. Our results provide a novel insight and arguments for policy makers to focus surveillance on the connections between firms, in addition to capital requirements directed at the nodes.

Spatial distribution and packing of xylem conduits.

PREMISE OF THE STUDY: The hydraulic properties of the xylem determine the ability of plants to transport water from the soil to the leaves and to cope with important stress factors such as frost and drought. Hydraulic properties have usually been studied as a function of the anatomy of xylem conduits and their pits, but recent studies have proposed that system-level properties, related to the topology of the xylem network, may also play a role. Here we study how the spatial arrangement of conduits in xylem cross sections affects the relationship between mean conduit lumen area and conduit density (packing function) across species. METHODS: Point pattern analysis was used to describe the spatial distribution of xylem conduits in 97 woody species. The effect of conduit aggregation on the packing function was tested using phylogenetic generalized least squares. A hydraulic model with an explicit description of the topology of the xylem network was used to interpret the functional significance of our findings. KEY RESULTS: The spatial arrangement of conduits affected the packing function across species, so that species with aggregated distributions tended to have lower conduit densities for a given conduit size and lower conduit lumen fractions. According to our modeling results, the higher conduit-to-conduit connectivity of species with aggregated distributions allows them to achieve higher hydraulic conductivity. Species with aggregated conduits, however, pay a cost in terms of increased vulnerability to embolism. CONCLUSIONS: The spatial arrangement of conduits affects the fundamental structural and functional attributes of the xylem.

Stand- and tree-level determinants of the drought response of Scots pine radial growth.

Characterizing the responses of key tree species to extreme climatic events may provide important information for predicting future forest responses to increased climatic variability. Here we aimed at determining which tree- and stand-level attributes were more closely associated with the effect of a severe drought on the radial growth of Scots pine, both in terms of immediate impact and recovery after the drought event. Our dataset included tree-ring series from 393 plots located close to the dry limit of the species range. Time series analysis and mixed-effects models were used to study the growth of each tree and its detailed response to a severe drought event that occurred in 1986. Our results showed that the radial growth responses of Scots pine were determined primarily by tree-level characteristics, such as age and previous growth rate, and secondarily by stand basal area and species richness, whereas local climate had a relatively minor effect. Fast-growing trees were more severely affected by the drought and retained proportionally lower growth rates up to three years after the episode. In absolute terms, however, fast-growing trees performed better both during and after the event. Older trees were found to be less resilient to drought. The effect of stand basal area and species richness indicated that competition for resources worsened the effects of drought, and suggested that the effect of interspecific competition may be particularly detrimental during the drought year.

A quantitative and statistically robust method for the determination of xylem conduit spatial distribution.

PREMISE OF THE STUDY: Because of their limited length, xylem conduits need to connect to each other to maintain water transport from roots to leaves. Conduit spatial distribution in a cross section plays an important role in aiding this connectivity. While indices of conduit spatial distribution already exist, they are not well defined statistically. • METHODS: We used point pattern analysis to derive new spatial indices. One hundred and five cross-sectional images from different species were transformed into binary images. The resulting point patterns, based on the locations of the conduit centers-of-area, were analyzed to determine whether they departed from randomness. Conduit distribution was then modeled using a spatially explicit stochastic model. • KEY RESULTS: The presence of conduit randomness, uniformity, or aggregation depended on the spatial scale of the analysis. The large majority of the images showed patterns significantly different from randomness at least at one spatial scale. A strong phylogenetic signal was detected in the spatial variables. • CONCLUSIONS: Conduit spatial arrangement has been largely conserved during evolution, especially at small spatial scales. Species in which conduits were aggregated in clusters had a lower conduit density compared to those with uniform distribution. Statistically sound spatial indices must be employed as an aid in the characterization of distributional patterns across species and in models of xylem water transport. Point pattern analysis is a very useful tool in identifying spatial patterns.

The relevance of xylem network structure for plant hydraulic efficiency and safety.

The xylem is one of the two long distance transport tissues in plants, providing a low resistance pathway for water movement from roots to leaves. Its properties determine how much water can be transported and transpired and, at the same time, the plant's vulnerability to transport dysfunctions (the formation and propagation of emboli) associated to important stress factors, such as droughts and frost. Both maximum transport efficiency and safety against embolism have classically been attributed to the properties of individual conduits or of the pit membrane connecting them. But this approach overlooks the fact that the conduits of the xylem constitute a network. The topology of this network is likely to affect its overall transport properties, as well as the propagation of embolism through the xylem, since, according to the air-seeding hypothesis, drought-induced embolism propagates as a contact process (i.e., between neighbouring conduits). Here we present a model of the xylem that takes into account its system-level properties, including the connectivity of the xylem network. With the tools of graph theory and assuming steady state and Darcy's flow we calculated the hydraulic conductivity of idealized wood segments at different water potentials. A Monte Carlo approach was adopted, varying the anatomical and topological properties of the segments within biologically reasonable ranges, based on data available from the literature. Our results showed that maximum hydraulic conductivity and vulnerability to embolism increase with the connectivity of the xylem network. This can be explained by the fact that connectivity determines the fraction of all the potential paths or conduits actually available for water transport and spread of embolism. It is concluded that the xylem can no longer be interpreted as the mere sum of its conduits, because the spatial arrangement of those conduits in the xylem network influences the main functional properties of this tissue. This brings new arguments into the long-standing discussion on the efficiency vs. safety trade-off in the plants' xylem.