On the multiple ecological roles of water in river networks

The distribution and movement of water can influence the state and dynamics of terrestrial and aquatic ecosystems through a diversity of mechanisms. These mechanisms can be organized into three general categories wherein water acts as (1) a resource or habitat for biota, (2) a vector for connectivity and exchange of energy, materials, and organisms, and (3) as an agent of geomorphic change and disturbance. These latter two roles are highlighted in current models, which emphasize hydrologic connectivity and geomorphic change as determinants of the spatial and temporal distributions of species and processes in river systems. Water availability, on the other hand, has received less attention as a driver of ecological pattern, despite the prevalence of intermittent streams, and strong potential for environmental change to alter the spatial extent of drying in many regions. Here we summarize long-term research from a Sonoran Desert watershed to illustrate how spatial patterns of ecosystem structure and functioning reflect shifts in the relative importance of different 'roles of water' across scales of drainage size. These roles are distributed and interact hierarchically in the landscape, and for the bulk of the drainage network it is the duration of water availability that represents the primary determinant of ecological processes. Only for the largest catchments, with the most permanent flow regimes, do flood-associated disturbances and hydrologic exchange emerge as important drivers of local dynamics. While desert basins represent an extreme case, the diversity of mechanisms by which the availability and flow of water influence ecosystem structure and functioning are general. Predicting how river ecosystems may respond to future environmental pressures will require clear understanding of how changes in the spatial extent and relative overlap of these different roles of water shape ecological patterns. © 2013 Sponseller et al.

Optimal Capital Requirements in Financial Networks with Fire Sales

I explore and analyze a problem of finding the socially optimal capital requirements for financial institutions considering two distinct channels of contagion: direct exposures among the institutions, as represented by a network and fire sales externalities, which reflect the negative price impact of massive liquidation of assets.These two channels amplify shocks from individual financial institutions to the financial system as a whole and thus increase the risk of joint defaults amongst the interconnected financial institutions; this is often referred to as systemic risk. In the model, there is a trade-off between reducing systemic risk and raising the capital requirements of the financial institutions. The policymaker considers this trade-off and determines the optimal capital requirements for individual financial institutions. I provide a method for finding and analyzing the optimal capital requirements that can be applied to arbitrary network structures and arbitrary distributions of investment returns.

In particular, I first consider a network model consisting only of direct exposures and show that the optimal capital requirements can be found by solving a stochastic linear programming problem. I then extend the analysis to financial networks with default costs and show the optimal capital requirements can be found by solving a stochastic mixed integer programming problem. The computational complexity of this problem poses a challenge, and I develop an iterative algorithm that can be efficiently executed. I show that the iterative algorithm leads to solutions that are nearly optimal by comparing it with lower bounds based on a dual approach. I also show that the iterative algorithm converges to the optimal solution.

Finally, I incorporate fire sales externalities into the model. In particular, I am able to extend the analysis of systemic risk and the optimal capital requirements with a single illiquid asset to a model with multiple illiquid assets. The model with multiple illiquid assets incorporates liquidation rules used by the banks. I provide an optimization formulation whose solution provides the equilibrium payments for a given liquidation rule.

I further show that the socially optimal capital problem using the ``socially optimal liquidation" and prioritized liquidation rules can be formulated as a convex and convex mixed integer problem, respectively. Finally, I illustrate the results of the methodology on numerical examples and

discuss some implications for capital regulation policy and stress testing.