Dominance analysis of linear complementarity systems

The paper extends the concepts of dominance and p-dissipativity to the non-smooth family of linear complementarity systems. Dominance generalizes incremental stability whereas p-dissipativity generalizes incremental passivity. The generalization aims at an interconnection theory for the design and analysis of switching and oscillatory systems. The approach is illustrated by a detailed study of classical electrical circuits that switch and oscillate

Per capita interactions and stress tolerance drive stress-induced changes in biodiversity effects on ecosystem functions

Environmental stress changes the relationship between biodiversity and ecosystem functions, but the underlying mechanisms are poorly understood. Because species interactions shape biodiversity-ecosystem functioning relationships, changes in per capita interactions under stress (as predicted by the stress gradient hypothesis) can be an important driver of stress-induced changes in these relationships. To test this hypothesis, we measure productivity in microalgae communities along a diversity and herbicide gradient. On the basis of additive partitioning and a mechanistic community model, we demonstrate that changes in per capita interactions do not explain effects of herbicide stress on the biodiversity-productivity relationship. Instead, assuming that the per capita interactions remain unaffected by stress, causing species densities to only change through differences in stress tolerance, suffices to predict the stress-induced changes in the biodiversity-productivity relationship and community composition. We discuss how our findings set the stage for developing theory on how environmental stress changes biodiversity effects on ecosystem functions

Mean Field Equilibrium in Dynamic Games with Complementarities

We study a class of stochastic dynamic games that exhibit strategic complementarities between players; formally, in the games we consider, the payoff of a player has increasing differences between her own state and the empirical distribution of the states of other players. Such games can be used to model a diverse set of applications, including network security models, recommender systems, and dynamic search in markets. Stochastic games are generally difficult to analyze, and these difficulties are only exacerbated when the number of players is large (as might be the case in the preceding examples). We consider an approximation methodology called mean field equilibrium to study these games. In such an equilibrium, each player reacts to only the long run average state of other players. We find necessary conditions for the existence of a mean field equilibrium in such games. Furthermore, as a simple consequence of this existence theorem, we obtain several natural monotonicity properties. We show that there exist a "largest" and a "smallest" equilibrium among all those where the equilibrium strategy used by a player is nondecreasing, and we also show that players converge to each of these equilibria via natural myopic learning dynamics; as we argue, these dynamics are more reasonable than the standard best response dynamics. We also provide sensitivity results, where we quantify how the equilibria of such games move in response to changes in parameters of the game (e.g., the introduction of incentives to players).Comment: 56 pages, 5 figure

Role of functionally dominant species in varying environmental regimes: evidence for the performance-enhancing effect of biodiversity

Background Theory suggests that biodiversity can act as a buffer against disturbances and environmental variability via two major mechanisms: Firstly, a stabilising effect by decreasing the temporal variance in ecosystem functioning due to compensatory processes; and secondly, a performance enhancing effect by raising the level of community response through the selection of better performing species. Empirical evidence for the stabilizing effect of biodiversity is readily available, whereas experimental confirmation of the performance-enhancing effect of biodiversity is sparse. Results Here, we test the effect of different environmental regimes (constant versus fluctuating temperature) on bacterial biodiversity-ecosystem functioning relations. We show that positive effects of species richness on ecosystem functioning are enhanced by stronger temperature fluctuations due to the increased performance of individual species. Conclusions Our results provide evidence for the performance enhancing effect and suggest that selection towards functionally dominant species is likely to benefit the maintenance of ecosystem functioning under more variable conditions

The Decentralization Tradeoff for Complementary Spillovers

We examine a symmetric two-district setting with spillovers of local public spending where a spill-in from the foreign spending is not a substitute, but a complement to domestic spending. Specifically, we assume production of two district-specific public goods out of two complementary district-specific inputs. We compare equilibria in non-cooperative decentralization and cooperative centralization for different spillovers, complementarities and cost-division rules, and control for the effects of strategic delegation and the feasibility of voluntary contributions to the input in the foreign district. We find that centralization welfare-dominates decentralization in most institutional settings and for a wide range of parameters, yet we can also identify necessary and sufficient conditions for decentralization to welfare-dominate centralization. The setup features three novelties: In the absence of transfers, welfare in decentralization increases in spillovers, strategic delegation in decentralization improves welfare, and centralized provision may be non-monotonic in spillovers.Spillover, Spill-in, Strategic complementarity, Decentralization theorem

Biomass production, symbiotic nitrogen fixation and inorganic N use in dual and tri-component annual intercrops

The interspecific complementary and competitive interactions between pea (Pisum sativum L.), barley (Hordeum vulgare L.) and oilseed rape (Brassica napus L.), grown as dual and tri-component intercrops were assessed in a field study in Denmark. Total biomass production and N use at two levels of N fertilisation (0.5 and 4.0 g N/m2), were measured at five harvests throughout a growing season. All intercrops displayed land equivalent ratio values close to or exceeding unity, indicating complementary use of growth resources. Whereas both rape and barley responded positively to increased N fertilisation, irrespective of whether they were grown as sole- or intercrops, pea was strongly suppressed when grown in intercrop. Of the three crops barley was the strongest competitor for both soil and fertiliser N, rape intermediate and pea the weakest. Faster initial growth of barley than pea and rape gave barley an initial competitive advantage, an advantage that in the two dual intercrops was strengthened by the addition of N. Apparently the competitive superiority of barley was less strong in the tri-component intercrop, indicating that the impact of the dominantmay, through improved growth of both rape and pea, have been diminished through indirect facilitation. Interspecific competition had a promoting effect on the percent of nitrogen derived from N2 fixation of pea, and most so at the low N fertilisation level. Results indicate that the benefits achieved from the association of a legume and nonlegume, in terms of N2 fixed were greatest when pea was grown in association with rape as opposed to barley which could indicate that the benefits achieved from the association of a legume and nonlegume are partly lost if the nonlegume is too strong a competitor