Synthesizing optimal bias in randomized self-stabilization.

Randomization is a key concept in distributed computing to tackle impossibility results. This also holds for self-stabilization in anonymous networks where coin flips are often used to break symmetry. Although the use of randomization in self-stabilizing algorithms is rather common, it is unclear what the optimal coin bias is so as to minimize the expected convergence time. This paper proposes a technique to automatically synthesize this optimal coin bias. Our algorithm is based on a parameter synthesis approach from the field of probabilistic model checking. It over- and under-approximates a given parameter region and iteratively refines the regions with minimal convergence time up to the desired accuracy. We describe the technique in detail and present a simple parallelization that gives an almost linear speed-up. We show the applicability of our technique to determine the optimal bias for the well-known Herman's self-stabilizing token ring algorithm. Our synthesis obtains that for small rings, a fair coin is optimal, whereas for larger rings a biased coin is optimal where the bias grows with the ring size. We also analyze a variant of Herman's algorithm that coincides with the original algorithm but deviates for biased coins. Finally, we show how using speed reducers in Herman's protocol improve the expected convergence time.

13C isotopic signature and C concentration of soil density fractions illustrate reduced C allocation to subalpine grassland soil under high atmospheric N deposition.

We followed soil C fluxes in a subalpine grassland system exposed to experimentally increased atmospheric N deposition for 7 years. Earlier we found that, different from the plant productivity response, the bulk soil C stock increase was highest at the medium, not the high N input as hypothesized. This implies that a smaller N-deposition rate has a greater potential to favor the biological greenhouse gas-sink. To help elucidate the mechanisms controlling those changes in SOC in response to N deposition, we produced four soil density fractions and analyzed soil organic C concentration [SOC], as well as δ13C signatures (δ13CSOC) of SOC components. Soil respired CO2 (δ13CCO2) was analyzed to better distinguish seasonal short term dynamics from N-deposition effects and to identify the predominant substrate of soil respiration. Both at the start of the experiment and after 7 years we found a strong, negative correlation between [SOC] and δ13CSOC of the soil density fractions in the control treatment, consistent with an advanced stage of microbial processing of SOC in fractions of higher density. During the experiment the [SOC] increased in the two lighter density fractions, but decreased in the two heavier fractions, suggesting a possible priming effect that accelerated decomposition of formerly recalcitrant (heavy) organic matter pools. The seasonal pattern of soil δ13CCO2 was affected by weather and canopy development, and δ13CCO2 values for the different N treatment levels indicated that soil respiration originated primarily from the lightest density fractions. Surprisingly, [SOC] increases were significantly higher under medium N deposition in the <1.8 fraction and in bulk soil, compared to the high N treatment. Analogously, the depletion of δ13CSOC was significantly higher in the medium compared to the high N treatment in the three lighter fractions. Thus, medium N deposition favored the highest C sequestration potential, compared to the low N control and the high N treatment. Clearly, our results show that it is inappropriate to use plant productivity N response as an indicator for shifts in SOC content in grassland ecosystems. Here, isotopic techniques illustrated why atmospheric N deposition of 14 kg N ha-1 yr-1 is below, and 54 kg N ha-1 yr-1 is above a threshold that tips the balance between new, assimilative gains and respiratory losses towards a net loss of [SOC] for certain soil fractions in the subalpine grassland.

Elevated ozone and nitrogen deposition affect nitrogen pools of subalpine grassland.

In a free-air fumigation experiment with subalpine grassland, we studied long-term effects of elevated ozone (O3) and nitrogen (N) deposition on ecosystem N pools and on the fate of anthropogenic N. At three times during the seventh year of exposure, N pools and recovery of a stable isotope tracer ((15)N) were determined in above- and belowground plant parts, and in the soil. Plants were much better competitors for (15)N than soil microorganisms. Plant N pools increased by 30-40% after N addition, while soil pools remained unaffected, suggesting that most of the extra N was taken up and stored in plant biomass, thus preventing the ecosystem from acquiring characteristics of eutrophication. Elevated O3 caused an increase of N in microbial biomass and in stabilized soil N, probably resulting from increased litter input and lower litter quality. Different from individual effects, the interaction between the pollutants remained partly unexplained.

High tolerance of subalpine grassland to long-term ozone exposure is independent of N input and climatic drivers.

In a seven-year study, we tested effects of increased N and O3 deposition and climatic conditions on biomass of subalpine grassland. Ozone risk was assessed as exposure (AOT40) and as stomatal flux (POD0,1). We hypothesized that productivity is higher under N- and lower under O3 deposition, with interactions with climatic conditions. Aboveground biomass was best correlated with growing-degree days for May (GDDMay). Nitrogen deposition increased biomass up to 60% in the highest treatment, and 30% in the lowest addition. Also belowground biomass showed a positive N-response. Ozone enrichment had no effect on biomass, and no interaction between O3 and N was observed. Growth response to N deposition was not correlated to GDDMay or precipitation, but indicated a cumulative effect over time. Productivity of subalpine grassland is tolerant to increasing ozone exposure, independent of N input and climatic drivers. N deposition rates at current critical loads, strongly increase the grassland yield.

Ozone visible symptoms and reduced root biomass in the subalpine species Pinus uncinata after two years of free-air ozone fumigation.

Concentrations of ozone often exceed the thresholds of forest protection in the Pyrenees, but the effect of ozone on Pinus uncinata, the dominant species in subalpine forests in this mountainous range, has not yet been studied. We conducted an experiment of free-air ozone fumigation with saplings of P. uncinata fumigated with ambient O(3) (AOT40 May-Oct: 9.2 ppm h), 1.5 × O(3amb) (AOT40 May-Oct: 19.2 ppm h), and 1.8 × O(3amb) (AOT40 May-Oct: 32.5 ppm h) during two growing seasons. We measured chlorophyll content and fluorescence, visible injury, gas exchange, and above- and below-ground biomass. Increased exposures to ozone led to a higher occurrence and intensity of visible injury from O(3) and a 24-29% reduction of root biomass, which may render trees more susceptible to other stresses such as drought. P. uncinata is thus a species sensitive to O(3), concentrations of which in the Pyrenees are already likely affecting this species.

Effects of combined ozone and nitrogen deposition on the in situ properties of eleven key plant species of a subalpine pasture.

Tropospheric O(3) and deposition of reactive N threaten the composition and function of natural and semi-natural vegetation even in remote regions. However, little is known about effects of these pollutants individually or in combination on plant species in alpine habitats. We analyzed 11 frequent plant species of a subalpine Geo-Montani-Nardetum pasture exposed at 2,000 m a.s.l. in the Swiss Alps during 3 years using a factorial free-air exposure system with three concentrations of O(3) and five rates of N application. The aim was to detect subtle effects on leaf chlorophyll and N concentrations, leaf weight, specific leaf area (SLA), and delta(18)O and delta(13)C as proxies for gas exchange. We expected that the species' responsiveness to O(3) and N would be related to their functional traits and that N-induced changes in these traits would modify the species' response to O(3) via increased growth and higher leaf conductance (g (s)). Most species reacted to N supply with the accumulation of N and chlorophyll, but with no change in SLA, g (s), and growth, except Carex sempervirens which showed increased water use efficiency and leaf weight. Elevated O(3) reduced g ( s ) in most species, but this was not related to a reduction in leaf weight, which was recorded in half of the species. Contrary to our expectation, the magnitude of the response to both O(3) and N was not related to species-specific traits such as SLA or g (s). No pronounced O(3) x N interactions were observed. In conclusion, since for most species neither N nor gas exchange limited growth, their short-term response to O(3) and N and to their combination was small. O(3) x N interactive effects are expected to be more pronounced in habitats where species are more responsive to N due to favorable growth conditions in terms of nutrient availability and temperature.

Nitrogen deposition but not ozone affects productivity and community composition of subalpine grassland after 3 yr of treatment.

A field experiment was established at 2000 m above sea level (asl) in the central Swiss Alps with the aim of investigating the effects of elevated ozone (O(3)) and nitrogen deposition (N), and of their combination, on above-ground productivity and species composition of subalpine grassland. One hundred and eighty monoliths were extracted from a species-rich Geo-Montani-Nardetum pasture and exposed in a free-air O(3)-fumigation system to one of three concentrations of O(3) (ambient, 1.2 x ambient, 1.6 x ambient) and five concentrations of additional N. Above-ground biomass, proportion of functional groups and normalized difference vegetation index (NDVI) were measured annually. After 3 yr of treatment, the vegetation responded to the N input with an increase in above-ground productivity and altered species composition, but without changes resulting from elevated O(3). N input > 10 kg N ha(-1) yr(-1) was sufficient to affect the composition of functional groups, with sedges benefiting over-proportionally. No interaction of O(3) x N was observed, except for NDVI; positive effects of N addition on canopy greenness were counteracted by accelerated leaf senescence in the highest O(3) treatment. The results suggest that effects of elevated O(3) on the productivity and floristic composition of subalpine grassland may develop slowly, regardless of the sensitive response to increasing N.

Genotype × elevated CO2 interaction and allocation in calcareous grassland species.

• Biomass of genotypes of Carex flacca and Bromus erectus under CO2 enrichment was measured to test for 'winners' and 'losers' within the populations. Allocation was studied to identify reasons for varying biomass responses of the genotypes. • In a first experiment, genotypes of both species were grown separately and mown five times. In a second experiment, introducing species interaction, species were grown together (using nine genotypes of each) and harvested destructively during that time. • The first experiment showed that growth stimulation across harvests (Bromus+15%; Carex+11%) and genotype × CO2 treatment interactions in single harvests was significant, but repeated measures ANOVA was not (Carex) or only marginally significant (Bromus). Destructive harvests in the competition experiment indicated a significant growth stimulation (Bromus+28%, Carex+35%), but no CO2  × genotype interaction was found. Similarly, ANOVA of dry matter allocation never indicated a significant CO2  × genotype interaction. • The lack of a sustained CO2  × genotype interaction in isolated and competitive growth conditions with good moisture supply suggests, that if there is such an interaction, it must be very small.

Soil moisture effects determine CO2 responses of grassland species.

It has been suggested that positive biomass responses of grassland to elevated CO2 result from moisture savings in the soil as opposed to direct photosynthetic stimulation. In order to test this hypothesis for calcareous grassland we subjected experimental communities consisting of two important graminoid components of such grasslands (Carex flacca and Bromus erectus) on natural substrate to a fully factorial treatment of ambient (360 ppm) and elevated (600 ppm) CO2 concentration and four irrigation regimes (9 mm, 18 mm, 27 mm and 36 mm week-1). Biomass stimulation under elevated CO2 was higher the lower the irrigation rate was. Superimposed on the effects of irrigation on soil moisture, elevated CO2-induced higher soil water contents in all irrigation treatments via reduced plant water consumption (on average one-third lower stomatal conductance). This led to eight different soil moisture regimes instead of the intended four. When growth parameters were plotted against the effective soil water content rather than irrigation treatment, the "pure" CO2 effect on total biomass and other traits became much smaller and completely disappeared for biomass per tiller, leaf area per ground area, leaf mass fraction (LMF) and root mass fraction (RMF). We conclude that the CO2 response observed in this graminoid system consisted of a small primary CO2 effect and a large secondary, CO2-induced, soil moisture effect. Thus, it is difficult to use responses to CO2 from experiments in which CO2-induced soil moisture savings occur to predict CO2 effects as long as future soil moisture regimes are not defined. We suggest that direct and indirect (moisture driven) CO2 effects should be strictly separated, which requires data to be tested against soil moisture.