Tropically convex constraint satisfaction

A semilinear relation S is max-closed if it is preserved by taking the componentwise maximum. The constraint satisfaction problem for max-closed semilinear constraints is at least as hard as determining the winner in Mean Payoff Games, a notorious problem of open computational complexity. Mean Payoff Games are known to be in the intersection of NP and co-NP, which is not known for max-closed semilinear constraints. Semilinear relations that are max-closed and additionally closed under translations have been called tropically convex in the literature. One of our main results is a new duality for open tropically convex relations, which puts the CSP for tropically convex semilinaer constraints in general into NP intersected co-NP. This extends the corresponding complexity result for scheduling under and-or precedence constraints, or equivalently the max-atoms problem. To this end, we present a characterization of max-closed semilinear relations in terms of syntactically restricted first-order logic, and another characterization in terms of a finite set of relations L that allow primitive positive definitions of all other relations in the class. We also present a subclass of max-closed constraints where the CSP is in P; this class generalizes the class of max-closed constraints over finite domains, and the feasibility problem for max-closed linear inequalities. Finally, we show that the class of max-closed semilinear constraints is maximal in the sense that as soon as a single relation that is not max-closed is added to L, the CSP becomes NP-hard.Comment: 29 pages, 2 figure

Dry zone forests of Fiji: species composition, life history traits, and conservation

Species composition and life history traits of trees in native forests in the dry zone of Fiji were investigated. Areas receiving less than 2500 mm yr-1 of rain and covered with native forest were identified using maps, aerial photographs, estimated climate (WorldClim), and field reconnaissance. Ten forest remnants were identified and species lists and data on natural history and disturbance were compiled. Cluster analysis and DECORANA identified two principal forest types, moist forest (MF) and tropical dry forest (TDF), each defined by unique climate, species composition, and tree life history characteristics. TDF (reported for the first time from Fiji) has a pronounced dry season (5 consecutive months with < 100 mm rainfall each) and several deciduous canopy species. MF lacks a pronounced dry season and has few deciduous species. The amount and variability of rainfall seem to influence the type of forest in a particular location and disturbance is negatively correlated with precipitation. TDF are probably Fiji's most endangered ecosystems

Non-Additive Effects on Decomposition from Mixing Litter of the Invasive Mikania micrantha H.B.K. with Native Plants

A common hypothesis to explain the effect of litter mixing is based on the difference in litter N content between mixed species. Although many studies have shown that litter of invasive non-native plants typically has higher N content than that of native plants in the communities they invade, there has been surprisingly little study of mixing effects during plant invasions. We address this question in south China where Mikania micrantha H.B.K., a non-native vine, with high litter N content, has invaded many forested ecosystems. We were specifically interested in whether this invader accelerated decomposition and how the strength of the litter mixing effect changes with the degree of invasion and over time during litter decomposition. Using litterbags, we evaluated the effect of mixing litter of M. micrantha with the litter of 7 native resident plants, at 3 ratios: M(1) (1∶4, = exotic:native litter), M(2) (1∶1) and M(3) (4∶1, = exotic:native litter) over three incubation periods. We compared mixed litter with unmixed litter of the native species to identify if a non-additive effect of mixing litter existed. We found that there were positive significant non-additive effects of litter mixing on both mass loss and nutrient release. These effects changed with native species identity, mixture ratio and decay times. Overall the greatest accelerations of mixture decay and N release tended to be in the highest degree of invasion (mix ratio M(3)) and during the middle and final measured stages of decomposition. Contrary to expectations, the initial difference in litter N did not explain species differences in the effect of mixing but overall it appears that invasion by M. micrantha is accelerating the decomposition of native species litter. This effect on a fundamental ecosystem process could contribute to higher rates of nutrient turnover in invaded ecosystems