Abstract
Livestock farmers rely on a high and stable grassland productivity for fodder production to sustain their livelihoods. Future drought events related to climate change, however, threaten grassland functionality in many regions across the globe. The introduction of sustainable grassland management could buffer these negative effects. According to the biodiversity–productivity hypothesis, productivity positively associates with local biodiversity. The biodiversity–insurance hypothesis states that higher biodiversity enhances the temporal stability of productivity. To date, these hypotheses have mostly been tested through experimental studies under restricted environmental conditions, hereby neglecting climatic variations at a landscape‐scale. Here, we provide a landscape‐scale assessment of the contribution of species richness, functional composition, temperature, and precipitation on grassland productivity. We found that the variation in grassland productivity during the growing season was best explained by functional trait composition. The community mean of plant preference for nutrients explained 24.8% of the variation in productivity and the community mean of specific leaf area explained 18.6%, while species richness explained only 2.4%. Temperature and precipitation explained an additional 22.1% of the variation in productivity. Our results indicate that functional trait composition is an important predictor of landscape‐scale grassland productivity.
Highlights
System verification requires comparing a system’s behavior against a specification
We extend the notions of natural projection and partial model checking from finite-state to symbolic transition systems and we show that the equivalence still holds
Our work provides results that build a bridge between supervisory control theory and formal verification
Summary
System verification requires comparing a system’s behavior against a specification. When the system is built from several components, we can distinguish between local and global specifications. Natural projection is often applied component-wise to solve the controller synthesis problem, i.e., for synthesizing local controllers from a global specification of an asynchronous discrete-event system [11]. We address the first remark about a formal bridge by showing that, under reasonable assumptions, natural projection reduces to partial model checking and, when cast in a common setting, they are equivalent To this end, we start by defining a common theoretical framework for both. We propose a new algorithm for partial model checking that operates directly on Labeled Transition Systems (LTS), rather than on the μ-calculus. Extends the statement of Theorem 3.2 to the s-LTSs, i.e., that establishes the correspondence between partial model checking and natural projection for s-LTSs. we define a new algorithm for symbolic partial model checking directly on s-LTSs, and we prove it correct with respect to the symbolic quotienting operator. All the additional material about (i) implementation of the algorithms, (ii) tool usage and (iii) replication of the experiments is available at https:// github.com/gabriele-costa/pests
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