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Plant phenology has been shifting dramatically in response to climate change, a shift that may have significant and widespread ecological consequences. Of particular concern are tropical biomes, which represent the most biodiverse and imperiled regions of the world. However, compared to temperate floras, we know little about phenological responses of tropical plants because long-term observational datasets from the tropics are sparse. Herbarium specimens have greatly increased our phenological knowledge in temperate regions, but similar data have been underutilized in the tropics and their suitability for this purpose has not been broadly validated. Here, we compare phenological estimates derived from field observational data (i.e., plot surveys) and herbarium specimens at various spatial and taxonomic scales to determine whether specimens can provide accurate estimations of reproductive timing and its spatial variation. Here we demonstrate that phenological estimates from field observations and herbarium specimens coincide well. Fewer than 5% of the species exhibited significant differences between flowering periods inferred from field observations versus specimens regardless of spatial aggregation. In contrast to studies based on field records, herbarium specimens sampled much larger geographic and climatic ranges, as has been documented previously for temperate plants, and effectively captured phenological responses across varied environments. Herbarium specimens are verified to be a vital resource for closing the gap in our phenological knowledge of tropical systems. Tropical plant reproductive phenology inferred from herbarium records are widely congruent with field observations, suggesting that they can (and should) be used to investigate phenological variation and their associated environmental cues more broadly across tropical biomes. 

A method is presented addressing quantitative assessment of tunnel roof stability, based on the kinematic approach of limit analysis. Long tunnels with both rectangular (flat-ceiling) and circular cross-sections are considered. The rock is considered to be governed by the Hoek-Brown strength envelope and the normality flow rule, and it is assumed to provide enough ductility at failure, making plasticity theorems applicable. A failing block in the collapse mechanism is separated from the stationary rock by a deformation band with a large gradient of velocity across its width. The shape of the block in the critical mechanism is found from the requirement of the mechanism’s kinematic admissibility and an optimization procedure consistent with respective measures of stability. Both the stability number and the supporting pressure needed for tunnel stability are calculated first. Although less commonly used in rock engineering, a procedure is developed for estimating the factor of safety, defined as the ratio of the rock shear strength determined from the Hoek-Brown criterion to the demand on the strength. Curiously, for flat-ceiling tunnels, such definition of the factor of safety yields results equivalent to the ratio of a dimensionless group dependent on the uniaxial compressive strength and the size of the tunnel to the stability number. Such an equivalency does not hold for tunnels with ceilings of finite curvature. Not surprisingly, all measures of tunnel roof stability are strongly dependent on the Geological Strength Index that describes the quality of the rock.