3,261 research outputs found

    The paradox of the clumps mathematically explained

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    The lumpy distribution of species along a continuous one-dimensional niche axis recently found by Scheffer and van Nes (Scheffer and van Ness 2006) is explained mathematically. We show that it emerges simply from the eigenvalue and eigenvectors of the community matrix. Both the transient patterns—lumps and gaps between them—as well as the asymptotic equilibrium are explained. If the species are evenly distributed along the niche axis, the emergence of these patterns can be demonstrated analytically. The more general case, of randomly distributed species, shows only slight deviations and is illustrated by numerical simulation. This is a robust result whenever the finiteness of the niche is taken into account: it can be extended to different analytic dependence of the interaction coefficients with the distance on the niche axis (i.e., different kernel interactions), different boundary conditions, etc. We also found that there is a critical value both for the width of the species distribution s and the number of species n below which the clusterization disappear

    Resilience: Accounting for the Noncomputable

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    Plans to solve complex environmental problems should always consider the role of surprise. Nevertheless, there is a tendency to emphasize known computable aspects of a problem while neglecting aspects that are unknown and failing to ask questions about them. The tendency to ignore the noncomputable can be countered by considering a wide range of perspectives, encouraging transparency with regard to conflicting viewpoints, stimulating a diversity of models, and managing for the emergence of new syntheses that reorganize fragmentary knowledg

    A geometric condition implying energy equality for solutions of 3D Navier-Stokes equation

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    We prove that every weak solution uu to the 3D Navier-Stokes equation that belongs to the class L3L9/2L^3L^{9/2} and \n u belongs to L3L9/5L^3L^{9/5} localy away from a 1/2-H\"{o}lder continuous curve in time satisfies the generalized energy equality. In particular every such solution is suitable.Comment: 10 page

    Use of open-top chambers to study the effect of climate change in aquatic ecosystems

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    The aim of this research was to explore the possibility to use inexpensive open-top chambers (OTCs) as passive artificial warming devices in experimental aquatic studies. Our results show that OTCs give a significant temperature increase compared with the control. The measured increase (up to an average of 2.3°C) corresponds with predicted climatic warming. Due to their open top, the light quantity and quality is only minimally reduced. We found that OTCs are especially suited for studying the effect of climate change in small waters as the vertical temperature gradients remain unchanged. They can also easily be transported to remote environments. We discuss other advantages and disadvantages of these devices for aquatic studies and compare them with other warming devices

    Omnivory by planktivores stabilizes plankton dynamics, but may either promote or reduce algal biomass

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    Classical models of phytoplankton–zooplankton interaction show that with nutrient enrichment such systems may abruptly shift from limit cycles to stable phytoplankton domination due to zooplankton predation by planktivorous fish. Such models assume that planktivorous fish eat only zooplankton, but there are various species of filter-feeding fish that may also feed on phytoplankton. Here, we extend these classical models to systematically explore the effects of omnivory by planktivorous fish. Our analysis indicates that if fish forage on phytoplankton in addition to zooplankton, the alternative attractors predicted by the classical models disappear for all realistic parameter settings, even if omnivorous fish have a strong preference for zooplankton. Our model also shows that the level of fish biomass above which zooplankton collapse should be higher when fish are omnivorous than when fish are zooplanktivorous. We also used the model to explore the potential effects of the now increasingly common practice of stocking lakes with filter-feeding fish to control cyanobacteria. Because omnivorous filter-feeding fish forage on phytoplankton as well as on the main grazers of phytoplankton, the net effect of such fish on the phytoplankton biomass is not obvious. Our model suggests that there may be a unimodal relationship between the biomass of omnivorous filter-feeding fish and the biomass of phytoplankton. This implies that to manage for reductions in phytoplankton biomass, heavy stocking or strong reduction of such fish is bes

    Effects of submerged vegetation on water clarity across climates

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    A positive feedback between submerged vegetation and water clarity forms the backbone of the alternative state theory in shallow lakes. The water clearing effect of aquatic vegetation may be caused by different physical, chemical, and biological mechanisms and has been studied mainly in temperate lakes. Recent work suggests differences in biotic interactions between (sub)tropical and cooler lakes might result in a less pronounced clearing effect in the (sub)tropics. To assess whether the effect of submerged vegetation changes with climate, we sampled 83 lakes over a gradient ranging from the tundra to the tropics in South America. Judged from a comparison of water clarity inside and outside vegetation beds, the vegetation appeared to have a similar positive effect on the water clarity across all climatic regions studied. However, the local clearing effect of vegetation decreased steeply with the contribution of humic substances to the underwater light attenuation. Looking at turbidity on a whole-lake scale, results were more difficult to interpret. Although lakes with abundant vegetation (>30%) were generally clear, sparsely vegetated lakes differed widely in clarity. Overall, the effect of vegetation on water clarity in our lakes appears to be smaller than that found in various Northern hemisphere studies. This might be explained by differences in fish communities and their relation to vegetation. For instance, unlike in Northern hemisphere studies, we find no clear relation between vegetation coverage and fish abundance or their diet preference. High densities of omnivorous fish and coinciding low grazing pressures on phytoplankton in the (sub)tropics may, furthermore, weaken the effect of vegetation on water clarity