Modulated structures in electroconvection in nematic liquid crystals

Motivated by experiments in electroconvection in nematic liquid crystals with homeotropic alignment we study the coupled amplitude equations describing the formation of a stationary roll pattern in the presence of a weakly-damped mode that breaks isotropy. The equations can be generalized to describe the planarly aligned case if the orienting effect of the boundaries is small, which can be achieved by a destabilizing magnetic field. The slow mode represents the in-plane director at the center of the cell. The simplest uniform states are normal rolls which may undergo a pitchfork bifurcation to abnormal rolls with a misaligned in-plane director.We present a new class of defect-free solutions with spatial modulations perpendicular to the rolls. In a parameter range where the zig-zag instability is not relevant these solutions are stable attractors, as observed in experiments. We also present two-dimensionally modulated states with and without defects which result from the destabilization of the one-dimensionally modulated structures. Finally, for no (or very small) damping, and away from the rotationally symmetric case, we find static chevrons made up of a periodic arrangement of defect chains (or bands of defects) separating homogeneous regions of oblique rolls with very small amplitude. These states may provide a model for a class of poorly understood stationary structures observed in various highly-conducting materials ("prechevrons" or "broad domains").Comment: 13 pages, 13 figure

An explanatory model for food-web structure and evolution

Food webs are networks describing who is eating whom in an ecological community. By now it is clear that many aspects of food-web structure are reproducible across diverse habitats, yet little is known about the driving force behind this structure. Evolutionary and population dynamical mechanisms have been considered. We propose a model for the evolutionary dynamics of food-web topology and show that it accurately reproduces observed food-web characteristic in the steady state. It is based on the observation that most consumers are larger than their resource species and the hypothesis that speciation and extinction rates decrease with increasing body mass. Results give strong support to the evolutionary hypothesis.Comment: 16 pages, 3 figure

Some Properties of the Speciation Model for Food-Web Structure - Mechanisms for Degree Distributions and Intervality

We present a mathematical analysis of the speciation model for food-web structure, which had in previous work been shown to yield a good description of empirical data of food-web topology. The degree distributions of the network are derived. Properties of the speciation model are compared to those of other models that successfully describe empirical data. It is argued that the speciation model unifies the underlying ideas of previous theories. In particular, it offers a mechanistic explanation for the success of the niche model of Williams and Martinez and the frequent observation of intervality in empirical food webs.Comment: 23 pages, 6 figures, minor rewrite

A general framework for combining ecosystem models

When making predictions about ecosystems, we often have available a number of different ecosystem models that attempt to represent their dynamics in a detailed mechanistic way. Each of these can be used as a simulator of large-scale experiments and make projections about the fate of ecosystems under different scenarios to support the development of appropriate management strategies. However, structural differences, systematic discrepancies and uncertainties lead to different models giving different predictions. This is further complicated by the fact that the models may not be run with the same functional groups, spatial structure or time scale. Rather than simply trying to select a “best” model, or taking some weighted average, it is important to exploit the strengths of each of the models, while learning from the differences between them. To achieve this, we construct a flexible statistical model of the relationships between a collection of mechanistic models and their biases, allowing for structural and parameter uncertainty and for different ways of representing reality. Using this statistical meta-model, we can combine prior beliefs, model estimates and direct observations using Bayesian methods and make coherent predictions of future outcomes under different scenarios with robust measures of uncertainty. In this study, we take a diverse ensemble of existing North Sea ecosystem models and demonstrate the utility of our framework by applying it to answer the question what would have happened to demersal fish if fishing was to stop

How trophic interaction strength depends on traits: A conceptual framework for representing multidimensional trophic niche spaces

A key problem in community ecology is to understand how individual-level traits give rise to population-level trophic interactions. Here, we propose a synthetic framework based on ecological considerations to address this question systematically. We derive a general functional form for the dependence of trophic interaction coefficients on trophically relevant quantitative traits of consumers and resources. The derived expression encompasses-and thus allows a unified comparison of-several functional forms previously proposed in the literature. Furthermore, we show how a community's, potentially low-dimensional, effective trophic niche space is related to its higher-dimensional phenotypic trait space. In this manner, we give ecological meaning to the notion of the "dimensionality of trophic niche space." Our framework implies a method for directly measuring this dimensionality. We suggest a procedure for estimating the relevant parameters from empirical data and for verifying that such data matches the assumptions underlying our derivation

How trophic interaction strength depends on traits: A conceptual framework for representing multidimensional trophic niche spaces

A key problem in community ecology is to understand how individual-level traits give rise to population-level trophic interactions. Here, we propose a synthetic framework based on ecological considerations to address this question systematically. We derive a general functional form for the dependence of trophic interaction coefficients on trophically relevant quantitative traits of consumers and resources. The derived expression encompasses-and thus allows a unified comparison of-several functional forms previously proposed in the literature. Furthermore, we show how a community's, potentially low-dimensional, effective trophic niche space is related to its higher-dimensional phenotypic trait space. In this manner, we give ecological meaning to the notion of the "dimensionality of trophic niche space." Our framework implies a method for directly measuring this dimensionality. We suggest a procedure for estimating the relevant parameters from empirical data and for verifying that such data matches the assumptions underlying our derivation

Electroconvection in a homeotropic bent-rod nematic liquid crystal beyond the dielectric inversion frequency

We characterize the structural transitions in an initially homeotropic bent-rod nematic liquid crystal excited by ac fields of frequency/well above the dielectric inversion point fi. From the measured principal dielectric constants and electrical conductivities of the compound, the Can-Helfrich conduction regime is anticipated to extend into the sub-megahertz region. Periodic patterned states occur through secondary bifurcations from the Freedericksz distorted state. An anchoring transition between the bend Freedericksz (BF) and degenerate planar (DP) states is detected. The BF state is metastable well above the Freedericksz threshold and gives way to the DP state, which persists in the field-off condition for several hours. Numerous +1 and -1 umbilics form at the onset of BF distortion, the former being largely of the chiral type. They survive in the DP configuration as linear defects, nonsingular in the core. In the BF regime, not far from fi, periodic Williams-like domains form around the umbilics; they drift along the director easy axis right from their onset. With increasing fi, the wave vector of the periodic domains switches from parallel to normal disposition with respect to the c vector. Well above fi, a broadband instability is found

Food web indicators under the Marine Strategy Framework Directive: From complexity to simplicity?

International audienceThe Marine Strategy Framework Directive (MSFD) requires that European Union Member States achieve "Good Environmental Status" (GES) in respect of 11 Descriptors of the marine environment by 2020. Of those, Descriptor 4, which focuses on marine food webs, is perhaps the most challenging to implement since the identification of simple indicators able to assess the health of highly dynamic and complex interactions is difficult. Here, we present the proposed food web criteria/indicators and analyse their theoretical background and applicability in order to highlight both the current knowledge gaps and the difficulties associated with the assessment of GES. We conclude that the existing suite of indicators gives variable focus to the three important food web properties: structure, functioning and dynamics, and more emphasis should be given to the latter two and the general principles that relate these three properties. The development of food web indicators should be directed towards more integrative and process-based indicators with an emphasis on their responsiveness to multiple anthropogenic pressures. © 2013 Elsevier Ltd

Distributional (In)Congruence of Biodiversity-Ecosystem Functioning

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