Anticoherence measures for pure spin states

The set of pure spin states with vanishing spin expectation value can be regarded as the set of the less coherent pure spin states. This set can be divided into a finite number of nested subsets on the basis of higher order moments of the spin operators. This subdivision relies on the notion of anticoherent spin state to order $t$: A spin state is said to be anticoherent to order $t$ if the moment of order $k$ of the spin components along any directions are equal for $k= 1, 2,\ldots, t$. Most spin states are neither coherent nor anticoherent, but can be arbitrary close to one or the other. In order to quantify the degree of anticoherence of pure spin states, we introduce the notion of anticoherence measures. By relying on the mapping between spin-$j$ states and symmetric states of $2j$ spin-$1/2$ (Majorana representation), we present a systematic way of constructing anticoherence measures to any order. We briefly discuss their connection with measures of quantum coherence. Finally, we illustrate our measures on various spin states and use them to investigate the problem of the existence of anticoherent spin states with degenerated Majorana points

Anticoherence of spin states with point group symmetries

We investigate multiqubit permutation-symmetric states with maximal entropy of entanglement. Such states can be viewed as particular spin states, namely anticoherent spin states. Using the Majorana representation of spin states in terms of points on the unit sphere, we analyze the consequences of a point-group symmetry in their arrangement on the quantum properties of the corresponding state. We focus on the identification of anticoherent states (for which all reduced density matrices in the symmetric subspace are maximally mixed) associated with point-group symmetric sets of points. We provide three different characterizations of anticoherence, and establish a link between point symmetries, anticoherence and classes of states equivalent through stochastic local operations with classical communication (SLOCC). We then investigate in detail the case of small numbers of qubits, and construct infinite families of anticoherent states with point-group symmetry of their Majorana points, showing that anticoherent states do exist to arbitrary order.Comment: 15 pages, 5 figure

Tensor Representation of Spin States

We propose a generalization of the Bloch sphere representation for arbitrary spin states. It provides a compact and elegant representation of spin density matrices in terms of tensors that share the most important properties of Bloch vectors. Our representation, based on covariant matrices introduced by Weinberg in the context of quantum field theory, allows for a simple parametrization of coherent spin states, and a straightforward transformation of density matrices under local unitary and partial tracing operations. It enables us to provide a criterion for anticoherence, relevant in a broader context such as quantum polarization of light.Comment: 5 pages + 7 pages of supplementary informatio

Effects of individual and population parameters on reproductive success in three sexually deceptive orchid species

Reproductive success (RS) in orchids in general, and in non-rewarding species specifically, is extremely low. RS is pollinator and pollination limited in food deceptive orchids, but this has rarely been studied in sexually deceptive orchid species. Here, we tested the effects of several individual (plant height, inflorescence size, nearest neighbour distance and flower position) and population (patch geometry, population density and size) parameters on RS in three sexually deceptive Ophrys (Orchidaceae) species. Inter-specific differences were observed in RS of flowers situated in the upper versus the lower part of the inflorescence, likely due to species-specific pollinator behaviour. For all three species examined, RS increased with increasing plant height, inflorescence size and nearest neighbour distance. RS generally increased with decreasing population density and increasing patch elongation. Given these results, we postulate that pollinator availability, rather than pollinator learning, is the most limiting factor in successful reproduction for sexually deceptive orchids. Our results also suggest that olfactory ‘display’ (i.e. versus optical display), in terms of inflorescence size (and covarying plant height), plays a key role in individual RS of sexually deceptive orchids. In this regard, several hypotheses are suggested and discusse

A stochastic movement simulator improves estimates of landscape connectivity

Acknowledgments This publication issued from the project TenLamas funded by the French Ministère de l'Energie, de l'Ecologie, du Développement Durable et de la Mer through the EU FP6 BiodivERsA Eranet; by the Agence Nationale de la Recherche (ANR) through the open call INDHET and 6th extinction MOBIGEN to V. M. Stevens, M. Baguette, and A. Coulon, and young researcher GEMS (ANR-13-JSV7-0010-01) to V. M. Stevens and M. Baguette; and by a VLIR-VLADOC scholarship awarded to J. Aben. L. Lens, J. Aben, D. Strubbe, and E. Matthysen are grateful to the Research Foundation Flanders (FWO) for financial support of fieldwork and genetic analysis (grant G.0308.13). V. M. Stevens and M. Baguette are members of the “Laboratoire d'Excellence” (LABEX) entitled TULIP (ANR-10-LABX-41). J. M. J. Travis and S. C. F. Palmer also acknowledge the support of NERC. A. Coulon and J. Aben contributed equally to the work.Peer reviewedPublisher PD

Variation within and between Closely Related Species Uncovers High Intra-Specific Variability in Dispersal

Mounting evidence shows that contrasting selection pressures generate variability in dispersal patterns among individuals or populations of the same species, with potential impacts on both species dynamics and evolution. However, this variability is hardly considered in empirical works, where a single dispersal function is considered to adequately reflect the species-specific dispersal ability, suggesting thereby that within-species variation is negligible as regard to inter-specific differences in dispersal abilities. We propose here an original method to make the comparison of intra- and inter-specific variability in dispersal, by decomposing the diversity of that trait along a phylogeny of closely related species. We used as test group European butterflies that are classic study organisms in spatial ecology. We apply the analysis separately to eight metrics that reflect the dispersal propensity, the dispersal ability or the dispersal efficiency of populations and species. At the inter-specific level, only the dispersal ability showed the signature of a phylogenetic signal while neither the dispersal propensity nor the dispersal efficiency did. At the within-species level, the partitioning of dispersal diversity showed that dispersal was variable or highly variable among populations: intra-specific variability represented from 11% to 133% of inter-specific variability in dispersal metrics. This finding shows that dispersal variation is far from negligible in the wild. Understanding the processes behind this high within-species variation should allow us to properly account for dispersal in demographic models. Accordingly, to encompass the within species variability in life histories the use of more than one value per trait per species should be encouraged in the construction of databases aiming at being sources for modelling purposes

Monitoring frequency influences the analysis of resting behaviour in a forest carnivore

Resting sites are key structures for many mammalian species, which can affect reproduction, survival, population density, and even species persistence in human-modified landscapes. As a consequence, an increasing number of studies has estimated patterns of resting site use by mammals, as well as the processes underlying these patterns, though the impact of sampling design on such estimates remain poorly understood. Here we address this issue empirically, based on data from 21 common genets radiotracked during 28 months in Mediterranean forest landscapes. Daily radiotracking data was thinned to simulate every other day and weekly monitoring frequencies, and then used to evaluate the impact of sampling regime on estimates of resting site use. Results showed that lower monitoring frequencies were associated with major underestimates of the average number of resting sites per animal, and of site reuse rates and sharing frequency, though no effect was detected on the percentage use of resting site types. Monitoring frequency also had a major impact on estimates of environmental effects on resting site selection, with decreasing monitoring frequencies resulting in higher model uncertainty and reduced power to identify significant explanatory variables. Our results suggest that variation in monitoring frequency may have had a strong impact on intra- and interspecific differences in resting site use patterns detected in previous studies. Given the errors and uncertainties associated with low monitoring frequencies, we recommend that daily or at least every other day monitoring should be used whenever possible in studies estimating resting site use patterns by mammals

A bird’s eye view: using circuit theory to study urban landscape connectivity for birds

Context Connectivity is fundamental to understanding how landscape form influences ecological function. However, uncertainties persist due to the difficulty and expense of gathering empirical data to drive or to validate connectivity models, especially in urban areas, where relationships are multifaceted and the habitat matrix cannot be considered to be binary. Objectives This research used circuit theory to model urban bird flows (i.e. ‘current’), and compared results to observed abundance. The aims were to explore the ability of this approach to predict wildlife flows and to test relationships between modelled connectivity and variation in abundance. Methods Circuitscape was used to model functional connectivity in Bedford, Luton/Dunstable, and Milton Keynes, UK, for great tits (Parus major) and blue tits (Cyanistes caeruleus), drawing parameters from published studies of woodland bird flows in urban environments. Model performance was then tested against observed abundance data. Results Modelled current showed a weak yet positive agreement with combined abundance for P. major and C. caeruleus. Weaker correlations were found for other woodland species, suggesting the approach may be expandable if re-parameterised. Conclusions Trees provide suitable habitat for urban woodland bird species, but their location in large, contiguous patches and corridors along barriers also facilitates connectivity networks throughout the urban matrix. Urban connectivity studies are well-served by the advantages of circuit theory approaches, and benefit from the empirical study of wildlife flows in these landscapes to parameterise this type of modelling more explicitly. Such results can prove informative and beneficial in designing urban green space and new developments

Demography and Dispersal Ability of a Threatened Saproxylic Beetle: A Mark-Recapture Study of the Rosalia Longicorn (Rosalia alpina)

The Rosalia longicorn or Alpine longhorn (Coleoptera: Cerambycidae) is an endangered and strictly protected icon of European saproxylic biodiversity. Despite its popularity, lack of information on its demography and mobility may compromise adoption of suitable conservation strategies. The beetle experienced marked retreat from NW part of its range; its single population survives N of the Alps and W of the Carpathians. The population inhabits several small patches of old beech forest on hill-tops of the Ralska Upland, Czech Republic. We performed mark-recapture study of the population and assessed its distribution pattern. Our results demonstrate the high mobility of the beetle, including dispersal between hills (up to 1.6 km). The system is thus interconnected; it contained ∼2000 adult beetles in 2008. Estimated population densities were high, ranging between 42 and 84 adult beetles/hectare a year. The population survives at a former military-training ground despite long-term isolation and low cover of mature beech forest (∼1%). Its survival could be attributed to lack of forestry activities between the 1950s and 1990s, slow succession preventing canopy closure and undergrowth expansion, and probably also to the distribution of habitat patches on conspicuous hill-tops. In order to increase chances of the population for long term survival, we propose to stop clear-cuts of old beech forests, increase semi-open beech woodlands in areas currently covered by conifer plantations and active habitat management at inhabited sites and their wider environs