Rough Sets Determined by Quasiorders

In this paper, the ordered set of rough sets determined by a quasiorder relation $R$ is investigated. We prove that this ordered set is a complete, completely distributive lattice. We show that on this lattice can be defined three different kinds of complementation operations, and we describe its completely join-irreducible elements. We also characterize the case in which this lattice is a Stone lattice. Our results generalize some results of J. Pomykala and J. A. Pomykala (1988) and M. Gehrke and E. Walker (1992) in case $R$ is an equivalence.Comment: 18 pages, major revisio

Fungal root endophyte associations of plants endemic to the Pamir Alay Mountains of Central Asia

The fungal root endophyte associations of 16 species from 12 families of plants endemic to the Pamir Alay Mountains of Central Asia are presented. The plants and soil samples were collected in Zeravshan and Hissar ranges within the central Pamir Alay mountain system. Colonization by arbuscular mycorrhizal fungi (AMF) was found in 15 plant species; in 8 species it was of the Arum type and in 4 of the Paris type, while 3 taxa revealed intermediate arbuscular mycorrhiza (AM) morphology. AMF colonization was found to be absent only in Matthiola integrifolia, the representative of the Brassicaceae family. The AM status and morphology are reported for the first time for all the species analyzed and for the genera Asyneuma, Clementsia, and Eremostachys. Mycelia of dark septate endophytes (DSE) accompanied the AMF colonization in ten plant species. The frequency of DSE occurrence in the roots was low in all the plants, with the exception of Spiraea baldschuanica. However, in the case of both low and higher occurrence, the percentage of DSE root colonization was low. Moreover, the sporangia of Olpidium spp. were sporadically found inside the root epidermal cells of three plant species. Seven AMF species (Glomeromycota) found in the trap cultures established with soils surrounding roots of the plants being studied were reported for the first time from this region of Asia. Our results provide information that might well be of use to the conservation and restoration programmes of these valuable plant species. The potential application of beneficial root-inhabiting fungi in active plant protection projects of rare, endemic and endangered plants is discussed

Monthly variation in the probability of presence of adult Culicoides populations in nine European countries and the implications for targeted surveillance

Background: Biting midges of the genus Culicoides (Diptera: Ceratopogonidae) are small hematophagous insects responsible for the transmission of bluetongue virus, Schmallenberg virus and African horse sickness virus to wild and domestic ruminants and equids. Outbreaks of these viruses have caused economic damage within the European Union. The spatio-temporal distribution of biting midges is a key factor in identifying areas with the potential for disease spread. The aim of this study was to identify and map areas of neglectable adult activity for each month in an average year. Average monthly risk maps can be used as a tool when allocating resources for surveillance and control programs within Europe. Methods : We modelled the occurrence of C. imicola and the Obsoletus and Pulicaris ensembles using existing entomological surveillance data from Spain, France, Germany, Switzerland, Austria, Denmark, Sweden, Norway and Poland. The monthly probability of each vector species and ensembles being present in Europe based on climatic and environmental input variables was estimated with the machine learning technique Random Forest. Subsequently, the monthly probability was classified into three classes: Absence, Presence and Uncertain status. These three classes are useful for mapping areas of no risk, areas of high-risk targeted for animal movement restrictions, and areas with an uncertain status that need active entomological surveillance to determine whether or not vectors are present. Results: The distribution of Culicoides species ensembles were in agreement with their previously reported distribution in Europe. The Random Forest models were very accurate in predicting the probability of presence for C. imicola (mean AUC = 0.95), less accurate for the Obsoletus ensemble (mean AUC = 0.84), while the lowest accuracy was found for the Pulicaris ensemble (mean AUC = 0.71). The most important environmental variables in the models were related to temperature and precipitation for all three groups. Conclusions: The duration periods with low or null adult activity can be derived from the associated monthly distribution maps, and it was also possible to identify and map areas with uncertain predictions. In the absence of ongoing vector surveillance, these maps can be used by veterinary authorities to classify areas as likely vector-free or as likely risk areas from southern Spain to northern Sweden with acceptable precision. The maps can also focus costly entomological surveillance to seasons and areas where the predictions and vector-free status remain uncertain

Stressed out symbiotes:hypotheses for the influence of abiotic stress on arbuscular mycorrhizal fungi

Abiotic stress is a widespread threat to both plant and soil communities. Arbuscular mycorrhizal (AM) fungi can alleviate effects of abiotic stress by improving host plant stress tolerance, but the direct effects of abiotic stress on AM fungi are less well understood. We propose two hypotheses predicting how AM fungi will respond to abiotic stress. The stress exclusion hypothesis predicts that AM fungal abundance and diversity will decrease with persistent abiotic stress. The mycorrhizal stress adaptation hypothesis predicts that AM fungi will evolve in response to abiotic stress to maintain their fitness. We conclude that abiotic stress can have effects on AM fungi independent of the effects on the host plant. AM fungal communities will change in composition in response to abiotic stress, which may mean the loss of important individual species. This could alter feedbacks to the plant community and beyond. AM fungi will adapt to abiotic stress independent of their host plant. The adaptation of AM fungi to abiotic stress should allow the maintenance of the plant-AM fungal mutualism in the face of changing climates. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s00442-016-3673-7) contains supplementary material, which is available to authorized users