Phase transition for cutting-plane approach to vertex-cover problem

We study the vertex-cover problem which is an NP-hard optimization problem and a prototypical model exhibiting phase transitions on random graphs, e.g., Erdoes-Renyi (ER) random graphs. These phase transitions coincide with changes of the solution space structure, e.g, for the ER ensemble at connectivity c=e=2.7183 from replica symmetric to replica-symmetry broken. For the vertex-cover problem, also the typical complexity of exact branch-and-bound algorithms, which proceed by exploring the landscape of feasible configurations, change close to this phase transition from "easy" to "hard". In this work, we consider an algorithm which has a completely different strategy: The problem is mapped onto a linear programming problem augmented by a cutting-plane approach, hence the algorithm operates in a space OUTSIDE the space of feasible configurations until the final step, where a solution is found. Here we show that this type of algorithm also exhibits an "easy-hard" transition around c=e, which strongly indicates that the typical hardness of a problem is fundamental to the problem and not due to a specific representation of the problem.Comment: 4 pages, 3 figure

Effects of patch size and density on flower visitation and seed set of wild plants: a pan-European approach

1. Habitat fragmentation can affect pollinator and plant population structure in terms of species composition, abundance, area covered and density of flowering plants. This, in turn, may affect pollinator visitation frequency, pollen deposition, seed set and plant fitness. 2. A reduction in the quantity of flower visits can be coupled with a reduction in the quality of pollination service and hence the plants’ overall reproductive success and long-term survival. Understanding the relationship between plant population size and⁄ or isolation and pollination limitation is of fundamental importance for plant conservation. 3. Weexamined flower visitation and seed set of 10 different plant species fromfive European countries to investigate the general effects of plant populations size and density, both within (patch level) and between populations (population level), on seed set and pollination limitation. 4. Wefound evidence that the effects of area and density of flowering plant assemblages were generally more pronounced at the patch level than at the population level. We also found that patch and population level together influenced flower visitation and seed set, and the latter increased with increasing patch area and density, but this effect was only apparent in small populations. 5. Synthesis. By using an extensive pan-European data set on flower visitation and seed set we have identified a general pattern in the interplay between the attractiveness of flowering plant patches for pollinators and density dependence of flower visitation, and also a strong plant species-specific response to habitat fragmentation effects. This can guide efforts to conserve plant–pollinator interactions, ecosystem functioning and plant fitness in fragmented habitats

Interactive Effects of Large- and Small-Scale Sources of Feral Honey-Bees for Sunflower in the Argentine Pampas

Pollinators for animal pollinated crops can be provided by natural and semi-natural habitats, ranging from large vegetation remnants to small areas of non-crop land in an otherwise highly modified landscape. It is unknown, however, how different small- and large-scale habitat patches interact as pollinator sources. In the intensively managed Argentine Pampas, we studied the additive and interactive effects of large expanses (up to 2200 ha) of natural habitat, represented by untilled isolated “sierras”, and narrow (3–7 m wide) strips of semi-natural habitat, represented by field margins, as pollinator sources for sunflower (Helianthus annus). We estimated visitation rates by feral honey-bees, Apis mellifera, and native flower visitors (as a group) at 1, 5, 25, 50 and 100 m from a field margin in 17 sunflower fields 0–10 km distant from the nearest sierra. Honey-bees dominated the pollinator assemblage accounting for >90% of all visits to sunflower inflorescences. Honey-bee visitation was strongly affected by proximity to the sierras decreasing by about 70% in the most isolated fields. There was also a decline in honey-bee visitation with distance from the field margin, which was apparent with increasing field isolation, but undetected in fields nearby large expanses of natural habitat. The probability of observing a native visitor decreased with isolation from the sierras, but in other respects visitation by flower visitors other than honey-bees was mostly unaffected by the habitat factors assessed in this study. Overall, we found strong hierarchical and interactive effects between the study large and small-scale pollinator sources. These results emphasize the importance of preserving natural habitats and managing actively field verges in the absence of large remnants of natural habitat for improving pollinator services

Enhancing soil organic matter as a route to the ecological intensification of European arable systems

Soil organic matter (SOM) is declining in most agricultural ecosystems, impacting on multiple ecosystem services including erosion and flood prevention, climate and greenhouse gas regulation as well as other services which underpin crop production, such as nutrient cycling and pest control. Ecological intensification aims to enhance crop productivity, by including regulating and supporting ecosystem services management into agricultural practices. We investigate the potential for increased SOM to support the ecological intensification of arable systems by reducing the need for nitrogen fertiliser application and pest control. Using a large-scale European field trial implemented across 84 fields in 5 countries we tested whether increased SOM (using soil organic carbon as a proxy) helps recover yield in the absence of conventional nitrogen fertiliser and whether this also supports crops less favourable to key aphid pests. Greater SOM increased yield by 10%, but did not offset nitrogen fertiliser application entirely, which improved yield by 30%. Crop pest responses depended on species: Metopolophium dirhodum were more abundant in fertilised plots with high crop biomass, and although population growth rates of Sitobion avenae were enhanced by nitrogen fertiliser application in a cage trial, field populations were not affected. We conclude that under increased SOM and reduced fertilizer application, pest pressure can be reduced, while partially compensating for yield deficits linked to fertiliser reduction. If the benefits of reduced fertiliser application and increased SOM are considered in a wider environmental context, then a yield cost may become acceptable. Maintaining or increasing SOM is critical for achieving ecological intensification of European cereal production

Honey bee foraging distance depends on month and forage type

To investigate the distances at which honey bee foragers collect nectar and pollen, we analysed 5,484 decoded waggle dances made to natural forage sites to determine monthly foraging distance for each forage type. Firstly, we found significantly fewer overall dances made for pollen (16.8 %) than for non-pollen, presumably nectar (83.2 %; P < 2.2 × 10−23). When we analysed distance against month and forage type, there was a significant interaction between the two factors, which demonstrates that in some months, one forage type is collected at farther distances, but this would reverse in other months. Overall, these data suggest that distance, as a proxy for forage availability, is not significantly and consistently driven by need for one type of forage over the other

The costs and benefits of pollinator dependence: empirically based simulations predict raspberry fruit quality

Globally, agriculture increasingly depends on pollinators to produce many seed and fruit crops. However, what constitutes optimal pollination service for pollinator-dependent crops remains unanswered. We developed a simulation model to identify the optimal pollination service that maximizes fruit quality in crops. The model depicts the pollination (i.e., autonomous self-fertilization, pollen deposition) and post-pollination (i.e., pollen germination, and time from germination to ovule fertilization) processes leading to fruit and seed set and allows for negative flower–pollinator interactions, specifically pistil damage. We parameterized and validated the model based on empirical observations of commercial raspberry in western Argentina. To assess the effects of pollination intensity for fruit production, we conducted simulations over a range of visit number per flower by the two primary managed pollinators worldwide, Apis mellifera and Bombus terrestris. Simulations identified that ~15–35 visits per flower by A. mellifera or ~10–20 visits by B. terrestris provide adequate pollination and maximize raspberry fruit quality (i.e., estimated as the proportion of ovules that develop into drupelets). Visits in excess of these optima reduce simulated fruit quality, and flowers receiving >670 honey bee visits or >470 bumble bee visits would produce fruits of poorer quality than those receiving no bee visits. The simulations generated consistent, unbiased predictions of fruit quality for 12 raspberry fields. This model could be adapted easily to other animal-pollinated crops and used to guide efficient pollinator management in any agro-ecosystem.Fil: Sáez, Agustín. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte. Instituto de Investigaciones en Biodiversidad y Medioambiente. Universidad Nacional del Comahue. Centro Regional Universidad Bariloche. Instituto de Investigaciones en Biodiversidad y Medioambiente; ArgentinaFil: Morales, Juan Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte. Instituto de Investigaciones en Biodiversidad y Medioambiente. Universidad Nacional del Comahue. Centro Regional Universidad Bariloche. Instituto de Investigaciones en Biodiversidad y Medioambiente; ArgentinaFil: Morales, Carolina Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte. Instituto de Investigaciones en Biodiversidad y Medioambiente. Universidad Nacional del Comahue. Centro Regional Universidad Bariloche. Instituto de Investigaciones en Biodiversidad y Medioambiente; ArgentinaFil: Harder, Lawrence D.. University of Calgary. Departament of Biological Sciences; CanadáFil: Aizen, Marcelo Adrian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte. Instituto de Investigaciones en Biodiversidad y Medioambiente. Universidad Nacional del Comahue. Centro Regional Universidad Bariloche. Instituto de Investigaciones en Biodiversidad y Medioambiente; Argentin

An integrative environmental pollen diversity assessment and its importance for the Sustainable Development Goals

Pollen is at once intimately part of the reproductive cycle of seed plants and simultaneously highly relevant for the environment (pollinators, vector for nutrients, or organisms), people (food safety and health), and climate (cloud condensation nuclei and climate reconstruction). We provide an interdisciplinary perspective on the many and connected roles of pollen to foster a better integration of the currently disparate fields of pollen research, which would benefit from the sharing of general knowledge, technical advancements, or data processing solutions. We propose a more interdisciplinary and holistic research approach that encompasses total environmental pollen diversity (ePD) (wind and animal and occasionally water distributed pollen) at multiple levels of diversity (genotypic, phenotypic, physiological, chemical, and functional) across space and time. This interdisciplinary approach holds the potential to contribute to pressing human issues, including addressing United Nations Sustainable Development Goals, fostering social and political awareness of these tiny yet important and fascinating particles