Significance: Agricultural landscape homogenization is a major ongoing threat to biodiversity and the delivery of key ecosystem services for human well-being. It is well known that increasing the amount of seminatural cover in agricultural landscapes has a positive effect on biodiversity. However, little is known about the role of the crop mosaic itself. Crop heterogeneity in the landscape had a much stronger effect on multitrophic diversity than the amount of seminatural cover in the landscape, across 435 agricultural landscapes located in 8 European and North American regions. Increasing crop heterogeneity can be an effective way to mitigate the impacts of farming on biodiversity without taking land out of production.

The upper and lower approximations of a fuzzy subset with respect to an indistinguish-ability operator are studied. Their relations with fuzzy rough sets are also investigated.

Summary: Weedy plants pose a major threat to food security, biodiversity, ecosystem services and consequently to human health and wellbeing. However, many currently used weed management approaches are increasingly unsustainable. To address this knowledge and practice gap, in June 2014, 35 weed and invasion ecologists, weed scientists, evolutionary biologists and social scientists convened a workshop to explore current and future perspectives and approaches in weed ecology and management. A horizon scanning exercise ranked a list of 124 pre‐submitted questions to identify a priority list of 30 questions. These questions are discussed under seven themed headings that represent areas for renewed and emerging focus for the disciplines of weed research and practice. The themed areas considered the need for transdisciplinarity, increased adoption of integrated weed management and agroecological approaches, better understanding of weed evolution, climate change, weed invasiveness and finally, disciplinary challenges for weed science. Almost all the challenges identified rested on the need for continued efforts to diversify and integrate agroecological, socio‐economic and technological approaches in weed management. These challenges are not newly conceived, though their continued prominence as research priorities highlights an ongoing intransigence that must be addressed through a more system‐oriented and transdisciplinary research agenda that seeks an embedded integration of public and private research approaches. This horizon scanning exercise thus set out the building blocks needed for future weed management research and practice; however, the challenge ahead is to identify effective ways in which sufficient research and implementation efforts can be directed towards these needs.

1 Agricultural intensification can cause a huge increase in productivity. However, associated costs in terms of reduced, self-regulation and increased reliance on external inputs for the control of pests, diseases and weeds are seldom taken into account or acknowledged. A pro-active approach in which ecosystems services are documented and potential effects of changes in agricultural practices evaluated may lead to more informed decisions prior to implementation. 2 We investigated the effects of management of cereal production in a semi-arid region on weed seed mortality caused by predators. Seed losses have a greater impact on weed population size than any other life cycle process and should therefore be of significance for natural weed control. We hypothesized that the conversion from rain-fed to irrigated production should lead to reduced and the adoption of no-till techniques to increased seed predation. 3 Seed removal and seed predator populations were monitored in irrigated (N= 3) and rain-fed cereal fields (N= 6) and field margins. Of the dryland fields half was conventionally tilled and the other half no-till. Seed removal (g g⁻¹ 2-days⁻¹) was followed from April 2007 until June 2008, using Petri-dishes and exclosure cages. Populations of harvester ants were estimated by direct nest counts; rodent populations by Sherman live traps. 4 Seed removal in dryland cereals, mainly by harvester ants Messor barbarus was high from mid April to mid October, and should cause a strong weed suppressive effect. Seed removal in irrigated cereals, mainly by granivorous rodents Mus spretus, was low. 5 Seed removal was higher in no-till than in conventional fields and corresponded to differences in harvester ant nest densities. 6 Synthesis and applications. Our results show that tillage and irrigation in a semi-arid cereal production system results in a reduction and total annihilation of granivorous harvester ants, respectively. The concurrent decline in weed seed mortality could lead to increased herbicide use and dependency. In particular, in areas where economic margins are small or the environmental costs of tillage and irrigation high, the increased costs of chemical weed control may exceed the benefits. Here, preserving biodiversity to enhance natural weed control is a viable alternative to agricultural intensification.

Increasing landscape heterogeneity by restoring semi‐natural elements to reverse farmland biodiversity declines is not always economically feasible or acceptable to farmers due to competition for land. We hypothesized that increasing the heterogeneity of the crop mosaic itself, hereafter referred to as crop heterogeneity, can have beneficial effects on within‐field plant diversity. Using a unique multi‐country dataset from a cross‐continent collaborative project covering 1,451 agricultural fields within 432 landscapes in Europe and Canada, we assessed the relative effects of compositional and configurational crop heterogeneity on within‐field plant diversity components. We also examined how these relationships were modulated by the position within the field. We found strong positive effects of configurational crop heterogeneity on within‐field plant alpha and gamma diversity in field interiors. These effects were as high as the effect of semi‐natural cover. In field borders, effects of crop heterogeneity were limited to alpha diversity. We suggest that a heterogeneous crop mosaic may overcome the high negative impact of management practices on plant diversity in field interiors, whereas in field borders, where plant diversity is already high, landscape effects are more limited. Synthesis and applications. Our study shows that increasing configurational crop heterogeneity is beneficial to within‐field plant diversity. It opens up a new effective and complementary way to promote farmland biodiversity without taking land out of agricultural production. We therefore recommend adopting manipulation of crop heterogeneity as a specific, effective management option in future policy measures, perhaps adding to agri‐environment schemes, to contribute to the conservation of farmland plant diversity.