Integrated crop pollination to buffer spatial and temporal variability in pollinator activity

Insect pollination improves the yield and quality of many crops, yet there is increasing evidence of insufficient insect pollinators limiting crop production. Effective Integrated Crop Pollination (ICP) involves adaptable, targeted and cost effective management of crop pollination and encourages the use of both wild and managed pollinators where appropriate. In this study we investigate how the addition of honeybee hives affects the community of insects visiting oilseed rape, and if hive number and location affect pollinator foraging and oilseed rape pollination in order to provide evidence for effective ICP. We found that introducing hives increased overall flower visitor numbers and altered the pollinator community, which became dominated by honeybees. Furthermore a greater number of hives did not increase bee numbers significantly but did result in honeybees foraging further into fields. The timing of surveys and proximity to the field edge influenced different pollinators in different ways and represents an example of spatial and temporal complementarity. For example dipteran flower visitor numbers declined away from the field edge whereas honeybees peaked at intermediate distances into the field. Furthermore, no significant effects of survey round on wild bees overall was observed but honeybee numbers were relatively lower during peak flowering and dipteran abundance was greater in later survey rounds. Thus combining diverse wild pollinators and managed species for crop pollination buffers spatial and temporal variation in flower visitation. However we found no effect of insect pollination on seed set or yield of oilseed rape in our trial, highlighting the critical need to understand crop demand for insect pollination before investments are made in managing pollination services

Ferromagnetic phase transition for the spanning-forest model (q \to 0 limit of the Potts model) in three or more dimensions

We present Monte Carlo simulations of the spanning-forest model (q \to 0 limit of the ferromagnetic Potts model) in spatial dimensions d=3,4,5. We show that, in contrast to the two-dimensional case, the model has a "ferromagnetic" second-order phase transition at a finite positive value w_c. We present numerical estimates of w_c and of the thermal and magnetic critical exponents. We conjecture that the upper critical dimension is 6.Comment: LaTex2e, 4 pages; includes 6 Postscript figures; Version 2 has expanded title as published in PR

Dynamic critical behavior of the Chayes-Machta-Swendsen-Wang algorithm

We study the dynamic critical behavior of the Chayes-Machta dynamics for the Fortuin-Kasteleyn random-cluster model, which generalizes the Swendsen-Wang dynamics for the q-state Potts model to noninteger q, in two and three spatial dimensions, by Monte Carlo simulation. We show that the Li-Sokal bound z \ge \alpha/\nu is close to but probably not sharp in d=2, and is far from sharp in d=3, for all q. The conjecture z \ge \beta/\nu is false (for some values of q) in both d=2 and d=3.Comment: Revtex4, 4 pages including 4 figure

Critical speeding-up in a local dynamics for the random-cluster model

We study the dynamic critical behavior of the local bond-update (Sweeny) dynamics for the Fortuin-Kasteleyn random-cluster model in dimensions d=2,3, by Monte Carlo simulation. We show that, for a suitable range of q values, the global observable S_2 exhibits "critical speeding-up": it decorrelates well on time scales much less than one sweep, so that the integrated autocorrelation time tends to zero as the critical point is approached. We also show that the dynamic critical exponent z_{exp} is very close (possibly equal) to the rigorous lower bound \alpha/\nu, and quite possibly smaller than the corresponding exponent for the Chayes-Machta-Swendsen-Wang cluster dynamics.Comment: LaTex2e/revtex4, 4 pages, includes 5 figure

Cluster simulations of loop models on two-dimensional lattices

We develop cluster algorithms for a broad class of loop models on two-dimensional lattices, including several standard O(n) loop models at n \ge 1. We show that our algorithm has little or no critical slowing-down when 1 \le n \le 2. We use this algorithm to investigate the honeycomb-lattice O(n) loop model, for which we determine several new critical exponents, and a square-lattice O(n) loop model, for which we obtain new information on the phase diagram.Comment: LaTex2e, 4 pages; includes 1 table and 2 figures. Totally rewritten in version 2, with new theory and new data. Version 3 as published in PR

Zero-free regions for multivariate Tutte polynomials (alias Potts-model partition functions) of graphs and matroids

The chromatic polynomial P_G(q) of a loopless graph G is known to be nonzero (with explicitly known sign) on the intervals (-\infty,0), (0,1) and (1,32/27]. Analogous theorems hold for the flow polynomial of bridgeless graphs and for the characteristic polynomial of loopless matroids. Here we exhibit all these results as special cases of more general theorems on real zero-free regions of the multivariate Tutte polynomial Z_G(q,v). The proofs are quite simple, and employ deletion-contraction together with parallel and series reduction. In particular, they shed light on the origin of the curious number 32/27.Comment: LaTeX2e, 49 pages, includes 5 Postscript figure

Absence of Phase Transition for Antiferromagnetic Potts Models via the Dobrushin Uniqueness Theorem

We prove that the $q$-state Potts antiferromagnet on a lattice of maximum coordination number $r$ exhibits exponential decay of correlations uniformly at all temperatures (including zero temperature) whenever $q > 2r$. We also prove slightly better bounds for several two-dimensional lattices: square lattice (exponential decay for $q \ge 7$), triangular lattice ($q \ge 11$), hexagonal lattice ($q \ge 4$), and Kagom\'e lattice ($q \ge 6$). The proofs are based on the Dobrushin uniqueness theorem.Comment: 32 pages including 3 figures. Self-unpacking file containing the tex file, the needed macros (epsf.sty, indent.sty, subeqnarray.sty, and eqsection.sty) and the 3 ps file

Assessing recovery from acidification of European surface waters in the year 2010: evaluation of projections made with the MAGIC model in 1995

In 1999 we used the MAGIC (Model of Acidification of Groundwater In Catchments) model to project acidification of acid-sensitive European surface waters in the year 2010, given implementation of the Gothenburg Protocol to the Convention on Long-Range Transboundary Air Pollution (LRTAP). A total of 202 sites in 10 regions in Europe were studied. These forecasts can now be compared with measurements for the year 2010, to give a “ground truth” evaluation of the model. The prerequisite for this test is that the actual sulfur and nitrogen deposition decreased from 1995 to 2010 by the same amount as that used to drive the model forecasts; this was largely the case for sulfur, but less so for nitrogen, and the simulated surface water [NO3–] reflected this difference. For most of the sites, predicted surface water recovery from acidification for the year 2010 is very close to the actual recovery observed from measured data, as recovery is predominantly driven by reductions in sulfur deposition. Overall these results show that MAGIC successfully predicts future water chemistry given known changes in acid deposition

Dynamic Critical Behavior of the Chayes-Machta Algorithm for the Random-Cluster Model. I. Two Dimensions

We study, via Monte Carlo simulation, the dynamic critical behavior of the Chayes-Machta dynamics for the Fortuin-Kasteleyn random-cluster model, which generalizes the Swendsen-Wang dynamics for the q-state Potts ferromagnet to non-integer q \ge 1. We consider spatial dimension d=2 and 1.25 \le q \le 4 in steps of 0.25, on lattices up to 1024^2, and obtain estimates for the dynamic critical exponent z_{CM}. We present evidence that when 1 \le q \lesssim 1.95 the Ossola-Sokal conjecture z_{CM} \ge \beta/\nu is violated, though we also present plausible fits compatible with this conjecture. We show that the Li-Sokal bound z_{CM} \ge \alpha/\nu is close to being sharp over the entire range 1 \le q \le 4, but is probably non-sharp by a power. As a byproduct of our work, we also obtain evidence concerning the corrections to scaling in static observables.Comment: LaTeX2e, 75 pages including 26 Postscript figure