A spatially explicit model for competition among specialists and generalists in a heterogeneous environment

Competition is a major force in structuring ecological communities. The strength of competition can be measured using the concept of a niche. A niche comprises the set of requirements of an organism in terms of habitat, environment and functional role. The more niches overlap, the stronger competition is. The niche breadth is a measure of specialization: the smaller the niche space of an organism, the more specialized the organism is. It follows that, everything else being equal, generalists tend to be more competitive than specialists. In this paper, we compare the outcome of competition among generalists and specialists in a spatial versus a nonspatial habitat in a heterogeneous environment. Generalists can utilize the entire habitat, whereas specialists are restricted to their preferred habitat type. We find that although competitiveness decreases with specialization, specialists are more competitive in a spatial than in a nonspatial habitat as patchiness increases.Comment: Published at http://dx.doi.org/10.1214/105051606000000394 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Spatially explicit non-Mendelian diploid model

We introduce a spatially explicit model for the competition between type $a$ and type $b$ alleles. Each vertex of the $d$-dimensional integer lattice is occupied by a diploid individual, which is in one of three possible states or genotypes: $aa$, $ab$ or $bb$. We are interested in the long-term behavior of the gene frequencies when Mendel's law of segregation does not hold. This results in a voter type model depending on four parameters; each of these parameters measures the strength of competition between genes during meiosis. We prove that with or without a spatial structure, type $a$ and type $b$ alleles coexist at equilibrium when homozygotes are poor competitors. The inclusion of a spatial structure, however, reduces the parameter region where coexistence occurs.Comment: Published in at http://dx.doi.org/10.1214/09-AAP598 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Stochastic spatial models of host-pathogen and host-mutualist interactions I

Mutualists and pathogens, collectively called symbionts, are ubiquitous in plant communities. While some symbionts are highly host-specific, others associate with multiple hosts. The outcomes of multispecies host-symbiont interactions with different degrees of specificity are difficult to predict at this point due to a lack of a general conceptual framework. Complicating our predictive power is the fact that plant populations are spatially explicit, and we know from past research that explicit space can profoundly alter plant-plant interactions. We introduce a spatially explicit, stochastic model to investigate the role of explicit space and host-specificity in multispecies host-symbiont interactions. We find that in our model, pathogens can significantly alter the spatial structure of plant communities, promoting coexistence, whereas mutualists appear to have only a limited effect. Effects are more pronounced the more host-specific symbionts are.Comment: Published at http://dx.doi.org/10.1214/105051605000000782 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Maullinia braseltonii sp. nov. (Rhizaria, Phytomyxea, Phagomyxida) : A Cyst-forming Parasite of the Bull Kelp Durvillaea spp. (Stramenopila, Phaeophyceae, Fucales)

Help in biomass collection by David J. Patiño (UACh), Liliana A. Muñoz (University of Aberdeen (UoA)) and Alexandra Mystikou (South Atlantic Environmental Research Institute & UoA), and in conducting electron microscopy by Gillian Milne (Aberdeen Microscopy Facility) is acknowledged. Thanks are due to the three anonymous reviewers, whose comments helped to improve the earlier version of this manuscript. PM was funded by Conicyt (BecasChile N° 72130422) for PhD studies at the University of Aberdeen, and by the NERC IOF Pump-priming (scheme NE/L013223/1) for activities at the Scottish Association for Marine Sciences. RW thanks financial support from Gobierno Regional de Los Lagos (projects FIC 2012 E7259-2 and FIC 2013 BIP30234872-0) and Fondef, Conicyt (HUAM AQ12I0010), which allows the sampling expeditions at Chiloe Island by David J. Patiño, Liliana Muñoz and PM. SN was funded by the Austrian Science Fund (FWF): grant J3175-B20 (Erwin Schrödinger Fellowship) and grant Y801-B16 (START-grant). PvW is supported by the UoA, BBSRC and NERC. Also, the MASTS pooling initiative (Marine Alliance for Science and Technology for Scotland, funded by the Scottish Funding Council and contributing institutions; grant reference HR09011) is gratefully acknowledged for its support to FCK. Finally, we would like to thank the UoA, Shackleton Fund (FCK) and the John Cheek Fund (FCK) for supporting the expeditions of Alexandra Mystikou, PvW and FCK to the Falkland Islands.Peer reviewedPublisher PD

Error-resistant Single Qubit Gates with Trapped Ions

Coherent operations constitutive for the implementation of single and multi-qubit quantum gates with trapped ions are demonstrated that are robust against variations in experimental parameters and intrinsically indeterministic system parameters. In particular, pulses developed using optimal control theory are demonstrated for the first time with trapped ions. Their performance as a function of error parameters is systematically investigated and compared to composite pulses.Comment: 5 pages 5 figure

High-order time-splitting Hermite and Fourier spectral methods

In this paper, we are concerned with the numerical solution of the time-dependent Gross-Pitaevskii Equation (GPE) involving a quasi-harmonic potential. Primarily, we consider discretisations that are based on spectral methods in space and higher-order exponential operator splitting methods in time. The resulting methods are favourable in view of accuracy and efficiency; moreover, geometric properties of the equation such as particle number and energy conservation are well captured. Regarding the spatial discretisation of the GPE, we consider two approaches. In the unbounded domain, we employ a spectral decomposition of the solution into Hermite basis functions: on the other hand. restricting the equation to a sufficiently large bounded domain, Fourier techniques are applicable. For the time integration of the GPE, we study various exponential operator splitting methods of convergence orders two, four, and six. Our main objective is to provide accuracy and efficiency comparisons of exponential operator splitting Fourier and Hermite pseudospectral methods for the time evolution of the GPE. Furthermore, we illustrate the effectiveness of higher-order time-splitting methods compared to standard integrators in a long-term integration

Deterministic/Fragmented-Stochastic Exchange for Large Scale Hybrid DFT Calculations

We develop an efficient approach to evaluate range-separated exact exchange for grid or plane-wave based representations within the Generalized Kohn-Sham DFT (GKS-DFT) framework. The Coulomb kernel is fragmented in reciprocal space, and we employ a mixed deterministic-stochastic representation, retaining long wavelength (low-$k$) contributions deterministically and using a sparse ("fragmented") stochastic basis for the high-$k$ part. Coupled with a projection of the Hamiltonian onto a subspace of valence and conduction states from a prior local-DFT calculation, this method allows for the calculation of long-range exchange of large molecular systems with hundreds and potentially thousands of coupled valence states delocalized over millions of grid points. We find that even a small number of valence and conduction states is sufficient for converging the HOMO and LUMO energies of the GKS-DFT. Excellent tuning of long-range separated hybrids (RSH) is easily obtained in the method for very large systems, as exemplified here for the chlorophyll hexamer of Photosystem II with 1,320 electrons.Comment: 9 pages, 3 figure