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

Composite absorbing potentials

The multiple scattering interferences due to the addition of several contiguous potential units are used to construct composite absorbing potentials that absorb at an arbitrary set of incident momenta or for a broad momentum interval.Comment: 9 pages, Revtex, 2 postscript figures. Accepted in Phys. Rev. Let

The spectacular evolution of Supernova 1996al over 15 years: a low energy explosion of a stripped massive star in a highly structured environment

Spectrophotometry of SN 1996al carried out throughout 15 years is presented. The early photometry suggests that SN 1996al is a Linear type-II supernova, with an absolute peak of Mv ~ -18.2 mag. Early spectra present broad, asymmetric Balmer emissions, with super-imposed narrow lines with P-Cygni profile, and He I features with asymmetric, broad emission components. The analysis of the line profiles shows that the H and He broad components form in the same region of the ejecta. By day +142, the Halpha profile dramatically changes: the narrow P-Cygni profile disappears, and the Halpha is fitted by three emission components, that will be detected over the remaining 15 yrs of the SN monitoring campaign. Instead, the He I emissions become progressively narrower and symmetric. A sudden increase in flux of all He I lines is observed between 300 and 600 days. Models show that the supernova luminosity is sustained by the interaction of low mass (~1.15 Msun) ejecta, expelled in a low kinetic energy (~ 1.6 x 10^50 erg) explosion, with highly asymmetric circumstellar medium. The detection of Halpha emission in pre-explosion archive images suggests that the progenitor was most likely a massive star (~25 Msun ZAMS) that had lost a large fraction of its hydrogen envelope before explosion, and was hence embedded in a H-rich cocoon. The low-mass ejecta and modest kinetic energy of the explosion are explained with massive fallback of material into the compact remnant, a 7-8 Msun black hole.Comment: 27 pages, 23 figures, Accepted for publication in MNRA

The Origin of Jovian Planets in Protostellar Disks: The Role of Dead Zones

The final masses of Jovian planets are attained when the tidal torques that they exert on their surrounding protostellar disks are sufficient to open gaps in the face of disk viscosity, thereby shutting off any further accretion. In sufficiently well-ionized disks, the predominant form of disk viscosity originates from the Magneto-Rotational Instability (MRI) that drives hydromagnetic disk turbulence. In the region of sufficiently low ionization rate -- the so-called dead zone -- turbulence is damped and we show that lower mass planets will be formed. We considered three ionization sources (X-rays, cosmic rays, and radioactive elements) and determined the size of a dead zone for the total ionization rate by using a radiative, hydrostatic equilibrium disk model developed by Chiang et al. (2001). We studied a range of surface mass density (Sigma_{0}=10^3 - 10^5 g cm^{-2}) and X-ray energy (kT_{x}=1 - 10 keV). We also compared the ionization rate of such a disk by X-rays with cosmic rays and find that the latter dominate X-rays in ionizing protostellar disks unless the X-ray energy is very high (5 - 10 keV). Among our major conclusions are that for typical conditions, dead zones encompass a region extending out to several AU -- the region in which terrestrial planets are found in our solar system. Our results suggest that the division between low and high mass planets in exosolar planetary systems is a consequence of the presence of a dead zone in their natal protoplanetary disks. We also find that the extent of a dead zone is mainly dependent on the disk's surface mass density. Our results provide further support for the idea that Jovian planets in exosolar systems must have migrated substantially inwards from their points of origin.Comment: 28 pages, 10 figures, accepted by Ap

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

A Search for Photometric Rotation Periods in Low-Mass Stars and Brown Dwarfs in the Pleiades

We have photometrically monitored (Cousins Ic) eight low mass stars and brown dwarfs which are probable members of the Pleiades. We derived rotation periods for two of the stars - HHJ409 and CFHT-PL8 - to be 0.258 d and 0.401 d, respectively. The masses of these stars are near 0.4 and 0.08 Msun, respectively; the latter is the second such object near the hydrogen-burning boundary for which a rotation period has been measured. We also observed HHJ409 in V; the relative amplitude in the two bands shows that the spots in that star are about 200 K cooler than the stellar effective temperature of 3560 K and have a filling factor on the order of 13%. With one possible exception, the remaining stars in the sample do not show photometric variations larger than the mean error of measurement. We also examined the M9.5V disk star 2MASSJ0149, which had previously exhibited a strong flare event, but did not detect any photometric variation.Comment: 13 pages, four figures. Accepted for publication in A

Brown dwarfs in the Hyades and beyond?

We have used both the Low-Resolution Imaging Spectrograph and the HIRES echelle spectrograph on the Keck telescopes to obtain spectra of twelve candidate members of the Hyades cluster identified by Leggett and Hawkins (1988, 1989). All of the objects are chromospherically-active, late-type M-dwarfs, with H$\alpha$ equivalent widths varying from 1 to 30\AA. Based on our measured radial velocities, the level of stellar activity and other spectroscopic features, only one of the twelve stars has properties consistent with cluster membership. We consider how this result affects estimates of the luminosity and mass function of the Hyades cluster. Five of the eleven field stars have weak K I 7665/7699\AA and CaH absorption as compared with M-dwarf standards of the same spectral type, suggesting a lower surface gravity. Two of these sources, LH0416+14 and LH0419+15, exhibit significant lithium 6708 \AA absorption. Based partly on parallax measurements by the US Naval Observatory (Harris et al, 1998), we identify all five as likely to be young, pre-main sequence objects in or near the Taurus-Auriga association at distances of between 150 and 250 parsecs. A comparison with theoretical models of pre-main sequence stars indicates masses of less than 0.05 M$_\odot$.Comment: to appear in AJ, January 1999; 34 pages, (Latex format), including 10 embedded postscript figures and two table