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

Polynominals related to powers of the Dedekind eta function

The vanishing properties of Fourier coefficients of integral powers of the Dedekind eta function correspond to the existence of integral roots of integer-valued polynomials Pn(x) introduced by M. Newman. In this paper we study the derivatives of these polynomials. We obtain non-vanishing results at integral points. As an application we prove that integral roots are simple if the index n of the polynomial is equal to a prime power pm or to pm + 1. We obtain a formula for the derivative of Pn(x) involving the polynomials of lower degree

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

Radiative transitions of the helium atom in highly magnetized neutron star atmospheres

Recent observations of thermally emitting isolated neutron stars revealed spectral features that could be interpreted as radiative transitions of He in a magnetized neutron star atmosphere. We present Hartree-Fock calculations of the polarization-dependent photoionization cross sections of the He atom in strong magnetic fields ranging from 10^12 G to 10^14 G. Convenient fitting formulae for the cross sections are given as well as related oscillator strengths for various bound-bound transitions. The effects of finite nucleus mass on the radiative absorption cross sections are examined using perturbation theory.Comment: 14 pages, 7 figures. Minor changes. MNRAS in pres