Diffusive logistic equation with non-linear boundary conditions

AbstractWe analyze the solutions of a population model with diffusion and logistic growth. In particular, we focus our study on a population living in a patch, Ω⊆Rn with n⩾1, that satisfies a certain non-linear boundary condition and on its survival when constant yield harvesting is introduced. We establish our existence results by the method of sub-super solutions

Modeling the effects of trait-mediated dispersal on coexistence of mutualists

© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0) Even though mutualistic interactions are ubiquitous in nature, we are still far from making good predictions about the fate of mutualistic communities under threats such as habitat fragmentation and climate change. Fragmentation often causes declines in abundance of a species due to increased susceptibility to edge effects between remnant habitat patches and lower quality “matrix” surrounding these focal patches. It has been argued that ecological communities are replete with trait-mediated indirect effects, and that these effects may sometimes contribute more to the dynamics of a population than direct density-mediated effects, e.g., lowering an organism\u27s fitness through competitive interactions. Although some studies have focused on trait-mediated behavior such as trait-mediated dispersal, in which an organism changes its dispersal patterns due to the presence of another species, they have been mostly limited to predator-prey systems-little is known regarding their effect on other interaction systems such as mutualism. Here, we explore consequences of fragmentation and trait-mediated dispersal on coexistence of a system of two mutualists by employing a model built upon the reaction diffusion framework. To distinguish between trait-mediated dispersal and density-mediated effects, we isolate effects of trait-mediated dispersal on the mutualistic system by excluding any direct density-mediated effects in the model. Our results demonstrate that fragmentation and trait-mediated dispersal can have important impacts on coexistence of mutualists. Specifically, one species can be better able to invade and persist than the other and be crucial to the success of the other species in the patch. Matrix quality degradation can also bring about a complete reversal of the role of which species is supporting the other\u27s persistence in the patch, even as the patch size remains constant. As most mutualistic relationships are identified based on density-mediated effects, such an effect may be easily overlooked

Variability in ornamentation of adult Dermacentor parumapertus Neumann (Acari: Ixodidae): implications for tick identification

Abstract The hard tick Dermacentor parumapertus is an ectoparasite commonly found on hares and rabbits and occurs over much of the western United States. These ticks are rarely encountered except by hunters or scientists collecting rabbits for study. Herein we describe 74 adult D. parumapertus ticks (21F, 53M) removed from 8 black-tailed jackrabbits, Lepus californicus, in central Utah, and 13 adult D. parumapertus (7F, 6M) found on 4 L. californicus in western Texas. The Utah ticks were barely ornamented. Females displayed only slight gray ornamentation near the posterior edge of the scutum and whitish-gray spots distally on the femur of legs II, III, and IV; males were completely devoid of any ornamentation. In contrast, Texas specimens were richly ornamented in white, closely resembling D. variabilis. Females were brightly marked with white (not gray) on the scutum and had white spots distally on all femurs. Males from Texas were variously ornamented along the posterolateral margins of the scutum and displayed white spots distally on all femurs. Documentation of this variability in ornamentation in D. parumapertus is important, particularly as white-marked specimens can easily be confused with D. variabilis and since both species have been reported from rabbit hosts

Modeling the effects of density dependent emigration, weak Allee effects, and matrix hostility on patch-level population persistence

© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0) The relationship between conspecific density and the probability of emigrating from a patch can play an essential role in determining the population-dynamic consequences of an Allee effect. In this paper, we model a population that inside a patch is diffusing and growing according to a weak Allee effect per-capita growth rate, but the emigration probability is dependent on conspecific density. The habitat patch is one-dimensional and is surrounded by a tuneable hostile matrix. We consider five different forms of density dependent emigration (DDE) that have been noted in previous empirical studies. Our models predict that at the patch-level, DDE forms that have a positive slope will counteract Allee effects, whereas, DDE forms with a negative slope will enhance them. Also, DDE can have profound effects on the dynamics of a population, including producing very complicated population dynamics with multiple steady states whose density profile can be either symmetric or asymmetric about the center of the patch. Our results are obtained mathematically through the method of sub-super solutions, time map analysis, and numerical computations using Wolfram Mathematica

Dyons and S-Duality in N=4 Supersymmetric Gauge Theory

We analyze the spectrum of dyons in N=4 supersymmetric Yang-Mills theory with gauge group SU(3) spontaneously broken down to U(1)xU(1). The Higgs fields select a natural basis of simple roots. Acting with S-duality on the W-boson states corresponding to simple roots leads to an orbit of BPS dyon states that are magnetically charged with respect to one of the U(1)'s. The corresponding monopole solutions can be obtained by embedding SU(2) monopoles into SU(3) and the S-duality predictions reduce to the SU(2) case. Acting with S-duality on the W-boson corresponding to a non-simple root leads to an infinite set of new S-duality predictions. The simplest of these corresponds to the existence of a harmonic form on the moduli space of SU(3) monopoles that have magnetic charge (1,1) with respect to the two U(1)'s. We argue that the moduli space is given by R^3x(R^1xM)/Z_2, where M is Euclidean Taub-NUT space, and that the latter admits the appropriate normalizable harmonic two form. We briefly discuss the generalizations to other gauge groups.Comment: 13 pages (Harvmac b), discrete identification corrected, reference adde

Recent Legal Litertature

Freund: The Police Power, Public Policy and Constitutional Rights; Parsons: The Law of Contracts; Baldwin: American Railroad Law; Gilbert (ed.): Street Railway Reports, Annotated, reporting the electric railway and street railway decisions of the Federal and State Courts in the United States, from April 1, 1903