Embedding Population Dynamics Models in Inference

Increasing pressures on the environment are generating an ever-increasing need to manage animal and plant populations sustainably, and to protect and rebuild endangered populations. Effective management requires reliable mathematical models, so that the effects of management action can be predicted, and the uncertainty in these predictions quantified. These models must be able to predict the response of populations to anthropogenic change, while handling the major sources of uncertainty. We describe a simple ``building block'' approach to formulating discrete-time models. We show how to estimate the parameters of such models from time series of data, and how to quantify uncertainty in those estimates and in numbers of individuals of different types in populations, using computer-intensive Bayesian methods. We also discuss advantages and pitfalls of the approach, and give an example using the British grey seal population.Comment: Published at http://dx.doi.org/10.1214/088342306000000673 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Building integral projection models with non-independent vital rates

Population dynamics are functions of several demographic processes including survival, reproduction, somatic growth, and maturation. The rates or probabilities for these processes can vary by time, by location, and by individual. These processes can co‐vary and interact to varying degrees, e.g., an animal can only reproduce when it is in a particular maturation state. Population dynamics models that treat the processes as independent may yield somewhat biased or imprecise parameter estimates, as well as predictions of population abundances or densities. However, commonly used integral projection models (IPMs) typically assume independence across these demographic processes. We examine several approaches for modelling between process dependence in IPMs and include cases where the processes co‐vary as a function of time (temporal variation), co‐vary within each individual (individual heterogeneity), and combinations of these (temporal variation and individual heterogeneity). We compare our methods to conventional IPMs, which treat vital rates independent, using simulations and a case study of Soay sheep (Ovis aries). In particular, our results indicate that correlation between vital rates can moderately affect variability of some population‐level statistics. Therefore, including such dependent structures is generally advisable when fitting IPMs to ascertain whether or not such between vital rate dependencies exist, which in turn can have subsequent impact on population management or life‐history evolution

COMPARING ESTIMATION PROCEDURES FOR DOSE-RESPONSE FUNCTIONS

The dose-response design is often used in agricultural research when it is necessary to measure a biological response at various levels of an experimental factor. This type of problem is common in chemical and pesticide research, however, it can also occur in other disciplines such as plant, animal, soil, and environmental sciences. While the analysis of dose-response data usually involves fitting a regression curve, the primary objective often centers on the estimation of dose related percentiles such as the LD50 or LC50. These measures are useful for comparing the relative efficacy of various treatments, however, the estimation of the specified percentiles is not always straightforward. Traditional methodology has relied on inverted solutions or asymptotic theory for statistical inference. More recently, computer intensive methods have been used to model dose-response relationships and can be more appropriate than traditional methods in some situations. This paper examines both the traditional and modem approaches to estimating doseresponse functions as they apply to binomial data. The techniques will be demonstrated using mortality data collected on black vine weevil eggs exposed to an organic pesticide treatment

Nakedness and curvature strength of shell-focusing singularity in the spherically symmetric space-time with vanishing radial pressure

It was recently shown that the metric functions which describe a spherically symmetric space-time with vanishing radial pressure can be explicitly integrated. We investigate the nakedness and curvature strength of the shell-focusing singularity in that space-time. If the singularity is naked, the relation between the circumferential radius and the Misner-Sharp mass is given by $R\approx 2y_{0} m^{\beta}$ with $1/3<\beta\le 1$ along the first radial null geodesic from the singularity. The $\beta$ is closely related to the curvature strength of the naked singularity. For example, for the outgoing or ingoing null geodesic, if the strong curvature condition (SCC) by Tipler holds, then $\beta$ must be equal to 1. We define the ``gravity dominance condition'' (GDC) for a geodesic. If GDC is satisfied for the null geodesic, both SCC and the limiting focusing condition (LFC) by Kr\'olak hold for $\beta=1$ and $y_{0}\ne 1$, not SCC but only LFC holds for $1/2\le \beta <1$, and neither holds for $1/3<\beta <1/2$, for the null geodesic. On the other hand, if GDC is satisfied for the timelike geodesic $r=0$, both SCC and LFC are satisfied for the timelike geodesic, irrespective of the value of $\beta$. Several examples are also discussed.Comment: 11 pages, Accepted for Publication in Classical and Quantum Gravity, References Updated, Grammatical Errors Correcte

Gp41-targeted antibodies restore infectivity of a fusion-deficient HIV-1 envelope glycoprotein

The HIV-1 envelope glycoprotein (Env) mediates viral entry via conformational changes associated with binding the cell surface receptor (CD4) and coreceptor (CCR5/CXCR4), resulting in subsequent fusion of the viral and cellular membranes. While the gp120 Env surface subunit has been extensively studied for its role in viral entry and evasion of the host immune response, the gp41 transmembrane glycoprotein and its role in natural infection are less well characterized. Here, we identified a primary HIV-1 Env variant that consistently supports \u3e300% increased viral infectivity in the presence of autologous or heterologous HIV-positive plasma. However, in the absence of HIV-positive plasma, viruses with this Env exhibited reduced infectivity that was not due to decreased CD4 binding. Using Env chimeras and sequence analysis, we mapped this phenotype to a change Q563R, in the gp41 heptad repeat 1 (HR1) region. We demonstrate that Q563R reduces viral infection by disrupting formation of the gp41 six-helix bundle required for virus-cell membrane fusion. Intriguingly, antibodies that bind cluster I epitopes on gp41 overcome this inhibitory effect, restoring infectivity to wild-type levels. We further demonstrate that the Q563R change increases HIV-1 sensitivity to broadly neutralizing antibodies (bNAbs) targeting the gp41 membrane-proximal external region (MPER). In summary, we identify an HIV-1 Env variant with impaired infectivity whose Env functionality is restored through the binding of host antibodies. These data contribute to our understanding of gp41 residues involved in membrane fusion and identify a mechanism by which host factors can alleviate a viral defect

General-relativistic Model of Magnetically Driven Jet

The general scheme for the construction of the general-relativistic model of the magnetically driven jet is suggested. The method is based on the usage of the 3+1 MHD formalism. It is shown that the critical points of the flow and the explicit radial behavior of the physical variables may be derived through the jet ``profile function."Comment: 12 pages, LaTex, no figure

Gravitational Waves around a Naked Singularity -- Odd-Parity Perturbation of Lemaitre-Tolman-Bondi Space-Time --

The motion of a spherical dust cloud is described by the Lemaitre-Tolman-Bondi solution and is completely specified by initial values of distributions of the rest mass density and specific energy of the dust fluid. From generic initial conditions of this spherically symmetric collapse, there appears a naked singularity at the symmetric center in the course of the gravitational collapse of the dust cloud. So this might be a counter example to the cosmic censorship hypothesis. To investigate the genericity of this example, we examine the stability of the `nakedness' of this singularity against odd-parity modes of non-spherical linear perturbations for the metric, i.e., linear gravitational waves. We find that the perturbations do not diverge but are well-behaved even in the neighborhood of the central naked singularity. This means that the naked singularity formation process is marginally stable against the odd-parity modes of linear gravitational waves.Comment: 19 pages, 12 figures, to be published in Physical Review

SP701-A-Growing and Harvesting Switchgrass for Ethanol Production in Tennessee

Switchgrass is a warm-season perennial grass native to North America. The plant can reach heights up to 10 feet with an extensive root system. Once established, switchgrass well-managed for biomass should have a productive life of 10-20 years. Within the stand, switchgrass is an extremely strong competitor. However, it is not considered an invasive plant. Switchgrass adapts well to a variety of soil and climatic conditions. It is most productive on moderately well to well-drained soils of medium fertility and a soil pH at 5.0 or above. The high cellulosic content of switchgrass makes it a favorable feedstock for ethanol production. It is anticipated that switchgrass can yield sufficient biomass to produce approximately 500 gallons of ethanol per acre. While the Tennessee Biofuels Initiative includes a demonstration plant to make ethanol from switchgrass, the market for switchgrass as an energy crop remains limited. Producers will likely need to be located within 30 to 50 miles of a cellulosic ethanol plant. Producing switchgrass for energy generally occurs under some form of contractual arrangement with the end-user. To reap potential benefits from using switchgrass for cellulosic ethanol production, the system of production must be profitable for farmers and energy producers, as well as cost effective for consumers