The effects of environmental perturbation and measurement error on estimates of the shape parameter in the theta-logistic model of population regulation

The theta-logistic is a widely used generalisation of the logistic model of regulated biological processes which is used in particular to model population regulation. Then the parameter theta gives the shape of the relationship between per-capita population growth rate and population size. Estimation of theta from population counts is however subject to bias, particularly when there are measurement errors. Here we identify factors disposing towards accurate estimation of theta by simulation of populations regulated according to the theta-logistic model. Factors investigated were measurement error, environmental perturbation and length of time series. Large measurement errors bias estimates of theta towards zero. Where estimated theta is close to zero, the estimated annual return rate may help resolve whether this is due to bias. Environmental perturbations help yield unbiased estimates of theta. Where environmental perturbations are large, estimates of theta are likely to be reliable even when measurement errors are also large. By contrast where the environment is relatively constant, unbiased estimates of theta can only be obtained if populations are counted precisely Our results have practical conclusions for the design of long-term population surveys. Estimation of the precision of population counts would be valuable, and could be achieved in practice by repeating counts in at least some years. Increasing the length of time series beyond ten or 20 years yields only small benefits. if populations are measured with appropriate accuracy, given the level of environmental perturbation, unbiased estimates can be obtained from relatively short censuses. These conclusions are optimistic for estimation of theta. (C) 2008 Elsevier B.V All rights reserved.

Compression of polyelectrolyte brushes in a salt-free theta solvent

This paper examines the normal force between two opposing polyelectrolyte brushes and the interpenetration of their chains that is responsible for sliding friction. It focuses on the special case of semi-dilute brushes in a salt-free theta solvent, for which Zhulina and Borisov [J. Chem. Phys., {\bf 107}, 5952, (1997)] have derived analytical predictions using the classical strong-stretching theory (SST) introduced by Semenov and developed by Milner, Witten and Cates. Interestingly, the SST predicts that the brushes contract maintaining a polymer-free gap as they are compressed together, which provides an explanation for the ultra-low frictional forces observed in experiment. We examine the degree to which the SST predictions are affected by chain fluctuations by employing self-consistent field theory (SCFT). While the normal force is relatively unaffected, fluctuations are found to have a strong impact on brush interpenetration. Even still, the contraction of the brushes does significantly prolong the onset of interpenetration, implying that a sizeable normal force can be achieved before the sliding friction becomes significant.

Effect of salt on the compression of polyelectrolyte brushes in a theta solvent

Classical strong-stretching theory (SST) predicts that, as opposing polyelectrolyte brushes are compressed together in a salt-free theta solvent, they contract so as to maintain a finite polymer-free gap, which offers a potential explanation for the ultra-low frictional forces observed in experiments even with the application of large normal forces. However, the SST ignores chain fluctuations, which would tend to close the gap resulting in physical contact and in turn significant friction. In a preceding study, we examined the effect of fluctuations using self-consistent field theory (SCFT) and illustrated that high normal forces can still be applied before the gap is destroyed. We now look at the effect of adding salt. It is found to reduce the long-range interaction between the brushes but has little effect on the short-range part, provided the concentration does not enter the salted-brush regime. Consequently, the maximum normal force between two planar brushes at the point of contact is remarkably unaffected by salt. For the crossed-cylinder geometry commonly used in experiments, however, there is a gradual reduction because in this case the long-range part of the interaction contributes to the maximum normal force.

New perspectives on the Northern Hemisphere winter storm tracks

The aim of this paper is to explore the use of both an Eulerian and system-centered method of storm track diagnosis applied to a wide range of meteorological fields at multiple levels to provide a range of perspectives on the Northern Hemisphere winter transient motions and to give new insight into the storm track organization and behavior. The data used are primarily from the European Centre for Medium-Range Weather Forecasts reanalyses project extended with operational analyses to the period 1979-2000. This is supplemented by data from the National Centers for Environmental Prediction and Goddard Earth Observing System 1 reanalyses. The range of fields explored include the usual mean sea level pressure and the lower- and upper-tropospheric height, meridional wind, vorticity, and temperature, as well as the potential vorticity (PV) on a 330-K isentropic surface (PV330) and potential temperature on a PV = 2 PVU surface (theta(PV2)). As well as reporting the primary analysis based on feature tracking, the standard Eulerian 2-6-day bandpass filtered variance analysis is also reported and contrasted with the tracking diagnostics. To enable the feature points to be identified as extrema for all the chosen fields, a planetary wave background structure is removed at each data time. The bandpass filtered variance derived from the different fields yield a rich picture of the nature and comparative magnitudes of the North Pacific and Atlantic storm tracks, and of the Siberian and Mediterranean candidates for storm tracks. The feature tracking allows the cyclonic and anticyclonic activities to be considered seperately. The analysis indicates that anticyclonic features are generally much weaker with less coherence than the cyclonic systems. Cyclones and features associated with them are shown to have much greater coherence and give tracking diagnostics that create a vivid storm track picture that includes the aspects highlighted by the variances as well as highlighting aspects that are not readily available from Eulerian studies. In particular, the upper-tropospheric features as shown by negative theta(PV2), for example, occur in a band spiraling around the hemisphere from the subtropical North Atlantic eastward to the high latitudes of the same ocean basin. Lower-troposphere storm tracks occupy more limited longitudinal sectors, with many of the individual storms possibly triggered from the upper-tropospheric disturbances in the spiral band of activity.

The diurnal course of soil moisture as measured by various dielectric sensors: Effects of soil temperature and the implications for evaporation estimates

Soil moisture content, theta, of a bare and vegetated UK gravelly sandy loam soil (in situ and repacked in small lysimeters) was measured using various dielectric instruments (single-sensor ThetaProbes, multi-sensor Profile Probes, and Aquaflex Sensors), at depths ranging between 0.03 and I m, during the summers of 2001 (in situ soil) and 2002 (mini-lysimeters). Half-hourly values of evaporation, E, were calculated from diurnal changes in total soil profile water content, using the soil water balance equation. For the bare soil field, Profile Probes and ML2x ThetaProbes indicated a diurnal course of theta that did not concur with typical soil physical observations: surface layer soil moisture content increased from early morning until about midday, after which theta declined, generally until the early evening. The unexpected course of theta was positively correlated to soil temperature, T-s, also at deeper depths. Aquaflex and ML1 ThetaProbe (older models) outputs, however, reflected common observations: 0 increased slightly during the night (capillary rise) and decreased from the morning until late afternoon (as a result of evaporation). For the vegetated plot, the spurious diurnal theta fluctuations were less obvious, because canopy shading resulted in lower amplitudes of T-s. The unrealistic theta profiles measured for the bare and vegetated field sites caused diurnal estimates of E to attain downward daytime and upward night-time values. In the mini-lysimeters, at medium to high moisture contents, theta values measured by (ML2x) ThetaProbes followed a relatively realistic course, and predictions of E from diurnal changes in vertically integrated theta generally compared well with lysimeter estimates of E. However, time courses of theta and E became comparable to those observed for the field plots when the soil in the lysimeters reached relatively low values of theta. Attempts to correct measured theta for fluctuations in T, revealed that no generally applicable formula could be derived. (c) 2005 Elsevier B.V. All rights reserved.

Variational calculations of rovibrational states: a precise high-energy potential surface for HCN [and discussion]

We report the results of variational calculations of the rovibrational energy levels of HCN for J = 0, 1 and 2, where we reproduce all the ca. 100 observed vibrational states for all observed isotopic species, with energies up to 18000 cm$^{-1}$, to about $\pm $1 cm$^{-1}$, and the corresponding rotational constants to about $\pm $0.001 cm$^{-1}$. We use a hamiltonian expressed in internal coordinates r$_{1}$, r$_{2}$ and $\theta $, using the exact expression for the kinetic energy operator T obtained by direct transformation from the cartesian representation. The potential energy V is expressed as a polynomial expansion in the Morse coordinates y$_{i}$ for the bond stretches and the interbond angle $\theta $. The basis functions are built as products of appropriately scaled Morse functions in the bond-stretches and Legendre or associated Legendre polynomials of cos $\theta $ in the angle bend, and we evaluate matrix elements by Gauss quadrature. The hamiltonian matripx is factorized using the full rovibrational symmetry, and the basis is contracted to an optimized form; the dimensions of the final hamiltonian matrix vary from 240 $\times $ 240 to 1000 $\times $ 1000.We believe that our calculation is converged to better than 1 cm$^{-1}$ at 18 000 cm$^{-1}$. Our potential surface is expressed in terms of 31 parameters, about half of which have been refined by least squares to optimize the fit to the experimental data. The advantages and disadvantages and the future potential of calculations of this type are discussed.

A note on the accuracy of PAC-likelihood inference with microsatellite data

Stephens and Donnelly have introduced a simple yet powerful importance sampling scheme for computing the likelihood in population genetic models. Fundamental to the method is an approximation to the conditional probability of the allelic type of an additional gene, given those currently in the sample. As noted by Li and Stephens, the product of these conditional probabilities for a sequence of draws that gives the frequency of allelic types in a sample is an approximation to the likelihood, and can be used directly in inference. The aim of this note is to demonstrate the high level of accuracy of "product of approximate conditionals" (PAC) likelihood when used with microsatellite data. Results obtained on simulated microsatellite data show that this strategy leads to a negligible bias over a wide range of the scaled mutation parameter theta. Furthermore, the sampling variance of likelihood estimates as well as the computation time are lower than that obtained with importance sampling on the whole range of theta. It follows that this approach represents an efficient substitute to IS algorithms in computer intensive (e.g. MCMC) inference methods in population genetics. (c) 2006 Elsevier Inc. All rights reserved.

A Bayesian approach to disease gene location using allelic association

A Bayesian approach to analysing data from family-based association studies is developed. This permits direct assessment of the range of possible values of model parameters, such as the recombination frequency and allelic associations, in the light of the data. In addition, sophisticated comparisons of different models may be handled easily, even when such models are not nested. The methodology is developed in such a way as to allow separate inferences to be made about linkage and association by including theta, the recombination fraction between the marker and disease susceptibility locus under study, explicitly in the model. The method is illustrated by application to a previously published data set. The data analysis raises some interesting issues, notably with regard to the weight of evidence necessary to convince us of linkage between a candidate locus and disease.

Population subdivision and molecular sequence variation: Theory and analysis of Drosophila ananassae data

Population subdivision complicates analysis of molecular variation. Even if neutrality is assumed, three evolutionary forces need to be considered: migration, mutation, and drift. Simplification can be achieved by assuming that the process of migration among and drift within subpopulations is occurring fast compared to Mutation and drift in the entire population. This allows a two-step approach in the analysis: (i) analysis of population subdivision and (ii) analysis of molecular variation in the migrant pool. We model population subdivision using an infinite island model, where we allow the migration/drift parameter Theta to vary among populations. Thus, central and peripheral populations can be differentiated. For inference of Theta, we use a coalescence approach, implemented via a Markov chain Monte Carlo (MCMC) integration method that allows estimation of allele frequencies in the migrant pool. The second step of this approach (analysis of molecular variation in the migrant pool) uses the estimated allele frequencies in the migrant pool for the study of molecular variation. We apply this method to a Drosophila ananassae sequence data set. We find little indication of isolation by distance, but large differences in the migration parameter among populations. The population as a whole seems to be expanding. A population from Bogor (Java, Indonesia) shows the highest variation and seems closest to the species center.

Synthesis, structure and magnetic characterisation of a new layered ammonium manganese(II) diphosphate hydrate, (NH4)(2)[Mn-3(P2O7)(2)(H2O)(2)]

A new layered ammonium manganese(II) diphosphate, (NH4)(2)[Mn-3(P2O7)(2)(H2O)(2)], has been synthesised under solvothermal conditions at 433 K in ethylene glycol and the structure determined at 293 K using single-crystal X-ray diffraction data (M-r = 584.82, monoclinic, space group P2(1)/a, a = 9.4610( 8), b = 8.3565( 7), c = 9.477(1) Angstrom, beta = 99.908(9) degrees, V = 738.07 Angstrom(3), Z = 2, R = 0.0351 and R-w = 0.0411 for 1262 observed data (I > 3(sigma(I))). The structure consists of chains of cis- and trans-edge sharing MnO6 octahedra linked via P2O7 units to form layers of formula [Mn3P4O14(H2O)(2)](2-) in the ab plane. Ammonium ions lie between the manganese-diphosphate layers. A network of interlayer and ammonium-layer based hydrogen bonding holds the structure together. Magnetic measurements indicate Curie - Weiss behaviour above 30 K with mu(eff) = 5.74(1) mu(B) and theta = -23(1) K, consistent with the presence of high-spin Mn2+ ions and antiferromagnetic interactions. However, the magnetic data reveal a spontaneous magnetisation at 5 K, indicating a canting of Mn2+ moments in the antiferromagnetic ground state. On heating (NH4)(2)[Mn-3(P2O7)(2)(H2O)(2)] in water at 433 K under hydrothermal conditions, Mn-5(HPO4)(2)(PO4)(2).4H(2)O, synthetic hureaulite, is formed.

Minimum neighborhood in a generalized cube

Generalized cubes are a subclass of hypercube-like networks, which include some hypercube variants as special cases. Let theta(G)(k) denote the minimum number of nodes adjacent to a set of k vertices of a graph G. In this paper, we prove theta(G)(k) >= -1/2k(2) + (2n - 3/2)k - (n(2) - 2) for each n-dimensional generalized cube and each integer k satisfying n + 2 <= k <= 2n. Our result is an extension of a result presented by Fan and Lin [J. Fan, X. Lin, The t/k-diagnosability of the BC graphs, IEEE Trans. Comput. 54 (2) (2005) 176-184]. (c) 2005 Elsevier B.V. All rights reserved.