Measuring departures from Hardy-Weinberg: a Markov chain Monte Carlo method for estimating the inbreeding coefficient

Many well-established statistical methods in genetics were developed in a climate of severe constraints on computational power. Recent advances in simulation methodology now bring modern, flexible statistical methods within the reach of scientists having access to a desktop workstation. We illustrate the potential advantages now available by considering the problem of assessing departures from Hardy-Weinberg (HW) equilibrium. Several hypothesis tests of HW have been established, as well as a variety of point estimation methods for the parameter which measures departures from HW under the inbreeding model. We propose a computational, Bayesian method for assessing departures from HW, which has a number of important advantages over existing approaches. The method incorporates the effects-of uncertainty about the nuisance parameters--the allele frequencies--as well as the boundary constraints on f (which are functions of the nuisance parameters). Results are naturally presented visually, exploiting the graphics capabilities of modern computer environments to allow straightforward interpretation. Perhaps most importantly, the method is founded on a flexible, likelihood-based modelling framework, which can incorporate the inbreeding model if appropriate, but also allows the assumptions of the model to he investigated and, if necessary, relaxed. Under appropriate conditions, information can be shared across loci and, possibly, across populations, leading to more precise estimation. The advantages of the method are illustrated by application both to simulated data and to data analysed by alternative methods in the recent literature.

Precision of quasi-optical null-balanced bridge techniques for transmission and reflection coefficient measurements

The precision of quasioptical null-balanced bridge instruments for transmission and reflection coefficient measurements at millimeter and submillimeter wavelengths is analyzed. A Jones matrix analysis is used to describe the amount of power reaching the detector as a function of grid angle orientation, sample transmittance/reflectance and phase delay. An analysis is performed of the errors involved in determining the complex transmission and reflection coefficient after taking into account the quantization error in the grid angle and micrometer readings, the transmission or reflection coefficient of the sample, the noise equivalent power of the detector, the source power and the post-detection bandwidth. For a system fitted with a rotating grid with resolution of 0.017 rad and a micrometer quantization error of 1 μm, a 1 mW source, and a detector with a noise equivalent power 5×10−9 W Hz−1/2, the maximum errors at an amplitude transmission or reflection coefficient of 0.5 are below ±0.025.

Modèle d'état à coefficient aléatoire: filtrage par densités approchées

Le filtrage de Bucy-Kalman s'applique au modèle d'état comprenant des équations linéaires bruitées, décrivant l'évolution de l'état et des équations linéaires bruitées d'observation . Ce filtrage consiste dans le cas gaussien, à calculer de façon récursive, la loi de probabilité, a posteriori, de l'état, au vu de l' observation actuelle et des observations passées . Le filtrage par densités approchées permet de traiter des équations d'état, non linéaires ou à bruits non Gaussiens. Pour un coefficient de rappel aléatoire, cas typique d'une situation de changements de modèles, l'article introduit une famille de lois de probabilité, paramétrées, bimodales servant, par ajustement des paramètres, à approcher les lois a posteriori de l'état aux divers instants . Les paramètres sont recalculés récursivement, lors des mises à jour et des prédictions.

A functional coefficient model view of the Feldstein–Horioka puzzle

What does the saving–investment (SI) relation really measure and how should the SI relation be measured? These are two of the most discussed issues triggered by the so-called Feldstein–Horioka puzzle. Based on panel data we introduce a new variant of functional coefficient models that allows to separate long and short to medium run parameter dependence. The new modeling framework is applied to uncover the determinants of the SI relation. Macroeconomic state variables such as openness, the age dependency ratio, government current and consumption expenditures are found to affect the SI relation significantly in the long run.

Catchment phosphorous losses: an export coefficient modelling approach with scenario analysis for water management

This paper presents the development of an export coefficient model to characterise the rates and sources of P export from land to water in four reservoir systems located in a semi-arid rural region in southern of Portugal. The model was developed to enable effective management of these important water resource systems under the EU Water Framework Directive. This is the first time such an approach has been fully adapted for the semi-arid systems typical of Mediterranean Europe. The sources of P loading delivered to each reservoir from its catchment were determined and scenario analysis was undertaken to predict the likely impact of catchment management strategies on the scale of rate of P loading delivered to each water body from its catchment. The results indicate the importance of farming and sewage treatment works/collective septic tanks discharges as the main contributors to the total diffuse and point source P loading delivered to the reservoirs, respectively. A reduction in the total P loading for all study areas would require control of farming practices and more efficient removal of P from human wastes prior to discharge to surface waters. The scenario analysis indicates a strategy based solely on reducing the agricultural P surplus may result in only a slow improvement in water quality, which would be unlikely to support the generation of good ecological status in reservoirs. The model application indicates that a reduction of P-inputs to the reservoirs should first focus on reducing P loading from sewage effluent discharges through the introduction of tertiary treatment (P-stripping) in all major residential areas. The fully calibrated export coefficient modelling approach transferred well to semi-arid regions, with the only significant limitation being the availability of suitable input data to drive the model. Further studies using this approach in semi-arid catchments are now needed to increase the knowledge of nutrient export behaviours in semi-arid regions.

Evaluation and management of the impact of land use change on the nitrogen and phosphorus load delivered to surface waters: the export coefficient modelling approach

A manageable, relatively inexpensive model was constructed to predict the loss of nitrogen and phosphorus from a complex catchment to its drainage system. The model used an export coefficient approach, calculating the total nitrogen (N) and total phosphorus (P) load delivered annually to a water body as the sum of the individual loads exported from each nutrient source in its catchment. The export coefficient modelling approach permits scaling up from plot-scale experiments to the catchment scale, allowing application of findings from field experimental studies at a suitable scale for catchment management. The catchment of the River Windrush, a tributary of the River Thames, UK, was selected as the initial study site. The Windrush model predicted nitrogen and phosphorus loading within 2% of observed total nitrogen load and 0.5% of observed total phosphorus load in 1989. The export coefficient modelling approach was then validated by application in a second research basin, the catchment of Slapton Ley, south Devon, which has markedly different catchment hydrology and land use. The Slapton model was calibrated within 2% of observed total nitrogen load and 2.5% of observed total phosphorus load in 1986. Both models proved sensitive to the impact of temporal changes in land use and management on water quality in both catchments, and were therefore used to evaluate the potential impact of proposed pollution control strategies on the nutrient loading delivered to the River Windrush and Slapton Ley

The Natural History of Slapton Ley Nature Reserve XVIII: nitrogen and phosphorus losses from the catchment - an export coefficient modelling approach

Nitrogen and phosphorus losses from the catchment of Slapton Ley, a small coastal lake in SW England, were calculated using an adaptation of a model developed by Jorgensen (1980). A detailed survey of the catchment revealed that its land use is dominated by both permanent and temporary grassland (respectively 38 and 32% of its total area), and that the remainder is made up of the cultivation of cereals and field vegetables, and market gardening. Livestock numbers in the catchment constitute ca. 6600 head of cattle, 10,000 sheep, 590 pigs, 1700 poultry and 58 horses. The permanent human population of the area is ca. 2000, served by two small gravity-fed sewage treatment works (STWs). Inputs to, and losses from, farmland in the catchment were computed using Jorgensen’s model, and coefficients derived from the data of Cooke (1976), Gostick (1982), Rast and Lee (1983) and Vollenweider (1968). Allowing for outputs from STWs, the total annual external load of N and P upon Slapton Ley is 160 t (35 kg ha-1) a-1 N, and 4.8 t (1.05 kg ha-1) a-1 P. Accordingly to Vollenweider (1968, 1975), such loadings exceed OECD permissible level by a factor of ca. 50 in the case of N, and ca. 5 in that of P. In order to reduce nutrient loads, attention would need to be paid to both STW and agricultural sources.

Determination of the gas diffusion coefficient of a peat grassland soil

Peatland habitats are important carbon stocks that also have the potential to be significant sources of greenhouse gases, particularly when subject to changes such as artificial drainage and application of fertilizer. Models aiming to estimate greenhouse gas release from peatlands require an accurate estimate of the diffusion coefficient of gas transport through soil (Ds). The availability of specific measurements for peatland soils is currently limited. This study measured Ds for a peat soil with an overlying clay horizon and compared values with those from widely available models. The Ds value of a sandy loam reference soil was measured for comparison. Using the Currie (1960) method, Ds was measured between an air-filled porosity (ϵ) range of 0 and 0.5 cm3 cm−3. Values of Ds for the peat cores ranged between 3.2 × 10−4 and 4.4 × 10−3 m2 hour−1, for loamy clay cores between 0 and 4.7 × 10−3 m2 hour−1 and for the sandy reference soil they were between 5.4 × 10−4 and 3.4 × 10−3 m2 hour−1. The agreement of measured and modelled values of relative diffusivity (Ds/D0, with D0 the diffusion coefficient through free air) varied with soil type; however, the Campbell (1985) model provided the best replication of measured values for all soils. This research therefore suggests that the use of the Campbell model in the absence of accurately measured Ds and porosity values for a study soil would be appropriate. Future research into methods to reduce shrinkage of peat during measurement and therefore allow measurement of Ds for a greater range of ϵ would be beneficial.

A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators

We study the homogeneous Riemann-Hilbert problem with a vanishing scalar-valued continuous coefficient. We characterize non-existence of nontrivial solutions in the case where the coefficient has its values along several rays starting from the origin. As a consequence, some results on injectivity and existence of eigenvalues of Toeplitz operators in Hardy spaces are obtained.

Phase separation and surface segregation in ceria-zirconia solid solutions

Using a combination of density functional theory calculations and statistical mechanics, we show that a wide range of intermediate compositions of ceria – zirconia solid solutions are thermodynamically metastable with respect to phase separation into Ce-rich and Zr-rich oxides. We estimate that the maximum equilibrium concentration of Zr in CeO2 at 1373 K is ~2%, and therefore equilibrated samples with higher Zr content are expected to exhibit heterogeneity at the atomic scale. We also demonstrate that in the vicinity of the (111) surface, cation redistribution at high temperatures will occur with significant Ce enrichment of the surface, which we attribute to the more covalent character of Zr-O bonds compared to Ce-O bonds. Although the kinetic barriers for cation diffusion normally prevent the decomposition/segregation of ceria-zirconia solid solutions in typical catalytic applications, the separation behaviour described here can be expected to occur in modern three-way catalytic converters, where very high temperatures are reached.

Urban segregation and inequality

This article reviews the shortcomings of the current UK planning system to address urban inequalities and segregation of impoverished communities.