A genome scan for eye color in 502 twin families: Most variation is due to a QTL on chromosome 15q

We have rated eye color on a 3-point scale (1=blue/grey, 2=hazel/green, 3=brown) in 502 twin families and carried out a 5-10 cM genome scan (400-757 markers). We analyzed eye color as a threshold trait and performed multipoint sib pair linkage analysis using variance components analysis in Mx. A lod of 19.2 was found at the marker D15S1002, less than 1 cM from OCA2, which has been previously implicated in eye color variation. We estimate that 74% of variance in eye color liability is due to this QTL and a further 18% due to polygenic effects. However, a large shoulder on this peak suggests that other loci affecting eye color may be telomeric of OCA2 and inflating the QTL estimate. No other peaks reached genome-wide significance, although lods >2 were seen on 5p and 14q and lods >1 were additionally seen on chromosomes 2, 3, 6, 7, 8, 9, 17 and 18. Most of these secondary peaks were reduced or eliminated when we repeated the scan as a two locus analysis with the 15q linkage included, although this does not necessarily exclude them as false positives. We also estimated the interaction between the 15q QTL and the other marker locus but there was only minor evidence for additive x additive epistasis. Elaborating the analysis to the full two-locus model including non-additive main effects and interactions did not strengthen the evidence for epistasis. We conclude that most variation in eye color in Europeans is due to polymorphism in OCA2 but that there may be modifiers at several other loci.

Increasing uncertainty: A definition

We present a definition of increasing uncertainty, in which an elementary increase in the uncertainty of any act corresponds to the addition of an 'elementary bet' that increases consumption by a fixed amount in (relatively) 'good' states and decreases consumption by a fixed (and possibly different) amount in (relatively) 'bad' states. This definition naturally gives rise to a dual definition of comparative aversion to uncertainty. We characterize this definition for a popular class of generalized models of choice under uncertainty.

Assumption-free estimation of heritability from genome-wide identity-by-descent sharing between full siblings

The study of continuously varying, quantitative traits is important in evolutionary biology, agriculture, and medicine. Variation in such traits is attributable to many, possibly interacting, genes whose expression may be sensitive to the environment, which makes their dissection into underlying causative factors difficult. An important population parameter for quantitative traits is heritability, the proportion of total variance that is due to genetic factors. Response to artificial and natural selection and the degree of resemblance between relatives are all a function of this parameter. Following the classic paper by R. A. Fisher in 1918, the estimation of additive and dominance genetic variance and heritability in populations is based upon the expected proportion of genes shared between different types of relatives, and explicit, often controversial and untestable models of genetic and non-genetic causes of family resemblance. With genome-wide coverage of genetic markers it is now possible to estimate such parameters solely within families using the actual degree of identity-by-descent sharing between relatives. Using genome scans on 4,401 quasi-independent sib pairs of which 3,375 pairs had phenotypes, we estimated the heritability of height from empirical genome-wide identity-by-descent sharing, which varied from 0.374 to 0.617 (mean 0.498, standard deviation 0.036). The variance in identity-by-descent sharing per chromosome and per genome was consistent with theory. The maximum likelihood estimate of the heritability for height was 0.80 with no evidence for non-genetic causes of sib resemblance, consistent with results from independent twin and family studies but using an entirely separate source of information. Our application shows that it is feasible to estimate genetic variance solely from within- family segregation and provides an independent validation of previously untestable assumptions. Given sufficient data, our new paradigm will allow the estimation of genetic variation for disease susceptibility and quantitative traits that is free from confounding with non-genetic factors and will allow partitioning of genetic variation into additive and non-additive components.

Genetic and Cultural Transmission of Smoking Initiation: An Extended Twin Kinship Model

Background Considerable evidence from twin and adoption studies indicates that genetic and shared environmental factors play a significant role in the initiation of smoking behavior. Although twin and adoption designs are powerful to detect genetic and environmental influences, they do not provide information on the processes of assortative mating and parent–offspring transmission and their contribution to the variability explained by genetic and/or environmental factors. Methods We examined the role of genetic and environmental factors for smoking initiation using an extended kinship design. This design allows the simultaneous testing of additive and non-additive genetic, shared and individual-specific environmental factors, as well as sex differences in the expression of genes and environment in the presence of assortative mating and combined genetic and cultural transmission. A dichotomous lifetime smoking measure was obtained from twins and relatives in the Virginia 30,000 sample. Results Results demonstrate that both genetic and environmental factors play a significant role in the liability to smoking initiation. Major influences on individual differences appeared to be additive genetic and unique environmental effects, with smaller contributions from assortative mating, shared sibling environment, twin environment, cultural transmission and resulting genotype–environment covariance. The finding of negative cultural transmission without dominance led us to investigate more closely two possible mechanisms for the lower parent–offspring correlations compared to the sibling and DZ twin correlations in subsets of the data: (i) age × gene interaction, and (ii) social homogamy. Neither mechanism provided a significantly better explanation of the data, although age regression was significant. Conclusions This study showed significant heritability, partly due to assortment, and significant effects of primarily non-parental shared environment on smoking initiation.

The utility and limitations of chloroplast DNA analysis for identifying native British oak stands and for guiding replanting strategy

We report a method using variation in the chloroplast genome (cpDNA) to test whether oak stands of unknown provenance are of native and/or local origin. As an example, a sample of test oaks, of mostly unknown status in relation to nativeness and localness, were surveyed for cpDNA type. The sample comprised 126 selected trees, derived from 16 British seed stands, and 75 trees, selected for their superior phenotype (201 tree samples in total). To establish whether these two test groups are native and local, their cpDNA type was compared with that of material from known autochthonous origin (results of a previous study which examined variation in 1076 trees from 224 populations distributed across Great Britain). In the previous survey of autochthonous material, four cpDNA types were identified as native; thus if a test sample possessed a new haplotype then it could be classed as non-native. Every one of the 201 test samples possessed one of the four cpDNA types found within the autochthonous sample. Therefore none could be proven to be introduced and, on this basis, was considered likely to be native. The previous study of autochthonous material also found that cpDNA variation was highly structured geographically and, therefore, if the cpDNA type of the test sample did not match that of neighbouring autochthonous trees then it could be considered to be non-local. A high proportion of the seed stand group (44.2 per cent) and the phenotypically superior trees (58.7 per cent) possessed a cpDNA haplotype which matched that of the neighbouring autochthonous trees and, therefore, can be considered as local, or at least cannot be proven to be introduced. The remainder of the test sample could be divided into those which did not grow in an area of overall dominance (18.7 per cent of seed stand trees and 28 per cent of phenotypically superior) and those which failed to match the neighbouring autochthonous haplotype (37.1 per cent and 13.3 per cent, respectively). Most of the non-matching test samples were located within 50 km of an area dominated by a matching autochthonous haplotype (96.0 per cent and 93.5 per cent, respectively), and potentially indicates only local transfer. Whilst such genetic fingerprinting tests have proven useful for assessing the origin of stands of unknown provenance, there are potential limitations to using a marker from the chloroplast genome (mostly adaptively neutral) for classifying seed material into categories which have adaptive implications. These limitations are discussed, particularly within the context of selecting adaptively superior material for restocking native forests.

Optimization of co-current spray drying process of sugar-rich foods. Part I - Moisture and glass transition temperature profile during drying

A steady state mathematical model for co-current spray drying was developed for sugar-rich foods with the application of the glass transition temperature concept. Maltodextrin-sucrose solution was used as a sugar-rich food model. The model included mass, heat and momentum balances for a single droplet drying as well as temperature and humidity profile of the drying medium. A log-normal volume distribution of the droplets was generated at the exit of the rotary atomizer. This generation created a certain number of bins to form a system of non-linear first-order differential equations as a function of the axial distance of the drying chamber. The model was used to calculate the changes of droplet diameter, density, temperature, moisture content and velocity in association with the change of air properties along the axial distance. The difference between the outlet air temperature and the glass transition temperature of the final products (AT) was considered as an indicator of stickiness of the particles in spray drying process. The calculated and experimental AT values were close, indicating successful validation of the model. (c) 2004 Elsevier Ltd. All rights reserved.

A theoretical comparison of two optimization methods for radiofrequency drive schemes in high frequency MRI resonators

In this paper, numerical simulations are used in an attempt to find optimal Source profiles for high frequency radiofrequency (RF) volume coils. Biologically loaded, shielded/unshielded circular and elliptical birdcage coils operating at 170 MHz, 300 MHz and 470 MHz are modelled using the FDTD method for both 2D and 3D cases. Taking advantage of the fact that some aspects of the electromagnetic system are linear, two approaches have been proposed for the determination of the drives for individual elements in the RF resonator. The first method is an iterative optimization technique with a kernel for the evaluation of RF fields inside an imaging plane of a human head model using pre-characterized sensitivity profiles of the individual rungs of a resonator; the second method is a regularization-based technique. In the second approach, a sensitivity matrix is explicitly constructed and a regularization procedure is employed to solve the ill-posed problem. Test simulations show that both methods can improve the B-1-field homogeneity in both focused and non-focused scenarios. While the regularization-based method is more efficient, the first optimization method is more flexible as it can take into account other issues such as controlling SAR or reshaping the resonator structures. It is hoped that these schemes and their extensions will be useful for the determination of multi-element RF drives in a variety of applications.

Efficient accommodation of local minima in watershed model calibration

The Gauss-Marquardt-Levenberg (GML) method of computer-based parameter estimation, in common with other gradient-based approaches, suffers from the drawback that it may become trapped in local objective function minima, and thus report optimized parameter values that are not, in fact, optimized at all. This can seriously degrade its utility in the calibration of watershed models where local optima abound. Nevertheless, the method also has advantages, chief among these being its model-run efficiency, and its ability to report useful information on parameter sensitivities and covariances as a by-product of its use. It is also easily adapted to maintain this efficiency in the face of potential numerical problems (that adversely affect all parameter estimation methodologies) caused by parameter insensitivity and/or parameter correlation. The present paper presents two algorithmic enhancements to the GML method that retain its strengths, but which overcome its weaknesses in the face of local optima. Using the first of these methods an intelligent search for better parameter sets is conducted in parameter subspaces of decreasing dimensionality when progress of the parameter estimation process is slowed either by numerical instability incurred through problem ill-posedness, or when a local objective function minimum is encountered. The second methodology minimizes the chance of successive GML parameter estimation runs finding the same objective function minimum by starting successive runs at points that are maximally removed from previous parameter trajectories. As well as enhancing the ability of a GML-based method to find the global objective function minimum, the latter technique can also be used to find the locations of many non-global optima (should they exist) in parameter space. This can provide a useful means of inquiring into the well-posedness of a parameter estimation problem, and for detecting the presence of bimodal parameter and predictive probability distributions. The new methodologies are demonstrated by calibrating a Hydrological Simulation Program-FORTRAN (HSPF) model against a time series of daily flows. Comparison with the SCE-UA method in this calibration context demonstrates a high level of comparative model run efficiency for the new method. (c) 2006 Elsevier B.V. All rights reserved.

The cross-entropy method for continuous multi-extremal optimization

In recent years, the cross-entropy method has been successfully applied to a wide range of discrete optimization tasks. In this paper we consider the cross-entropy method in the context of continuous optimization. We demonstrate the effectiveness of the cross-entropy method for solving difficult continuous multi-extremal optimization problems, including those with non-linear constraints.