Calibration and sensitivity analysis of a river water quality model under unsteady flow conditions

Water quality models generally require a relatively large number of parameters to define their functional relationships, and since prior information on parameter values is limited, these are commonly defined by fitting the model to observed data. In this paper, the identifiability of water quality parameters and the associated uncertainty in model simulations are investigated. A modification to the water quality model `Quality Simulation Along River Systems' is presented in which an improved flow component is used within the existing water quality model framework. The performance of the model is evaluated in an application to the Bedford Ouse river, UK, using a Monte-Carlo analysis toolbox. The essential framework of the model proved to be sound, and calibration and validation performance was generally good. However some supposedly important water quality parameters associated with algal activity were found to be completely insensitive, and hence non-identifiable, within the model structure, while others (nitrification and sedimentation) had optimum values at or close to zero, indicating that those processes were not detectable from the data set examined. (C) 2003 Elsevier Science B.V. All rights reserved.

Sensitivity analysis of a cyanobacterial growth and movement model under two different flow regimes

Bloom-forming and toxin-producing cyanobacteria remain a persistent nuisance across the world. Modelling cyanobacterial behaviour in freshwaters is an important tool for understanding their population dynamics and predicting the location and timing of the bloom events in lakes, reservoirs and rivers. A new deterministic–mathematical model was developed, which simulates the growth and movement of cyanobacterial blooms in river systems. The model focuses on the mathematical description of the bloom formation, vertical migration and lateral transport of colonies within river environments by taking into account the major factors that affect the cyanobacterial bloom formation in rivers including light, nutrients and temperature. A parameter sensitivity analysis using a one-at-a-time approach was carried out. There were two objectives of the sensitivity analysis presented in this paper: to identify the key parameters controlling the growth and movement patterns of cyanobacteria and to provide a means for model validation. The result of the analysis suggested that maximum growth rate and day length period were the most significant parameters in determining the population growth and colony depth, respectively.

Improving power and accuracy of genome-wide association studies via a multi-locus mixed linear model methodology

Genome-wide association studies (GWAS) have been widely used in genetic dissection of complex traits. However, common methods are all based on a fixed-SNP-effect mixed linear model (MLM) and single marker analysis, such as efficient mixed model analysis (EMMA). These methods require Bonferroni correction for multiple tests, which often is too conservative when the number of markers is extremely large. To address this concern, we proposed a random-SNP-effect MLM (RMLM) and a multi-locus RMLM (MRMLM) for GWAS. The RMLM simply treats the SNP-effect as random, but it allows a modified Bonferroni correction to be used to calculate the threshold p value for significance tests. The MRMLM is a multi-locus model including markers selected from the RMLM method with a less stringent selection criterion. Due to the multi-locus nature, no multiple test correction is needed. Simulation studies show that the MRMLM is more powerful in QTN detection and more accurate in QTN effect estimation than the RMLM, which in turn is more powerful and accurate than the EMMA. To demonstrate the new methods, we analyzed six flowering time related traits in Arabidopsis thaliana and detected more genes than previous reported using the EMMA. Therefore, the MRMLM provides an alternative for multi-locus GWAS.

The effect of doubled CO2 and model basic state biases on the monsoon-ENSO system. II: Changing ENSO regimes

Integrations of a fully-coupled climate model with and without flux adjustments in the equatorial oceans are performed under 2×CO2 conditions to explore in more detail the impact of increased greenhouse gas forcing on the monsoon-ENSO system. When flux adjustments are used to correct some systematic model biases, ENSO behaviour in the modelled future climate features distinct irregular and periodic (biennial) regimes. Comparison with the observed record yields some consistency with ENSO modes primarily based on air-sea interaction and those dependent on basinwide ocean wave dynamics. Simple theory is also used to draw analogies between the regimes and irregular (stochastically forced) and self-excited oscillations respectively. Periodic behaviour is also found in the Asian-Australian monsoon system, part of an overall biennial tendency of the model under these conditions related to strong monsoon forcing and increased coupling between the Indian and Pacific Oceans. The tropospheric biennial oscillation (TBO) thus serves as a useful descriptor for the coupled monsoon-ENSO system in this case. The presence of obvious regime changes in the monsoon-ENSO system on interdecadal timescales, when using flux adjustments, suggests there may be greater uncertainty in projections of future climate, although further modelling studies are required to confirm the realism and cause of such changes.

Spatial analysis of the error in a model of soil nitrogen

Models of the dynamics of nitrogen in soil (soil-N) can be used to aid the fertilizer management of a crop. The predictions of soil-N models can be validated by comparison with observed data. Validation generally involves calculating non-spatial statistics of the observations and predictions, such as their means, their mean squared-difference, and their correlation. However, when the model predictions are spatially distributed across a landscape the model requires validation with spatial statistics. There are three reasons for this: (i) the model may be more or less successful at reproducing the variance of the observations at different spatial scales; (ii) the correlation of the predictions with the observations may be different at different spatial scales; (iii) the spatial pattern of model error may be informative. In this study we used a model, parameterized with spatially variable input information about the soil, to predict the mineral-N content of soil in an arable field, and compared the results with observed data. We validated the performance of the N model spatially with a linear mixed model of the observations and model predictions, estimated by residual maximum likelihood. This novel approach allowed us to describe the joint variation of the observations and predictions as: (i) independent random variation that occurred at a fine spatial scale; (ii) correlated random variation that occurred at a coarse spatial scale; (iii) systematic variation associated with a spatial trend. The linear mixed model revealed that, in general, the performance of the N model changed depending on the spatial scale of interest. At the scales associated with random variation, the N model underestimated the variance of the observations, and the predictions were correlated poorly with the observations. At the scale of the trend, the predictions and observations shared a common surface. The spatial pattern of the error of the N model suggested that the observations were affected by the local soil condition, but this was not accounted for by the N model. In summary, the N model would be well-suited to field-scale management of soil nitrogen, but suited poorly to management at finer spatial scales. This information was not apparent with a non-spatial validation. (c),2007 Elsevier B.V. All rights reserved.

North Atlantic Oscillation response to transient greenhouse gas forcing and the impact on European winter climate: a CMIP2 multi-model assessment

This study investigates the response of wintertime North Atlantic Oscillation (NAO) to increasing concentrations of atmospheric carbon dioxide (CO2) as simulated by 18 global coupled general circulation models that participated in phase 2 of the Coupled Model Intercomparison Project (CMIP2). NAO has been assessed in control and transient 80-year simulations produced by each model under constant forcing, and 1% per year increasing concentrations of CO2, respectively. Although generally able to simulate the main features of NAO, the majority of models overestimate the observed mean wintertime NAO index of 8 hPa by 5-10 hPa. Furthermore, none of the models, in either the control or perturbed simulations, are able to reproduce decadal trends as strong as that seen in the observed NAO index from 1970-1995. Of the 15 models able to simulate the NAO pressure dipole, 13 predict a positive increase in NAO with increasing CO2 concentrations. The magnitude of the response is generally small and highly model-dependent, which leads to large uncertainty in multi-model estimates such as the median estimate of 0.0061 +/- 0.0036 hPa per %CO2. Although an increase of 0.61 hPa in NAO for a doubling in CO2 represents only a relatively small shift of 0.18 standard deviations in the probability distribution of winter mean NAO, this can cause large relative increases in the probabilities of extreme values of NAO associated with damaging impacts. Despite the large differences in NAO responses, the models robustly predict similar statistically significant changes in winter mean temperature (warmer over most of Europe) and precipitation (an increase over Northern Europe). Although these changes present a pattern similar to that expected due to an increase in the NAO index, linear regression is used to show that the response is much greater than can be attributed to small increases in NAO. NAO trends are not the key contributor to model-predicted climate change in wintertime mean temperature and precipitation over Europe and the Mediterranean region. However, the models' inability to capture the observed decadal variability in NAO might also signify a major deficiency in their ability to simulate the NAO-related responses to climate change.

Identifying adaptive genetic divergence among populations from genome scans

The identification of signatures of natural selection in genomic surveys has become an area of intense research, stimulated by the increasing ease with which genetic markers can be typed. Loci identified as subject to selection may be functionally important, and hence (weak) candidates for involvement in disease causation. They can also be useful in determining the adaptive differentiation of populations, and exploring hypotheses about speciation. Adaptive differentiation has traditionally been identified from differences in allele frequencies among different populations, summarised by an estimate of F-ST. Low outliers relative to an appropriate neutral population-genetics model indicate loci subject to balancing selection, whereas high outliers suggest adaptive (directional) selection. However, the problem of identifying statistically significant departures from neutrality is complicated by confounding effects on the distribution of F-ST estimates, and current methods have not yet been tested in large-scale simulation experiments. Here, we simulate data from a structured population at many unlinked, diallelic loci that are predominantly neutral but with some loci subject to adaptive or balancing selection. We develop a hierarchical-Bayesian method, implemented via Markov chain Monte Carlo (MCMC), and assess its performance in distinguishing the loci simulated under selection from the neutral loci. We also compare this performance with that of a frequentist method, based on moment-based estimates of F-ST. We find that both methods can identify loci subject to adaptive selection when the selection coefficient is at least five times the migration rate. Neither method could reliably distinguish loci under balancing selection in our simulations, even when the selection coefficient is twenty times the migration rate.

Sparse model identification using orthogonal forward regression with basis pursuit and D-optimality

An efficient model identification algorithm for a large class of linear-in-the-parameters models is introduced that simultaneously optimises the model approximation ability, sparsity and robustness. The derived model parameters in each forward regression step are initially estimated via the orthogonal least squares (OLS), followed by being tuned with a new gradient-descent learning algorithm based on the basis pursuit that minimises the l(1) norm of the parameter estimate vector. The model subset selection cost function includes a D-optimality design criterion that maximises the determinant of the design matrix of the subset to ensure model robustness and to enable the model selection procedure to automatically terminate at a sparse model. The proposed approach is based on the forward OLS algorithm using the modified Gram-Schmidt procedure. Both the parameter tuning procedure, based on basis pursuit, and the model selection criterion, based on the D-optimality that is effective in ensuring model robustness, are integrated with the forward regression. As a consequence the inherent computational efficiency associated with the conventional forward OLS approach is maintained in the proposed algorithm. Examples demonstrate the effectiveness of the new approach.

M-estimator, and D-optimality model construction using orthogonal forward regression

This correspondence introduces a new orthogonal forward regression (OFR) model identification algorithm using D-optimality for model structure selection and is based on an M-estimators of parameter estimates. M-estimator is a classical robust parameter estimation technique to tackle bad data conditions such as outliers. Computationally, The M-estimator can be derived using an iterative reweighted least squares (IRLS) algorithm. D-optimality is a model structure robustness criterion in experimental design to tackle ill-conditioning in model Structure. The orthogonal forward regression (OFR), often based on the modified Gram-Schmidt procedure, is an efficient method incorporating structure selection and parameter estimation simultaneously. The basic idea of the proposed approach is to incorporate an IRLS inner loop into the modified Gram-Schmidt procedure. In this manner, the OFR algorithm for parsimonious model structure determination is extended to bad data conditions with improved performance via the derivation of parameter M-estimators with inherent robustness to outliers. Numerical examples are included to demonstrate the effectiveness of the proposed algorithm.

Backward elimination model construction for regression and classification using leave-one-out criteria

A fundamental principle in practical nonlinear data modeling is the parsimonious principle of constructing the minimal model that explains the training data well. Leave-one-out (LOO) cross validation is often used to estimate generalization errors by choosing amongst different network architectures (M. Stone, "Cross validatory choice and assessment of statistical predictions", J. R. Stast. Soc., Ser. B, 36, pp. 117-147, 1974). Based upon the minimization of LOO criteria of either the mean squares of LOO errors or the LOO misclassification rate respectively, we present two backward elimination algorithms as model post-processing procedures for regression and classification problems. The proposed backward elimination procedures exploit an orthogonalization procedure to enable the orthogonality between the subspace as spanned by the pruned model and the deleted regressor. Subsequently, it is shown that the LOO criteria used in both algorithms can be calculated via some analytic recursive formula, as derived in this contribution, without actually splitting the estimation data set so as to reduce computational expense. Compared to most other model construction methods, the proposed algorithms are advantageous in several aspects; (i) There are no tuning parameters to be optimized through an extra validation data set; (ii) The procedure is fully automatic without an additional stopping criteria; and (iii) The model structure selection is directly based on model generalization performance. The illustrative examples on regression and classification are used to demonstrate that the proposed algorithms are viable post-processing methods to prune a model to gain extra sparsity and improved generalization.

Nonlinear model structure design and construction using orthogonal least squares and D-optimality design

A very efficient learning algorithm for model subset selection is introduced based on a new composite cost function that simultaneously optimizes the model approximation ability and model robustness and adequacy. The derived model parameters are estimated via forward orthogonal least squares, but the model subset selection cost function includes a D-optimality design criterion that maximizes the determinant of the design matrix of the subset to ensure the model robustness, adequacy, and parsimony of the final model. The proposed approach is based on the forward orthogonal least square (OLS) algorithm, such that new D-optimality-based cost function is constructed based on the orthogonalization process to gain computational advantages and hence to maintain the inherent advantage of computational efficiency associated with the conventional forward OLS approach. Illustrative examples are included to demonstrate the effectiveness of the new approach.

Nonlinear model structure detection using optimum experimental design and orthogonal least squares

A very efficient learning algorithm for model subset selection is introduced based on a new composite cost function that simultaneously optimizes the model approximation ability and model adequacy. The derived model parameters are estimated via forward orthogonal least squares, but the subset selection cost function includes an A-optimality design criterion to minimize the variance of the parameter estimates that ensures the adequacy and parsimony of the final model. An illustrative example is included to demonstrate the effectiveness of the new approach.

Deposition of charged inhaled aerosols with transient airflow in sequential lung airway model

Transport and deposition of charged inhaled aerosols in double planar bifurcation representing generation three to five of human respiratory system has been studied under a light activity breathing condition. Both steady and oscillatory laminar inhalation airflow is considered. Particle trajectories are calculated using a Lagrangian reference frame, which is dominated by the fluid force driven by airflow, gravity force and electrostatic forces (both of space and image charge forces). The particle-mesh method is selected to calculate the space charge force. This numerical study investigates the deposition efficiency in the three-dimensional model under various particle sizes, charge values, and inlet particle distribution. Numerical results indicate that particles carrying an adequate level of charge can improve deposition efficiency in the airway model.

Selfishness and altruism can coexist when help is subject to diminishing returns

Altruism and selfishness are 30–50% heritable in man in both Western and non-Western populations. This genetically based variation in altruism and selfishness requires explanation. In non-human animals, altruism is generally directed towards relatives, and satisfies the condition known as Hamilton's rule. This nepotistic altruism evolves under natural selection only if the ratio of the benefit of receiving help to the cost of giving it exceeds a value that depends on the relatedness of the individuals involved. Standard analyses assume that the benefit provided by each individual is the same but it is plausible in some cases that as more individuals contribute, help is subject to diminishing returns. We analyse this situation using a single-locus two-allele model of selection in a diploid population with the altruistic allele dominant to the selfish allele. The analysis requires calculation of the relationship between the fitnesses of the genotypes and the frequencies of the genes. The fitnesses vary not only with the genotype of the individual but also with the distribution of phenotypes amongst the sibs of the individual and this depends on the genotypes of his parents. These calculations are not possible by direct fitness or ESS methods but are possible using population genetics. Our analysis shows that diminishing returns change the operation of natural selection and the outcome can now be a stable equilibrium between altruistic and selfish alleles rather than the elimination of one allele or the other. We thus provide a plausible genetic model of kin selection that leads to the stable coexistence in the same population of both altruistic and selfish individuals. This may explain reported genetic variation in altruism in man.