A model for predicting the future incidence of coronary heart disease within percentiles of coronary heart disease risk

Background We present a method (The CHD Prevention Model) for modelling the incidence of fatal and nonfatal coronary heart disease (CHD) within various CHD risk percentiles of an adult population. The model provides a relatively simple tool for lifetime risk prediction for subgroups within a population. It allows an estimation of the absolute primary CHD risk in different populations and will help identify subgroups of the adult population where primary CHD prevention is most appropriate and cost-effective. Methods The CHD risk distribution within the Australian population was modelled, based on the prevalence of CHD risk, individual estimates of integrated CHD risk, and current CHD mortality rates. Predicted incidence of first fatal and nonfatal myocardial infarction within CHD risk strata of the Australian population was determined. Results Approximately 25% of CHD deaths were predicted to occur amongst those in the top 10 percentiles of integrated CHD risk, regardless of age group or gender. It was found that while all causes survival did not differ markedly between percentiles of CHD risk before the ages of around 50-60, event-free survival began visibly to differ about 5 years earlier. Conclusions The CHD Prevention Model provides a means of predicting future CHD incidence amongst various strata of integrated CHD risk within an adult population. It has significant application both in individual risk counselling and in the identification of subgroups of the population where drug therapy to reduce CHD risk is most cost-effective. J Cardiovasc Risk 8:31-37 (C) 2001 Lippincott Williams & Wilkins.

Physical function interfering with pain and symptoms in fibromyalgia patients

Objectives. The aim of this study was to assess the relationship between variables of physical assessment - muscular strength, flexibility and dynamic balance - with pain, pain threshold, and fibromyalgia symptoms (FM). Methods. Our sample consists of 55 women, with age ranging from 30 to 55 years (mean of 46.5, (standard deviation, SD=6.6)), mean body mass index (BMI) of 28.7(3.8) and diagnosed for FM according to the American College of Rheumatology criteria. Pain intensity was measured using a visual analogue scale (VAS) and pain threshold (PT) using Fisher`s dolorimeter. FM symptoms were assessed by the Fibromyalgia Impact Questionnaire (FIQ); flexibility by the third finger to floor test (3FF); the muscular strength index (MSI) by the maximum volunteer isometric contraction at flexion and extension of right knee and elbow using a force transducer, dynamic balance by the time to get up and go (TUG) test and the functional reach test (FRT). Data were analysed using Pearson`s correlation, as well as simple and multivariate regression tests, with significance level of 5%. Results. PT and FIQ were weakly but significantly correlated with the TUG, MSI and 3FF as well as VAS with the TUG and MSI (p<0.05). VAS, PT and FIQ was not correlated with FRT. Simple regression suggests that, alone, TUG, FR, MSI and 3FF are low predictors of VAS, PT and FIQ. For the VAS, the best predictive model includes TUG and MSI, explaining 12.6% of pain. variability. For TP and total symptoms, as obtained by the FIQ, most predictive model includes 3FF and MSI, which respectively respond by 30% and 21% of the variability. Conclusion. Muscular strength, flexibility and balance are associated with pain, pain threshold, and symptoms in FM patients.

Review and future directions in the modelling and control of continuous drum granulation

Many granulation plants operate well below design capacity, suffering from high recycle rates and even periodic instabilities. This behaviour cannot be fully predicted using the present models. The main objective of the paper is to provide an overview of the current status of model development for granulation processes and suggest future directions for research and development. The end-use of the models is focused on the optimal design and control of granulation plants using the improved predictions of process dynamics. The development of novel models involving mechanistically based structural switching methods is proposed in the paper. A number of guidelines are proposed for the selection of control relevant model structures. (C) 2002 Published by Elsevier Science B.V.

Pharmacogenetics-based population pharmacokinetic analysis of efavirenz in HIV-1-infected individuals.

Besides CYP2B6, other polymorphic enzymes contribute to efavirenz (EFV) interindividual variability. This study was aimed at quantifying the impact of multiple alleles on EFV disposition. Plasma samples from 169 human immunodeficiency virus (HIV) patients characterized for CYP2B6, CYP2A6, and CYP3A4/5 allelic diversity were used to build up a population pharmacokinetic model using NONMEM (non-linear mixed effects modeling), the aim being to seek a general approach combining genetic and demographic covariates. Average clearance (CL) was 11.3 l/h with a 65% interindividual variability that was explained largely by CYP2B6 genetic variation (31%). CYP2A6 and CYP3A4 had a prominent influence on CL, mostly when CYP2B6 was impaired. Pharmacogenetics fully accounted for ethnicity, leaving body weight as the only significant demographic factor influencing CL. Square roots of the numbers of functional alleles best described the influence of each gene, without interaction. Functional genetic variations in both principal and accessory metabolic pathways demonstrate a joint impact on EFV disposition. Therefore, dosage adjustment in accordance with the type of polymorphism (CYP2B6, CYP2A6, or CYP3A4) is required in order to maintain EFV within the therapeutic target levels.

Population pharmacokinetic-pharmacodynamic modelling of angiotensin receptor blockade in healthy volunteers.

OBJECTIVE: To compare the pharmacokinetic and pharmacodynamic characteristics of angiotensin II receptor antagonists as a therapeutic class. DESIGN: Population pharmacokinetic-pharmacodynamic modelling study. METHODS: The data of 14 phase I studies with 10 different drugs were analysed. A common population pharmacokinetic model (two compartments, mixed zero- and first-order absorption, two metabolite compartments) was applied to the 2685 drug and 900 metabolite concentration measurements. A standard nonlinear mixed effect modelling approach was used to estimate the drug-specific parameters and their variabilities. Similarly, a pharmacodynamic model was applied to the 7360 effect measurements, i.e. the decrease of peak blood pressure response to intravenous angiotensin challenge recorded by finger photoplethysmography. The concentration of drug and metabolite in an effect compartment was assumed to translate into receptor blockade [maximum effect (Emax) model with first-order link]. RESULTS: A general pharmacokinetic-pharmacodynamic (PK-PD) model for angiotensin antagonism in healthy individuals was successfully built up for the 10 drugs studied. Representatives of this class share different pharmacokinetic and pharmacodynamic profiles. Their effects on blood pressure are dose-dependent, but the time course of the effect varies between the drugs. CONCLUSIONS: The characterisation of PK-PD relationships for these drugs gives the opportunity to optimise therapeutic regimens and to suggest dosage adjustments in specific conditions. Such a model can be used to further refine the use of this class of drugs.

Prediction of infant drug exposure through breastfeeding: population PK modeling and simulation of fluoxetine

BACKGROUND: Risks of significant infant drug exposurethrough breastmilk are poorly defined for many drugs, and largescalepopulation data are lacking. We used population pharmacokinetics(PK) modeling to predict fluoxetine exposure levels ofinfants via mother's milk in a simulated population of 1000 motherinfantpairs.METHODS: Using our original data on fluoxetine PK of 25breastfeeding women, a population PK model was developed withNONMEM and parameters, including milk concentrations, wereestimated. An exponential distribution model was used to account forindividual variation. Simulation random and distribution-constrainedassignment of doses, dosing time, feeding intervals and milk volumewas conducted to generate 1000 mother-infant pairs with characteristicssuch as the steady-state serum concentrations (Css) and infantdose relative to the maternal weight-adjusted dose (relative infantdose: RID). Full bioavailability and a conservative point estimate of1-month-old infant CYP2D6 activity to be 20% of the adult value(adjusted by weigth) according to a recent study, were assumed forinfant Css calculations.RESULTS: A linear 2-compartment model was selected as thebest model. Derived parameters, including milk-to-plasma ratios(mean: 0.66; SD: 0.34; range, 0 - 1.1) were consistent with the valuesreported in the literature. The estimated RID was below 10% in >95%of infants. The model predicted median infant-mother Css ratio was0.096 (range 0.035 - 0.25); literature reported mean was 0.07 (range0-0.59). Moreover, the predicted incidence of infant-mother Css ratioof >0.2 was less than 1%.CONCLUSION: Our in silico model prediction is consistent withclinical observations, suggesting that substantial systemic fluoxetineexposure in infants through human milk is rare, but further analysisshould include active metabolites. Our approach may be valid forother drugs. [supported by CIHR and Swiss National Science Foundation(SNSF)]

The population genetics of clonal and partially clonal diploids.

The consequences of variable rates of clonal reproduction on the population genetics of neutral markers are explored in diploid organisms within a subdivided population (island model). We use both analytical and stochastic simulation approaches. High rates of clonal reproduction will positively affect heterozygosity. As a consequence, nearly twice as many alleles per locus can be maintained and population differentiation estimated as F(ST) value is strongly decreased in purely clonal populations as compared to purely sexual ones. With increasing clonal reproduction, effective population size first slowly increases and then points toward extreme values when the reproductive system tends toward strict clonality. This reflects the fact that polymorphism is protected within individuals due to fixed heterozygosity. Contrarily, genotypic diversity smoothly decreases with increasing rates of clonal reproduction. Asexual populations thus maintain higher genetic diversity at each single locus but a lower number of different genotypes. Mixed clonal/sexual reproduction is nearly indistinguishable from strict sexual reproduction as long as the proportion of clonal reproduction is not strongly predominant for all quantities investigated, except for genotypic diversities (both at individual loci and over multiple loci).

Pharmacogenetics-based population pharmacokinetic analysis of etravirine in HIV-1 infected individuals.

OBJECTIVES: Etravirine (ETV) is metabolized by cytochrome P450 (CYP) 3A, 2C9, and 2C19. Metabolites are glucuronidated by uridine diphosphate glucuronosyltransferases (UGT). To identify the potential impact of genetic and non-genetic factors involved in ETV metabolism, we carried out a two-step pharmacogenetics-based population pharmacokinetic study in HIV-1 infected individuals. MATERIALS AND METHODS: The study population included 144 individuals contributing 289 ETV plasma concentrations and four individuals contributing 23 ETV plasma concentrations collected in a rich sampling design. Genetic variants [n=125 single-nucleotide polymorphisms (SNPs)] in 34 genes with a predicted role in ETV metabolism were selected. A first step population pharmacokinetic model included non-genetic and known genetic factors (seven SNPs in CYP2C, one SNP in CYP3A5) as covariates. Post-hoc individual ETV clearance (CL) was used in a second (discovery) step, in which the effect of the remaining 98 SNPs in CYP3A, P450 cytochrome oxidoreductase (POR), nuclear receptor genes, and UGTs was investigated. RESULTS: A one-compartment model with zero-order absorption best characterized ETV pharmacokinetics. The average ETV CL was 41 (l/h) (CV 51.1%), the volume of distribution was 1325 l, and the mean absorption time was 1.2 h. The administration of darunavir/ritonavir or tenofovir was the only non-genetic covariate influencing ETV CL significantly, resulting in a 40% [95% confidence interval (CI): 13-69%] and a 42% (95% CI: 17-68%) increase in ETV CL, respectively. Carriers of rs4244285 (CYP2C19*2) had 23% (8-38%) lower ETV CL. Co-administered antiretroviral agents and genetic factors explained 16% of the variance in ETV concentrations. None of the SNPs in the discovery step influenced ETV CL. CONCLUSION: ETV concentrations are highly variable, and co-administered antiretroviral agents and genetic factors explained only a modest part of the interindividual variability in ETV elimination. Opposing effects of interacting drugs effectively abrogate genetic influences on ETV CL, and vice-versa.

Population viscosity can promote the evolution of altruistic sterile helpers and eusociality.

Because it increases relatedness between interacting individuals, population viscosity has been proposed to favour the evolution of altruistic helping. However, because it increases local competition between relatives, population viscosity may also act as a brake for the evolution of helping behaviours. In simple models, the kin selected fecundity benefits of helping are exactly cancelled out by the cost of increased competition between relatives when helping occurs after dispersal. This result has lead to the widespread view, especially among people working with social organisms, that special conditions are required for the evolution of altruism. Here, we re-examine this result by constructing a simple population genetic model where we analyse whether the evolution of a sterile worker caste (i.e. an extreme case of altruism) can be selected for by limited dispersal. We show that a sterile worker caste can be selected for even under the simplest life-cycle assumptions. This has relevant consequences for our understanding of the evolution of altruism in social organisms, as many social insects are characterized by limited dispersal and significant genetic population structure.

Linking landscape- and population ecology for large population management modelling: the case of Ibex (capra ibex) in Switzerland

La biologie de la conservation est communément associée à la protection de petites populations menacées d?extinction. Pourtant, il peut également être nécessaire de soumettre à gestion des populations surabondantes ou susceptibles d?une trop grande expansion, dans le but de prévenir les effets néfastes de la surpopulation. Du fait des différences tant quantitatives que qualitatives entre protection des petites populations et contrôle des grandes, il est nécessaire de disposer de modèles et de méthodes distinctes. L?objectif de ce travail a été de développer des modèles prédictifs de la dynamique des grandes populations, ainsi que des logiciels permettant de calculer les paramètres de ces modèles et de tester des scénarios de gestion. Le cas du Bouquetin des Alpes (Capra ibex ibex) - en forte expansion en Suisse depuis sa réintroduction au début du XXème siècle - servit d?exemple. Cette tâche fut accomplie en trois étapes : En premier lieu, un modèle de dynamique locale, spécifique au Bouquetin, fut développé : le modèle sous-jacent - structuré en classes d?âge et de sexe - est basé sur une matrice de Leslie à laquelle ont été ajoutées la densité-dépendance, la stochasticité environnementale et la chasse de régulation. Ce modèle fut implémenté dans un logiciel d?aide à la gestion - nommé SIM-Ibex - permettant la maintenance de données de recensements, l?estimation automatisée des paramètres, ainsi que l?ajustement et la simulation de stratégies de régulation. Mais la dynamique d?une population est influencée non seulement par des facteurs démographiques, mais aussi par la dispersion et la colonisation de nouveaux espaces. Il est donc nécessaire de pouvoir modéliser tant la qualité de l?habitat que les obstacles à la dispersion. Une collection de logiciels - nommée Biomapper - fut donc développée. Son module central est basé sur l?Analyse Factorielle de la Niche Ecologique (ENFA) dont le principe est de calculer des facteurs de marginalité et de spécialisation de la niche écologique à partir de prédicteurs environnementaux et de données d?observation de l?espèce. Tous les modules de Biomapper sont liés aux Systèmes d?Information Géographiques (SIG) ; ils couvrent toutes les opérations d?importation des données, préparation des prédicteurs, ENFA et calcul de la carte de qualité d?habitat, validation et traitement des résultats ; un module permet également de cartographier les barrières et les corridors de dispersion. Le domaine d?application de l?ENFA fut exploré par le biais d?une distribution d?espèce virtuelle. La comparaison à une méthode couramment utilisée pour construire des cartes de qualité d?habitat, le Modèle Linéaire Généralisé (GLM), montra qu?elle était particulièrement adaptée pour les espèces cryptiques ou en cours d?expansion. Les informations sur la démographie et le paysage furent finalement fusionnées en un modèle global. Une approche basée sur un automate cellulaire fut choisie, tant pour satisfaire aux contraintes du réalisme de la modélisation du paysage qu?à celles imposées par les grandes populations : la zone d?étude est modélisée par un pavage de cellules hexagonales, chacune caractérisée par des propriétés - une capacité de soutien et six taux d?imperméabilité quantifiant les échanges entre cellules adjacentes - et une variable, la densité de la population. Cette dernière varie en fonction de la reproduction et de la survie locale, ainsi que de la dispersion, sous l?influence de la densité-dépendance et de la stochasticité. Un logiciel - nommé HexaSpace - fut développé pour accomplir deux fonctions : 1° Calibrer l?automate sur la base de modèles de dynamique (par ex. calculés par SIM-Ibex) et d?une carte de qualité d?habitat (par ex. calculée par Biomapper). 2° Faire tourner des simulations. Il permet d?étudier l?expansion d?une espèce envahisseuse dans un paysage complexe composé de zones de qualité diverses et comportant des obstacles à la dispersion. Ce modèle fut appliqué à l?histoire de la réintroduction du Bouquetin dans les Alpes bernoises (Suisse). SIM-Ibex est actuellement utilisé par les gestionnaires de la faune et par les inspecteurs du gouvernement pour préparer et contrôler les plans de tir. Biomapper a été appliqué à plusieurs espèces (tant végétales qu?animales) à travers le Monde. De même, même si HexaSpace fut initialement conçu pour des espèces animales terrestres, il pourrait aisément être étndu à la propagation de plantes ou à la dispersion d?animaux volants. Ces logiciels étant conçus pour, à partir de données brutes, construire un modèle réaliste complexe, et du fait qu?ils sont dotés d?une interface d?utilisation intuitive, ils sont susceptibles de nombreuses applications en biologie de la conservation. En outre, ces approches peuvent également s?appliquer à des questions théoriques dans les domaines de l?écologie des populations et du paysage.<br/><br/>Conservation biology is commonly associated to small and endangered population protection. Nevertheless, large or potentially large populations may also need human management to prevent negative effects of overpopulation. As there are both qualitative and quantitative differences between small population protection and large population controlling, distinct methods and models are needed. The aim of this work was to develop theoretical models to predict large population dynamics, as well as computer tools to assess the parameters of these models and to test management scenarios. The alpine Ibex (Capra ibex ibex) - which experienced a spectacular increase since its reintroduction in Switzerland at the beginning of the 20th century - was used as paradigm species. This task was achieved in three steps: A local population dynamics model was first developed specifically for Ibex: the underlying age- and sex-structured model is based on a Leslie matrix approach with addition of density-dependence, environmental stochasticity and culling. This model was implemented into a management-support software - named SIM-Ibex - allowing census data maintenance, parameter automated assessment and culling strategies tuning and simulating. However population dynamics is driven not only by demographic factors, but also by dispersal and colonisation of new areas. Habitat suitability and obstacles modelling had therefore to be addressed. Thus, a software package - named Biomapper - was developed. Its central module is based on the Ecological Niche Factor Analysis (ENFA) whose principle is to compute niche marginality and specialisation factors from a set of environmental predictors and species presence data. All Biomapper modules are linked to Geographic Information Systems (GIS); they cover all operations of data importation, predictor preparation, ENFA and habitat suitability map computation, results validation and further processing; a module also allows mapping of dispersal barriers and corridors. ENFA application domain was then explored by means of a simulated species distribution. It was compared to a common habitat suitability assessing method, the Generalised Linear Model (GLM), and was proven better suited for spreading or cryptic species. Demography and landscape informations were finally merged into a global model. To cope with landscape realism and technical constraints of large population modelling, a cellular automaton approach was chosen: the study area is modelled by a lattice of hexagonal cells, each one characterised by a few fixed properties - a carrying capacity and six impermeability rates quantifying exchanges between adjacent cells - and one variable, population density. The later varies according to local reproduction/survival and dispersal dynamics, modified by density-dependence and stochasticity. A software - named HexaSpace - was developed, which achieves two functions: 1° Calibrating the automaton on the base of local population dynamics models (e.g., computed by SIM-Ibex) and a habitat suitability map (e.g. computed by Biomapper). 2° Running simulations. It allows studying the spreading of an invading species across a complex landscape made of variously suitable areas and dispersal barriers. This model was applied to the history of Ibex reintroduction in Bernese Alps (Switzerland). SIM-Ibex is now used by governmental wildlife managers to prepare and verify culling plans. Biomapper has been applied to several species (both plants and animals) all around the World. In the same way, whilst HexaSpace was originally designed for terrestrial animal species, it could be easily extended to model plant propagation or flying animals dispersal. As these softwares were designed to proceed from low-level data to build a complex realistic model and as they benefit from an intuitive user-interface, they may have many conservation applications. Moreover, theoretical questions in the fields of population and landscape ecology might also be addressed by these approaches.

Control and Simulation of Batch Crystallization

Concerning process control of batch cooling crystallization the present work focused on the cooling profile and seeding technique. Secondly, the influence of additives on batch-wise precipitation process was investigated. Moreover, a Computational Fluid Dynamics (CFD) model for simulation of controlled batch cooling crystallization was developed. A novel cooling model to control supersaturation level during batch-wise cooling crystallization was introduced. The crystallization kinetics together with operating conditions, i.e. seed loading, cooling rate and batch time, were taken into account in the model. Especially, the supersaturation- and suspension density- dependent secondary nucleation was included in the model. The interaction between the operating conditions and their influence on the control target, i.e. the constant level of supersaturation, were studied with the aid of a numerical solution for the cooling model. Further, the batch cooling crystallization was simulated with the ideal mixing model and CFD model. The moment transformation of the population balance, together with the mass and heat balances, were solved numerically in the simulation. In order to clarify a relationship betweenthe operating conditions and product sizes, a system chart was developed for anideal mixing condition. The utilization of the system chart to determine the appropriate operating condition to meet a required product size was introduced. With CFD simulation, batch crystallization, operated following a specified coolingmode, was studied in the crystallizers having different geometries and scales. The introduced cooling model and simulation results were verified experimentallyfor potassium dihydrogen phosphate (KDP) and the novelties of the proposed control policies were demonstrated using potassium sulfate by comparing with the published results in the literature. The study on the batch-wise precipitation showed that immiscible additives could promote the agglomeration of a derivative of benzoic acid, which facilitated the filterability of the crystal product.

Optimisation de l’administration des médicaments chez les enfants transplantés grâce à la pharmacocinétique de population

Ce travail de thèse porte sur l’application de la pharmacocinétique de population dans le but d’optimiser l’utilisation de certains médicaments chez les enfants immunosupprimés et subissant une greffe. Parmi les différents médicaments utilisés chez les enfants immunosupprimés, l’utilisation du busulfan, du tacrolimus et du voriconazole reste problématique, notamment à cause d’une très grande variabilité interindividuelle de leur pharmacocinétique rendant nécessaire l’individualisation des doses par le suivi thérapeutique pharmacologique. De plus, ces médicaments n’ont pas fait l’objet d’études chez les enfants et les doses sont adaptées à partir des adultes. Cette dernière pratique ne prend pas en compte les particularités pharmacologiques qui caractérisent l’enfant tout au long de son développement et rend illusoire l’extrapolation aux enfants des données acquises chez les adultes. Les travaux effectués dans le cadre de cette thèse ont étudié successivement la pharmacocinétique du busulfan, du voriconazole et du tacrolimus par une approche de population en une étape (modèles non-linéaires à effets mixtes). Ces modèles ont permis d’identifier les principales sources de variabilités interindividuelles sur les paramètres pharmacocinétiques. Les covariables identifiées sont la surface corporelle et le poids. Ces résultats confirment l’importance de tenir en compte l’effet de la croissance en pédiatrie. Ces paramètres ont été inclus de façon allométrique dans les modèles. Cette approche permet de séparer l’effet de la mesure anthropométrique d’autres covariables et permet la comparaison des paramètres pharmacocinétiques en pédiatrie avec ceux des adultes. La prise en compte de ces covariables explicatives devrait permettre d’améliorer la prise en charge a priori des patients. Ces modèles développés ont été évalués pour confirmer leur stabilité, leur performance de simulation et leur capacité à répondre aux objectifs initiaux de la modélisation. Dans le cas du busulfan, le modèle validé a été utilisé pour proposer par simulation une posologie qui améliorerait l’atteinte de l’exposition cible, diminuerait l’échec thérapeutique et les risques de toxicité. Le modèle développé pour le voriconazole, a permis de confirmer la grande variabilité interindividuelle dans sa pharmacocinétique chez les enfants immunosupprimés. Le nombre limité de patients n’a pas permis d’identifier des covariables expliquant cette variabilité. Sur la base du modèle de pharmacocinétique de population du tacrolimus, un estimateur Bayesien a été mis au point, qui est le premier dans cette population de transplantés hépatiques pédiatriques. Cet estimateur permet de prédire les paramètres pharmacocinétiques et l’exposition individuelle au tacrolimus sur la base d’un nombre limité de prélèvements. En conclusion, les travaux de cette thèse ont permis d’appliquer la pharmacocinétique de population en pédiatrie pour explorer les caractéristiques propres à cette population, de décrire la variabilité pharmacocinétique des médicaments utilisés chez les enfants immunosupprimés, en vue de l’individualisation du traitement. Les outils pharmacocinétiques développés s’inscrivent dans une démarche visant à diminuer le taux d'échec thérapeutique et l’incidence des effets indésirables ou toxiques chez les enfants immunosupprimés suite à une transplantation.

Population Assessment of an Endangered Shorebird: the Piping Plover (Charadrius melodus melodus) in Eastern Canada

Small, at-risk populations are those for which accurate demographic information is most crucial to conservation and recovery, but also where data collection is constrained by logistical challenges and small sample sizes. Migratory animals in particular may experience a wide range of threats to survival and reproduction throughout each annual cycle, and identification of life stages most critical to persistence may be especially difficult for these populations. The endangered eastern Canadian breeding population of Piping Plover (Charadrius melodus melodus) was estimated at only 444 adults in 2005, and extensive effort has been invested in conservation activities, reproductive monitoring, and marking of individual birds, providing a comprehensive data set on population dynamics since 1998. We used these data to build a matrix projection model for two Piping Plover population segments that nest in eastern Canada in order to estimate both deterministic and stochastic rates of population growth (λd and λs, respectively). Annual population censuses suggested moderate growth in abundance between 1998–2003, but vital rate estimates indicated that this temporary growth may be replaced by declines in the long term, both in southern Nova Scotia (λd = 1.0043, λs = 0.9263) and in the Gulf of St. Lawrence (λd = 0.9651, λs = 0.8214). Nonetheless, confidence intervals on λ estimates were relatively wide, highlighting remaining uncertainty in future population trajectories. Differences in projected growth between regions appear to be driven by low estimated juvenile post-fledging survival in the Gulf, but threats to juveniles of both population segments following departure from nesting beaches remain unidentified. Similarly, λ in both population segments was particularly sensitive to changes in adult survival as expected for most migratory birds, but very little is understood about the threats to Piping Plover survival during migration and overwintering. Consequently, we suggest that future recovery efforts for these and other vulnerable migrants should quantify and manage the largely unknown sources of both adult and juvenile mortality during non-breeding seasons while maintaining current levels of nesting habitat protection.

How many facets are needed to represent the surface energy balance of an urban area?

We investigate the question of how many facets are needed to represent the energy balance of an urban area by developing simplified 3-, 2- and 1-facet versions of a 4-facet energy balance model of two-dimensional streets and buildings. The 3-facet model simplifies the 4-facet model by averaging over the canyon orientation, which results in similar net shortwave and longwave balances for both wall facets, but maintains the asymmetry in the heat fluxes within the street canyon. For the 2-facet model, on the assumption that the wall and road temperatures are equal, the road and wall facets can be combined mathematically into a single street-canyon facet with effective values of the heat transfer coefficient, albedo, emissivity and thermodynamic properties, without further approximation. The 1-facet model requires the additional assumption that the roof temperature is also equal to the road and wall temperatures. Idealised simulations show that the geometry and material properties of the walls and road lead to a large heat capacity of the combined street canyon, whereas the roof behaves like a flat surface with low heat capacity. This means that the magnitude of the diurnal temperature variation of the street-canyon facets are broadly similar and much smaller than the diurnal temperature variation of the roof facets. Consequently, the approximation that the street-canyon facets have similar temperatures is sound, and the road and walls can be combined into a single facet. The roof behaves very differently and a separate roof facet is required. Consequently, the 2-facet model performs similarly to the 4-facet model, while the 1-facet model does not. The models are compared with previously published observations collected in Mexico City. Although the 3- and 2-facet models perform better than the 1-facet model, the present models are unable to represent the phase of the sensible heat flux. This result is consistent with previous model comparisons, and we argue that this feature of the data cannot be produced by a single column model. We conclude that a 2-facet model is necessary, and for numerical weather prediction sufficient, to model an urban surface, and that this conclusion is robust and therefore applicable to more general geometries.

Quantifying uncertainty in critical loads: (B) acidity mass balance critical loads on a sensitive site

This paper reports an uncertainty analysis of critical loads for acid deposition for a site in southern England, using the Steady State Mass Balance Model. The uncertainty bounds, distribution type and correlation structure for each of the 18 input parameters was considered explicitly, and overall uncertainty estimated by Monte Carlo methods. Estimates of deposition uncertainty were made from measured data and an atmospheric dispersion model, and hence the uncertainty in exceedance could also be calculated. The uncertainties of the calculated critical loads were generally much lower than those of the input parameters due to a "compensation of errors" mechanism - coefficients of variation ranged from 13% for CLmaxN to 37% for CL(A). With 1990 deposition, the probability that the critical load was exceeded was > 0.99; to reduce this probability to 0.50, a 63% reduction in deposition is required; to 0.05, an 82% reduction. With 1997 deposition, which was lower than that in 1990, exceedance probabilities declined and uncertainties in exceedance narrowed as deposition uncertainty had less effect. The parameters contributing most to the uncertainty in critical loads were weathering rates, base cation uptake rates, and choice of critical chemical value, indicating possible research priorities. However, the different critical load parameters were to some extent sensitive to different input parameters. The application of such probabilistic results to environmental regulation is discussed.