An investigation into effects of long-distance seed dispersal on organelle population genetic structure and colonization rate: a model analysis

A simulation-based modelling approach is used to examine the effects of stratified seed dispersal (representing the distribution of the majority of dispersal around the maternal parent and also rare long-distance dispersal) on the genetic structure of maternally inherited genomes and the colonization rate of expanding plant populations. The model is parameterized to approximate postglacial oak colonization in the UK, but is relevant to plant populations that exhibit stratified seed dispersal. The modelling approach considers the colonization of individual plants over a large area (three 500 km x 10 km rolled transects are used to approximate a 500 km x 300 km area). Our approach shows how the interaction of plant population dynamics with stratified dispersal can result in a spatially patchy haplotype structure. We show that while both colonization speeds and the resulting genetic structure are influenced by the characteristics of the dispersal kernel, they are robust to changes in the periodicity of long-distance events, provided the average number of long-distance dispersal events remains constant. We also consider the effects of additional physical and environmental mechanisms on plant colonization. Results show significant changes in genetic structure when the initial colonization of different haplotypes is staggered over time and when a barrier to colonization is introduced. Environmental influences on survivorship and fecundity affect both the genetic structure and the speed of colonization. The importance of these mechanisms in relation to the postglacial spread and genetic structure of oak in the UK is discussed.

Process systems modelling and applications in granulation: A review

Granulation is one of the fundamental operations in particulate processing and has a very ancient history and widespread use. Much fundamental particle science has occurred in the last two decades to help understand the underlying phenomena. Yet, until recently the development of granulation systems was mostly based on popular practice. The use of process systems approaches to the integrated understanding of these operations is providing improved insight into the complex nature of the processes. Improved mathematical representations, new solution techniques and the application of the models to industrial processes are yielding better designs, improved optimisation and tighter control of these systems. The parallel development of advanced instrumentation and the use of inferential approaches provide real-time access to system parameters necessary for improvements in operation. The use of advanced models to help develop real-time plant diagnostic systems provides further evidence of the utility of process system approaches to granulation processes. This paper highlights some of those aspects of granulation. (c) 2005 Elsevier Ltd. All rights reserved.

Modelling nucleation in wet granulation

Nucleation is the first stage in any granulation process where binder liquid first comes into contact with the powder. This paper investigates the nucleation process where binder liquid is added to a fine powder with a spray nozzle. The dimensionless spray flux approach of Hapgood et al. (Powder Technol. 141 (2004) 20) is extended to account for nonuniform spray patterns and allow for overlap of nuclei granules rather than spray drops. A dimensionless nuclei distribution function which describes the effects of the design and operating parameters of the nucleation process (binder spray characteristics, the nucleation area ratio between droplets and nuclei and the powder bed velocity) on the fractional surface area coverage of nuclei on a moving powder bed is developed. From this starting point, a Monte Carlo nucleation model that simulates full nuclei size distributions as a function of the design and operating parameters that were implemented in the dimensionless nuclei distribution function is developed. The nucleation model was then used to investigate the effects of the design and operating parameters on the formed nuclei size distributions and to correlate these effects to changes of the dimensionless nuclei distribution function. Model simulations also showed that it is possible to predict nuclei size distributions beyond the drop controlled nucleation regime in Hapgood's nucleation regime map. Qualitative comparison of model simulations and experimental nucleation data showed similar shapes of the nuclei size distributions. In its current form, the nucleation model can replace the nucleation term in one-dimensional population balance models describing wet granulation processes. Implementation of more sophisticated nucleation kinetics can make the model applicable to multi-dimensional population balance models.

Assessing the impacts of grazing levels on bird density in woodland habitat: a Bayesian approach using expert opinion

Many studies on birds focus on the collection of data through an experimental design, suitable for investigation in a classical analysis of variance (ANOVA) framework. Although many findings are confirmed by one or more experts, expert information is rarely used in conjunction with the survey data to enhance the explanatory and predictive power of the model. We explore this neglected aspect of ecological modelling through a study on Australian woodland birds, focusing on the potential impact of different intensities of commercial cattle grazing on bird density in woodland habitat. We examine a number of Bayesian hierarchical random effects models, which cater for overdispersion and a high frequency of zeros in the data using WinBUGS and explore the variation between and within different grazing regimes and species. The impact and value of expert information is investigated through the inclusion of priors that reflect the experience of 20 experts in the field of bird responses to disturbance. Results indicate that expert information moderates the survey data, especially in situations where there are little or no data. When experts agreed, credible intervals for predictions were tightened considerably. When experts failed to agree, results were similar to those evaluated in the absence of expert information. Overall, we found that without expert opinion our knowledge was quite weak. The fact that the survey data is quite consistent, in general, with expert opinion shows that we do know something about birds and grazing and we could learn a lot faster if we used this approach more in ecology, where data are scarce. Copyright (c) 2005 John Wiley & Sons, Ltd.

Estimates of sex- and age-class-specific survival probabilities for a southern Great Barrier Reef green sea turtle population

Sex- and age-class-specific survival probabilities of a southern Great Barrier Reef green sea turtle population were estimated using a capture - mark - recapture (CMR) study and a Cormack - Jolly - Seber (CJS) modelling approach. The CMR history profiles for 954 individual turtles tagged over a 9-year period ( 1984 - 1992) were classified into three age classes ( adult, subadult, juvenile) based on somatic growth and reproductive traits. Reduced-parameter CJS models, accounting for constant survival and time-specific recapture, fitted best for all age classes. There were no significant sex-specific differences in either survival or recapture probabilities for any age class. Mean annual adult survival was estimated at 0.9482 (95% CI: 0.92 - 0.98) and was significantly higher than survival for either subadults or juveniles. Mean annual subadult survival was 0.8474 ( 95% CI: 0.79 - 0.91), which was not significantly different from mean annual juvenile survival estimated at 0.8804 ( 95% CI: 0.84 - 0.93). The time-specific adult recapture probabilities were a function of sampling effort but this was not the case for either juveniles or subadults. The sampling effort effect was accounted for explicitly in the estimation of adult survival and recapture probabilities. These are the first comprehensive sex- and age-class-specific survival and recapture probability estimates for a green sea turtle population derived from a long-term CMR program.

Trait physiology and crop modelling as a framework to link phenotypic complexity to underlying genetic systems

New tools derived from advances in molecular biology have not been widely adopted in plant breeding for complex traits because of the inability to connect information at gene level to the phenotype in a manner that is useful for selection. In this study, we explored whether physiological dissection and integrative modelling of complex traits could link phenotype complexity to underlying genetic systems in a way that enhanced the power of molecular breeding strategies. A crop and breeding system simulation study on sorghum, which involved variation in 4 key adaptive traits-phenology, osmotic adjustment, transpiration efficiency, stay-green-and a broad range of production environments in north-eastern Australia, was used. The full matrix of simulated phenotypes, which consisted of 547 location-season combinations and 4235 genotypic expression states, was analysed for genetic and environmental effects. The analysis was conducted in stages assuming gradually increased understanding of gene-to-phenotype relationships, which would arise from physiological dissection and modelling. It was found that environmental characterisation and physiological knowledge helped to explain and unravel gene and environment context dependencies in the data. Based on the analyses of gene effects, a range of marker-assisted selection breeding strategies was simulated. It was shown that the inclusion of knowledge resulting from trait physiology and modelling generated an enhanced rate of yield advance over cycles of selection. This occurred because the knowledge associated with component trait physiology and extrapolation to the target population of environments by modelling removed confounding effects associated with environment and gene context dependencies for the markers used. Developing and implementing this gene-to-phenotype capability in crop improvement requires enhanced attention to phenotyping, ecophysiological modelling, and validation studies to test the stability of candidate genetic regions.

Approximating persistence in a general class of population processes

We provide a general framework for estimating persistence in populations which may be affected by catastrophic events, and which are either unbounded or have very large ceilings. We model the population using a birth-death process modified to allow for downward jumps of arbitrary size. For such processes, it is typically necessary to truncate the process in order to make the evaluation of expected extinction times (and higher-order moments) computationally feasible. Hence, we give particular attention to the selection of a cut-off point at which to truncate the process, and we present a simple method for obtaining quantitative indicators of the suitability of a chosen cut-off. (c) 2005 Elsevier Inc. All rights reserved.

Optimal design for model discrimination and parameter estimation for itraconazole population pharmacokinetics in cystic fibrosis patients

Optimal sampling times are found for a study in which one of the primary purposes is to develop a model of the pharmacokinetics of itraconazole in patients with cystic fibrosis for both capsule and solution doses. The optimal design is expected to produce reliable estimates of population parameters for two different structural PK models. Data collected at these sampling times are also expected to provide the researchers with sufficient information to reasonably discriminate between the two competing structural models.

Analysis of population pharmacokinetic data using NONMEM and WinBUGS

The aim of this report is to describe the use of WinBUGS for two datasets that arise from typical population pharmacokinetic studies. The first dataset relates to gentamicin concentration-time data that arose as part of routine clinical care of 55 neonates. The second dataset incorporated data from 96 patients receiving enoxaparin. Both datasets were originally analyzed by using NONMEM. In the first instance, although NONMEM provided reasonable estimates of the fixed effects parameters it was unable to provide satisfactory estimates of the between-subject variance. In the second instance, the use of NONMEM resulted in the development of a successful model, albeit with limited available information on the between-subject variability of the pharmacokinetic parameters. WinBUGS was used to develop a model for both of these datasets. Model comparison for the enoxaparin dataset was performed by using the posterior distribution of the log-likelihood and a posterior predictive check. The use of WinBUGS supported the same structural models tried in NONMEM. For the gentamicin dataset a one-compartment model with intravenous infusion was developed, and the population parameters including the full between-subject variance-covariance matrix were available. Analysis of the enoxaparin dataset supported a two compartment model as superior to the one-compartment model, based on the posterior predictive check. Again, the full between-subject variance-covariance matrix parameters were available. Fully Bayesian approaches using MCMC methods, via WinBUGS, can offer added value for analysis of population pharmacokinetic data.

Pharmacokinetic-pharmacodynamic modelling of QT interval prolongation following citalopram overdoses

Aims To develop a pharmacokinetic-pharmacodynamic model describing the time-course of QT interval prolongation after citalopram overdose and to evaluate the effect of charcoal on the relative risk of developing abnormal QT and heart-rate combinations. Methods Plasma concentrations and electrocardiograph (ECG) data from 52 patients after 62 citalopram overdose events were analysed in WinBUGS using a Bayesian approach. The reported doses ranged from 20 to 1700 mg and on 17 of the events a single dose of activated charcoal was administered. The developed pharmacokinetic-pharmacodynamic model was used for predicting the probability of having abnormal combinations of QT-RR, which was assumed to be related to an increased risk for torsade de pointes (TdP). Results The absolute QT interval was related to the observed heart rate with an estimated individual heart-rate correction factor [alpha = 0.36, between-subject coefficient of variation (CV) = 29%]. The heart-rate corrected QT interval was linearly dependent on the predicted citalopram concentration (slope = 40 ms l mg(-1), between-subject CV = 70%) in a hypothetical effect-compartment (half-life of effect-delay = 1.4 h). The heart-rate corrected QT was predicted to be higher in women than in men and to increase with age. Administration of activated charcoal resulted in a pronounced reduction of the QT prolongation and was shown to reduce the risk of having abnormal combinations of QT-RR by approximately 60% for citalopram doses above 600 mg. Conclusion Citalopram caused a delayed lengthening of the QT interval. Administration of activated charcoal was shown to reduce the risk that the QT interval exceeds a previously defined threshold and therefore is expected to reduce the risk of TdP.

Modelling cell lifespan and proliferation: is likelihood to die or to divide independent of age?

In cell lifespan studies the exponential nature of cell survival curves is often interpreted as showing the rate of death is independent of the age of the cells within the population. Here we present an alternative model where cells that die are replaced and the age and lifespan of the population pool is monitored until a, steady state is reached. In our model newly generated individual cells are given a determined lifespan drawn from a number of known distributions including the lognormal, which is frequently found in nature. For lognormal lifespans the analytic steady-state survival curve obtained can be well-fit by a single or double exponential, depending on the mean and standard deviation. Thus, experimental evidence for exponential lifespans of one and/or two populations cannot be taken as definitive evidence for time and age independence of cell survival. A related model for a dividing population in steady state is also developed. We propose that the common adoption of age-independent, constant rates of change in biological modelling may be responsible for significant errors, both of interpretation and of mathematical deduction. We suggest that additional mathematical and experimental methods must be used to resolve the relationship between time and behavioural changes by cells that are predominantly unsynchronized.

Cognitive modelling and the behaviour genetics of reading

While it is well known that reading is highly heritable, less has been understood about the bases of these genetic influences. In this paper, we review the research that we have been conducting in recent years to examine genetic and environmental influences on the particular reading processes specified in the dual-route cognitive model of reading. We argue that a detailed understanding of the role of genetic factors in reading acquisition requires the delineation and measurement of precise phenotypes, derived from well-articulated models of the reading process. We report evidence for independent genetic influences on the lexical and nonlexical reading processes represented in the dual-route model, based on studies of children with particular subtypes of dyslexia, and on univariate and multivariate genetic modelling of reading performance in the normally reading population.

Customised birthweight: Coefficients for an Australian population and validation of the model

Background: Published birthweight references in Australia do not fully take into account constitutional factors that influence birthweight and therefore may not provide an accurate reference to identify the infant with abnormal growth. Furthermore, studies in other regions that have derived adjusted (customised) birthweight references have applied untested assumptions in the statistical modelling. Aims: To validate the customised birthweight model and to produce a reference set of coefficients for estimating a customised birthweight that may be useful for maternity care in Australia and for future research. Methods: De-identified data were extracted from the clinical database for all births at the Mater Mother's Hospital, Brisbane, Australia, between January 1997 and June 2005. Births with missing data for the variables under study were excluded. In addition the following were excluded: multiple pregnancies, births less than 37 completed week's gestation, stillbirths, and major congenital abnormalities. Multivariate analysis was undertaken. A double cross-validation procedure was used to validate the model. Results: The study of 42 206 births demonstrated that, for statistical purposes, birthweight is normally distributed. Coefficients for the derivation of customised birthweight in an Australian population were developed and the statistical model is demonstrably robust. Conclusions: This study provides empirical data as to the robustness of the model to determine customised birthweight. Further research is required to define where normal physiology ends and pathology begins, and which segments of the population should be included in the construction of a customised birthweight standard.

Extinction times for a birth-death process with two phases

Many populations have a negative impact on their habitat or upon other species in the environment if their numbers become too large. For this reason they are often subjected to some form of control. One common control regime is the reduction regime: when the population reaches a certain threshold it is controlled (for example culled) until it falls below a lower predefined level. The natural model for such a controlled population is a birth-death process with two phases, the phase determining which of two distinct sets of birth and death rates governs the process. We present formulae for the probability of extinction and the expected time to extinction, and discuss several applications. (c) 2006 Elsevier Inc. All rights reserved.

Multidimensional modelling to investigate interspecies hydrogen transfer in anaerobic biofilms

Anaerobic digestion is a multistep process, mediated by a functionally and phylogenetically diverse microbial population. One of the crucial steps is oxidation of organic acids, with electron transfer via hydrogen or formate from acetogenic bacteria to methanogens. This syntrophic microbiological process is strongly restricted by a thermodynamic limitation on the allowable hydrogen or formate concentration. In order to study this process in more detail, we developed an individual-based biofilm model which enables to describe the processes at a microbial resolution. The biochemical model is the ADM1, implemented in a multidimensional domain. With this model, we evaluated three important issues for the syntrophic relationship: (i) is there a fundamental difference in using hydrogen or formate as electron carrier? (ii) Does a thermodynamic-based inhibition function produced substantially different results from an empirical function? and; (iii) Does the physical colocation of acetogens and methanogens follow directly from a general model. Hydrogen or formate as electron carrier had no substantial impact on model results. Standard inhibition functions or thermodynamic inhibition function gave similar results at larger substrate field grid sizes (> 10 mu m), but at smaller grid sizes, the thermodynamic-based function reduced the number of cells with long interspecies distances (> 2.5 mu m). Therefore, a very fine grid resolution is needed to reflect differences between the thermodynamic function, and a more generic inhibition form. The co-location of syntrophic bacteria was well predicted without a need to assume a microbiological based mechanism (e.g., through chemotaxis) of biofilm formation.