Stochastic models for mainland-island metapopulations in static and dynamic landscapes

This paper has three primary aims: to establish an effective means for modelling mainland-island metapopulations inhabiting a dynamic landscape: to investigate the effect of immigration and dynamic changes in habitat on metapopulation patch occupancy dynamics; and to illustrate the implications of our results for decision-making and population management. We first extend the mainland-island metapopulation model of Alonso and McKane [Bull. Math. Biol. 64:913-958,2002] to incorporate a dynamic landscape. It is shown, for both the static and the dynamic landscape models, that a suitably scaled version of the process converges to a unique deterministic model as the size of the system becomes large. We also establish that. under quite general conditions, the density of occupied patches, and the densities of suitable and occupied patches, for the respective models, have approximate normal distributions. Our results not only provide us with estimates for the means and variances that are valid at all stages in the evolution of the population, but also provide a tool for fitting the models to real metapopulations. We discuss the effect of immigration and habitat dynamics on metapopulations, showing that mainland-like patches heavily influence metapopulation persistence, and we argue for adopting measures to increase connectivity between this large patch and the other island-like patches. We illustrate our results with specific reference to examples of populations of butterfly and the grasshopper Bryodema tuberculata.

La Mettrie and charlatanism: The dynamics of recognition and denunciation

This paper contributes to a genealogy of charlatanism by tracing two figures which eventually come to overlap: the street charlatan or operator, known for his eloquence and deceptive skill, and the comically incompetent doctor, represented classically in France in the theatre of Molière. The paper argues that eighteenth-century France gives the term 'charlatan' new moral weight while extending it to fields outside medicine, most notably to philosophy. Some examples of the denunciation of charlatans are examined, and it is suggested that denunciation was usually both extensible and reversible. La Mettrie appears in this regard as the very type of the denouncer denounced. He was a doctor-philosopher who vigorously decried the Paris Faculty of Medicine as a group of charlatans, even though his own medical qualifications were anything but impressive, and he was in turn reviled by Diderot as the most charlatanic and unworthy of philosophers.

Stochastic delay differential equations for genetic regulatory networks

Time delay is an important aspect in the modelling of genetic regulation due to slow biochemical reactions such as gene transcription and translation, and protein diffusion between the cytosol and nucleus. In this paper we introduce a general mathematical formalism via stochastic delay differential equations for describing time delays in genetic regulatory networks. Based on recent developments with the delay stochastic simulation algorithm, the delay chemical masterequation and the delay reaction rate equation are developed for describing biological reactions with time delay, which leads to stochastic delay differential equations derived from the Langevin approach. Two simple genetic regulatory networks are used to study the impact of' intrinsic noise on the system dynamics where there are delays. (c) 2006 Elsevier B.V. All rights reserved.

Stochastic modelling of the invasion process of nematodes in fly larvae

Stochastic models based on Markov birth processes are constructed to describe the process of invasion of a fly larva by entomopathogenic nematodes. Various forms for the birth (invasion) rates are proposed. These models are then fitted to data sets describing the observed numbers of nematodes that have invaded a fly larval after a fixed period of time. Non-linear birthrates are required to achieve good fits to these data, with their precise form leading to different patterns of invasion being identified for three populations of nematodes considered. One of these (Nemasys) showed the greatest propensity for invasion. This form of modelling may be useful more generally for analysing data that show variation which is different from that expected from a binomial distribution.

Evolving noisy oscillatory dynamics in genetic regulatory networks

We introduce a genetic programming (GP) approach for evolving genetic networks that demonstrate desired dynamics when simulated as a discrete stochastic process. Our representation of genetic networks is based on a biochemical reaction model including key elements such as transcription, translation and post-translational modifications. The stochastic, reaction-based GP system is similar but not identical with algorithmic chemistries. We evolved genetic networks with noisy oscillatory dynamics. The results show the practicality of evolving particular dynamics in gene regulatory networks when modelled with intrinsic noise.

The effect of non-standard employment on work-family balance

Across the last four decades, the structure of the Australian labour market has changed profoundly as non-standard forms of employment have become more prevalent. According to many researchers, the growth of non-standard work has been driven by employee preferences, particularly among married women, for greater flexibility to balance paid work with domestic responsibilities and other non-work related pursuits. In contrast, other researchers argue that the increasing prevalence of non-standard employment reflects employer demands for greater staffing flexibility. From this perspective, non-standard forms of employment are considered to have a negative effect on work-family balance. This paper explores whether non-standard employment is associated with improved or poorer work-to-family conflict and tests whether experiences vary by gender. It concentrates on three common forms of non-standard employment: part-time employment, casual and fixed-term work contracts and flexible scheduling practices (such as evening work, weekend work and irregular rostering). Analysis is based on 2299 employed parents from the first wave of the Household, Income and Labour Dynamics on Australia (HILDA) project. Results show that few scheduling measures are significant determinants of work-family balance. However, part-time employment is associated with reduced work-to-family strain for both men and women, even after controlling for various other employment and household related characteristics. Casual employment, in contrast, incurs the cost of poorer work-family balance for men. Surprisingly, HILDA data show that overall men experience greater work-to-family strain than women.

Parallel implementation of stochastic simulation for large scale cellular processes

Experimental and theoretical studies have shown the importance of stochastic processes in genetic regulatory networks and cellular processes. Cellular networks and genetic circuits often involve small numbers of key proteins such as transcriptional factors and signaling proteins. In recent years stochastic models have been used successfully for studying noise in biological pathways, and stochastic modelling of biological systems has become a very important research field in computational biology. One of the challenge problems in this field is the reduction of the huge computing time in stochastic simulations. Based on the system of the mitogen-activated protein kinase cascade that is activated by epidermal growth factor, this work give a parallel implementation by using OpenMP and parallelism across the simulation. Special attention is paid to the independence of the generated random numbers in parallel computing, that is a key criterion for the success of stochastic simulations. Numerical results indicate that parallel computers can be used as an efficient tool for simulating the dynamics of large-scale genetic regulatory networks and cellular processes

Structure and dynamics of a gene network model incorporating small RNAs

As advances in molecular biology continue to reveal additional layers of complexity in gene regulation, computational models need to incorporate additional features to explore the implications of new theories and hypotheses. It has recently been suggested that eukaryotic organisms owe their phenotypic complexity and diversity to the exploitation of small RNAs as signalling molecules. Previous models of genetic systems are, for several reasons, inadequate to investigate this theory. In this study, we present an artificial genome model of genetic regulatory networks based upon previous work by Torsten Reil, and demonstrate how this model generates networks with biologically plausible structural and dynamic properties. We also extend the model to explore the implications of incorporating regulation by small RNA molecules in a gene network. We demonstrate how, using these signals, highly connected networks can display dynamics that are more stable than expected given their level of connectivity.

Vibrational dynamics and structure of natural feldspars

The present study gives a contribution to the knowledge on the Na-feldspar and plagioclases, extending the database of the Raman spectra of plagioclases with different chemical compositions and structural orders. This information may be used for the future planetary explorations by “rovers”, for the investigation of ceramics nanocrystal materials and for the mineralogical phase identification in sediments. Na-feldspar and plagioclase solid solution have been investigated by Raman spectroscopy in order to determine the relationships between the vibrational changes and the plagioclase crystal chemistry and structure. We focused on the Raman micro-spectroscopy technique, being a non-destructive method, suited for contactless analysis with high spatial resolution. Chemical and structural analyses have been performed on natural samples to test the usefulness of Raman spectroscopy as a tool in the study of the pressure-induced structural deformations, the disordering processes due to change in the Al-Si distribution in the tetrahedral sites and, finally, in the determination of the anorthitic content (Anx) in plagioclase minerals. All the predicted 39 Ag Raman active modes have been identified and assigned to specific patterns of atomic vibrational motion. A detailed comparison between experimental and computed Raman spectra has been performed and previous assignments have been revised, solving some discrepancies reported in recent literature. The ab initio calculation at the hybrid HF/DFT level with the WC1LYP Hamiltonian has proven to give excellent agreement between calculated and experimentally measured Raman wavenumbers and intensities in triclinic minerals. A short digression on the 36 infrared active modes of Na-feldspar has been done too. The identification of all 39 computed Raman modes in the experimentally measured spectra of the fully ordered Na-feldspar, known as low albite, along with the detailed description of each vibrational mode, has been essential to extend the comparative analysis to the high pressure and high temperature structural forms of albite, which reflect the physical–chemical conditions of the hosting rocks. The understanding of feldspar structure response to pressure and temperature is crucial in order to constrain crustal behaviour. The compressional behaviour of the Na-feldspar has been investigated for the first time by Raman spectroscopy. The absence of phase transitions and the occurrence of two secondary compression mechanisms acting at different pressures have been confirmed. Moreover, Raman data suggest that the internal structural changes are confined to a small pressure interval, localized around 6 GPa, not spread out from 4 to 8 GPa as suggested by previous X-rays studies on elasticity. The dominant compression mechanisms act via tetrahedral tilting, while the T-O bond lengths remain nearly constant at moderate compressional regimes. At the spectroscopic level, this leads to the strong pressure dependencies of T-O-T bending modes, as found for the four modes at 478, 508, 578 and 815 cm-1. The Al-Si distribution in the tetrahedral sites affects also the Raman spectrum of Na-feldspar. In particular, peak broadening is more sensitive than peak position to changes in the degree of order. Raman spectroscopy is found to be a good probe for local ordering, in particular being sensitive to the first annealing steps, when the macroscopic order parameter is still high. Even though Raman data are scattered and there are outliers in the estimated values of the degree of order, the average peak linewidths of the Na-feldspar characteristic doublet band, labelled here as υa and υb, as a function of the order parameter Qod show interesting trends: both peak linewidths linearly increase until saturation. From Qod values lower than 0.6, peak broadening is no more affected by the Al-Si distribution. Moreover, the disordering process is found to be heterogeneous. SC-XRD and Raman data have suggested an inter-crystalline inhomogeneity of the samples, i.e., the presence of regions with different defect density on the micrometric scale. Finally, the influence of Ca-Na substitution in the plagioclase Raman spectra has been investigated. Raman spectra have been collected on a series of well characterized natural, low structural plagioclases. The variations of the Raman modes as a function of the chemical composition and the structural order have been determined. The number of the observed Raman bands at each composition gives information about the unit-cell symmetry: moving away from the C1 structures, the number of the Raman bands enhances, as the number of formula units in the unit cell increases. The modification from an “albite-like” Raman spectrum to a more “anorthite-like” spectrum occurs from sample An78 onwards, which coincides with the appearance of c reflections in the diffraction patterns of the samples. The evolution of the Raman bands υa and υb displays two changes in slope at ~An45 and ~An75: the first one occurs between e2 and e1 plagioclases, the latter separates e1 and I1 plagioclases with only b reflections in their diffraction patterns from I1 and P1 samples having b and c reflections too. The first variation represents exactly the e2→e1 phase transitions, whereas the second one corresponds in good approximation to the C1→I1 transition, which has been determined at ~An70 by previous works. The I1→P1 phase transition in the anorthite-rich side of the solid solution is not highlighted in the collected Raman spectra. Variations in peak broadening provide insights into the behaviour of the order parameter on a local scale, suggesting an increase in the structural disorder within the solid solution, as the structures have to incorporate more Al atoms to balance the change from monovalent to divalent cations. All the information acquired on these natural plagioclases has been used to produce a protocol able to give a preliminary estimation of the chemical composition of an unknown plagioclase from its Raman spectrum. Two calibration curves, one for albite-rich plagioclases and the other one for the anorthite-rich plagioclases, have been proposed by relating the peak linewidth of the most intense Raman band υa and the An content. It has been pointed out that the dependence of the composition from the linewidth can be obtained only for low structural plagioclases with a degree of order not far away from the references. The proposed tool has been tested on three mineralogical samples, two of meteoric origin and one of volcanic origin. Chemical compositions by Raman spectroscopy compare well, within an error of about 10%, with those obtained by elemental techniques. Further analyses on plagioclases with unknown composition will be necessary to validate the suggested method and introduce it as routine tool for the determination of the chemical composition from Raman data in planetary missions.

The dynamics of a genetic algorithm under stabilizing selection

A formalism recently introduced by Prugel-Bennett and Shapiro uses the methods of statistical mechanics to model the dynamics of genetic algorithms. To be of more general interest than the test cases they consider. In this paper, the technique is applied to the subset sum problem, which is a combinatorial optimization problem with a strongly non-linear energy (fitness) function and many local minima under single spin flip dynamics. It is a problem which exhibits an interesting dynamics, reminiscent of stabilizing selection in population biology. The dynamics are solved under certain simplifying assumptions and are reduced to a set of difference equations for a small number of relevant quantities. The quantities used are the population's cumulants, which describe its shape, and the mean correlation within the population, which measures the microscopic similarity of population members. Including the mean correlation allows a better description of the population than the cumulants alone would provide and represents a new and important extension of the technique. The formalism includes finite population effects and describes problems of realistic size. The theory is shown to agree closely to simulations of a real genetic algorithm and the mean best energy is accurately predicted.

Modelling the dynamics of genetic algorithms using statistical mechanics

A formalism for modelling the dynamics of Genetic Algorithms (GAs) using methods from statistical mechanics, originally due to Prugel-Bennett and Shapiro, is reviewed, generalized and improved upon. This formalism can be used to predict the averaged trajectory of macroscopic statistics describing the GA's population. These macroscopics are chosen to average well between runs, so that fluctuations from mean behaviour can often be neglected. Where necessary, non-trivial terms are determined by assuming maximum entropy with constraints on known macroscopics. Problems of realistic size are described in compact form and finite population effects are included, often proving to be of fundamental importance. The macroscopics used here are cumulants of an appropriate quantity within the population and the mean correlation (Hamming distance) within the population. Including the correlation as an explicit macroscopic provides a significant improvement over the original formulation. The formalism is applied to a number of simple optimization problems in order to determine its predictive power and to gain insight into GA dynamics. Problems which are most amenable to analysis come from the class where alleles within the genotype contribute additively to the phenotype. This class can be treated with some generality, including problems with inhomogeneous contributions from each site, non-linear or noisy fitness measures, simple diploid representations and temporally varying fitness. The results can also be applied to a simple learning problem, generalization in a binary perceptron, and a limit is identified for which the optimal training batch size can be determined for this problem. The theory is compared to averaged results from a real GA in each case, showing excellent agreement if the maximum entropy principle holds. Some situations where this approximation brakes down are identified. In order to fully test the formalism, an attempt is made on the strong sc np-hard problem of storing random patterns in a binary perceptron. Here, the relationship between the genotype and phenotype (training error) is strongly non-linear. Mutation is modelled under the assumption that perceptron configurations are typical of perceptrons with a given training error. Unfortunately, this assumption does not provide a good approximation in general. It is conjectured that perceptron configurations would have to be constrained by other statistics in order to accurately model mutation for this problem. Issues arising from this study are discussed in conclusion and some possible areas of further research are outlined.

Noisy fitness evaluation in genetic algorithms and the dynamics of learning

A theoretical model is presented which describes selection in a genetic algorithm (GA) under a stochastic fitness measure and correctly accounts for finite population effects. Although this model describes a number of selection schemes, we only consider Boltzmann selection in detail here as results for this form of selection are particularly transparent when fitness is corrupted by additive Gaussian noise. Finite population effects are shown to be of fundamental importance in this case, as the noise has no effect in the infinite population limit. In the limit of weak selection we show how the effects of any Gaussian noise can be removed by increasing the population size appropriately. The theory is tested on two closely related problems: the one-max problem corrupted by Gaussian noise and generalization in a perceptron with binary weights. The averaged dynamics can be accurately modelled for both problems using a formalism which describes the dynamics of the GA using methods from statistical mechanics. The second problem is a simple example of a learning problem and by considering this problem we show how the accurate characterization of noise in the fitness evaluation may be relevant in machine learning. The training error (negative fitness) is the number of misclassified training examples in a batch and can be considered as a noisy version of the generalization error if an independent batch is used for each evaluation. The noise is due to the finite batch size and in the limit of large problem size and weak selection we show how the effect of this noise can be removed by increasing the population size. This allows the optimal batch size to be determined, which minimizes computation time as well as the total number of training examples required.

Towards a framework for combining stochastic and deterministic descriptions of nonstationary financial time series

We present in this paper ideas to tackle the problem of analysing and forecasting nonstationary time series within the financial domain. Accepting the stochastic nature of the underlying data generator we assume that the evolution of the generator's parameters is restricted on a deterministic manifold. Therefore we propose methods for determining the characteristics of the time-localised distribution. Starting with the assumption of a static normal distribution we refine this hypothesis according to the empirical results obtained with the methods anc conclude with the indication of a dynamic non-Gaussian behaviour with varying dependency for the time series under consideration.

Flexibility of short-strand RNA in aqueous solution as revealed by molecular dynamics simulation:are A′-RNA and A-RNA distinct conformational structures?

We use molecular dynamics simulations to compare the conformational structure and dynamics of a 21-base pair RNA sequence initially constructed according to the canonical A-RNA and A'-RNA forms in the presence of counterions and explicit water. Our study aims to add a dynamical perspective to the solid-state structural information that has been derived from X-ray data for these two characteristic forms of RNA. Analysis of the three main structural descriptors commonly used to differentiate between the two forms of RNA namely major groove width, inclination and the number of base pairs in a helical twist over a 30 ns simulation period reveals a flexible structure in aqueous solution with fluctuations in the values of these structural parameters encompassing the range between the two crystal forms and more. This provides evidence to suggest that the identification of distinct A-RNA and A'-RNA structures, while relevant in the crystalline form, may not be generally relevant in the context of RNA in the aqueous phase. The apparent structural flexibility observed in our simulations is likely to bear ramifications for the interactions of RNA with biological molecules (e.g. proteins) and non-biological molecules (e.g. non-viral gene delivery vectors). © CSIRO 2009.