Interacting populations in heterogeneous environments

To optimally manage a metapopulation, managers and conservation biologists can favor a type of habitat spatial distribution (e.g. aggregated or random). However, the spatial distribution that provides the highest habitat occupancy remains ambiguous and numerous contradictory results exist. Habitat occupancy depends on the balance between local extinction and colonization. Thus, the issue becomes even more puzzling when various forms of relationships - positive or negative co-variation - between local extinction and colonization rate within habitat types exist. Using an analytical model we demonstrate first that the habitat occupancy of a metapopulation is significantly affected by the presence of habitat types that display different extinction-colonization dynamics, considering: (i) variation in extinction or colonization rate and (ii) positive and negative co-variation between the two processes within habitat types. We consequently examine, with a spatially explicit stochastic simulation model, how different degrees of habitat aggregation affect occupancy predictions under similar scenarios. An aggregated distribution of habitat types provides the highest habitat occupancy when local extinction risk is spatially heterogeneous and high in some places, while a random distribution of habitat provides the highest habitat occupancy when colonization rates are high. Because spatial variability in local extinction rates always favors aggregation of habitats, we only need to know about spatial variability in colonization rates to determine whether aggregating habitat types increases, or not, metapopulation occupancy. From a comparison of the results obtained with the analytical and with the spatial-explicit stochastic simulation model we determine the conditions under which a simple metapopulation model closely matches the results of a more complex spatial simulation model with explicit heterogeneity.

Stochastic time-concentration activity models for cytotoxicity in 3D brain cell cultures.

BACKGROUND: In vitro aggregating brain cell cultures containing all types of brain cells have been shown to be useful for neurotoxicological investigations. The cultures are used for the detection of nervous system-specific effects of compounds by measuring multiple endpoints, including changes in enzyme activities. Concentration-dependent neurotoxicity is determined at several time points. METHODS: A Markov model was set up to describe the dynamics of brain cell populations exposed to potentially neurotoxic compounds. Brain cells were assumed to be either in a healthy or stressed state, with only stressed cells being susceptible to cell death. Cells may have switched between these states or died with concentration-dependent transition rates. Since cell numbers were not directly measurable, intracellular lactate dehydrogenase (LDH) activity was used as a surrogate. Assuming that changes in cell numbers are proportional to changes in intracellular LDH activity, stochastic enzyme activity models were derived. Maximum likelihood and least squares regression techniques were applied for estimation of the transition rates. Likelihood ratio tests were performed to test hypotheses about the transition rates. Simulation studies were used to investigate the performance of the transition rate estimators and to analyze the error rates of the likelihood ratio tests. The stochastic time-concentration activity model was applied to intracellular LDH activity measurements after 7 and 14 days of continuous exposure to propofol. The model describes transitions from healthy to stressed cells and from stressed cells to death. RESULTS: The model predicted that propofol would affect stressed cells more than healthy cells. Increasing propofol concentration from 10 to 100 μM reduced the mean waiting time for transition to the stressed state by 50%, from 14 to 7 days, whereas the mean duration to cellular death reduced more dramatically from 2.7 days to 6.5 hours. CONCLUSION: The proposed stochastic modeling approach can be used to discriminate between different biological hypotheses regarding the effect of a compound on the transition rates. The effects of different compounds on the transition rate estimates can be quantitatively compared. Data can be extrapolated at late measurement time points to investigate whether costs and time-consuming long-term experiments could possibly be eliminated.

Conditioning of stochastic 3-D fracture networks to hydrological and geophysical data

The geometry and connectivity of fractures exert a strong influence on the flow and transport properties of fracture networks. We present a novel approach to stochastically generate three-dimensional discrete networks of connected fractures that are conditioned to hydrological and geophysical data. A hierarchical rejection sampling algorithm is used to draw realizations from the posterior probability density function at different conditioning levels. The method is applied to a well-studied granitic formation using data acquired within two boreholes located 6 m apart. The prior models include 27 fractures with their geometry (position and orientation) bounded by information derived from single-hole ground-penetrating radar (GPR) data acquired during saline tracer tests and optical televiewer logs. Eleven cross-hole hydraulic connections between fractures in neighboring boreholes and the order in which the tracer arrives at different fractures are used for conditioning. Furthermore, the networks are conditioned to the observed relative hydraulic importance of the different hydraulic connections by numerically simulating the flow response. Among the conditioning data considered, constraints on the relative flow contributions were the most effective in determining the variability among the network realizations. Nevertheless, we find that the posterior model space is strongly determined by the imposed prior bounds. Strong prior bounds were derived from GPR measurements and helped to make the approach computationally feasible. We analyze a set of 230 posterior realizations that reproduce all data given their uncertainties assuming the same uniform transmissivity in all fractures. The posterior models provide valuable statistics on length scales and density of connected fractures, as well as their connectivity. In an additional analysis, effective transmissivity estimates of the posterior realizations indicate a strong influence of the DFN structure, in that it induces large variations of equivalent transmissivities between realizations. The transmissivity estimates agree well with previous estimates at the site based on pumping, flowmeter and temperature data.

Uncertainty Quantification Of A Semi-Supervised Support Vector Regression Reservoir Model

Uncertainty quantification of petroleum reservoir models is one of the present challenges, which is usually approached with a wide range of geostatistical tools linked with statistical optimisation or/and inference algorithms. Recent advances in machine learning offer a novel approach to model spatial distribution of petrophysical properties in complex reservoirs alternative to geostatistics. The approach is based of semisupervised learning, which handles both ?labelled? observed data and ?unlabelled? data, which have no measured value but describe prior knowledge and other relevant data in forms of manifolds in the input space where the modelled property is continuous. Proposed semi-supervised Support Vector Regression (SVR) model has demonstrated its capability to represent realistic geological features and describe stochastic variability and non-uniqueness of spatial properties. On the other hand, it is able to capture and preserve key spatial dependencies such as connectivity of high permeability geo-bodies, which is often difficult in contemporary petroleum reservoir studies. Semi-supervised SVR as a data driven algorithm is designed to integrate various kind of conditioning information and learn dependences from it. The semi-supervised SVR model is able to balance signal/noise levels and control the prior belief in available data. In this work, stochastic semi-supervised SVR geomodel is integrated into Bayesian framework to quantify uncertainty of reservoir production with multiple models fitted to past dynamic observations (production history). Multiple history matched models are obtained using stochastic sampling and/or MCMC-based inference algorithms, which evaluate posterior probability distribution. Uncertainty of the model is described by posterior probability of the model parameters that represent key geological properties: spatial correlation size, continuity strength, smoothness/variability of spatial property distribution. The developed approach is illustrated with a fluvial reservoir case. The resulting probabilistic production forecasts are described by uncertainty envelopes. The paper compares the performance of the models with different combinations of unknown parameters and discusses sensitivity issues.

Rates of cultural change and patterns of cultural accumulation in stochastic models of social transmission.

Cultural variation in a population is affected by the rate of occurrence of cultural innovations, whether such innovations are preferred or eschewed, how they are transmitted between individuals in the population, and the size of the population. An innovation, such as a modification in an attribute of a handaxe, may be lost or may become a property of all handaxes, which we call "fixation of the innovation." Alternatively, several innovations may attain appreciable frequencies, in which case properties of the frequency distribution-for example, of handaxe measurements-is important. Here we apply the Moran model from the stochastic theory of population genetics to study the evolution of cultural innovations. We obtain the probability that an initially rare innovation becomes fixed, and the expected time this takes. When variation in cultural traits is due to recurrent innovation, copy error, and sampling from generation to generation, we describe properties of this variation, such as the level of heterogeneity expected in the population. For all of these, we determine the effect of the mode of social transmission: conformist, where there is a tendency for each naïve newborn to copy the most popular variant; pro-novelty bias, where the newborn prefers a specific variant if it exists among those it samples; one-to-many transmission, where the variant one individual carries is copied by all newborns while that individual remains alive. We compare our findings with those predicted by prevailing theories for rates of cultural change and the distribution of cultural variation.

Stochastic Population Projection for Germany - based on the Quadratic Spline approach to modelling age specific fertility rates

This contribution builds upon a former paper by the authors (Lipps and Betz 2004), in which a stochastic population projection for East- and West Germany is performed. Aim was to forecast relevant population parameters and their distribution in a consistent way. We now present some modifications, which have been modelled since. First, population parameters for the entire German population are modelled. In order to overcome the modelling problem of the structural break in the East during reunification, we show that the adaptation process of the relevant figures by the East can be considered to be completed by now. As a consequence, German parameters can be modelled just by using the West German historic patterns, with the start-off population of entire Germany. Second, a new model to simulate age specific fertility rates is presented, based on a quadratic spline approach. This offers a higher flexibility to model various age specific fertility curves. The simulation results are compared with the scenario based official forecasts for Germany in 2050. Exemplary for some population parameters (e.g. dependency ratio), it can be shown that the range spanned by the medium and extreme variants correspond to the s-intervals in the stochastic framework. It seems therefore more appropriate to treat this range as a s-interval covering about two thirds of the true distribution.

On the problematic of reserving and stochastic loss models

Abstract Traditionally, the common reserving methods used by the non-life actuaries are based on the assumption that future claims are going to behave in the same way as they did in the past. There are two main sources of variability in the processus of development of the claims: the variability of the speed with which the claims are settled and the variability between the severity of the claims from different accident years. High changes in these processes will generate distortions in the estimation of the claims reserves. The main objective of this thesis is to provide an indicator which firstly identifies and quantifies these two influences and secondly to determine which model is adequate for a specific situation. Two stochastic models were analysed and the predictive distributions of the future claims were obtained. The main advantage of the stochastic models is that they provide measures of variability of the reserves estimates. The first model (PDM) combines one conjugate family Dirichlet - Multinomial with the Poisson distribution. The second model (NBDM) improves the first one by combining two conjugate families Poisson -Gamma (for distribution of the ultimate amounts) and Dirichlet Multinomial (for distribution of the incremental claims payments). It was found that the second model allows to find the speed variability in the reporting process and development of the claims severity as function of two above mentioned distributions' parameters. These are the shape parameter of the Gamma distribution and the Dirichlet parameter. Depending on the relation between them we can decide on the adequacy of the claims reserve estimation method. The parameters have been estimated by the Methods of Moments and Maximum Likelihood. The results were tested using chosen simulation data and then using real data originating from the three lines of business: Property/Casualty, General Liability, and Accident Insurance. These data include different developments and specificities. The outcome of the thesis shows that when the Dirichlet parameter is greater than the shape parameter of the Gamma, resulting in a model with positive correlation between the past and future claims payments, suggests the Chain-Ladder method as appropriate for the claims reserve estimation. In terms of claims reserves, if the cumulated payments are high the positive correlation will imply high expectations for the future payments resulting in high claims reserves estimates. The negative correlation appears when the Dirichlet parameter is lower than the shape parameter of the Gamma, meaning low expected future payments for the same high observed cumulated payments. This corresponds to the situation when claims are reported rapidly and fewer claims remain expected subsequently. The extreme case appears in the situation when all claims are reported at the same time leading to expectations for the future payments of zero or equal to the aggregated amount of the ultimate paid claims. For this latter case, the Chain-Ladder is not recommended.

The handaxe and the microscope: individual and social learning in a multidimensional model of adaptation

When individuals learn by trial-and-error, they perform randomly chosen actions and then reinforce those actions that led to a high payoff. However, individuals do not always have to physically perform an action in order to evaluate its consequences. Rather, they may be able to mentally simulate actions and their consequences without actually performing them. Such fictitious learners can select actions with high payoffs without making long chains of trial-and-error learning. Here, we analyze the evolution of an n-dimensional cultural trait (or artifact) by learning, in a payoff landscape with a single optimum. We derive the stochastic learning dynamics of the distance to the optimum in trait space when choice between alternative artifacts follows the standard logit choice rule. We show that for both trial-and-error and fictitious learners, the learning dynamics stabilize at an approximate distance of root n/(2 lambda(e)) away from the optimum, where lambda(e) is an effective learning performance parameter depending on the learning rule under scrutiny. Individual learners are thus unlikely to reach the optimum when traits are complex (n large), and so face a barrier to further improvement of the artifact. We show, however, that this barrier can be significantly reduced in a large population of learners performing payoff-biased social learning, in which case lambda(e) becomes proportional to population size. Overall, our results illustrate the effects of errors in learning, levels of cognition, and population size for the evolution of complex cultural traits. (C) 2013 Elsevier Inc. All rights reserved.

Stochastic inversion of tracer test and electrical geophysical data to estimate hydraulic conductivities.

Quantifying the spatial configuration of hydraulic conductivity (K) in heterogeneous geological environments is essential for accurate predictions of contaminant transport, but is difficult because of the inherent limitations in resolution and coverage associated with traditional hydrological measurements. To address this issue, we consider crosshole and surface-based electrical resistivity geophysical measurements, collected in time during a saline tracer experiment. We use a Bayesian Markov-chain-Monte-Carlo (McMC) methodology to jointly invert the dynamic resistivity data, together with borehole tracer concentration data, to generate multiple posterior realizations of K that are consistent with all available information. We do this within a coupled inversion framework, whereby the geophysical and hydrological forward models are linked through an uncertain relationship between electrical resistivity and concentration. To minimize computational expense, a facies-based subsurface parameterization is developed. The Bayesian-McMC methodology allows us to explore the potential benefits of including the geophysical data into the inverse problem by examining their effect on our ability to identify fast flowpaths in the subsurface, and their impact on hydrological prediction uncertainty. Using a complex, geostatistically generated, two-dimensional numerical example representative of a fluvial environment, we demonstrate that flow model calibration is improved and prediction error is decreased when the electrical resistivity data are included. The worth of the geophysical data is found to be greatest for long spatial correlation lengths of subsurface heterogeneity with respect to wellbore separation, where flow and transport are largely controlled by highly connected flowpaths.

Modélisation par automate cellulaire des phénomènes diagénétiques des plateformes carbonatées : calibration et paramétrage à partir de deux cas d'études : l'Urgonien du Vercors (Crétacé inférieur, SE France) et les Calcaires Gris du Mont Compomolon (Lias, NE Italie)

Une fois déposé, un sédiment est affecté au cours de son enfouissement par un ensemble de processus, regroupé sous le terme diagenèse, le transformant parfois légèrement ou bien suffisamment pour le rendre méconnaissable. Ces modifications ont des conséquences sur les propriétés pétrophysiques qui peuvent être positives ou négatives, c'est-à-dire les améliorer ou bien les détériorer. Une voie alternative de représentation numérique des processus, affranchie de l'utilisation des réactions physico-chimiques, a été adoptée et développée en mimant le déplacement du ou des fluides diagénétiques. Cette méthode s'appuie sur le principe d'un automate cellulaire et permet de simplifier les phénomènes sans sacrifier le résultat et permet de représenter les phénomènes diagénétiques à une échelle fine. Les paramètres sont essentiellement numériques ou mathématiques et nécessitent d'être mieux compris et renseignés à partir de données réelles issues d'études d'affleurements et du travail analytique effectué. La représentation des phénomènes de dolomitisation de faible profondeur suivie d'une phase de dédolomitisation a été dans un premier temps effectuée. Le secteur concerne une portion de la série carbonatée de l'Urgonien (Barrémien-Aptien), localisée dans le massif du Vercors en France. Ce travail a été réalisé à l'échelle de la section afin de reproduire les géométries complexes associées aux phénomènes diagénétiques et de respecter les proportions mesurées en dolomite. De plus, la dolomitisation a été simulée selon trois modèles d'écoulement. En effet, la dédolomitisation étant omniprésente, plusieurs hypothèses sur le mécanisme de dolomitisation ont été énoncées et testées. Plusieurs phases de dolomitisation per ascensum ont été également simulées sur des séries du Lias appartenant aux formations du groupe des Calcaire Gris, localisées au nord-est de l'Italie. Ces fluides diagénétiques empruntent le réseau de fracturation comme vecteur et affectent préférentiellement les lithologies les plus micritisées. Cette étude a permis de mettre en évidence la propagation des phénomènes à l'échelle de l'affleurement. - Once deposited, sediment is affected by diagenetic processes during their burial history. These diagenetic processes are able to affect the petrophysical properties of the sedimentary rocks and also improve as such their reservoir capacity. The modelling of diagenetic processes in carbonate reservoirs is still a challenge as far as neither stochastic nor physicochemical simulations can correctly reproduce the complexity of features and the reservoir heterogeneity generated by these processes. An alternative way to reach this objective deals with process-like methods, which simplify the algorithms while preserving all geological concepts in the modelling process. The aim of the methodology is to conceive a consistent and realistic 3D model of diagenetic overprints on initial facies resulting in petrophysical properties at a reservoir scale. The principle of the method used here is related to a lattice gas automata used to mimic diagenetic fluid flows and to reproduce the diagenetic effects through the evolution of mineralogical composition and petrophysical properties. This method developed in a research group is well adapted to handle dolomite reservoirs through the propagation of dolomitising fluids and has been applied on two case studies. The first study concerns a mid-Cretaceous rudist and granular platform of carbonate succession (Urgonian Fm., Les Gorges du Nan, Vercors, SE France), in which several main diagenetic stages have been identified. The modelling in 2D is focused on dolomitisation followed by a dédolomitisation stage. For the second study, data collected from outcrops on the Venetian platform (Lias, Mont Compomolon NE Italy), in which several diagenetic stages have been identified. The main one is related to per ascensum dolomitisation along fractures. In both examples, the evolution of the effects of the mimetic diagenetic fluid on mineralogical composition can be followed through space and numerical time and help to understand the heterogeneity in reservoir properties. Carbonates, dolomitisation, dédolomitisation, process-like modelling, lattice gas automata, random walk, memory effect.

A model for the evolution of reinforcement learning in fluctuating games

Many species are able to learn to associate behaviours with rewards as this gives fitness advantages in changing environments. Social interactions between population members may, however, require more cognitive abilities than simple trial-and-error learning, in particular the capacity to make accurate hypotheses about the material payoff consequences of alternative action combinations. It is unclear in this context whether natural selection necessarily favours individuals to use information about payoffs associated with nontried actions (hypothetical payoffs), as opposed to simple reinforcement of realized payoff. Here, we develop an evolutionary model in which individuals are genetically determined to use either trial-and-error learning or learning based on hypothetical reinforcements, and ask what is the evolutionarily stable learning rule under pairwise symmetric two-action stochastic repeated games played over the individual's lifetime. We analyse through stochastic approximation theory and simulations the learning dynamics on the behavioural timescale, and derive conditions where trial-and-error learning outcompetes hypothetical reinforcement learning on the evolutionary timescale. This occurs in particular under repeated cooperative interactions with the same partner. By contrast, we find that hypothetical reinforcement learners tend to be favoured under random interactions, but stable polymorphisms can also obtain where trial-and-error learners are maintained at a low frequency. We conclude that specific game structures can select for trial-and-error learning even in the absence of costs of cognition, which illustrates that cost-free increased cognition can be counterselected under social interactions.

A comprehensive model for quantum noise characterization in digital mammography.

NlmCategory="UNASSIGNED">A version of cascaded systems analysis was developed specifically with the aim of studying quantum noise propagation in x-ray detectors. Signal and quantum noise propagation was then modelled in four types of x-ray detectors used for digital mammography: four flat panel systems, one computed radiography and one slot-scan silicon wafer based photon counting device. As required inputs to the model, the two dimensional (2D) modulation transfer function (MTF), noise power spectra (NPS) and detective quantum efficiency (DQE) were measured for six mammography systems that utilized these different detectors. A new method to reconstruct anisotropic 2D presampling MTF matrices from 1D radial MTFs measured along different angular directions across the detector is described; an image of a sharp, circular disc was used for this purpose. The effective pixel fill factor for the FP systems was determined from the axial 1D presampling MTFs measured with a square sharp edge along the two orthogonal directions of the pixel lattice. Expectation MTFs were then calculated by averaging the radial MTFs over all possible phases and the 2D EMTF formed with the same reconstruction technique used for the 2D presampling MTF. The quantum NPS was then established by noise decomposition from homogenous images acquired as a function of detector air kerma. This was further decomposed into the correlated and uncorrelated quantum components by fitting the radially averaged quantum NPS with the radially averaged EMTF(2). This whole procedure allowed a detailed analysis of the influence of aliasing, signal and noise decorrelation, x-ray capture efficiency and global secondary gain on NPS and detector DQE. The influence of noise statistics, pixel fill factor and additional electronic and fixed pattern noises on the DQE was also studied. The 2D cascaded model and decompositions performed on the acquired images also enlightened the observed quantum NPS and DQE anisotropy.