Sources Of Stochasticity Research Articles

The motility-matrix production switch in Bacillus subtilis-a modeling perspective.

Phenotype switching can be triggered by external stimuli and by intrinsic stochasticity. Here, we focus on the motility-matrix production switch in Bacillus subtilis. We use modeling to describe the SinR-SlrR bistable switch and its regulation by SinI and to distinguish different sources of stochasticity. Our simulations indicate that intrinsic fluctuations in the synthesis of SinI are insufficient to drive spontaneous switching and suggest that switching is triggered by upstream noise from the Spo0A phosphorelay. IMPORTANCE The switch from motility to matrix production is the first step toward biofilm formation and, thus, to multicellular behavior in Bacillus subtilis. The transition is governed by a bistable switch based on the interplay of the regulators SinR and SlrR, while SinI transmits upstream signals to that switch. Quantitative modeling can be used to study the switching dynamics. Here, we build such a model step by step to describe the dynamics of the switch and its regulation and to study how spontaneous switching is triggered by upstream noise from the Spo0A phosphorelay.

A model of replicating coupled oscillators generates naturally occurring cell networks.

When a founder cell and its progeny divide with incomplete cytokinesis, a network forms in which each intercellular bridge corresponds to a past mitotic event. Such networks are required for gamete production in many animals, and different species have evolved diverse final network topologies. Although mechanisms regulating network assembly have been identified in particular organisms, we lack a quantitative framework to understand network assembly and inter-species variability. Motivated by cell networks responsible for oocyte production in invertebrates, where the final topology is typically invariant within each species, we devised a mathematical model for generating cell networks, in which each node is an oscillator and, after a full cycle, the node produces a daughter to which it remains connected. These cell cycle oscillations are transient and coupled via diffusion over the edges of the network. By variation of three biologically motivated parameters, our model generates nearly all such networks currently reported across invertebrates. Furthermore, small parameter variations can rationalize cases of intra-species variation. Because cell networks outside of the ovary often form less deterministically, we propose model generalizations to account for sources of stochasticity.

Analytical formulation for explaining the variations in traffic states: A fundamental diagram modeling perspective with stochastic parameters

Despite the simplicity and practicality of (deterministic) fundamental diagram models in highway traffic flow theory, the wide scattering effect observed in empirical data remains highly controversial, particularly for explaining traffic state variations. Owing to the analytical properties of the fundamental diagram modeling approach, in this study, we proposed an analytical and quantitative method for analyzing traffic state variations. We investigated the scattering effect in the fundamental diagram and proposed two stochastic fundamental diagram (SFD) models with lognormal and skew-normal distributions to explain the variations in traffic states. The first SFD model assumes that the scattering effect results from stochasticity in both the free-flow speed and the speed at critical density. Both random variables were assumed to follow the lognormal distribution. In the second SFD model, an integrated error term that was assumed to follow the skew-normal distribution over different density ranges was appended to the deterministic fundamental diagram. The properties of these two SFD models were analyzed and compared, and the parameters in these SFD models were calibrated using real-world loop detector data. The observed scatters from the empirical data were reproduced well by the simulated fundamental diagram model, indicating the validity of the proposed SFD models for explaining traffic state variations. Using these two analytical SFD models, we can analyze the stochastic capacity of freeways with closed forms. More importantly, the sources of stochasticity in freeway capacity can be traced in terms of randomly distributed parameters in fundamental diagram models.

Stochastic processes in the structure and functioning of soil biodiversity

Ecologists are increasingly recognizing the importance of stochastic processes in generating spatial and temporal variation in biological communities. This variation is very high in soil, which hosts not <¼ of all biodiversity on Earth and is central to how terrestrial ecosystems respond to perturbations. Measurement errors, demographic stochasticity (individual variability in traits such as birth and death rates), and environmental stochasticity (fluctuations in environmental properties) are the three main sources of stochasticity in ecology. Here, we synthesize how these three sources of stochasticity are quantified and incorporated in the study of soil biodiversity, highlighting current limits, possible solutions, and future research needs. We stress the relevance of all these factors to our future understanding of terrestrial ecosystems via plant-soil and soil-climate interactions and feedbacks. In soil, measurement errors are due to the small size, high abundance, and broad distributions of soil organisms, which limit sampling in space and especially over time. We argue that positive autocorrelation is a main characteristic of soil environmental properties, which may have important consequences on the response of soil biota to perturbations. At a local scale, large populations of soil organisms also imply a minor role of demographic stochasticity. Despite demographic stochasticity being a less significant source of variability than environmental stochasticity, we show that demographic stochasticity can be sizeable, but that within soil systems, stochasticity of environmental conditions must be accounted for. Explicit consideration of stochastic processes in soil biodiversity research is essential to our future understanding of the processes that control soil biodiversity. In classical ecology, stochasticity implies probabilistic predictions in terms of population growth, extinction, species coexistence, and community diversity. In soil, stochasticity implies very variable responses to climate change and the soil-climate feedback. Future studies will have to identify the major sources of environmental stochasticity with a particular focus on the interaction between multiple global change factors.

Designing an optimal large‐scale reintroduction plan for a critically endangered species

Abstract Optimization methods are routinely used for landscape‐level conservation planning, but still underused in supporting species recovery programs. A possible barrier is the difficulty in representing and optimizing complex multidimensional problems: for example, many species recovery programs require management at the population level, but also allocation of effort and resources across populations and over time. Optimization methods can help, but they must strike a balance: too much realism can be computationally unfeasible, but too much simplification can limit relevance for complex programs, exactly where decision support might be most needed. We show how integer linear programming can be used to solve such a complex problem, combining multiple site‐level demographic models with realistic management constraints under different sources of stochasticity and uncertainty. We apply this protocol to reintroduction planning for the critically endangered Montseny brook newt Calotriton arnoldi, optimizing site restoration efforts, captive releases from limited and variable stocks, and short‐ and long‐term monitoring, all across 17 sites over 10 years. For C. arnoldi, the optimal solution was generally to open as many sites as possible, as soon as allowed by budget, and to reinforce sites with additional releases. The number of new populations that could be established was limited not only by the high initial costs of restoring and preparing sites for releases, but also because opening new sites would require subsequent monitoring, eventually adding up to unsustainable costs. Synthesis and applications. Our results suggest releases of Calotriton arnoldi should be dictated first by habitat restoration capacity, then by long‐term sustainability. More generally, our study shows how quantitative decision‐support methods can improve the value of science for conservation, and help managers find solutions to complex problems. However, deploying those methods requires close collaboration between managers and scientists, to ensure models are realistic, results are relevant, and the whole process is informative.

Sources of Stochasticity in the Growth of Cloud Droplets: Supersaturation Fluctuations versus Turbulent Transport

Abstract The role played by fluctuations of supersaturation in the growth of cloud droplets is examined in this study. The stochastic condensation framework and the three regimes of activation of cloud droplets— namely, mean dominant, fluctuation influenced, and fluctuation dominant—are used for analyzing the data from high-resolution large-eddy simulations of the Pi convection-cloud chamber. Based on a detailed budget analysis the significance of all the terms in the evolution of the droplet size distribution equation is evaluated in all three regimes. The analysis indicates that the mean-growth rate is a dominant process in shaping the droplet size distribution in all three regimes. Turbulence introduces two sources of stochasticity, turbulent transport and particle lifetime, and supersaturation fluctuations. The transport of cloud droplets plays an important role in all three regimes, whereas the direct effect of supersaturation fluctuations is primarily related to the activation and growth of the small droplets in the fluctuation-influenced and fluctuation-dominant regimes. We compare our results against the previous studies (experimental and theory) of the Pi chamber, and discuss the limitations of the existing models based on the stochastic condensation framework. Furthermore, we extend the discussion of our results to atmospheric clouds, and in particular focus on recent adiabatic turbulent cloud parcel simulations based on the stochastic condensation framework, and emphasize the importance of entrainment/mixing and turbulent transport in shaping the droplet size distribution.

High-throughput determination of dry mass of single bacterial cells by ultrathin membrane resonators

How bacteria are able to maintain their size remains an open question. Techniques that can measure the biomass (dry mass) of single cells with high precision and high-throughput are demanded to elucidate this question. Here, we present a technological approach that combines the transport, guiding and focusing of individual bacteria from solution to the surface of an ultrathin silicon nitride membrane resonator in vacuum. The resonance frequencies of the membrane undergo abrupt variations at the instants where single cells land on the membrane surface. The resonator design displays a quasi-symmetric rectangular shape with an extraordinary capture area of 0.14 mm2, while maintaining a high mass resolution of 0.7 fg (1 fg = 10−15 g) to precisely resolve the dry mass of single cells. The small rectangularity of the membrane provides unprecedented frequency density of vibration modes that enables to retrieve the mass of individual cells with high accuracy by specially developed inverse problem theory. We apply this approach for profiling the dry mass distribution in Staphylococcus epidermidis and Escherichia coli cells. The technique allows the determination of the dry mass of single bacterial cells with an accuracy of about 1% at an unparalleled throughput of 20 cells/min. Finally, we revisit Koch & Schaechter model developed during 60 s to assess the intrinsic sources of stochasticity that originate cell size heterogeneity in steady-state populations. The results reveal the importance of mass resolution to correctly describe these mechanisms.

An empirical review of ICES reference points

Abstract The International Council for the Exploration of the Sea (ICES) has provided scientific stock advice based on reference points to manage fisheries in the North Atlantic Ocean and adjacent seas for decades. ICES advice integrates the precautionary approach with the objective of achieving maximum sustainable yield. Here, we examine ICES reference point evolution over the last 25 yr and provide a comprehensive empirical review of current ICES reference points for data-rich stocks (Category 1; 79 stocks). The consistency of reference point estimation with the ICES guidelines is evaluated. We demonstrate: (1) how the framework has evolved over time in an intergovernmental setting, (2) that multiple precautionary components and sources of stochasticity are included, (3) that the relationship and historical context of stock size and recruitment are crucial for non-proxy reference points, (4) that reference points are reviewed frequently, taking into account fluctuations and multiple sources of variability, (5) that there are occasional inconsistencies with the guidelines, and (6) that more comprehensive and clearer documentation is needed. Simplifying the stock-recruit typology and developing quantitative criteria would assist with this critically important classification. We recommend a well-documented, transparent, and reproducible framework, and periodic syntheses comparing applications across all stocks.

Reducing Uncertainty in the Onset of Combustion Instabilities Using Dynamic Pressure Information and Bayesian Neural Networks

Abstract Modern low-emission combustion systems with improved fuel-air mixing are more prone to combustion instabilities and, therefore, use advanced control methods to balance minimum NOx emissions and the presence of thermoacoustic combustion instabilities. The exact operating conditions at which the system encounters an instability are uncertain because of sources of stochasticity, such as turbulent combustion, and the influence of hidden variables, such as unmeasured wall temperatures or differences in machine geometry within manufacturing tolerances. Practical systems tend to be more elaborate than laboratory systems and tend to have less instrumentation, meaning that they suffer more from uncertainty induced by hidden variables. In many commercial systems, the only direct measurement of the combustor comes from a dynamic pressure sensor. In this study, we train a Bayesain Neural Network to predict the probability of onset of thermoacoustic instability at various times in the future, using only dynamic pressure measurements and the current operating condition. We show that on a practical system, the error in the onset time predicted by the Bayesain Neural Networks is 45% lower than the error when using the operating condition alone and more informative than the warning provided by commonly used precursor detection methods. This is demonstrated on two systems: (i) a premixed hydrogen/methane annular combustor, where the hidden variables are wall temperatures that depend on the rate of change of operating condition, and (ii) full-scale prototype combustion system, where the hidden variables arise from differences between the systems.

A guide to state–space modeling of ecological time series

AbstractState–space models (SSMs) are an important modeling framework for analyzing ecological time series. These hierarchical models are commonly used to model population dynamics, animal movement, and capture–recapture data, and are now increasingly being used to model other ecological processes. SSMs are popular because they are flexible and they model the natural variation in ecological processes separately from observation error. Their flexibility allows ecologists to model continuous, count, binary, and categorical data with linear or nonlinear processes that evolve in discrete or continuous time. Modeling the two sources of stochasticity separately allows researchers to differentiate between biological variation and imprecision in the sampling methodology, and generally provides better estimates of the ecological quantities of interest than if only one source of stochasticity is directly modeled. Since the introduction of SSMs, a broad range of fitting procedures have been proposed. However, the variety and complexity of these procedures can limit the ability of ecologists to formulate and fit their own SSMs. We provide the knowledge for ecologists to create SSMs that are robust to common, and often hidden, estimation problems, and the model selection and validation tools that can help them assess how well their models fit their data. We present a review of SSMs that will provide a strong foundation to ecologists interested in learning about SSMs, introduce new tools to veteran SSM users, and highlight promising research directions for statisticians interested in ecological applications. The review is accompanied by an in‐depth tutorial that demonstrates how SSMs can be fitted and validated in R. Together, the review and tutorial present an introduction to SSMs that will help ecologists to formulate, fit, and validate their models.

Evaluating Meta-Reinforcement Learning through a HVAC Control Benchmark (Student Abstract)

Meta-Reinforcement Learning (RL) algorithms promise to leverage prior task experience to quickly learn new unseen tasks. Unfortunately, evaluating meta-RL algorithms is complicated by a lack of suitable benchmarks. In this paper we propose adapting a challenging real-world heating, ventilation and air-conditioning (HVAC) control benchmark for meta-RL. Unlike existing benchmark problems, HVAC control has a broader task distribution, and sources of exogenous stochasticity from price and weather predictions which can be shared across task definitions. This can enable greater differentiation between the performance of current meta-RL approaches, and open the way for future research into algorithms that can adapt to entirely new tasks not sampled from the current task distribution.

A Strategic Markovian Traffic Equilibrium Model for Capacitated Networks

In the realm of traffic assignment over a network involving rigid arc capacities, the aim of the present work is to generalize the model of Marcotte, Nguyen, and Schoeb [Marcotte P, Nguyen S, Schoeb A (2004) A strategic flow model of traffic assignment in static capacitated networks. Oper. Res. 52(2):191–212.] by casting it within a stochastic user equilibrium framework. The strength of the proposed model is to incorporate two sources of stochasticity stemming, respectively, from the users’ imperfect knowledge regarding arc costs (represented by a discrete choice model) and the probability of not accessing saturated arcs. Moreover, the arc-based formulation extends the Markovian traffic equilibrium model of Baillon and Cominetti [Baillon JB, Cominetti R ( 2008 ) Markovian traffic equilibrium. Math. Programming 111(1-2):33–56.] through the explicit consideration of capacities. This paper is restricted to the case of acyclic networks, for which we present solution algorithms and numerical experiments.

Demography_Lab, an educational application to evaluate population growth: Unstructured and matrix models.

Training in Population Ecology asks for scalable applications capable of embarking students on a trip from basic concepts to the projection of populations under the various effects of density dependence and stochasticity. Demography_Lab is an educational tool for teaching Population Ecology aspiring to cover such a wide range of objectives. The application uses stochastic models to evaluate the future of populations. Demography_Lab may accommodate a wide range of life cycles and can construct models for populations with and without an age or stage structure. Difference equations are used for unstructured populations and matrix models for structured populations. Both types of models operate in discrete time. Models can be very simple, constructed with very limited demographic information or parameter‐rich, with a complex density‐dependence structure and detailed effects of the different sources of stochasticity. Demography_Lab allows for deterministic projections, asymptotic analysis, the extraction of confidence intervals for demographic parameters, and stochastic projections. Stochastic population growth is evaluated using up to three sources of stochasticity: environmental and demographic stochasticity and sampling error in obtaining the projection matrix. The user has full control on the effect of stochasticity on vital rates. The effect of the three sources of stochasticity may be evaluated independently for each vital rate. The user has also full control on density dependence. It may be included as a ceiling population size controlling the number of individuals in the population or it may be evaluated independently for each vital rate. Sensitivity analysis can be done for the asymptotic population growth rate or for the probability of extinction. Elasticity of the probability of extinction may be evaluated in response to changes in vital rates, and in response to changes in the intensity of density dependence and environmental stochasticity.

Modeling transport of antibiotic resistant bacteria in aquatic environment using stochastic differential equations

Contaminated sites are recognized as the “hotspot” for the development and spread of antibiotic resistance in environmental bacteria. It is very challenging to understand mechanism of development of antibiotic resistance in polluted environment in the presence of different anthropogenic pollutants. Uncertainties in the environmental processes adds complexity to the development of resistance. This study attempts to develop mathematical model by using stochastic partial differential equations for the transport of fluoroquinolone and its resistant bacteria in riverine environment. Poisson’s process is assumed for the diffusion approximation in the stochastic partial differential equations (SPDE). Sensitive analysis is performed to evaluate the parameters and variables for their influence over the model outcome. Based on their sensitivity, the model parameters and variables are chosen and classified into environmental, demographic, and anthropogenic categories to investigate the sources of stochasticity. Stochastic partial differential equations are formulated for the state variables in the model. This SPDE model is then applied to the 100 km stretch of river Musi (South India) and simulations are carried out to assess the impact of stochasticity in model variables on the resistant bacteria population in sediments. By employing the stochasticity in model variables and parameters we came to know that environmental and anthropogenic variations are not able to affect the resistance dynamics at all. Demographic variations are able to affect the distribution of resistant bacteria population uniformly with standard deviation between 0.087 and 0.084, however, is not significant to have any biological relevance to it. The outcome of the present study is helpful in simplifying the model for practical applications. This study is an ongoing effort to improve the model for the transport of antibiotics and transport of antibiotic resistant bacteria in polluted river. There is a wide gap between the knowledge of stochastic resistant bacterial growth dynamics and the knowledge of transport of antibiotic resistance in polluted aquatic environment, this study is one step towards filling up that gap.

Systematic model reduction captures the dynamics of extrinsic noise in biochemical subnetworks.

We consider the general problem of describing the dynamics of subnetworks of larger biochemical reaction networks, e.g., protein interaction networks involving complex formation and dissociation reactions. We propose the use of model reduction strategies to understand the "extrinsic" sources of stochasticity arising from the rest of the network. Our approaches are based on subnetwork dynamical equations derived by projection methods and path integrals. The results provide a principled derivation of different components of the extrinsic noise that is observed experimentally in cellular biochemical reactions, over and above the intrinsic noise from the stochasticity of biochemical events in the subnetwork. We explore several intermediate approximations to assess systematically the relative importance of different extrinsic noise components, including initial transients, long-time plateaus, temporal correlations, multiplicative noise terms, and nonlinear noise propagation. The best approximations achieve excellent accuracy in quantitative tests on a simple protein network and on the epidermal growth factor receptor signaling network.

A Stochastic Model for Predicting Age and Mass at Maturity of Insects

Variation in age and mass at maturity is commonly observed in populations, even among individuals with the same genetic and environmental backgrounds. Accounting for such individual variation with a stochastic model is important for estimating optimal evolutionary strategies and for understanding potential trade-offs among life-history traits. However, most studies employ stochastic models that are either phenomenological or account for variation in only one life-history trait. We propose a model based on the developmental biology of the moth Manduca sexta that accounts for stochasticity in two key life-history traits, age and mass at maturity. The model is mechanistic, describing feeding behavior and common insect developmental processes, including the degradation of juvenile hormone prior to molting. We derive a joint probability density function for the model and explore how the distribution of age and mass at maturity is affected by different parameter values. We find that the joint distribution is generally nonnormal and highly sensitive to parameter values. In addition, our model predicts previously observed effects of temperature change and nutritional quality on the expected values of insect age and mass. Our results highlight the importance of integrating multiple sources of stochasticity into life-history models.

Total cost optimization of submersible irrigation pump maintenance using simulation

PurposeThe unpredictable failure of submersible pump (SP) in groundwater irrigation systems has considerable negative economic consequences. The purpose of this paper is to develop a total cost minimization model that aims to optimize maintenance actions for SP. It reports on simulation-based stochastic scenario analysis for evaluating total cost of maintenance.Design/methodology/approachStochastic simulation modeling has been performed for failure of pump motor and corresponding maintenance. Five alternative scenarios were compared for total cost over 15 years starting with empirical data from a northern Ethiopian site. Downtime probabilities and spare part supply uncertainty have been considered in the mathematical model. The model is also validated using multiple ways.FindingsThe scenario comparisons indicate that despite the challenges of accessing SP doing one motor rewinding for each purchased pump system upon failure (preferably with shorter supply lead time and variability) seems to result in lowest overall costs for the time horizon considered.Practical implicationsThe model should help to make informed practical decision regarding planning and management of SP failure systems in a developing economy context. This should, therefore, lead to better revenue for smallholder farmers and improved food security in similar context.Originality/valueThere are limited number of publications that consider the life cycle costs with stochastic analysis when it comes to maintenance of SPs. To the best of the authors’ knowledge, no paper has previously directly addressed maintenance cost optimization for SP in irrigation. The study could be used to develop more sophisticated stochastic models with more efficient algorithms and consideration of additional sources of stochasticity for such system.

Intraindividual variability in behavior shapes fitness landscapes.

Although intraindividual variability (IIV) in behavior is fundamental to ecological dynamics, the factors that contribute to the expression of IIV are poorly understood. Using an individual‐based model, this study examined the effects of stochasticity on the evolution of IIV represented by the residual variability of behavior. The model describes a population of prey with nonoverlapping generations, in which prey take refuge upon encountering a predator. The strategy of a prey is characterized by the mean and IIV (i.e., standard deviation) of hiding duration. Prey with no IIV will spend the same duration hiding in a refuge at each predator encounter, while prey with IIV will have variable hiding durations among encounters. For the sources of stochasticity, within‐generation stochasticity (represented by random predator encounters) and between‐generation stochasticity (represented by random resource availability) were considered. Analysis of the model indicates that individuals with high levels of IIV are maintained in a population in the presence of between‐generation stochasticity even though the optimal strategy in each generation is a strategy with no IIV, regardless of the presence or absence of within‐generation stochasticity. This contradictory pattern emerges because the mean behavioral trait and IIV do not independently influence fitness (e.g., the sign of the selection gradient with respect to IIV depends on the mean trait). Consequently, even when evolution eventually leads toward a strategy with no IIV (i.e., the optimal strategy), greater IIV may be transiently selected. Between‐generation stochasticity consistently imposes such transient selection and maintain high levels of IIV in a population.

Stochasticity in social structure and mating system drive extinction risk

AbstractAs anthropogenic activities continue to threaten species across the globe, many populations have seen dramatic reductions in abundance from historical values. While the underlying causes are varied, such long‐term population declines greatly increase these species’ susceptibility to extinction via stochastic processes. Previous research has established that demographic stochasticity and environmental stochasticity play important roles in extinction risk, but few studies have investigated the role of stochasticity in social dynamics, such as group formation and mating systems. Here, we developed a suite of simulation models incorporating different combinations of stochastic processes, while also varying group size and mating system. Using these models, we evaluated the interacting effects of different mating systems coupled with varied sources of stochasticity on extinction risk. Extinction risk was generally higher for populations with mating systems more dependent on even sex ratios in groups (e.g., monogamy). However, in more flexible mating systems (e.g., polygynandry), stochasticity in the formation of individual groups actually reduced extinction risk in certain scenarios. By identifying the factors most important to the stochastic extinction risk of species with different mating systems and social structures, we provide insight into conservation and management strategies for such species facing population declines.

Causation and chance: Detection of deterministic and stochastic ingredients in psychotherapy processes

A novel methodology for the empirical analysis of processes in psychotherapy was developed and tested. This method is based on the Fokker-Planck equation (FPE), a probabilistic model that detects the deterministic and stochastic components of a process. The deterministic component is given by the potential function underlying the process. The FPE application can be used to visualize the attractor (or in the case of multistability, attractors) of the dynamics, and the sources of stochasticity. The FPE app can also be employed in two-dimensional systems, for example, client’s and therapist’s coupled processes; then the method is run on the cross-correlations of the time series. Signatures were defined that merge the functions retrieved from the methodology into numerical values, and may serve to detect associations with conventional self-report measures of psychotherapy. The method was tested in a case series where client’s and therapist’s heart rate, heart rate variability and respiration were monitored in 20 psychotherapy sessions. The FPE app works well with time series of high resolution and adequate observation numbers, which renders it applicable to nonverbal and physiological time series.