A stochastic model for the membrane potential of a stimulated neuron

We present a simple model describing the transition between the prefiring, firing and postfiring phases of a single neuron in a large neural net. Using typical values for the physiological parameters that enter the model, we find average interspike times that are close to those reported in experimental measurements.     

Effect of an exponentially decaying threshold on the firing statistics of a stochastic integrate-and-fire neuron

We study a white-noise driven integrate-and-fire (IF) neuron with a time-dependent threshold. We give analytical expressions for mean and variance of the interspike interval assuming that the modification of the threshold value is small. It is shown that the variability of the interval can become both smaller or larger than in the case of constant threshold depending on the decay rate of threshold. We also show that the relative variability is minimal for a certain finite decay rate of the threshold. Furthermore, for slow threshold decay the leaky IF model shows a minimum in the coefficient of variation whenever the firing rate of the neuron matches the decay rate of the threshold. This novel effect can be seen if the firing rate is changed by varying the noise intensity or the mean input current.     

A stochastic formulation of the gompertzian growth model for in vitro bactericidal kinetics: parameter estimation and extinction probability

Time-kill curves have frequently been employed to study the antimicrobial effects of antibiotics. The relevance of pharmacodynamic modeling to these investigations has been emphasized in many studies of bactericidal kinetics. Stochastic models are needed that take into account the randomness of the mechanisms of both bacterial growth and bacteria-drug interactions. However, most of the models currently used to describe antibiotic activity against microorganisms are deterministic. In this paper we examine a stochastic differential equation representing a stochastic version of a pharmacodynamic model of bacterial growth undergoing random fluctuations, and derive its solution, mean value and covariance structure. An explicit likelihood function is obtained both when the process is observed continuously over a period of time and when data is sampled at time points, as is the custom in these experimental conditions. Some asymptotic properties of the maximum likelihood estimators for the model parameters are discussed. The model is applied to analyze in vitro time-kill data and to estimate model parameters; the probability of the bacterial population size dropping below some critical threshold is also evaluated. Finally, the relationship between bacterial extinction probability and the pharmacodynamic parameters estimated is discussed.     

Derivation of stochastic partial differential equations for size- and age-structured populations

Stochastic partial differential equations (SPDEs) for size-structured and age- and size-structured populations are derived from basic principles, i.e. from the changes that occur in a small time interval. Discrete stochastic models of size-structured and age-structured populations are constructed, carefully taking into account the inherent randomness in births, deaths, and size changes. As the time interval decreases, the discrete stochastic models lead to systems of Itô stochastic differential equations. As the size and age intervals decrease, SPDEs are derived for size-structured and age- and size-structured populations. Comparisons between numerical solutions of the SPDEs and independently formulated Monte Carlo calculations support the accuracy of the derivations.     

Identification and comparison of stochastic metabolic/hemodynamic models (sMHM) for the generation of the BOLD signal

This paper extends a previously formulated deterministic metabolic/hemodynamic model for the generation of blood oxygenated level dependent (BOLD) responses to include both physiological and observation stochastic components (sMHM). This adds a degree of flexibility when fitting the model to actual data by accounting for un-modelled activity. We then show how the innovation method can be used to estimate unobserved metabolic/hemodynamic as well as vascular variables of the sMHM, from simulated and actual BOLD data. The proposed estimation method allowed for doing model comparison by calculating the model’s AIC and BIC. This methodology was then used to select between different neurovascular coupling assumptions underlying sMHM. The proposed framework was first validated on simulations and then applied to BOLD data from a motor task experiment. The models under comparison in the analysis of the actual data considered that vascular response was coupled to: (I) inhibition, (II) excitation, (III) both excitation and inhibition. Data was best described by model II, although model III was also supported.     

A comparison of persistence-time estimation for discrete and continuous stochastic population models that include demographic and environmental variability

A discrete-time Markov chain model, a continuous-time Markov chain model, and a stochastic differential equation model are compared for a population experiencing demographic and environmental variability. It is assumed that the environment produces random changes in the per capita birth and death rates, which are independent from the inherent random (demographic) variations in the number of births and deaths for any time interval. An existence and uniqueness result is proved for the stochastic differential equation system. Similarities between the models are demonstrated analytically and computational results are provided to show that estimated persistence times for the three stochastic models are generally in good agreement when the models satisfy certain consistency conditions.     

Validation of a heterogeneous elastic-biphasic model for the numerical simulation of the PDL

An elastic-biphasic model for the simulation of the periodontal ligament (PDL) and the adjacent tooth is presented and investigated. The PDL is modelled as a biphasic material following the work of Ehlers and Markert (2001 EhlersW, MarkertB. 2001. A linear viscoelastic biphasic model for soft tissues based on the theory of porous media. ASME J Biomech Eng. 128:418–424.[Crossref], [Web of Science ®] , [Google Scholar]), whereas the tooth is modelled as a linear elastic body. A spatial discretisation scheme is proposed based on mixed finite elements for the spatial discretisation. Due to nonlinearity in the model, a predictor–corrector scheme is employed as a temporal discretisation scheme. In order to validate the PDL model, in vitro measurements are compared with numerical simulations. The numerical simulations are performed using geometries resulting from micro-CT scanner of the same porcine tooth, which was employed for the invitro measurements.     

On a stochastic model of a molecular genetic system capable of differentiation and reproduction of the initial state

A model of the system, consisting of a cyclic 3-operonic subsystem, related to a 2-operonic trigger by direct and feedback connections, is built. The operons of this system are functionally connected by repressers. The basic postulates are: a) the repressers are stable; b) during cell division each molecule of represser and respective mRNA has equal probability to find itself in any daughter cell. Computer simulation demonstrates that after few cell divisions, analogues of somatic cell, maintaining the system for some successive divisions, and of generative cells, where by the system returns to the initial state, appear. A scheme of molecular genetic control system, producing a lot of different cell types in course of successive cell divisions, is proposed.     

On the effects of the spatial distribution in an epidemic model based on cellular automaton

Several theoretical studies on disease propagation assume that individuals belonging to different groups regarding their health conditions are homogeneously distributed over the space. This is the well-known homogenous mixing assumption, which supports epidemiological models written in terms of ordinary differential or difference equations. Here, we consider that the host population infected by a contagious pathogen is composed by two groups with distinct traits and habits, which can be homogeneously mixed or not. The pathogen propagation is modeled by using an asynchronous probabilistic cellular automaton. Our main goal is to examine how a heterogeneous spatial distribution of these groups affects the endemic state. We noted that homogeneous distribution favors the occurrence of oscillations in the population composition. Surprisingly, we found out that the propagation dynamics of the heterogeneous distribution can also be described by a set of ordinary difference equations.     

Modelling the effects of field spatial scale and natural enemy colonization behaviour on pest suppression in diversified agroecosystems

1. Diversifying agroecosystems by establishing or retaining natural vegetation in and around crop areas has long been recognized as a potentially effective means of bolstering pest control as a result of attracting more numerous and diverse natural enemies, although outcomes are inconsistent across species.
2. Little is known about the underlying mechanisms driving such differences in species responses, creating challenges for determining how best to manage landscapes for maximizing environmental services such as biological control.
3. The present study addresses gaps in our understanding of the link between noncrop vegetation in field margins and pest suppression by using a system of partial differential equations to model population‐level predator–prey interactions, as well as spatial processes, aiming to capture the dynamics of crop plants, herbivores and two generalist predators.
4. We focus on differences in how two predators (a carabid and a ladybird beetle) colonize crop fields where they forage for prey, examining differences in how they move into the fields from adjacent vegetation as a potential driver of differences in overall pest suppression.
5. The results obtained demonstrate that predator colonization behaviour and spatial scale are important factors with respect to determining the effectiveness of biological control.

     

Sensitivity analysis of the tree distribution model Phenofit to climatic input characteristics: implications for climate impact assessment

Species distributions are already affected by climate change. Forecasting their long‐term evolution requires models with thoroughly assessed validation. Our aim here is to demonstrate that the sensitivity of such models to climate input characteristics may complicate their validation and introduce uncertainties in their predictions. In this study, we conducted a sensitivity analysis of a process‐based tree distribution model Phenofit to climate input characteristics. This analysis was conducted for two North American trees which differ greatly in their distribution and eight different types of climate input for the historic period which differ in their spatial (local or gridded data) and temporal (daily vs. monthly) resolution as well as their type (locally recorded, extrapolated or simulated by General Circulation Models). We show that the climate data resolution (spatial and temporal) and their type, highly affect the model predictions. The sensitivity analysis also revealed, the importance, for global climate change impact assessment, of (i) the daily variability of temperatures in modeling the biological processes shaping species distribution, (ii) climate data at high latitudes and elevations and (iii) climate data with high spatial resolution.     

A new mathematical model for combining growth and energy intake in animals: The case of the growing pig

A simultaneous model for analysis of net energy intake and growth curves is presented, viewing the animal's responses as a two dimensional outcome. The model is derived from four assumptions: (1) the intake is a quadratic function of metabolic weight; (2) the rate of body energy accretion represents the difference between intake and maintenance; (3) the relationship between body weight and body energy is allometric and (4) animal intrinsic variability affects the outcomes so the intake and growth trajectories are realizations of a stochastic process. Data on cumulated net energy intake and body weight measurements registered from weaning to maturity were available for 13 pigs. The model was fitted separately to 13 datasets. Furthermore, slaughter data obtained from 170 littermates was available for validation of the model. The parameters of the model were estimated by maximum likelihood within a stochastic state space model framework where a transform-both-sides approach was adopted to obtain constant variance. A suitable autocorrelation structure was generated by the stochastic process formulation. The pigs’ capacity for intake and growth were quantified by eight parameters: body weight at maximum rate of intake (149-281 kg); maximum rate of intake (25.7-35.7 MJ/day); metabolic body size exponent (fixed: 0.75); the daily maintenance requirement per kg metabolic body size (0.232-0.303 MJ/(day×kg^0.75)); reciprocal scaled energy density ; a dimensional exponent, θ₆ (0.730-0.867); coefficient for animal intrinsic variability in intake (0.120-0.248 MJ^0.5) and coefficient for animal intrinsic variability in growth (0.029-0.065 kg^0.5). Model parameter values for maintenance requirements and body energy gains were in good agreement with those obtained from slaughter data. In conclusion, the model provides biologically relevant parameter values, which cannot be derived by traditional analysis of growth and energy intake data.     

The effects of archipelago spatial structure on island diversity and endemism: predictions from a spatially‐structured neutral model

Islands are particularly suited to testing hypotheses about the ecological and evolutionary mechanisms underpinning community assembly. Yet the complex spatial arrangements of real island systems have received little attention from both empirical studies and theoretical models. Here, we investigate the extent to which the spatial structure of archipelagos affects species diversity and endemism. We start by proposing a new spatially structured neutral model that explicitly considers archipelago structure, and then investigate its predictions under a diversity of scenarios. Our results suggest that considering the spatial structure of archipelagos is crucial to understanding their diversity and endemism, with structured island systems acting both as “museums” and “cradles” of biodiversity. These dynamics of diversification may change the traditionally expected pattern of decrease in species richness with distance from the mainland, even potentially leading to increasing patterns for taxa with high speciation rates in archipelagos off species‐poor continental areas. Our results also predict that, within spatially structured archipelagos, metapopulation dynamics and evolutionary processes can generate higher diversity on islands more centrally placed than at the periphery. We derive from our results a set of theoretical predictions, potentially testable with empirical data.     

RATP: a model for simulating the spatial distribution of radiation absorption, transpiration and photosynthesis within canopies: application to an isolated tree crown

The model RATP (radiation absorption, transpiration and photosynthesis) is presented. The model was designed to simulate the spatial distribution of radiation and leaf-gas exchanges within vegetation canopies as a function of canopy structure, canopy microclimate within the canopy and physical and physiological leaf properties. The model uses a three-dimensional (3D) representation of the canopy (i.e. an array of 3D cells, each characterized by a leaf area density). Radiation transfer is computed by a turbid medium analogy, transpiration by the leaf energy budget approach, and photosynthesis by the Farquhar model, each applied for sunlit and shaded leaves at the individual 3D cell-scale. The model typically operates at a 20–30 min time step. The RATP model was applied to an isolated, 20-year-old walnut tree grown in the field. The spatial distribution of wind speed, stomatal response to environmental variables, and light acclimation of leaf photosynthetic properties were taken into account. Model outputs were compared with data acquired in the field. The model was shown to simulate satisfactorily the intracrown distribution of radiation regime, transpiration and photosynthetic rates, at shoot or branch scales.     

A model for the neuronal substrate of dead reckoning and memory in arthropods: a comparative computational and behavioral study

Returning to the point of departure after exploring the environment is a key capability for most animals. In the absence of landmarks, this task will be solved by integrating direction and distance traveled over time. This is referred to as path integration or dead reckoning. An important question is how the nervous systems of navigating animals such as the 1 mm³ brain of ants can integrate local information in order to make global decision. In this article we propose a neurobiologically plausible system of storing and retrieving direction and distance information. The path memory of our model builds on the well established concept of population codes, moreover our system does not rely on trigonometric functions or other complex non-linear operations such as multiplication, but only uses biologically plausible operations such as integration and thresholding. We test our model in two paradigms; in the first paradigm the system receives input from a simulated compass, in the second paradigm, the model is tested against behavioral data recorded from 17 ants. We were able to show that our path memory system was able to reliably encode and compute the angle of the vector pointing to the start location, and that the system stores the total length of the trajectory in a dependable way. From the structure and behavior of our model, we derive testable predictions both at the level of observable behavior as well as on the anatomy and physiology of its underlying neuronal substrate.     

Modulatory effects of parallel fiber and molecular layer interneuron synaptic activity on purkinje cell responses to ascending segment input: a modeling study

Based on anatomical, physiological, and model-based studies, it has been proposed that synapses associated with the ascending segment of granule cell axons provide the principle excitatory drive on Purkinje cells which is then modulated by the more numerous parallel fiber synapses. In this study we have evaluated this idea using a detailed compartmental model of a cerebellar Purkinje cell by providing identical ascending segment synaptic inputs during different levels of random parallel fiber and molecular interneuron input. Results suggest that background inputs from parallel fibers and molecular layer interneurons can have a substantial effect on the response of Purkinje cells to ascending segment inputs. Interestingly, these effects are not reflected in the average firing rate of the Purkinje cell and are thus entirely dendritic in effect. These results are considered in the context of the known segregated spatial distribution of the parallel fibers and ascending segment synapses and a new hypothesis concerning the functional organization of cerebellar cortical circuitry.     

Modelling the effects of climate change on the distribution and production of marine fishes: accounting for trophic interactions in a dynamic bioclimate envelope model

Climate change has already altered the distribution of marine fishes. Future predictions of fish distributions and catches based on bioclimate envelope models are available, but to date they have not considered interspecific interactions. We address this by combining the species‐based Dynamic Bioclimate Envelope Model (DBEM) with a size‐based trophic model. The new approach provides spatially and temporally resolved predictions of changes in species' size, abundance and catch potential that account for the effects of ecological interactions. Predicted latitudinal shifts are, on average, reduced by 20% when species interactions are incorporated, compared to DBEM predictions, with pelagic species showing the greatest reductions. Goodness‐of‐fit of biomass data from fish stock assessments in the North Atlantic between 1991 and 2003 is improved slightly by including species interactions. The differences between predictions from the two models may be relatively modest because, at the North Atlantic basin scale, (i) predators and competitors may respond to climate change together; (ii) existing parameterization of the DBEM might implicitly incorporate trophic interactions; and/or (iii) trophic interactions might not be the main driver of responses to climate. Future analyses using ecologically explicit models and data will improve understanding of the effects of inter‐specific interactions on responses to climate change, and better inform managers about plausible ecological and fishery consequences of a changing environment.     

Exploring the spatial distribution of light interception and photosynthesis of canopies by means of a functional-structural plant model

Background and Aims

At present most process-based models and the majority of three-dimensional models include simplifications of plant architecture that can compromise the accuracy of light interception simulations and, accordingly, canopy photosynthesis. The aim of this paper is to analyse canopy heterogeneity of an explicitly described tomato canopy in relation to temporal dynamics of horizontal and vertical light distribution and photosynthesis under direct- and diffuse-light conditions.

Methods

Detailed measurements of canopy architecture, light interception and leaf photosynthesis were carried out on a tomato crop. These data were used for the development and calibration of a functional–structural tomato model. The model consisted of an architectural static virtual plant coupled with a nested radiosity model for light calculations and a leaf photosynthesis module. Different scenarios of horizontal and vertical distribution of light interception, incident light and photosynthesis were investigated under diffuse and direct light conditions.

Key Results

Simulated light interception showed a good correspondence to the measured values. Explicitly described leaf angles resulted in higher light interception in the middle of the plant canopy compared with fixed and ellipsoidal leaf-angle distribution models, although the total light interception remained the same. The fraction of light intercepted at a north–south orientation of rows differed from east–west orientation by 10 % on winter and 23 % on summer days. The horizontal distribution of photosynthesis differed significantly between the top, middle and lower canopy layer. Taking into account the vertical variation of leaf photosynthetic parameters in the canopy, led to approx. 8 % increase on simulated canopy photosynthesis.

Conclusions

Leaf angles of heterogeneous canopies should be explicitly described as they have a big impact both on light distribution and photosynthesis. Especially, the vertical variation of photosynthesis in canopy is such that the experimental approach of photosynthesis measurements for model parameterization should be revised.