Stochastic determinants of assemblage patterns in coral reef fishes: a quantification by means of two models

Synopsis One perspective emphasizing the importance of stochastic processes in determining coral reef fish assemblages implies that there is little organization in species richness, abundance structure, and spatial distribution. We examine the degree to which this perspective is correct by analyzing distribution of fishes on a collection of patch reefs (Discovery Bay, Jamaica). We ask the question whether these patches accumulate species and individuals in a manner consistent with stochastic expectations. To address this question we use two conceptual models, each permitting a different insight. One assumes that fish are distributed stochastically on patches while the other assumes presence of restrictions on fish distribution due to habitat structure. For each conceptual model we use two types of benchmark: we compare observed patterns to those predicted by theoretical models, and we also compare observed patterns to those obtained from a random reallocation of fish individuals to patches. We found that the conceptual model assuming stochastic processes appeared to provide weaker explanation of patterns than the conceptual model that includes restrictions due to habitat structure. Further, and more importantly, we found that (i) the community is shaped by a mixture of stochastic and non-stochastic mechanisms, and (ii) the stochastic assembly processes decrease in importance for species restricted to fewer microhabitat types and sites. Our study therefore indicates that patches do accumulate individuals and species in a manner consistent with stochastic expectations, however, this applies primarily to the habitat generalists (unrestricted species). By the same token, increased habitat specialization by some species imposes constraints on the stochastic model such that it eventually fails.     

Comparing Stochastically Restricted Estimators in a Linear Regression Model

The minimum dispersion linear unbiased estimators of the vector of parameters in a linear regression model are compared when the parameters of the model are subject to stochastic linear restrictions with different dispersion matrices of the disturbances involved in them.     

Estimating transition probabilities of singly and doubly stochastic matrices

Vector quadratic programming techniques, based on the classical theory of vector quadratic forms, subjected to linear restrictions, minimization techniques are applied to the estimation of the transition probabilities of singly and doubly stochastic matrices.     

A Note on Comparing Stochastically Restricted Linear Estimators in a Regression Model

In his recent paper Liski (1989) derived conditions for superiority of the minimum dispersion estimator over another with respect to the covariance matrix when the parameter vector of a regression model is subject to competing stochastic restrictions. The aim of this note is to provide another necessary and sufficient condition which admits an easier interpretation of superiority related to the covariance matrix criterion.     

Most of the long-term genetic gain from optimum-contribution selection can be realised with restrictions imposed during optimisation

Background

We tested the hypothesis that optimum-contribution selection (OCS) with restrictions imposed during optimisation realises most of the long-term genetic gain realised by OCS without restrictions.

Methods

We used stochastic simulation to estimate long-term rates of genetic gain realised by breeding schemes that applied OCS without and with restrictions imposed during optimisation, where long-term refers to generations 23 to 25 (approximately). Six restrictions were imposed. Five of these removed solutions from the solution space. The sixth removed records of selection decisions made at earlier selection times. We also simulated a conventional breeding scheme with truncation selection as a reference point. Generations overlapped, selection was for a single trait, and the trait was observed for all selection candidates prior to selection.

Results

OCS with restrictions realised 67 to 99% of the additional gain realised by OCS without restrictions, where additional gain was the difference in the long-term rates of genetic gain realised by OCS without restrictions and our reference point with truncation selection. The only exceptions were those restrictions that removed all solutions near the optimum solution from the solution space and the restriction that removed records of selection decisions made at earlier selection times. Imposing these restrictions realised only −12 to 46% of the additional gain.

Conclusions

Most of the long-term genetic gain realised by OCS without restrictions can be realised by OCS with restrictions imposed during optimisation, provided the restrictions do not remove all solutions near the optimum from the solution space and do not remove records of earlier selection decisions. In breeding schemes where OCS cannot be applied optimally because of biological and logistical restrictions, OCS with restrictions provides a useful alternative. Not only does it realise most of the long-term genetic gain, OCS with restrictions enables OCS to be tailored to individual breeding schemes.     

Additive‐Multiplicative Regression Models for Spatio‐Temporal Epidemics

An extension of the stochastic susceptible–infectious–recovered (SIR) model is proposed in order to accommodate a regression context for modelling infectious disease data. The proposal is based on a multivariate counting process specified by conditional intensities, which contain an additive epidemic component and a multiplicative endemic component. This allows the analysis of endemic infectious diseases by quantifying risk factors for infection by external sources in addition to infective contacts. Inference can be performed by considering the full likelihood of the stochastic process with additional parameter restrictions to ensure non‐negative conditional intensities. Simulation from the model can be performed by Ogata's modified thinning algorithm. As an illustrative example, we analyse data provided by the Federal Research Centre for Virus Diseases of Animals, Wusterhausen, Germany, on the incidence of the classical swine fever virus in Germany during 1993–2004.     

Diffusion Restrictions Surrounding Mitochondria: A Mathematical Model of Heart Muscle Fibers

Several experiments on permeabilized heart muscle fibers suggest the existence of diffusion restrictions grouping mitochondria and surrounding ATPases. The specific causes of these restrictions are not known, but intracellular structures are speculated to act as diffusion barriers. In this work, we assume that diffusion restrictions are induced by sarcoplasmic reticulum (SR), cytoskeleton proteins localized near SR, and crowding of cytosolic proteins. The aim of this work was to test whether such localization of diffusion restrictions would be consistent with the available experimental data and evaluate the extent of the restrictions. For that, a three-dimensional finite-element model was composed with the geometry based on mitochondrial and SR structural organization. Diffusion restrictions induced by SR and cytoskeleton proteins were varied with other model parameters to fit the set of experimental data obtained on permeabilized rat heart muscle fibers. There are many sets of model parameters that were able to reproduce all experiments considered in this work. However, in all the sets, <5-6% of the surface formed by SR and associated cytoskeleton proteins is permeable to metabolites. Such a low level of permeability indicates that the proteins should play a dominant part in formation of the diffusion restrictions.     

Stochastic resonance as a possible mechanism of amplification of weak electric signals in living cells

The most important but still unresolved problem in bioelectromagnetics is the interaction of weak electromagnetic fields (EMFs) with living cells. Thermal and other types of noise pose restrictions in cell detection of weak signals. As a consequence, some extant experimental results that indicate low-intensity field effects cannot be accounted for, and this renders the results themselves questionable. One way out of this dead end is to search for possible mechanisms of signal amplification. In this paper, we discuss a general mechanism in which a weak signal is amplified by system noise itself. This mechanism was discovered several years ago in physics and is known, in its simplest form, as a stochastic resonance. It was shown that signal amplification may exceed a factor of 1000, which renders existing estimations of EMF thresholds highly speculative. The applicability of the stochastic resonance concept to cells is discussed particularly with respect to the possible role of the cell membrane in the amplification process. © 1994 Wiley-Liss, Inc.     

A method for estimating stochastic noise in large genetic regulatory networks

MOTIVATION: Genetic regulatory networks are often affected by stochastic noise, due to the low number of molecules taking part in certain reactions. The networks can be simulated using stochastic techniques that model each reaction as a stochastic event. As models become increasingly large and sophisticated, however, the solution time can become excessive; particularly if one wishes to determine the effect on noise of changes to a series of parameters, or the model structure. Methods are therefore required to rapidly estimate stochastic noise. RESULTS: This paper presents an algorithm, based on error growth techniques from non-linear dynamics, to rapidly estimate the noise characteristics of genetic networks of arbitrary size. The method can also be used to determine analytical solutions for simple sub-systems. It is demonstrated on a number of cases, including a prototype model of the galactose regulatory pathway in yeast. AVAILABILITY: A software tool which incorporates the algorithm is available for use as part of the stochastic simulation package Dizzy. It is available for download at http://labs.systemsbiology.net/bolouri/software/Dizzy/ CONTACT: dorrell@systemsbiology.org SUPPLEMENTARY INFORMATION: A conceptual model of the regulatory part of the galactose utilization pathway in yeast, used as an example in the paper, is available at http://labs.systemsbiology.net/bolouri/models/galconcept.dizzy     

Segregated mathematical model for growth of anchorage-dependent MDCK cells in microcarrier culture

To describe the growth behavior of anchorage-dependent mammalian cells in microcarrier systems, various approaches comprising deterministic and stochastic single cell models as well as automaton-based models have been presented in the past. The growth restriction of these often contact-inhibited cells by spatial effects is described at levels with different complexity but for the most part not taking into account their metabolic background. Compared to suspension cell lines these cells have a comparatively long lag phase required for attachment and start of proliferation on the microcarrier. After an initial phase of exponential growth only a moderate specific growth rate is achieved due to restrictions in space available for cell growth, limiting medium components, and accumulation of growth inhibitors. Here, a basic deterministic unstructured segregated cell model for growth of Madin Darby Canine Kidney (MDCK) cells used in influenza vaccine production is described. Four classes of cells are considered: cells on microcarriers, cells in suspension, dead cells, and lysed cells. Based on experimental data, cell attachment and detachment is taken explicitly into account. The model allows simulation of the overall growth behavior in microcarrier culture, including the lag phase. In addition, it describes the time course of uptake and release of key metabolites and the identification of parameters relevant for the design and optimization of vaccine manufacturing processes.     

Positive Effect of Noises on Sensory Systems

1　IntroductionStochasticresonanceisthe phenomenonthatanonzeronoiseleveloptimizesthesystemperformanceinnon linearfield .Especially ,ithelpstodetectandtransferthesmallsignalinalargenoisybackground .Inthenondynamicalsystemorthethresholddetectionsys tem ,thethresholdcrossingisatypicalnon linearphe nomenonandcanresultinastochasticresonance[1] .Asingleneuronwiththresholdbehaviorcanberegardedasasimplethresholddetector ;hencethestochasticres onancephenomenaofneuronhavenaturallybeenstud ied[2 ,3] .Re…     

Prediction of the intramembranous tissue formation during perisprosthetic healing with uncertainties. Part 1. Effect of the variability of each biochemical factor

A stochastic model is proposed to predict the intramembranous process in periprosthetic healing in the early post-operative period. The methodology was validated by a canine experimental model. In this first part, the effects of each individual uncertain biochemical factor on the bone-implant healing are examined, including the coefficient of osteoid synthesis, the coefficients of haptotactic and chemotactic migration of osteoblastic population and the radius of the drill hole. A multi-phase reactive model solved by an explicit finite difference scheme is combined with the polynomial chaos expansion to solve the stochastic system. In the second part, combined biochemical factors are considered to study a real configuration of clinical acts.     

Persistence in stochastic food web models

A sufficient condition is given for stochastic boundedness persistence of a top predator in generalized Lotka-Volterra-type stochastic food web models in arbitrary bounded regions of state space. The main result indicates that persistence in the corresponding deterministic system is preserved in the stochastic system if the intensities of the random fluctuations are not too large. This work was supported, in part, by the U. S. Environmental Protection Agency under Grant No. CR 807830.     

The augmentation algorithm and molecular phylogenetic trees

Summary The augmentation procedure of G.W. Moore leads to correct estimates of the total number of nucleotide substitutions separating two genes descendent from a common ancestor provided the data base is sufficiently dense. These estimates are in agreement with the true distance values from simulations of known evolutionary pathways. The estimates, on the average, are unbiased: they neither overaugment nor underaugment seriously. The variance of the population of augmented distance values reflects accurately the variance of the population of true distance values and is thus not abnormally large due to procedural defects in the algorithm.The augmented distances are in agreement with stochastic models tested on real data when the latter take proper account of the restricted mutability of codons resulting from natural selection.When the experimental data base is not dense, the augmented distance values and population variance may underestimate both the true distance values and their variance. This has a logical consequence that there exist significant and numerous errors in the ancestral sequences reconstructed by the parsimony principle from such data bases.The restrictions, resulting from natural selection, on the mutability of different nucleotide sites is shown to bear critically on the accuracy of estimates of the total number of nucleotide replacements made by stochastic models.     

One- and multi-locus multi-allele selection models in a random environment

Summary We deduce conditions for stochastic local stability of general perturbed linear stochastic difference equations widely applicable in population genetics. The findings are adapted to evaluate the stability properties of equilibria in classical one- and multi-locus multi-allele selection models influenced by random temporal variation in selection intensities. As an example of some conclusions and biological interpretations we analyse a special one-locus multi-allele model in more detail.This work was supported in part by Stiftung Volkswagenwerk.     

Statistical alignment based on fragment insertion and deletion models

Motivation: The topic of this paper is the estimation of alignments and mutation rates based on stochastic sequence-evolution models that allow insertions and deletions of subsequences ('fragments') and not just single bases. The model we propose is a variant of a model introduced by Thorne et al., (J. Mol. Evol., 34, 3-16, 1992). The computational tractability of the model depends on certain restrictions in the insertion/deletion process; possible effects we discuss. Results: The process of fragment insertion and deletion in the sequence-evolution model induces a hidden Markov structure at the level of alignments and thus makes possible efficient statistical alignment algorithms. As an example we apply a sampling procedure to assess the variability in alignment and mutation parameter estimates for HVR1 sequences of human and orangutan, improving results of previous work. Simulation studies give evidence that estimation methods based on the proposed model also give satisfactory results when applied to data for which the restrictions in the insertion/deletion process do not hold. Availability: The source code of the software for sampling alignments and mutation rates for a pair of DNA sequences according to the fragment insertion and deletion model is freely available from http://www.math.uni-frankfurt.de/~stoch/software/mcmcsalut under the terms of the GNU public license (GPL, 2000).     

A new explanation of the glitch phenomenon

Summary We consider a discrete model for asynchronous circuits and show that, under very mild restrictions, this model excludes the existence of glitch-free arbiters. This result contradicts a long standing conjecture that the nonexistence of glitch-free arbiters is due to the continuous nature of such circuits.Work supported in part by Office of Naval Research Contract N00014-89-J-1913     

Signal detection theory,detectability and stochastic resonance effects

 Stochastic resonance is a phenomenon in which the performance of certain non-linear detectors can be enhanced by the addition of appropriate levels of random noise. Signal detection theory offers a powerful tool for analysing this type of system, through an ability to separate detection processes into reception and classification, with the former generally being linear and the latter always non-linear. Through appropriate measures of signal detectability it is possible to decide whether a local improvement in detection via stochastic resonance occurs due to the non-linear effects of the classification process. In this case, improvement of detection through the addition of noise can never improve detection beyond that of a corresponding adaptive system. Signal detection and stochastic resonance is investigated in several integrate-and-fire neuron models. It is demonstrated that the stochastic resonance observed in spiking models is caused by non-linear properties of the spike-generation process itself. The true detectability of the signal, as seen by the receiver part of the spiking neuron (the integrator part), decreases monotonically with input noise level for all signal and noise intensities. Received: 3 April 2001 / Accepted in revised form: 8 March 2002     

Developmental Plasticity of Postweanling Cotton Rats (Sigmodon hispidus) as an Adaptation to Nutritionally Stochastic Environments

Elucidating interrelationships between rate of growth and sexual maturation in unpredictable or stochastic environments could increase our understanding of life-history strategies of small mammals. It has been hypothesized that species living in environments where food availability is unpredictable might become sexually mature at smaller sizes and channel excess energy into reproduction rather than into compensatory growth. We explored this hypothesis in female cotton rats (Sigmodon hispidus) by feeding variable levels of dietary protein during early postweanling development (14–45days of age) and monitoring compensatory growth and fitness after nutritional rehabilitation (45–100days of age). Growth was optimum in females fed diets containing 16% protein, with minimal requirements estimated to be 12%. Females fed diets containing <12% protein exhibited suppressed development, including delayed puberty. However, these nulliparous females demonstrated compensatory growth during the early period of nutritional rehabilitation, regardless of the severity of previous restrictions in protein. No long-lasting fitness consequences from postweanling nutritional restrictions were apparent as we observed no difference in date of conception, body mass of dams at parturition, litter size, or rate of growth of neonates. We offer a possible adaptive explanation for this observed plasticity in growth and development. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Minimal Model of Signaling Network Elucidates Cell-to-Cell Stochastic Variability in Apoptosis

Background

Signaling networks are designed to sense an environmental stimulus and adapt to it. We propose and study a minimal model of signaling network that can sense and respond to external stimuli of varying strength in an adaptive manner. The structure of this minimal network is derived based on some simple assumptions on its differential response to external stimuli.

Methodology

We employ stochastic differential equations and probability distributions obtained from stochastic simulations to characterize differential signaling response in our minimal network model. Gillespie''s stochastic simulation algorithm (SSA) is used in this study.

Conclusions/Significance

We show that the proposed minimal signaling network displays two distinct types of response as the strength of the stimulus is decreased. The signaling network has a deterministic part that undergoes rapid activation by a strong stimulus in which case cell-to-cell fluctuations can be ignored. As the strength of the stimulus decreases, the stochastic part of the network begins dominating the signaling response where slow activation is observed with characteristic large cell-to-cell stochastic variability. Interestingly, this proposed stochastic signaling network can capture some of the essential signaling behaviors of a complex apoptotic cell death signaling network that has been studied through experiments and large-scale computer simulations. Thus we claim that the proposed signaling network is an appropriate minimal model of apoptosis signaling. Elucidating the fundamental design principles of complex cellular signaling pathways such as apoptosis signaling remains a challenging task. We demonstrate how our proposed minimal model can help elucidate the effect of a specific apoptotic inhibitor Bcl-2 on apoptotic signaling in a cell-type independent manner. We also discuss the implications of our study in elucidating the adaptive strategy of cell death signaling pathways.