Asymptotic and explicit formulae for a non-markovian model with linear transition rule

Asymptotic and explicit formulae are obtained for the n-step stochastic kernel of a special class of non-MARKOVIAN models with linear transition rule which occur in learning theory, adaption theory, control theory, and biological research.     

Potential Distribution and Risk Assessment of an Invasive Plant Species: A Case Study of Hymenachne amplexicaulis in Australia

Given the limited resources available for weed management, a strategic approach is required to give the “best bang for your buck.” The current study incorporates: (1) a model ensemble approach to identify areas of uncertainty and commonality regarding a species invasive potential, (2) current distribution of the invaded species, and (3) connectivity of systems to identify target regions and focus efforts for more effective management. Uncertainty in the prediction of suitable habitat for H. amplexicaulis (study species) in Australia was addressed in an ensemble-forecasting approach to compare distributional scenarios from four models (CLIMATCH; CLIMEX; boosted regression trees [BRT]; maximum entropy [Maxent]). Models were built using subsets of occurrence and environmental data. Catchment risk was determined through incorporating habitat suitability, the current abundance and distribution of H. amplexicaulis, and catchment connectivity. Our results indicate geographic differences between predictions of different approaches. Despite these differences a number of catchments in northern, central, and southern Australia were identified as high risk of invasion or further spread by all models suggesting they should be given priority for the management of H. amplexicaulis. The study also highlighted the utility of ensemble approaches in indentifying areas of uncertainty and commonality regarding the species’ invasive potential.     

Stochastic models of tumor growth and the probability of elimination by cytotoxic cells

The probability of tumor extinction due to the action of cytotoxic cell populations is investigated by several one dimensional stochastic models of the population growth and elimination processes of a tumor. The several models are made necessary by the nonlinearity of the processes and the different parameter ranges explored. The deterministic form of the model is where γ₀, k′₆ and k ₁ are positive constants. The parameter of most import is which determines the stability of the T = 0 equilibrium. With an initial tumor size of one, a (linear) branching process is used to estimate the extinction probability. However, in the case λ = 0 when the linearization of the deterministic model gives no information (T = 0 is actually unstable) the branching model is unsatisfactory. This makes necessary the utilization of a density-dependent branching process to approximate the population. Through scaling a diffusion limit is reached which enables one to again compute the probability of extinction. For populations away from one a sequence of density-dependent jump Markov processes are approximated by a sequence of diffusion processes. In limiting cases, the estimates of extinction correspond to that computed from the original branching process. Table 1 summarizes the results.     

Assessment of the risk of a bluetongue outbreak in Europe caused by Culicoides midges introduced through intracontinental transport and trade networks

The importation of infected hosts and the arrival of windborne infected Culicoides (Diptera: Ceratopogonidae) were considered unlikely mechanisms for bluetongue virus (BTV) incursion into a BTV‐free area during the recent BTV serotype 8 (BTV‐8) epidemic in northern Europe. Therefore, alternative mechanisms need to be considered. Air, sea and land transport networks continue to expand, and an important consequence of this is vector‐borne pathogen importation. One important aspect of bluetongue (BT) epidemiology not yet addressed is the potential movement of infected Culicoides via transport and trade networks. Therefore, a risk assessment model was constructed to assess the probability of a BTV outbreak as a consequence of the introduction of Culicoides via these networks. The model was applied to calculate the risk for a BTV‐8 epidemic in Spain in 2007 caused by the introduction of Culicoides from affected northern European countries. The mean weighted annual risk for an outbreak caused by transportation of a single vector from an affected northern European country varied from 1.8 × 10^?7 to 3.0 × 10^?13, with the highest risks associated with Culicoides imported from Belgium, the Netherlands, Germany and France. For this mechanism to pose a significant risk to BTV‐free countries, a large number of vectors would have to be transported.     

Resistance to change and vulnerability to stress: autistic‐like features of GAP43‐deficient mice

There is an urgent need for animal models of autism spectrum disorder (ASD) to understand the underlying pathology and facilitate development and testing of new treatments. The synaptic growth‐associated protein‐43 (GAP43) has recently been identified as an autism candidate gene of interest. Our previous studies show many brain abnormalities in mice lacking one allele for GAP43 [GAP43 (+/?)] that are consistent with the disordered connectivity theory of ASD. Thus, we hypothesized that GAP43 (+/?) mice would show at least some autistic‐like behaviors. We found that GAP43 (+/?) mice, relative to wild‐type (+/+) littermates, displayed resistance to change, consistent with one of the diagnostic criteria for ASD. GAP43 (+/?) mice also displayed stress‐induced behavioral withdrawal and anxiety, as seen in many autistic individuals. In addition, both GAP43 (+/?) mice and (+/+) littermates showed low social approach and lack of preference for social novelty, consistent with another diagnostic criterion for ASD. This low sociability is likely because of the mixed C57BL/6J 129S3/SvImJ background. We conclude that GAP43 deficiency leads to the development of a subset of autistic‐like behaviors. As these behaviors occur in a mouse that displays disordered connectivity, we propose that future anatomical and functional studies in this mouse may help uncover underlying mechanisms for these specific behaviors. Strain‐specific low sociability may be advantageous in these studies, creating a more autistic‐like environment for study of the GAP43‐mediated deficits of resistance to change and vulnerability to stress.     

On the stock estimation for some fishery systems

In this work we address the stock estimation problem for two fishery models. We show that a tool from nonlinear control theory called “observer” can be helpful to deal with the resource stock estimation in the field of renewable resource management. It is often difficult or expensive to measure all the state variables characterising the evolution of a given population system, therefore the question arises whether from the observation of certain indicators of the considered system, the whole state of the population system can be recovered or at least estimated. The goal of this paper is to show how some techniques of control theory can be applied for the approximate estimation of the unmeasurable state variables using only the observed data together with the dynamical model describing the evolution of the system. More precisely we shall consider two fishery models and we shall show how to built for each model an auxiliary dynamical system (the observer) that uses the available data (the total of caught fish) and which produces a dynamical estimation of the unmeasurable stock state x(t). Moreover the convergence speed of towards x(t) can be chosen.     

Holling's “hungry mantid” model for the invertebrate functional response considered as a Markov process. Part I: The full model and some of its limits

In this paper we give an analytical reformulation of Holling's (1966) simulation model for invertebrate predatory behaviour. To this end we represent a population of predators as a frequency distribution over a space of (physiological) states. The functional response of a predator is calculated from the (stable) equilibrium distribution of its state as a function of prey density.Starting from the general model various other models are obtained by limit processes, some of them new and some of them old. The more interesting of which will be studied in further papers in this series.List of Notation a rate constant of digestion - b maximum of rate constant of prey encounter in the mantid - b maximum pursuit duration in the mantid (_p(0)) - c satiation threshold for search - c satiation threshold for pursuit in the mantid: c=c(b-D_s/v)/b - D _m maximum sighting distance - D _p pursuit distance - D _s strike distance - expectation operator - f, f ₀ rate of change of satiation during search - f ₁ rate of change of satiation during prey handling - F functional response: number of prey eaten per unit of time by one predator - g rate constant of effective prey encounter in the gobbler and sucker - g₀ rate constant of prey encounter - g₁ probability of no prey loss from pursuit - g₂ probability of no prey escaping during pursuit - H Holling secretary correction factor in the sucker: fraction of the time spent searching - k _R density of R - k_T probability density of maximum prey handling time - K probability that maximum prey handling time is _e, i.e. pursuit duration is zero - K _R distribution function of R - N number of prey caught - p (marginal) density of S - p₀ density of S in search - p₁ simultaneous density of S and T - P probability - p ₁ marginal density of S in handling prey - q probability of strike success - R ratio of realized to maximum sighting distance - s, S satiation - satiation axis - t time - handling time axis - u eating speed - U homogeneous(0,1) random variable - v pursuit speed - V exponential(1) random variable - w prey weight - W exponential(_m) random variable - x prey density - ratio of maximum successful pursuit duration to meal duration (_pm/_e) - _pm - relative duration of successful pursuit (_p/_pm) - ratio of shortest to largest sighting distance - x_e - time already spent handling a prey item - rate of prey loss during prey handling - prey escape rate during pursuit - prey biomass density (xw) - , T maximum time still to be spent handling a prey item - _e meal duration - _m maximum handling time ( _e+ _p) - _p duration of successful pursuit - _pm maximum duration of successful pursuit (_p(0)) - hazard rate - _m maximum of hazard rate - scaled functional response (wF) - minimal i-state space     

An assessment of Gallistel's (2012) rationalistic account of extinction phenomena

Gallistel (2012) asserts that animals use rationalistic reasoning (i.e., information theory and Bayesian inference) to make decisions that underlie select extinction phenomena. Rational processes are presumed to lead to evolutionarily optimal behavior. Thus, Gallistel's model is a type of optimality theory. But optimality theory is only a theory, a theory about an ideal organism, and its predictions frequently deviate appreciably from observed behavior of animals in the laboratory and the real world. That is, behavior of animals is often far from optimal, as is evident in many behavioral phenomena. Hence, appeals to optimality theory to explain, rather than illuminate, actual behavior are misguided.     

A generalized transition model for grouped longitudinal categorical data

Transition models are an important framework that can be used to model longitudinal categorical data. They are particularly useful when the primary interest is in prediction. The available methods for this class of models are suitable for the cases in which responses are recorded individually over time. However, in many areas, it is common for categorical data to be recorded as groups, that is, different categories with a number of individuals in each. As motivation we consider a study in insect movement and another in pig behaviou. The first study was developed to understand the movement patterns of female adults of Diaphorina citri, a pest of citrus plantations. The second study investigated how hogs behaved under the influence of environmental enrichment. In both studies, the number of individuals in different response categories was observed over time. We propose a new framework for considering the time dependence in the linear predictor of a generalized logit transition model using a quantitative response, corresponding to the number of individuals in each category. We use maximum likelihood estimation and present the results of the fitted models under stationarity and non-stationarity assumptions, and use recently proposed tests to assess non-stationarity. We evaluated the performance of the proposed model using simulation studies under different scenarios, and concluded that our modeling framework represents a flexible alternative to analyze grouped longitudinal categorical data.     

Multivariate meta‐analysis with an increasing number of parameters

Meta‐analysis can average estimates of multiple parameters, such as a treatment's effect on multiple outcomes, across studies. Univariate meta‐analysis (UVMA) considers each parameter individually, while multivariate meta‐analysis (MVMA) considers the parameters jointly and accounts for the correlation between their estimates. The performance of MVMA and UVMA has been extensively compared in scenarios with two parameters. Our objective is to compare the performance of MVMA and UVMA as the number of parameters, p, increases. Specifically, we show that (i) for fixed‐effect (FE) meta‐analysis, the benefit from using MVMA can substantially increase as p increases; (ii) for random effects (RE) meta‐analysis, the benefit from MVMA can increase as p increases, but the potential improvement is modest in the presence of high between‐study variability and the actual improvement is further reduced by the need to estimate an increasingly large between study covariance matrix; and (iii) when there is little to no between‐study variability, the loss of efficiency due to choosing RE MVMA over FE MVMA increases as p increases. We demonstrate these three features through theory, simulation, and a meta‐analysis of risk factors for non‐Hodgkin lymphoma.     

长白山暗针叶林群落物种多样性维持机制

植物群落物种多样性维持机制一直是生态学研究的热点话题,其中生态位理论和中性理论是被普遍接受的两种理论观点,但是目前关于生态位理论和中性理论在群落物种多样性维持中的相对重要性还没有统一定论。基于长白山暗针叶林群落数据,采用单物种-面积关系模型探究特定树种对邻域物种丰富度的影响,并借助同质性和异质性泊松零模型检验其显著性。(1)群落水平上,在3—15 m空间尺度上,促进种占据优势地位,在>15 m空间尺度上,中性种逐渐取代促进种起主导作用,抑制种比例较低,并且随着空间尺度变化幅度不大。(2)物种水平上,采用同质性泊松零模型检验树种对邻域物种丰富度的影响,臭冷杉、花楷槭、青楷槭在0—20 m空间尺度上对邻域物种丰富度增加起促进作用,黄花落叶松、鱼鳞云杉在0—20 m空间尺度上抑制了邻域物种丰富度增加。花楸树、黑桦和硕桦在全部研究尺度上表现为中性种,髭脉槭、大青杨、红松等在不同研究尺度上表现为不同的作用效果。剔除了生境过滤作用的异质性泊松零模型检验结果与同质性泊松零模型结果差异不显著,表明研究样地内生境过滤作用对多样性格局形成影响不大,各树种间的相互作用对群落物种组成影响较大,进一步证明...     

Understanding and Application of Learning Theory in UK-based Equestrians

Learning in equines occurs through a predictable chain of stimulus–response–consequence processing. Whether the behavior persists will depend on the nature and timing of the consequence, whether it punishes or reinforces the response behavior. Knowledge and application of learning theory in UK-based equestrians was assessed by an online survey which probed three aspects of knowledge and understanding. Fifty-eight UK individuals (91% female) took part in the study and had an average of 12.4 years’ equestrian experience. Almost one-third (31%) described themselves as professional equestrians. A questionnaire was used to assess participants’ ability to identify and describe terminology associated with learning theory; self-report on their own knowledge and training methodology; and to express how they would respond in different training situations. Human-focused educational strategies were tested to assess their effectiveness and suitability for increasing understanding of learning theory. Professional equestrians expressed higher levels of subjective knowledge than amateurs (t₍₂₇₎ = –2.752, p = 0.018), with a moderate positive correlation between subjective knowledge and observer-scored knowledge (r = 0.443, p < 0.001). Professionals scored higher than amateurs on all questions asked, however a deficit of knowledge was observed across the board; in particular, in defining positive punishment (professional 38.8%, amateur 12.5% successful) and negative reinforcement (professional 33%, amateur 12.5% successful). Application of both an educational video and a leaflet increased respondents’ ability to correctly define terminology (Video t₍₈₎ = –4.07, p = 0.004: Leaflet t₍₁₂₎ = –5.02, p < 0.001). Improving understanding and application of learning theory in amateurs and professionals alike has the potential to improve equine welfare and training outcomes for both leisure and performance horses through reducing wastage attributed to behavioral problems or poor training.     

On the Asymptotic Behaviour of the Population Number

We consider the stochastic model of an asexual population in which the number of couples formed in some generation is random variable depending on the number of individuals in that generation only. The conditions of convergence were obtained almost everywhere and in mean square of the normalized number of individuals in the n-th generation. These results may be considered as the generalization of some known statements about the models constructed on the basis of the branching processses theory.     

A population‐based temporal logic gate for timing and recording chemical events

Engineered bacterial sensors have potential applications in human health monitoring, environmental chemical detection, and materials biosynthesis. While such bacterial devices have long been engineered to differentiate between combinations of inputs, their potential to process signal timing and duration has been overlooked. In this work, we present a two‐input temporal logic gate that can sense and record the order of the inputs, the timing between inputs, and the duration of input pulses. Our temporal logic gate design relies on unidirectional DNA recombination mediated by bacteriophage integrases to detect and encode sequences of input events. For an E. coli strain engineered to contain our temporal logic gate, we compare predictions of Markov model simulations with laboratory measurements of final population distributions for both step and pulse inputs. Although single cells were engineered to have digital outputs, stochastic noise created heterogeneous single‐cell responses that translated into analog population responses. Furthermore, when single‐cell genetic states were aggregated into population‐level distributions, these distributions contained unique information not encoded in individual cells. Thus, final differentiated sub‐populations could be used to deduce order, timing, and duration of transient chemical events.     

Optimal stomatal conductance in relation to photosynthesis in climatically contrasting Eucalyptus species under drought

Models of stomatal conductance (g_s) are based on coupling between g_s and CO₂ assimilation (A_net), and it is often assumed that the slope of this relationship (‘g₁’) is constant across species. However, if different plant species have adapted to different access costs of water, then there will be differences in g₁ among species. We hypothesized that g₁ should vary among species adapted to different climates, and tested the theory and its linkage to plant hydraulics using four Eucalyptus species from different climatic origins in a common garden. Optimal stomatal theory predicts that species from sub‐humid zones have a lower marginal water cost of C gain, hence lower g₁ than humid‐zone species. In agreement with the theory that g₁ is related to tissue carbon costs for water supply, we found a relationship between wood density and g₁ across Eucalyptus species of contrasting climatic origins. There were significant reductions in the parameter g₁ during drought in humid but not sub‐humid species, with the latter group maintaining g₁ in drought. There are strong differences in stomatal behaviour among related tree species in agreement with optimal stomatal theory, and these differences are consistent with the economics involved in water uptake and transport for carbon gain.     

Modeling the role of the close‐range effect and environmental variables in the occurrence and spread of Phragmites australis in four sites on the Finnish coast of the Gulf of Finland and the Archipelago Sea

Phragmites australis, a native helophyte in coastal areas of the Baltic Sea, has significantly spread on the Finnish coast in the last decades raising ecological questions and social interest and concern due to the important role it plays in the ecosystem dynamics of shallow coastal areas. Despite its important implications on the planning and management of the area, predictive modeling of Phragmites distribution is not well studied. We examined the prevalence and progression of Phragmites in four sites along the Southern Finnish coast in multiple time frames in relation to a number of predictors. We also analyzed patterns of neighborhood effect on the expansion and disappearance of Phragmites in a cellular data model. We developed boosted regression trees models to predict Phragmites occurrences and produce maps of habitat suitability. Various Phragmites spread figures were observed in different areas and time periods, with a minimum annual expansion rate of 1% and a maximum of 8%. The water depth, shore openness, and proximity to river mouths were found influential in Phragmites distribution. The neighborhood configuration partially explained the dynamics of Phragmites colonies. The boosted regression trees method was successfully used to interpolate and extrapolate Phragmites distributions in the study sites highlighting its potential for assessing habitat suitability for Phragmites along the Finnish coast. Our findings are useful for a number of applications. With variables easily available, delineation of areas susceptible for Phragmites colonization allows early management plans to be made. Given the influence of reed beds on the littoral species and ecosystem, these results can be useful for the ecological studies of coastal areas. We provide estimates of habitat suitability and quantification of Phragmites expansion in a form suitable for dynamic modeling, which would be useful for predicting future Phragmites distribution under different scenarios of land cover change and Phragmites spatial configuration.     

A statistical approach to quasi-extinction forecasting

Forecasting population decline to a certain critical threshold (the quasi-extinction risk) is one of the central objectives of population viability analysis (PVA), and such predictions figure prominently in the decisions of major conservation organizations. In this paper, we argue that accurate forecasting of a population's quasi-extinction risk does not necessarily require knowledge of the underlying biological mechanisms. Because of the stochastic and multiplicative nature of population growth, the ensemble behaviour of population trajectories converges to common statistical forms across a wide variety of stochastic population processes. This paper provides a theoretical basis for this argument. We show that the quasi-extinction surfaces of a variety of complex stochastic population processes (including age-structured, density-dependent and spatially structured populations) can be modelled by a simple stochastic approximation: the stochastic exponential growth process overlaid with Gaussian errors. Using simulated and real data, we show that this model can be estimated with 20-30 years of data and can provide relatively unbiased quasi-extinction risk with confidence intervals considerably smaller than (0,1). This was found to be true even for simulated data derived from some of the noisiest population processes (density-dependent feedback, species interactions and strong age-structure cycling). A key advantage of statistical models is that their parameters and the uncertainty of those parameters can be estimated from time series data using standard statistical methods. In contrast for most species of conservation concern, biologically realistic models must often be specified rather than estimated because of the limited data available for all the various parameters. Biologically realistic models will always have a prominent place in PVA for evaluating specific management options which affect a single segment of a population, a single demographic rate, or different geographic areas. However, for forecasting quasi-extinction risk, statistical models that are based on the convergent statistical properties of population processes offer many advantages over biologically realistic models.     

Mathematical properties of neuronal TD-rules and differential Hebbian learning: a comparison

A confusingly wide variety of temporally asymmetric learning rules exists related to reinforcement learning and/or to spike-timing dependent plasticity, many of which look exceedingly similar, while displaying strongly different behavior. These rules often find their use in control tasks, for example in robotics and for this rigorous convergence and numerical stability is required. The goal of this article is to review these rules and compare them to provide a better overview over their different properties. Two main classes will be discussed: temporal difference (TD) rules and correlation based (differential hebbian) rules and some transition cases. In general we will focus on neuronal implementations with changeable synaptic weights and a time-continuous representation of activity. In a machine learning (non-neuronal) context, for TD-learning a solid mathematical theory has existed since several years. This can partly be transfered to a neuronal framework, too. On the other hand, only now a more complete theory has also emerged for differential Hebb rules. In general rules differ by their convergence conditions and their numerical stability, which can lead to very undesirable behavior, when wanting to apply them. For TD, convergence can be enforced with a certain output condition assuring that the δ-error drops on average to zero (output control). Correlation based rules, on the other hand, converge when one input drops to zero (input control). Temporally asymmetric learning rules treat situations where incoming stimuli follow each other in time. Thus, it is necessary to remember the first stimulus to be able to relate it to the later occurring second one. To this end different types of so-called eligibility traces are being used by these two different types of rules. This aspect leads again to different properties of TD and differential Hebbian learning as discussed here. Thus, this paper, while also presenting several novel mathematical results, is mainly meant to provide a road map through the different neuronally emulated temporal asymmetrical learning rules and their behavior to provide some guidance for possible applications.     

A SPATIALLY EXPLICIT STOCHASTIC MODEL DEMONSTRATES THE FEASIBILITY OF WRIGHT'S SHIFTING BALANCE THEORY

Recently there has been a resurgence of theoretical papers exploring Wright's Shifting Balance Theory (SBT) of evolution. The SBT explains how traits which must pass through an adaptive valley may evolve in substructured populations. It has been suggested that Phase III of the SBT (the spread of new advantageous traits through the populations) proceeds only under a very restricted set of conditions. We show that Phase III can proceed under a much broader set of conditions in models that properly incorporate a key feature of Wright's theory: local, random migration of discrete individuals.