数学生态学随机模型

本文引入了数学生态学随机模型,建立了这类模型的向后和向前方程,最后给出了一个例子。     

Some Mathematical Models for Line Transect Sampling

ANDERSON and POSPAHALA (1970) investigated the estimation of wildlife population size using the belt or line transect sampling method and devised a correction for bias, thus leading to an estimator with interesting characteristics. This work was given a uniform mathematical framework in BURNHAM and ANDERSON (1976). In this paper we extend that mathematical framework to several different sampling models, and a number of interesting discrete probability distributions emerge.     

Mathematical Models for Hantavirus Infection in Rodents

Hantavirus pulmonary syndrome is an emerging disease of humans that is carried by wild rodents. Humans are usually exposed to the virus through geographically isolated outbreaks. The driving forces behind these outbreaks is poorly understood. Certainly, one key driver of the emergence of these viruses is the virus population dynamics within the rodent population. Two new mathematical models for hantavirus infection in rodents are formulated and studied. The new models include the dynamics of susceptible, exposed, infective, and recovered male and female rodents. The first model is a system of ordinary differential equations while the second model is a system of stochastic differential equations. These new models capture some of the realistic dynamics of the male/female rodent hantavirus interaction: higher seroprevalence in males and variability in seroprevalence levels.     

Evaluation of PVA Models of Arboreal Marsupials: Coupling Models with Long-term Monitoring Data

This paper reports the outcomes of a novel inter-twining of long-term monitoring data and population modelling to assess the accuracy of predictions of a Population Viability Analysis (PVA) model. In particular, the relative effectiveness of different management options for reserving areas from timber harvesting was assessed for two forest-dependent arboreal marsupials, the greater glider (Petauroides volans) and Leadbeater's Possum (Gymnobelideus leadbeateri). We used data from 7 years of monitoring conducted at 161 sites to assess and modify, where appropriate, previous population models of the two species of arboreal marsupials. The results indicated that the importance of food resources for both had been underestimated in past work. Despite this, the modified models that included increased importance of food availability did not change the predicted risks of decline substantially, particularly for Leadbeater's Possum. Importantly, past conclusions about the optimal sizes of patches to reserve within the forests used wood production were robust to changes in the model. This is a valuable finding because the work we report is one of the first to empirically test the robustness of the relative predictions of a PVA model. Nevertheless, the new insights we derived from this study have implications both for: (1) the implementation of our ongoing long-term monitoring study, in particular the value of what can be termed ȁ8adaptive monitoring', and, (2) the establishment of a new silvicultural experiment designed to better create habitat for arboreal marsupials within logged and regenerated sites.     

Log-linear Models for Polytomous Data

The present study discusses two variants of linear logistic models for polytomous variables for ?unordered”? and for ?ordered”? categories (polydimensional and one-dimensional model). The ML-estimation equations and the possibilities to test the validity of the model are given for both. A test for goodness-of-fit (external validity) and a test for equality of the parameter estimates for split data (interval validity) are suggested. In addition, statistical tests for the significance of individual parameters on the basis of the information matrix and likelihood ratio tests for one or more parameters are described. The presentation is completed by an empirical example from the area of audiology.     

Models for Ordinal Agreement Data

Statistical models can be used to describe the probabilistic structure underlying cross‐classified agreement data. This article explains how models for ordinal agreement data can be understood in terms of an association component and an agreement component. The association component accounts for the positive association typically present in ordinal ratings of two observers. The agreement component specifies a model for the diagonal cells of the cross‐classified ratings. Several models for ordinal agreement data proposed in the literature are special cases of this approach. A new log‐linear model for agreement data that can also be understood in terms of the two components is presented and illustrated using data from a case‐control study of coronary heart disease.     

Mathematical Models of Cell Motility

Cell motility is an essential biological action in the creation, operation and maintenance of our bodies. Developing mathematical models elucidating cell motility will greatly advance our understanding of this fundamental biological process. With accurate models it is possible to explore many permutations of the same event and concisely investigate their outcome. While great advancements have been made in experimental studies of cell motility, it now has somewhat fallen on mathematical models to taking a leading role in future developments. The obvious reason for this is the complexity of cell motility. Employing the processing power of today’s computers will give researches the ability to run complex biophysical and biochemical scenarios, without the inherent difficulty and time associated with in vitro investigations. Before any great advancement can be made, the basics of cell motility will have to be well-defined. Without this, complicated mathematical models will be hindered by their inherent conjecture. This review will look at current mathematical investigations of cell motility, explore the reasoning behind such work and conclude with how best to advance this interesting and challenging research area.     

松林复合经营模式的试验与评价

复合经营系统就是在某一特定的自然环境区域中,根据不同的生物学特性,组成空间的多层次结构、时间的有序配置,以充分利用光热资源、空间资源和土地资源。以物质和能量的多级利用,有效地提高生态、经济和社会效益［１～３］。通过对复合经营系统的实践和研究,积累和总...     

种群数学模型的基本性质

种群数学模型的建立有赖于对生物背景的各种似是而非的假设,然而,在建模过程中,这些假定常常容易得到不当的结合和表达,常常些关于生物背景的清晰而明确的假设被不适当地处理或者甚至被抛开,事实上,即使是某些赫赫有名的种群数学模型也难以完全避免这种缺陷,这一点在我们本文中提及并讨论,要使得所建立的模型在逻辑上可信正确。我们必须确保关于其背景的各种假设得到的始终如一和恰如其分的协调组合。本本文中,我们测试了由Arditi和Michalski在1996年提出的几条建模标准,对于斑块模型,我们在他们的基础上增加了一条模型。我们同时在单种群的其他特殊情形方面的建方面增列了一些重要的标准。按照Arditi和Mchalski的标准以及其他著名的生物建模假定,我们建立了一些有意义的三维捕食－食饵种群模型（比率依赖型）,我们还讨论了种群各种振动现象的建模。     

Mathematical Programming Models for Determining the Optimal Location of Beehives

Farmers frequently decide where to locate the colonies of their domesticated eusocial bees, especially given the following mutually exclusive scenarios: (i) there are limited nectar and pollen sources within the vicinity of the apiary that cause competition among foragers; and (ii) there are fewer pollinators compared to the number of inflorescence that may lead to suboptimal pollination of crops. We hypothesize that optimally distributing the beehives in the apiary can help address the two scenarios stated above. In this paper, we develop quantitative models (specifically using linear programming) for addressing the two given scenarios. We formulate models involving the following factors: (i) fuzzy preference of the beekeeper; (ii) number of available colonies; (iii) unknown-but-bounded strength of colonies; (iv) probabilistic carrying capacity of the plant clusters; and (v) spatial orientation of the apiary.     

Mathematical Models Light Up Plant Signaling

Plants respond to changes in the environment by triggering a suite of regulatory networks that control and synchronize molecular signaling in different tissues, organs, and the whole plant. Molecular studies through genetic and environmental perturbations, particularly in the model plant Arabidopsis thaliana, have revealed many of the mechanisms by which these responses are actuated. In recent years, mathematical modeling has become a complementary tool to the experimental approach that has furthered our understanding of biological mechanisms. In this review, we present modeling examples encompassing a range of different biological processes, in particular those regulated by light. Current issues and future directions in the modeling of plant systems are discussed.     

Bayesian Neural Network Models for Censored Data

Neural networks are considered by many to be very promising tools for classification and prediction. The flexibility of the neural network models often result in over-fit. Shrinking the parameters using a penalized likelihood is often used in order to overcome such over-fit. In this paper we extend the approach proposed by FARAGGI and SIMON (1995a) to modeling censored survival data using the input-output relationship associated with a single hidden layer feed-forward neural network. Instead of estimating the neural network parameters using the method of maximum likelihood, we place normal prior distributions on the parameters and make inferences based on derived posterior distributions of the parameters. This Bayesian formulation will result in shrinking the parameters of the neural network model and will reduce the over-fit compared with the maximum likelihood estimators. We illustrate our proposed method on a simulated and a real example.