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。     

Baseline criteria and the evolution of hosts and parasites: D0, R0 and competition for resources between strains

Our understanding of the evolution of diseases has been greatly aided by the use of baseline criteria. Here we examine the theoretical and biological relationships of the well known baseline criteria for the evolution of disease (R0) and the recently introduced corresponding criterion for the evolution of resistance in hosts (D0). We show that there is a formal theoretical equivalence between the two criteria and discuss the characteristics of seperability that determine whether the criteria define the course of evolution. These theoretical determinants correspond biologically to whether strains compete for resources or not. We discuss the biological application of the criteria and argue that D0 may be less widely applicable than R0, but does determine the evolution of resistance in populations with fixed carrying capacities.     

一个设立海洋保护区的捕鱼模型的生物经济分析

考虑一个设立海洋保护区的捕鱼模型．从生物学和经济学两个角度研究海洋保护区的作用．给出所研究系统的生物和经济平衡点以及平衡点的局部稳定性,不稳定性,全局稳定性的条件．研究结果说明设立海洋保护区对于保护海洋资源是一种有效途径,保护区内的鱼群即使在对非保护区进行连续捕捞的情形下也能够保持在一个适当的水平．进一步研究了最优收获策略,并对所得结果的生物经济解释予以说明．     

Large-amplitude,short-wave peristalsis and its implications for transport

Valveless, tubular pumps are widespread in the animal kingdom, but the mechanism by which these pumps generate fluid flow is often in dispute. Where the pumping mechanism of many organs was once described as peristalsis, other mechanisms, such as dynamic suction pumping, have been suggested as possible alternative mechanisms. Peristalsis is often evaluated using criteria established in a technical definition for mechanical pumps, but this definition is based on a small-amplitude, long-wave approximation which biological pumps often violate. In this study, we use a direct numerical simulation of large-amplitude, short-wave peristalsis to investigate the relationships between fluid flow, compression frequency, compression wave speed, and tube occlusion. We also explore how the flows produced differ from the criteria outlined in the technical definition of peristalsis. We find that many of the technical criteria are violated by our model: Fluid flow speeds produced by peristalsis are greater than the speeds of the compression wave; fluid flow is pulsatile; and flow speed have a nonlinear relationship with compression frequency when compression wave speed is held constant. We suggest that the technical definition is inappropriate for evaluating peristalsis as a pumping mechanism for biological pumps because they too frequently violate the assumptions inherent in these criteria. Instead, we recommend that a simpler, more inclusive definition be used for assessing peristalsis as a pumping mechanism based on the presence of non-stationary compression sites that propagate unidirectionally along a tube without the need for a structurally fixed flow direction.     

Stability and selection in self-reproducing macromolecular systems

In this paper we develop stability criteria applicable to Eigen's model for the selection and evolution of biological macromolecules. We show that it is possible to characterize the time evolution of the macromolecular system by Lyapounov-like functionals. The Lyapounov method is used to discuss the general stability of the system and the metastable nature of the selected states are discussed.     

Functional tissue engineering of tendon: Establishing biological success criteria for improving tendon repair

Improving tendon repair using Functional Tissue Engineering (FTE) principles has been the focus of our laboratory over the last decade. Although our primary goals were initially focused only on mechanical outcomes, we are now carefully assessing the biological properties of our tissue-engineered tendon repairs so as to link biological influences with mechanics. However, given the complexities of tendon development and healing, it remains challenging to determine which aspects of tendon biology are the most important to focus on in the context of tissue engineering. To address this problem, we have formalized a strategy to identify, prioritize, and evaluate potential biological success criteria for tendon repair. We have defined numerous biological properties of normal tendon relative to cellular phenotype, extracellular matrix and tissue ultra-structure that we would like to reproduce in our tissue-engineered repairs and prioritized these biological criteria by examining their relative importance during both normal development and natural tendon healing. Here, we propose three specific biological criteria which we believe are essential for normal tendon function: (1) scleraxis-expressing cells; (2) well-organized and axially-aligned collagen fibrils having bimodal diameter distribution; and (3) a specialized tendon-to-bone insertion site. Moving forward, these biological success criteria will be used in conjunction with our already established mechanical success criteria to evaluate the effectiveness of our tissue-engineered tendon repairs.     

A theoretical framework for biological control of soil-borne plant pathogens: Identifying effective strategies

We develop and analyse a flexible compartmental model of the interaction between a plant host, a soil-borne pathogen and a microbial antagonist, for use in optimising biological control. By extracting invasion and persistence thresholds of host, pathogen and biological control agent, performing an equilibrium analysis, and numerical investigation of sensitivity to parameters and initial conditions, we determine criteria for successful biological control. We identify conditions for biological control (i) to prevent a pathogen entering a system, (ii) to eradicate a pathogen that is already present and, if that is not possible, (iii) to reduce the density of the pathogen. Control depends upon the epidemiology of the pathogen and how efficiently the antagonist can colonise particular habitats (i.e. healthy tissue, infected tissue and/or soil-borne inoculum). A sharp transition between totally effective control (i.e. eradication of the pathogen) and totally ineffective control can follow slight changes in biologically interpretable parameters or to the initial amounts of pathogen and biological control agent present. Effective biological control requires careful matching of antagonists to pathosystems. For preventative/eradicative control, antagonists must colonise susceptible hosts. However, for reduction in disease prevalence, the range of habitat is less important than the antagonist's bulking-up efficiency.     

A diffuse biosemiotic model for cell-to-tissue computational closure

The adoption of diffuse rationality creates a practical bridge between biosemiotics and computation in formulating local-to-global self-consistent criteria for cellular-to-tissue interfacing and for the emergence of life and consciousness. Nature is always complex, the more so at biological membranic inter-scalar interfaces. We present an evolutionary model of the relationship between autonomy and dependence across scales, and describe the implications of its alternating complex-rational-complex nature.     

Classification of Time Series Gene Expression in Clinical Studies via Integration of Biological Network

The increasing availability of time series expression datasets, although promising, raises a number of new computational challenges. Accordingly, the development of suitable classification methods to make reliable and sound predictions is becoming a pressing issue. We propose, here, a new method to classify time series gene expression via integration of biological networks. We evaluated our approach on 2 different datasets and showed that the use of a hidden Markov model/Gaussian mixture models hybrid explores the time-dependence of the expression data, thereby leading to better prediction results. We demonstrated that the biclustering procedure identifies function-related genes as a whole, giving rise to high accordance in prognosis prediction across independent time series datasets. In addition, we showed that integration of biological networks into our method significantly improves prediction performance. Moreover, we compared our approach with several state-of–the-art algorithms and found that our method outperformed previous approaches with regard to various criteria. Finally, our approach achieved better prediction results on early-stage data, implying the potential of our method for practical prediction.     

When the optimal is not the best: parameter estimation in complex biological models

Background

The vast computational resources that became available during the past decade enabled the development and simulation of increasingly complex mathematical models of cancer growth. These models typically involve many free parameters whose determination is a substantial obstacle to model development. Direct measurement of biochemical parameters in vivo is often difficult and sometimes impracticable, while fitting them under data-poor conditions may result in biologically implausible values.

Results

We discuss different methodological approaches to estimate parameters in complex biological models. We make use of the high computational power of the Blue Gene technology to perform an extensive study of the parameter space in a model of avascular tumor growth. We explicitly show that the landscape of the cost function used to optimize the model to the data has a very rugged surface in parameter space. This cost function has many local minima with unrealistic solutions, including the global minimum corresponding to the best fit.

Conclusions

The case studied in this paper shows one example in which model parameters that optimally fit the data are not necessarily the best ones from a biological point of view. To avoid force-fitting a model to a dataset, we propose that the best model parameters should be found by choosing, among suboptimal parameters, those that match criteria other than the ones used to fit the model. We also conclude that the model, data and optimization approach form a new complex system and point to the need of a theory that addresses this problem more generally.     

Putting the Biological Species Concept to the Test: Using Mating Networks to Delimit Species

Although interfertility is the key criterion upon which Mayr’s biological species concept is based, it has never been applied directly to delimit species under natural conditions. Our study fills this gap. We used the interfertility criterion to delimit two closely related oak species in a forest stand by analyzing the network of natural mating events between individuals. The results reveal two groups of interfertile individuals connected by only few mating events. These two groups were largely congruent with those determined using other criteria (morphological similarity, genotypic similarity and individual relatedness). Our study, therefore, shows that the analysis of mating networks is an effective method to delimit species based on the interfertility criterion, provided that adequate network data can be assembled. Our study also shows that although species boundaries are highly congruent across methods of species delimitation, they are not exactly the same. Most of the differences stem from assignment of individuals to an intermediate category. The discrepancies between methods may reflect a biological reality. Indeed, the interfertility criterion is an environment-dependant criterion as species abundances typically affect rates of hybridization under natural conditions. Thus, the methods of species delimitation based on the interfertility criterion are expected to give results slightly different from those based on environment-independent criteria (such as the genotypic similarity criteria). However, whatever the criterion chosen, the challenge we face when delimiting species is to summarize continuous but non-uniform variations in biological diversity. The grade of membership model that we use in this study appears as an appropriate tool.     

Halting indigenous biodiversity decline: ambiguity, equity, and outcomes in RMA assessment of significance

In New Zealand, assessment of ?significance? is undertaken to give effect to a legal requirement for local authorities to provide for protection of significant sites under the Resource Management Act (1991). The ambiguity of the statute enables different interests to define significance according to their goals: vested interests (developers), local authorities, and non-vested interests in pursuit of protection of environmental public goods may advance different definitions. We examine two sets of criteria used for assessment of significance for biological diversity under the Act. Criteria adapted from the 1980s Protected Natural Areas Programme are inadequate to achieve the maintenance of biological diversity if ranking is used to identify only highest priority sites. Norton and Roper-Lindsay (2004) propose a narrow definition of significance and criteria that identify only a few high-quality sites as significant. Both sets are likely to serve the interests of developers and local authorities, but place the penalty of uncertainty on non-vested interests seeking to maintain biological diversity, and are likely to exacerbate the decline of biological diversity and the loss of landscape-scale processes required for its persistence. When adopting criteria for assessment of significance, we suggest local authorities should consider whose interests are served by different criteria sets, and who will bear the penalty of uncertainty regarding biological diversity outcomes. They should also ask whether significance criteria are adequate, and sufficiently robust to the uncertainty inherent in the assessment of natural values, to halt the decline of indigenous biological diversity.     

Quantitative classification of life-style types in predaceous phytoseiid mites

Classification of species into different functional groups based on biological criteria has been a difficult problem in ecology. The difficulty mainly arises because natural classification patterns are not necessarily mutually exclusive. The more group characteristics overlap, the more difficult it is to identify the membership of a species in the overlapping portions of any two groups. In this paper, we present an application of discriminant analysis by creating classification models from life history and morphological data for two specialist and two generalist life-styles type of predaceous phytoseiid mites. Two stages can be distinguished in our method: life-style group membership assignment and trait variable evaluation. We use a Bayesian framework to create a classifier system to locate or assign species within a mixture of trait distributions. The method assumes that a mixture of trait distributions can represent the multiple dimensions of biological data. The mixture is most evident near the boundaries between groups. Because of the complexity of analytical solution, an iterative method is used to estimate the unknown means, variances, and mixing proportion between groups. We also developed a criterion based on information theory to evaluate model performance with different combinations of input variables and different hypotheses. We present a working example of our proposed methods. We apply these methods to the problem of selecting key species for inoculative release and for classical introductions of biological pest control agents.     

Escaping the mouse trap: the selection of new Evo-Devo model species

Among the many, sometimes contradictory, criteria that have been used for promoting model species, the most prominent has probably been their relevance for understanding human biology. Recently however, the debate has partly shifted from the search for evolutionary conservation (medicine-driven models) to a better understanding of the generative mechanisms underlying biological diversity (Evo-Devo-driven models). Integration of multiple disciplines, beyond developmental genetics and evolutionary molecular genetics, as well as of innovative technologies will help biologists to open the massive realm of living species to genome manipulation and phenotypic investigation. However, a consensual list of model species must still be reached for optimizing the interplay between in silico analyses and in vivo experiments, and we claim that the Evo-Devo community should play a more energetic role in this endeavor. We discuss here a few criteria and limitations of major relevance to the choice of model species for Evo-Devo studies, and promote the use of a pragmatic approach. Finally, given the difficulties related to manipulating and breeding model species, we suggest the development of Evo-Devo virtual zoos maintaining breeding colonies of a selected set of species and from which eggs or staged embryos are available on order.     

Evidence for a Causal Link between Exposure to an Insecticide Formulation and Declines in Catch of Atlantic Salmon

We report a case study showing relationships between historical insecticide applications (1973 to 1990) of an aminocarb formulation (Matacil® 1.8D ) containing 4-nonylphenol (4-NP) and catch data for Atlantic salmon (Salmo salar) populations. To address the hypothesis that Matacil® 1.8D caused reductions in Atlantic salmon catch, seven epidemiological criteria are used to evaluate causality between the stressor and effect. These criteria include: strength of association; consistency of association; specificity of association; time order; biological gradient; experimental support; and biological plausibility. We conclude that the general weight-of-evidence supporting the seven epidemiological criteria is consistent with a causal relationship between declines in salmon catch and Matacil® 1.8D exposure during parr-smolt transformation (PST). If the effects exerted by 4-NP are due to its activity as a weak estrogen, then hormonal activity stemming from other sources (e.g., domestic sewage, agricultural, industrial) might influence present day salmon populations.     

A method for molecular phylogeny construction by direct use of nucleotide sequence data

Summary A method for molecular phylogeny construction is newly developed. The method, called the stepwise ancestral sequence method, estimates molecular phylogenetic trees and ancestral sequences simultaneously on the basis of parsimony and sequence homology. For simplicity the emphasis is placed more on parsiomony than on sequence homology in the present study, though both are certainly important. Because parsimony alone will sometimes generate plural candidate trees, the method retains not one but five candidates from which one can then single out the final tree taking other criteria into account.The properties and performance of the method are then examined by simulating an evolving gene along a model phylogenetic tree. The estimated trees are found to lie in a narrow range of the parsimony criteria used in the present study. Thus, other criteria such as biological evidence and likelihood are necessary to single out the correct tree among them, with biological evidence taking precedence over any other criterion. The computer simulation also reveals that the method satisfactorily estimates both tree topology and ancestral sequences, at least for the evolutionary model used in the present study.     

Modification of protein stability by introduction of disulfide bridges and prolines: geometric criteria for mutation sites

We define geometrical parameters to characterize disulfide bridges using x-ray crystal structure data on small molecules and use them to suggest replacements of amino acids by cysteines in order to introduce disulfide bridges to increase thermal stability in proteins. We also define geometric parameters to identify target amino acids for replacements by prolines in order to conserve desired structural attributes in the vicinity of disulfide mutations leading to further structural and thermal stability of proteins. The geometric criteria are applied to the serine protease, subtilisin, to model stereochemically favorable disulfide mutants without altering the active site geometry, implying conservation of native biological activity.     

Periodic solutions in modelling lagoon ecological interactions

In this paper we present and analyze a nutrient-oxygen-phytoplankton-zooplankton mathematical model simulating lagoon ecological interactions. We obtain sufficient conditions, based on principal eigenvalue criteria – for the existence of periodic solutions. A decoupled model which arises in the high nutrient regime is then considered in further detail for gathering some explicit conditions on parameters and averages of exogenous inputs needed for coexistence. An application to Italian coastal lagoons is finally obtained by parameter estimation and comparison with real data. A biological interpretation of the mathematical results is also presented. Research supported by NSERC (Canada) and Regione Toscana (Italy).     

What mechanisms can’t do: Explanatory frameworks and the function of the p53 gene in molecular oncology

What has been called the new mechanistic philosophy conceives of mechanisms as the main providers of biological explanation. We draw on the characterization of the p53 gene in molecular oncology, to show that explaining a biological phenomenon (cancer, in our case) implies instead a dynamic interaction between the mechanistic level—rendered at the appropriate degree of ontological resolution—and far more general explanatory tools that perform a fundamental epistemic role in the provision of biological explanations. We call such tools “explanatory frameworks”. They are called frameworks to stress their higher level of generality with respect to bare mechanisms; on the other hand, they are called explanatory because, as we show in this paper, their importance in explaining biological phenomena is not secondary with respect to mechanisms. We illustrate how explanatory frameworks establish selective and local criteria of causal relevance that drive the search for, characterisation and usage of biological mechanisms. Furthermore, we show that explanatory frameworks allow for changes of scientific perspective on the causal relevance of mechanisms going beyond the account provided by the new mechanistic philosophy.