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  • Springer  (173,866)
  • MDPI Publishing
  • 2000-2004  (173,866)
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Year
  • 11
    Electronic Resource
    Electronic Resource
    Self-organization, scale and stability in a spatial predator-prey interaction (2000)
    Springer
    Bulletin of mathematical biology 62 (2000), S. 61-86 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Simple predator-prey models often predict extreme instability in interactions where the prey are depressed well below their carrying capacity. Although the behaviour of some laboratory systems conforms to this pattern, field and mesocosm studies generally show prolonged co-existence of prey and predator. Prominent among the possible causes of this discrepancy are the effects of spatial heterogeneity. In this paper we show that both discrete and continuous representations of the spatial Rosenzweig-McArthur model with immobile prey can be stabilized by self-organized prey heterogeneity. This concordance of behaviour closely parallels that which we have previously established in the context of invasion waves. We use the continuous model variant to calculate the characteristic spatial scales of the self-organized structures. The discrete variant forms the basis of a simulation study demonstrating the variety of stable structures and elucidating their relation to the history of the system. We note that all stable prey distributions take the form of a network of occupied patches separated by prey-free regions, and liken the process which generates such assemblages to the formation of a landscape mozaic.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1999.0130
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  • 12
    Electronic Resource
    Electronic Resource
    Book reviews (2000)
    Springer
    Bulletin of mathematical biology 62 (2000), S. 395-398 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1999.0105
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  • 13
    Electronic Resource
    Electronic Resource
    Calculation of the cumulative distribution function of the time to a small observable tumor (2000)
    Springer
    Bulletin of mathematical biology 62 (2000), S. 229-240 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Multistage mathematical models of carcinogenesis (when applied to tumor incidence data) have historically assumed that the growth kinetics of cells in the malignant state are disregarded and the formation of a single malignant cell is equated with the emergence of a detectable tumor. The justification of this simplification is, from a mathematical point of view, to make the estimation of tumor incidence rates tractable. However, analytical forms are not mandatory in the estimation of tumor incidence rates. Portier et al. (1996b, Math. Biosci. 135, 129–146) have demonstrated the utility of the Kolmogorov backward equations in numerically calculating tumor incidence. By extending their results, the cumulative distribution function of the time to a small observable tumor may be numerically obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1999.0148
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  • 14
    Electronic Resource
    Electronic Resource
    Time-dependent closed form solutions for fully competitive enzyme reactions (2000)
    Springer
    Bulletin of mathematical biology 62 (2000), S. 321-336 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An analytic formalism developed earlier to describe the time evolution of the basic enzyme reaction is extended to fully competitive systems. Time-dependent closed form solutions are derived for the three nominal cases of competition: even, slow and fast inhibitors, allowing for the first time the complete characterization of the reactions. In agreement with previous work, the time-independent Michaelis-Menten approach is shown to be inaccurate when a fast inhibitor is present. The validity of the quasi-steady-state approximation on which the present framework is based is also revised.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1999.0156
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  • 15
    Electronic Resource
    Electronic Resource
    Using parasites as biological tags of fish populations: A dynamical model (2000)
    Springer
    Bulletin of mathematical biology 62 (2000), S. 87-99 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A simple model of macroparasitic infections has been used to evaluate the potential use of parasites as biological tags of fish populations. In the model, the parasite-host interaction is regulated by a birth-death process, and parasites can only be acquired by the non-specific migratory host population in a particular area of the space domain. In this case, we show that parasites can be succesfully used for stocks identification and to describe the migratory routes taken by some marine fish species.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1999.0142
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  • 16
    Electronic Resource
    Electronic Resource
    Equilibrium stability of single-species metapopulations (2000)
    Springer
    Bulletin of mathematical biology 62 (2000), S. 155-161 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We investigate the effect of migration between local populations of a single discrete-generation species living in a ring or an array of habitats. The commonly used symmetric dispersal assumption is relaxed to include the biologically more reasonable asymmetric dispersion. It is demonstrated analytically that density independent migration has no effect on the equilibrium stability of individual populations. However, the positive equilibrium may be destabilizing if the migration is density dependent in such a way that it increases with increasing population density at the source patch.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1999.0145
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  • 17
    Electronic Resource
    Electronic Resource
    Fast subsystem bifurcations in strongly coupled heterogeneous collections of excitable cells (2000)
    Springer
    Bulletin of mathematical biology 62 (2000), S. 101-120 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A continuum model for a heterogeneous collection of excitable cells electrically coupled through gap junctions is introduced and analysed using spatial averaging, asymptotic and numerical techniques. Heterogeneity is modelled by imposing a spatial dependence on parameters which define the single cell model and a diffusion term is used to model the gap junction coupling. For different parameter values, single cell models can exhibit bursting, beating and a myriad of other complex oscillations. A procedure for finding asymptotic estimates of the thresholds between these (synchronous) behaviors in the cellular aggregates is described for the heterogeneous case where the coupling strength is strong. This procedure is tested on a model of a strongly coupled heterogeneous collection of bursting and beating cells. Since isolated pancreatic β-cells have been observed to both burst and beat, this test of the spatial averaging techniques provides a possible explanation to measured discrepancies between the electrical activities of isolated β-cells and coupled collections (islets) of β-cells.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1999.0143
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  • 18
    Electronic Resource
    Electronic Resource
    Moment expansions in spatial ecological models and moment closure through Gaussian approximation (2000)
    Springer
    Bulletin of mathematical biology 62 (2000), S. 595-632 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We describe the dynamics of competing species in terms of interactions between spatial moments. We close the moment hierarchy by employing a Gaussian approximation which assumes that fluctuations are independent and distributed normally about the mean values. The Gaussian approximation provides the lowest-order systematic correction to the mean-field approximation by incorporating the effect of fluctuations. When there are no fluctuations in the system, the mean equations agree with the Gaussian approximation as the fluctuations are weak. As the fluctuations gain strength, they influence the mean quantities and hence the Gaussian approximation departs from the mean-field approximation. At large fluctuation levels, the Gaussian approximation breaks down, as may be explained by the bimodality and skewness of the fluctuation distribution of the partial differential equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1999.0119
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  • 19
    Electronic Resource
    Electronic Resource
    Multipole approach to the inverse problem in electrocardiology: Convergence of the multipole equivalent generator on the inhomogeneous body conductor (2000)
    Springer
    Bulletin of mathematical biology 62 (2000), S. 543-583 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The multipole approach to the inverse electrocardiological problem consists of estimating the multipole components of the cardiac electric generator, starting from the measured body surface potential. This paper presents a critical investigation of the basic premise for the applicability of the multipole approach, namely the convergence of the multipole equivalent generator for the heart on the surface of an inhomogeneous body conductor. As an extension to multipole theory, a criterion for the convergence is derived. Based on realistic models for the body conductor and the cardiac electric generator, we observe that the criterion is not strictly satisfied in realistic conditions. Numerical simulations with the same models point out that the multipole equivalent generator is indeed not convergent in the strict mathematical sense. On the other hand, we show that the multipole equivalent generator yields a rather close approximation of the electrocardiological potential for intermediate values of the order of the multipole generator. A discussion is given on how to explain the apparently ambiguous results for the estimation of cardiac multipole components.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.2000.0169
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  • 20
    Electronic Resource
    Electronic Resource
    The effect of incubation time distribution on the extinction characteristics of a rabies epizootic (2000)
    Springer
    Bulletin of mathematical biology 62 (2000), S. 633-656 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The continuous model of Anderson et al. (1981), Nature 289, 765–771, is successful in describing certain characteristics of rabies epizootics, in particular, the secondary recurrences which follow the initial outbreak; however, it also predicts the occurrence of exponentially small minima in the infected population, which would realistically imply extinction of the virus. Here we show that inclusion of a more realistic distribution of incubation times in the model can explain why extinction will not occur, and we give explicit parametric estimates for the minimum infected fox density which will occur in the model, in terms of the incubation time distribution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1999.0170
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