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Mathematics for Ecology and Environmental Sciences

Yasuhiro Takeuchi ; Yoh Iwasa ; Kazunori Sato (eds.)

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Institución detectada Año de publicación Navegá Descargá Solicitá
No detectada 2007 SpringerLink

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Tipo de recurso:

libros

ISBN impreso

978-3-540-34427-8

ISBN electrónico

978-3-540-34428-5

Editor responsable

Springer Nature

País de edición

Reino Unido

Fecha de publicación

Información sobre derechos de publicación

© Springer-Verlag Berlin Heidelberg 2007

Tabla de contenidos

Ecology as a Modern Science

Kazunori Sato; Yoh Iwasa; Yasuhiro Takeuchi

In this paper, we propose an architecture of accounting and payment services for service-oriented grid computing systems. The proposed accounting and payment services provide the mechanisms for service providers to be paid for authorized use of their resources. It supports the recording of usage data, secure storage of that data, analysis of that data for purposes of billing and so forth. It allows a variety of payment methods, it is scalable, secure, convenient, and reduce the overall cost of payment processing while taking into account requirements of Grid computing systems.

Pp. 1-3

Physiologically Structured Population Models: Towards a General Mathematical Theory

Odo Diekmann; Mats Gyllenberg; Johan Metz

We review the state-of-the-art concerning a mathematical framework for general physiologically structured population models. When individual development is affected by the population density, such models lead to quasilinear equations. We show how to associate a dynamical system (defined on an infinite dimensional state space) to the model and how to determine the steady states. Concerning the principle of linearized stability, we offer a conjecture as well as some preliminary steps towards a proof.

Pp. 5-20

A Survey of Indirect Reciprocity

Hannelore Brandt; Hisashi Ohtsuki; Yoh Iwasa; Karl Sigmund

This survey deals with indirect reciprocity, i. e. with the possibility that altruistic acts are returned, not by the recipient, but by a third party. After briefly sketching how this question is dealt with in classical game theory, we turn to models from evolutionary game theory. We describe recent work on the assessment of interactions, and the evolutionary stability of strategies for indirect reciprocation. All stable strategies (the ‘leading eight’) distinguish between justified and non-justified defections, and therefore are based on non-costly punishment. Next we consider the replicator dynamics of populations consisting of defectors, discriminators and undiscriminating altruists. We stress that errors can destabilise cooperation for strategies not distinguishing justified from unjustified defections, but that a fixed number of rounds, or the assumption of an individual’s social network growing with age, can lead to cooperation based on a stable mixture of undiscriminating altruists and of discriminators who do not distinguish between justified and unjustified defection. We describe previous work using agent-based simulations for ‘binary score’ and ‘full score’ models. Finally, we survey the recent results on experiments with the indirect reciprocation game.

Pp. 21-49

The Effects of Migration on Persistence and Extinction

Jingan Cui; Yasuhiro Takeuchi

The interrelationship between organisms and the environment is essential to the stability or permanence of an ecological system, and the effect of migration on the possibility of species coexistence in an ecological community has been an important subject of research in population biology. Numerous types of models have been proposed and have been used to describe movement or dispersal of population individuals among patches. Some of the existing models deal with a single population dispersing among patches and others deal with predator-prey and competition interactions in patchy environments. Most previous models are based on autonomous ordinary differential equations. Recently, some authors have also studied the influence of migration on time-dependent population models.

In this chapter, we attempt to review key related research and introduce a set of new results for time-dependent population models in patchy environments. We consider a single-species model described by a set of autonomous ordinary differential equations or non-autonomous equations with periodic functions or with dispersal time delays. Also, we consider an age-structure model with or without dispersal delays. Further, we discuss predator-prey or competitive models described by autonomous or time-dependent ordinary differential equations.

Pp. 51-80

Sexual Reproduction Process on One-Dimensional Stochastic Lattice Model

Kazunori Sato

I consider the stochastic lattice model for sexual reproduction process on one-dimensional lattice investigated by [], [] and []. This model concerns the reproduction to the empty neighboring habitat by a pair of individuals on one-dimensional lattice. [] and [] mathematically analysed the model with rapid stirring and long-range interaction, respectively. In this chapter, after reviewing the process with rapid stirring briefly, I concentrate on the case with the nearest neighboring interactions and without stirring, and the qualitative features of the dynamics for this model are studied by using pair approximation, which shows the comparative difference from the mean-field approximation.

Pp. 81-92

A Mathematical Model of Gene Transfer in a Biofilm

Mudassar Imran; Hal L. Smith

Based on our previous work, a model of plasmid transfer between micro-organisms in a heterogeneous environment consisting of a biofilm immersed in a fluid medium is constructed. A review of previous modeling of gene transfer is provided in order to place our work in context. The key question is whether the plasmid can persist in the bacterial population. We answer this question by constructing a basic reproductive number which takes into account the advantages conferred by the plasmid and its costs to the bacterial host.

Pp. 93-123

Nonlinearity and Stochasticity in Population Dynamics

J. M. Cushing

Theoretical studies of population dynamics and ecological interactions tend to focus on asymptotic attractors of mathematical models. Modeling and experimental studies show, however, that even in controlled laboratory conditions the attractors of mathematical models are likely to be insufficient to explain observed temporal patterns in data. Instead, one is more likely to see a collage of many patterns that resemble various dynamics predicted by a deterministic model that arise during randomly occurring temporal episodes. These deterministic “signals” might include patterns characteristic of a model attractor (or several model attractors — even from possibly different deterministic models), transients both near and far from attractors, and/or unstable invariant sets and their stable manifolds. This paper discusses several examples taken from experimental projects in population dynamics that illustrate these and other tenets.

Pp. 125-144

The Adaptive Dynamics of Community Structure

Ulf Dieckmann; Åke Brännström; Reinier HilleRisLambers; Hiroshi C. Ito

I consider the stochastic lattice model for sexual reproduction process on one-dimensional lattice investigated by [], [] and []. This model concerns the reproduction to the empty neighboring habitat by a pair of individuals on one-dimensional lattice. [] and [] mathematically analysed the model with rapid stirring and long-range interaction, respectively. In this chapter, after reviewing the process with rapid stirring briefly, I concentrate on the case with the nearest neighboring interactions and without stirring, and the qualitative features of the dynamics for this model are studied by using pair approximation, which shows the comparative difference from the mean-field approximation.

Pp. 145-177