Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben

1986 | Buch

A Gentle Introduction to Structured Population Models: Three Worked Examples Kapitel lesen Erstes Kapitel lesen

The Dynamics of Physiologically Structured Populations

herausgegeben von: J. A. J. Metz, O. Diekmann

Verlag: Springer Berlin Heidelberg

Buchreihe : Lecture Notes in Biomathematics

Enthalten in: Professional Book Archive

Einloggen, um Zugang zu erhalten
insite
SUCHEN

Inhaltsverzeichnis

Frontmatter

Mathematical Models for Physiologically Structured Populations a Systematic Exposition

Frontmatter
I. A Gentle Introduction to Structured Population Models: Three Worked Examples
Abstract
In population models the basic unit is the individual. Therefore it is the task of the model builder to translate his/her knowledge about mechanisms on the individual level into models for the change in the number of such individuals.Generally, if one talks to an experimental ecologist (s)he has all kinds of alluring stories to tell about such mechanisms. However, as soon as it comes to writing down equations usually all that remains is but a handwaving reference when some mathematically convenient relationship between, say, death rate and population size is pulled mit of the hat. The main reason for this unsatisfactory state of affairs probably is that applied mathematics seems to revolve around differential equation models which in the simplest case of ordinary differential equations necessarily start at a rather high phenomenologicallevel. And biologists cannot but comply (but see e.g. MCKENDRICK (1926) for an early exception!). What clearly is needed, therefore, is a model1ing methodology which in principle can accomodate any necessary amouot of biological detail and yet is sufficiently near to the mainstream of applied mathematics that its toolscan be brought to bear. This is the backgrouod to our elforts as set forward in these notes.
J. A. J. Metz, O. Diekmann
II. The Cell Size Distribution and Semigroups of Linear Operators
Abstract
In this ehapter we present relevant parts of the theory of strongly continuous semigroups of linear operators in thecontext of a concrete example: the time evolution of the size distribution of a proliferating cell population. Our aim is to give a motivated introduction to the general mathematical theory of linear semigroups and to demonstrate its usefulness for the study of density independent struetured population models. We want to show that abstract arguments and concrete calculations may be combined to arrive at streng conclusions.
O. Diekmann
III. Formulating Models for Structured Populations
Abstract
By now the examples from chapter I and/or the subsequent theoretical elaboration in chapter 11 shou,ld have given you a taste lor structured population models. In this chapter we shall develop a do-it-yoursell kit enabling you to build models incorporating various amounts of biological detail.
J. A. J. Metz, O. Diekmann
IV. Age Dependence
Abstract
On the whole the theory of structured population models is still in statu nascendi. We have a firm idea where the linear theory is heading, but a great deal of work remains to be done to get even a semblance of completeness, and Dur present understanding of nonlinear problems is scanty at best (but developing rapidly!). However, there is one specific area that is already well past puberty: that purely age dependent problems.
J. A. J. Metz, O. Diekmann
V. The Dynamical Behaviour of the Age-Size-Distribution of a Cell Population
Abstract
It is appropriate to think of the celI cyde as an ordered sequenceof biochemical events, such as the synthesis of RNA and proteins and the replication of DNA, finally ending up in cell division. The rate at which these biochemical events, such as the increase of structural materials, proceed may heavily depend on volume (size) through such factors as diffusion times and surfaceto volume ratios. In section 1.4 and chapter II we therefore considered the case that the position of a particular cell in its cycle was adequately described by its size. However, some of the biochentical reactions seem to proceed sequentiaIly during a cell's Iife cyc1e and for such reactions cell age provides a better description.
H. J. A. M. Heijmans
VI. Nonlinear Dynamical Systems: Worked Examples, Perspectives and Open Problems
Abstract
A first and important step in tbe construction of a mathematical model of a (biologieal) system consists of the choice of astate space. Tbe mathematical state should be a convenient representation of those physiological, chemical, physical and other relevant properties which in our conception of (or hypotheses about) reality uniquely determine the future, in the sense that for a given time course of experimental or environmental conditions (the input) we obtain a unique time course of the quantities we are interested in (the output). In seetion III.2 we made some remarks about the choice of astate space and about the construction of astate space from input-output data. Moreover, we presented a precise mathematical reformulation of the intuitive definition of "state" above in terms of a family of operators with a sentigroup property.
O. Diekmann, H. J. A. M. Heijmans

From Physiological Ecology to Population Dynamics a Collection of Papers

Frontmatter
I. Individuals and laboratory populations
Abstract
The basic strategy of the structured approach to population dynamics, as advocated in these notes, starts from mechanistic considerations on the individual level incorporating various amounts of detail about the underlying physiology. The resultingi-model is used as the substrate lor subsequent p- modelling. In the end we may say that we have explained populationphenomena from considerations on the i-level.
S. A. L. M. Kooijman, M. W. Sabelis, J. van der Meer, W. E. M. Laane
II. Field populations
Abstract
The main reason to study laboratory populations is that they may serve as simplified models of field populations. The i-machinery is by definition a property of individuals , and as such independent of whether we deal with these individuals in the lab or in the field. What is different, however, is the structure of the environment. In the field this in general is much less homogeneous, both in space and in time. As Dur i-models are necessarily simplified and the quality of a simplification is dependent both on the range and the temporal dynamies of the inputs encauntered by the individuals, the transplantation of lab based models 10 the field is not straightforward. Moreover, often the species we are interested in are difficult 10 keep in the laboratory other than for short parts of their life cycle. As a result structured models for field populations offen have population data as their main empirical basis, even if they are theoretically based on our preconceptions about the adequate state representation of individuals. The resulting necessity of deducing details of the supposedly underlying i-model from population data leads inexorably to the so-called inverse problem: the deduction of (some of) the assumptions of a model from its predictions.
Niels Daan, Nico M. van Straalen, Tom Aldenberg
III. Cell populations
Abstract
In the case of cell poplulations we seldomly can do any direct measurements on the level of the individuals. So in cell biology the inverse problem is paramount: we have to infer the dynamical properties of the individuals from population observations. The paper by Voorn & Koch exemplifies this (also compare part A section 1.4.4). In it a very general procedure is described for connecting various size related statistics on the p- and --levels.
Wim J. Voorn, Arthur L. Koch, P. A. C. Raats
IV. Numerical approaches
Abstract
To arrive at a workable mode lling methodology the theoretical approaches have 10 be complemented by efficient numerical lechniques for exploring the models so conceived. Tbus far the problem of numerically calculating solutions of structured population equ at ions has received little attentio n except for the simplesi case of pure age dependence. Tbe two papers in Ibis section both deal with models in which the r-state variable und er consideration is physiological age (compare part A. remark fV.1.2.3).
J. Goudriaan, W. S. C. Gurney, R. M. Nisbet, S. P. Blythe
V. Analytical approaches and novel type of i-state
Abstract
Population dynamical models generally are constructed either to rnimic the behaviour of some specific population OI to illustrate some conceptual issue. Models of the first type are either completely specified or at worst belang to a low dimensional parametrie family, allowing their properties to be studied numerically. The quantitative matehing of observations and model predictions also instills an implicit trust in the aceuracy of the numerical technique. In the second case numerical methods may be used in the construction of examples OI counter examples, but we have to ascertain the essential correctness of the numeries in an independent manner. However, analytical methods are to be preferred as only these allow us to inter in a general fashion the potential consequences of large classes of mechanisms.
Horst R. Thieme
Backmatter
Metadaten
Titel
The Dynamics of Physiologically Structured Populations
herausgegeben von
J. A. J. Metz
O. Diekmann
Copyright-Jahr
1986
Verlag
Springer Berlin Heidelberg
Electronic ISBN
978-3-662-13159-6
Print ISBN
978-3-540-16786-0
DOI
https://doi.org/10.1007/978-3-662-13159-6