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Erschienen in:
Stochastic Optimal Foraging Theory Kapitel lesen Erstes Kapitel lesen

2013 | OriginalPaper | Buchkapitel

The Mathematical Analysis of Biological Aggregation and Dispersal: Progress, Problems and Perspectives

verfasst von : Hans G. Othmer, Chuan Xue

Erschienen in: Dispersal, Individual Movement and Spatial Ecology

Verlag: Springer Berlin Heidelberg

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Abstract

Motile organisms alter their movement in response to signals in their environment for a variety of reasons, such as to find food or mates or to escape danger. In populations of individuals this often this leads to large-scale pattern formation in the form of coherent movement or localized aggregates of individuals, and an important question is how the individual-level decisions are translated into population-level behavior. Mathematical models are frequently developed for a population-level description, and while these are often phenomenological, it is important to understand how individual-level properties can be correctly embedded in the population-level models. We discuss several classes of models that are used to describe individual movement and indicate how they can be translated into population-level models.

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Vorheriges Kapitel Beyond Optimal Searching: Recent Developments in the Modelling of Animal Movement Patterns as Lévy Walks
Nächstes Kapitel Hybrid Modelling of Individual Movement and Collective Behaviour
Fußnoten
1
In this section the weight w may be equivalent to the signal S used earlier, or some function of it.
 
2
These equations are the restriction of (54) to one-space dimension only when the speeds s  ±  are constant, and in that case the moment equations close at the second level for constant λ [73]. We consider the more general case for illustrative purposes.
 
3
In [41] this estimate appears with the L 2-norm squared, but it is clear from the proof that there should be no square.
 
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Metadaten
Titel
The Mathematical Analysis of Biological Aggregation and Dispersal: Progress, Problems and Perspectives
verfasst von
Hans G. Othmer
Chuan Xue
Copyright-Jahr
2013
Verlag
Springer Berlin Heidelberg
Buch
Dispersal, Individual Movement and Spatial Ecology

Print ISBN: 978-3-642-35496-0

Electronic ISBN: 978-3-642-35497-7

Copyright-Jahr: 2013

DOI
https://doi.org/10.1007/978-3-642-35497-7_4