Stochastic foundations in movement ecology. Anomalous diffusion, front propagation and random searches
type: Item
instance of: scholarly article
title: Stochastic foundations in movement ecology. Anomalous diffusion, front propagation and random searches
zbMATH Open document ID: 1295.92010
DOI: 10.1007/978-3-642-39010-4
author: Yanyan Li
published in: Springer Series in Synergetics
publication date: 2014-06-26T00:00:00Z
review text: This book, written in an interdisciplinary spirit and for a broad (but mathematically minded) audience, attempts to provide an overview of the essential mathematical, physical and modelling aspects which describe the motion of living entities at various scales. Since the movement of living entities involves a certain level of randomness, the mathematical scaffolding of the book lies in the theory of stochastic processes, rather than being deterministic. A distinguishing feature is the emphasis put on the multilevel description of stochastic processes and stochastic dispersal models (called microscopic, mesoscopic and macroscopic levels therein). Clear distinctions between these levels of description are made, their characteristic features, fundamental assumptions, advantages and limitations being highlighted. This book is divided into three parts. The first part, consisting in two chapters, provides a survey of the essential results in probability theory (first chapter) and an introduction to the concept of stochastic processes and of their micro, meso and macroscopic descriptions (second chapter). The reader is also generously provided with many concrete examples from population ecology. The second part of the book, consisting in four chapters, provides a comprehensive review of the stochastic modelling approach towards describing ecological movements. Chapter 3 refers to micro, meso and macroscopic definitions of dispersal and their ability (or lack thereof) to incorporate nontrivial effects such as memory (correlations), finite jump speeds, long-distance dispersal and velocity drifts. It also describes the opposite of dispersal, aggregation, in the form of animal grouping. This chapter does not only state and describe, but also discuss, explain and clarify, passing through multiple levels of description (micro, meso and macro) whenever necessary. Chapter 4 shows how differentiation on multiple levels of description helps when introducing more advanced concepts su…
reviewed by: Paul Georgescu
Mathematics Subject Classification ID: 92-02
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 92D50
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 92C17
Mathematics Subject Classification ID: 92B15
zbMATH DE Number: 6309037
zbMATH Keywords: stochastic processes
zbMATH Keywords: movement ecology
zbMATH Keywords: dispersal
zbMATH Keywords: random searches
zbMATH Keywords: front propagation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-642-39010-4
OpenAlex ID: W2481093941
Wikidata QID: Q57029460
description: scientific article