Diffusion and Ecological Problems

by Okubo, Akira; Levin, Simon A.

• ISBN13: 9780387986760
• ISBN10: 0387986766
• Edition: 2nd
• Format: Hardcover
• Copyright: 2002-04-01
• Publisher: Springer Verlag

Summary

This book surveys a wide variety of mathematical models of diffusion in the ecological context. It is written with the primary intent of providing scientists, particularly physicists but also biologists, with some background in the mathematics and physics of diffusion, and shows how they can be applied to ecological problems. The secondary intent is to provide a specialized textbook for graduate students who are interested in mathematical ecology. The reader is assumed to have a basic knowledge of probability and differential equations. Each chapter in this new edition has been substantially updated by appropriate leading researchers in the field, and contains much new material covering developments in the field in the last 20 years.

Table of Contents

Preface to the Second Edition	vii
Preface to the First Edition	ix
Contributors	xix
Introduction: The Mathematics of Ecological Diffusion	1	(9)
Akira Okubo
A History of Research on Diffusion in Ecology	1	(3)
The Value of Mathematical Models	4	(2)
Deterministic Versus Stochastic Methods	6	(4)
The Basics of Diffusion	10	(21)
Akira Okubo
Simon A. Levin
Random Variables	10	(1)
The Random Walk and Diffusion	11	(3)
Fick's Equation of Diffusion	14	(1)
Turbulence and Turbulent Diffusion	15	(3)
Diffusion in a Force Field	18	(2)
The Theory of Diffusion in Natural Environments: Physical Diffusion	20	(11)
Diffusion in Atmospheric Boundary Layers	26	(1)
Oceanographic and Limnological Diffusion	27	(4)
Passive Diffusion in Ecosystems	31	(76)
Akira Okubo
Josef David Ackerman
Dennis P. Swaney
Diffusion Within and Above Plant Canopies	32	(15)
Terrestrial Plant Canopies	32	(7)
Aquatic Plant Canopies	39	(8)
Diffusion of Nutrients in the Sea	47	(15)
Subsurface Productivity and Chlorophyll Maximum	53	(1)
Flocs, Aggregates, and Marine Snow	54	(5)
Benthic--Pelagic Coupling	59	(3)
Diffusion of Spores	62	(22)
Settling Velocity	63	(4)
Diffusion Model	67	(6)
Experiments on Spore Dispersal	73	(3)
Vertical Distributions over Wide Regions	76	(3)
Wind and Water Pollination	79	(5)
Dispersal of Gametes and Organisms	84	(7)
Broadcast Spawners and External Fertilization	85	(3)
The Dispersal of Fish Eggs and Larvae in the Sea	88	(3)
Transport Across the Solid Interface	91	(16)
Fluid Exchange in Animal Burrows	92	(12)
Bioturbation and Related Effects	104	(1)
Notes on Solute Transport in Soils and Sediments	105	(2)
Diffusion of ``Smell'' and ``Taste'': Chemical Communication	107	(20)
Akira Okubo
Robert A. Armstrong
Jeannette Yen
Diffusion of Insect Pheromones	107	(8)
Instantaneous Emission in Still Air	108	(2)
Continuous Emission in Still Air	110	(1)
Continuous Emission from a Moving Source	111	(1)
Continuous Emission of Pheromone in a Wind	112	(3)
A Diffusion Problem Concerning the Migration of Green Turtles	115	(4)
Chemical Communication in Aquatic Organisms	119	(8)
Temporal and Spatial Scales for Chemical Communication	119	(4)
Models of Chemical Communication in Aquatic Organisms	123	(1)
An Inverse Problem: Estimating the ``Statistical Funnel'' of Sediment Traps	124	(3)
Mathematical Treatment of Biological Diffusion	127	(43)
Akira Okubo
Daniel Grunbaum
Animal Motion and the Balance of Acting Forces	128	(3)
Taxis and the Equation of Motion	131	(2)
Extension of the Random Walk Model and the Equation of Biodiffusion	133	(18)
Correlated Random Walks	137	(3)
Patlak's Model	140	(3)
The Fokker--Planck Equations	143	(8)
Application to Taxis	151	(6)
Simulation of Taxis	157	(1)
Advection--Diffusion Models for Biodiffusion	158	(3)
Internal State-mediated Taxis	161	(9)
An Example: Receptor Kinetics-based Taxis	162	(8)
Some Examples of Animal Diffusion	170	(27)
Akira Okubo
Peter Kareiva
Population Pressure and Dispersal	170	(2)
Horizontal and Vertical Distributions of Insects in the Atmosphere: Insect Dispersal	172	(14)
Dispersal of Insects	173	(8)
Mathematical Models for Insect Dispersal	181	(5)
Diffusion Models for Homing and Migration of Animals	186	(5)
Model for Muskrat Dispersal and Biological Invasions in General	191	(3)
The Dispersal of Animal-Borne Plants	194	(1)
Diffusion Models as a Standard Tool in Animal Ecology	195	(2)
The Dynamics of Animal Grouping	197	(41)
Akira Okubo
Daniel Grunbaum
Leah Edelstein-Keshet
Physical Distinction Between Diffusion and Grouping	197	(3)
Formulation of Swarming by a Generalized Diffusion Equation	200	(2)
Insect Swarming	202	(7)
Locust Swarms	202	(1)
Experimental Techniques	203	(1)
Mosquitoes, Flies, and Midges	204	(4)
Marine Zooplankton Swarming	208	(1)
Fish Schooling	209	(6)
Simulation Model for Animal Grouping	215	(4)
The Split and Amalgamation of Herds	219	(3)
The Ecological or Evolutional Significance of Grouping	222	(5)
Linking Individuals, Groups, and Populations: The Biological Context of Mathematical Models of Grouping	227	(2)
Continum Approximations for Density Distributions Within Social Group	229	(5)
Energy-Potential Analogy	230	(1)
Integral Equations for Group Dynamics	231	(1)
Poisson-Point Assumption	232	(2)
Dynamics of Groups in Social Grouping Populations	234	(4)
Spatially Explicit Group-Size Distribution Models	235	(3)
Animal Movements in Home Range	238	(30)
Akira Okubo
Louis Gross
The Size of the Home Range and Its Relation to Animal Weight and Energy Requirements	239	(1)
Mathematical Models for Animal Dispersal in Home Ranges	240	(2)
Simulation of Animal Movement in Home Ranges	242	(6)
Animal Dispersal and Settling in New Home Ranges	248	(2)
Strategies of Movement for Resource Utilization	250	(8)
Data on Animal Movements	258	(3)
Case Study: Florida Panther	259	(2)
Home-Range Estimation	261	(1)
Allometric Relations Between Body Size and Home Range	261	(1)
Individual-based Models of Movement	262	(2)
Corridors and Movement	263	(1)
Food Density and Home-Range Size	264	(1)
Diffusion Models	264	(4)
Boundary Effects	265	(1)
Movement in Heterogeneous Environments	266	(1)
Multiple Scales and Foraging	266	(2)
Patchy Distribution and Diffusion	268	(30)
Akira Okubo
James G. Mitchell
Role of Diffusion in Plankton Patchiness	269	(5)
Spectra of Turbulence and Patchiness	274	(6)
Plankton Distribution in Convection Cells	280	(7)
Bioconvection	287	(4)
Microscale Patchiness	291	(3)
Diffusion and the Entropy of Patchiness	294	(4)
Population Dynamics in Temporal and Spatial Domains	298	(76)
Akira Okubo
Alan Hastings
Thomas Powell
Mathematical Representation of Intra-and Interspecific Interactions in Temporal and Spatial Domains: Advection--Diffusion--Reaction Equations	299	(5)
Single-Species Population Dynamics with Dispersal	304	(17)
Some Simple Population Models and Associated Travelling Frontal Waves	304	(6)
The Critical Size Problem	310	(7)
Population Balance with Diffusion and Direct Immigration-Emigration: Invasion and Settlement of New Species	317	(4)
Two- and Multispecies Population Dynamics with Dispersal	321	(53)
Lotka--Volterra Predator--Prey Model	322	(4)
Travelling Waves	326	(7)
The Effect of Cross-Diffusion	333	(1)
The Effect of Advective Flow on Predator--Prey Systems	334	(2)
The Effect of Density-Dependent Dispersal on Population Dynamics	336	(7)
The Effect of Dispersal on Competing Populations	343	(5)
Pattern-Developing Instability in Diffusion--Reaction Systems: The Development of Patchiness	348	(9)
Nonlinear Stability Analysis for Diffusion--Reaction Systems	357	(7)
Models of Age-Dependent Dispersal	364	(10)
References	374	(69)
Author Index	443	(16)
Subject Index	459