Ecological Dynamics

by Gurney, W. S. C.; Nisbet, R. M.

• ISBN13: 9780195104431
• ISBN10: 0195104439
• Format: Hardcover
• Copyright: 1998-04-16
• Publisher: Oxford University Press

Summary

Ecological Dynamics is unique in that it can serve both as an introductory text in numerous ecology courses and as a resource for more advanced work. It provides a flexible introduction to ecological dynamics that is accessible to students with limited previous mathematical and computationalexperience, yet also offers glimpses into the state of the art in the field. The book is divided into three parts: Part I, Methodologies and Techniques, defines the authors' modeling philosophy, focusing on models rather than ecology, and introduces essential concepts for describing and analyzing dynamical systems. Part II, Individuals to Ecosystems, the core of thebook, describes the formulation and analysis of models of individual organisms, populations, and ecosystems. Part III, Focus on Structure, introduces more advanced readers to models of 'structured' and spatially extended populations. Approximately 25% of the book is devoted to case studies drawnfrom the authors' research. Readers are guided through the many judgment calls involved in model formulation, shown the key steps in model analysis, and offered the authors' interpretation of the results. All chapters end with exercises and projects. While the book is designed to be independent ofany particular computing environment, a well-tested software package (SOLVER),including programs for solution of differential and difference equations, is available via the World Wide Web at http://www.stams.strath.ac.uk/external/solver. Ideal for courses in modeling ecological and environmental change, Ecological Dynamics can also be used in other courses such as theoretical ecology, population ecology, mathematical biology and ecology, and quantitative ecology.

Table of Contents

Preface	xi
PART I METHODOLOGIES AND TECHNIQUES	1	(78)
1 Ecological Modelling	1	(18)
1.1 Ecology	1	(1)
1.2 Models, mathematics, and ecological theory	2	(1)
1.3 Deterministic models	3	(7)
1.3.1 State variables	3	(1)
1.3.2 Modelling in discrete time	4	(2)
1.3.3 Modelling in continuous time	6	(4)
1.4 Balance equations	10	(2)
1.4.1 Balance equations for chemically inert materials	10	(1)
1.4.2 Balance equation for an open population	11	(1)
1.4.3 More complex balance equations	12	(1)
1.5 Formulating deterministic models	12	(2)
1.5.1 A model of an open population	13	(1)
1.5.2 A model of a closed population	13	(1)
1.5.3 A model of toxicant in a lake	14	(1)
1.6 Deterministic models in a random world	14	(5)
1.6.1 Random environments and random processes	14	(1)
1.6.2 Stochastic models	15	(2)
1.6.3 Deterministic models	17	(2)
2 Dynamics	19	(30)
2.1 Dynamic equations	19	(1)
2.1.1 Analytic and numerical solutions	19	(1)
2.2 Simple dynamic patterns	20	(7)
2.2.1 Geometric growth	21	(1)
2.2.2 Oscillations	22	(2)
2.2.3 Attractors	24	(3)
2.3 Complex dynamics in a fish population model	27	(4)
2.4 Analysis of discrete-time models	31	(4)
2.4.1 Equilibrium and stability in the mussel model	31	(1)
2.4.2 Local stability analysis	32	(3)
2.5 Analysis of continuous-time models	35	(6)
2.5.1 The logistic model	36	(1)
2.5.2 Local stability analysis: One differential equation	37	(1)
2.5.3 The Lotka-Volterra model	38	(2)
2.5.4 Local stability analysis: Two differential equations	40	(1)
2.6 Non-autonomous dynamics	41	(5)
2.6.1 Geometric and exponential growth	42	(2)
2.6.2 Fluctuations around equilibrium	44	(2)
2.7 Sources and suggested further reading	46	(1)
2.8 Exercises and project	46	(3)
3 A Dynamicist's Toolbox	49	(30)
3.1 Dimensional analysis and scaling	50	(4)
3.1.1 Logistic model	50	(2)
3.1.2 Reducing equations to dimensionless form	52	(1)
3.1.3 Dynamical information from dimensional analysis	53	(1)
3.2 Analysis of dynamics near equilibrium	54	(7)
3.2.1 Local linearisation and the characteristic equation	54	(3)
3.2.2 Local stability	57	(2)
3.2.3 Local instability and the onset of oscillations	59	(2)
3.3 Discrete versus continuous models	61	(5)
3.3.1 Time is continuous	61	(1)
3.3.2 Logistic growth: A cautionary tale	61	(3)
3.3.3 Predator-prey interaction: A semi-empirical formulation	64	(2)
3.4 Modelling age structure	66	(3)
3.4.1 Age-structure models in discrete time	66	(1)
3.4.2 Age-structure models in continuous time	67	(2)
3.5 Balance equations for spatially explicit models	69	(5)
3.5.1 Discrete time and space	69	(2)
3.5.2 Continuous time and space	71	(3)
3.6 Exercises and project	74	(5)
PART II INDIVIDUALS TO ECOSYSTEMS	79	(144)
4 Modelling Individuals	79	(39)
4.1 Survival and reproduction	79	(6)
4.1.1 Per-capita mortality rate	79	(1)
4.1.2 Age-independent mortality	80	(1)
4.1.3 Age-dependent mortality	81	(2)
4.1.4 Fecundity schedule and lifetime reproductive output	83	(2)
4.2 Feeding and the functional response	85	(8)
4.2.1 The Holling disc equation	86	(2)
4.2.2 Reward-dependent searching	88	(2)
4.2.3 Two types of food	90	(1)
4.2.4 Consumer strategy	91	(2)
4.3 The energetics of growth and reproduction	93	(10)
4.3.1 Balancing income and costs	94	(1)
4.3.2 Growth in a constant environment	95	(2)
4.3.3 Exponential and von Bertalanffy growth	97	(2)
4.3.4 The interaction between reproduction and growth	99	(4)
4.4 Life history selection	103	(2)
4.5 Case studies	105	(9)
4.5.1 Growth and reproduction in an abyssal sea urchin	105	(5)
4.5.2 Pollution of the marine environment	110	(4)
4.6 Sources and suggested further reading	114	(1)
4.7 Exercises and projects	114	(4)
5 Single-species Populations	118	(30)
5.1 Geometric and exponential population growth	118	(5)
5.1.1 Discrete generations	118	(1)
5.1.2 Continuous reproduction	119	(2)
5.1.3 Variable environments, small populations, and extinction	121	(2)
5.2 Density dependence	123	(8)
5.2.1 Discrete generation models with density dependence	125	(4)
5.2.2 Density dependence in continuous-time models	129	(2)
5.3 Evolutionary change	131	(1)
5.4 Case studies	132	(13)
5.4.1 Dynamics of a small bird population	132	(3)
5.4.2 Energy-limited growth of a waterflea population	135	(4)
5.4.3 The impact of a power plant on a coastal fishery	139	(6)
5.5 Sources and suggested further reading	145	(1)
5.6 Exercises and project	145	(3)
6 Interacting Populations	148	(35)
6.1 Discrete-time consumer-resource models	148	(6)
6.1.1 Plants and herbivores	148	(3)
6.1.2 Parasitoids and hosts	151	(3)
6.2 Predator-prey systems	154	(10)
6.2.1 The Lotka-Volterra model	155	(4)
6.2.2 Self-limiting prey	159	(2)
6.2.3 The paradox of enrichment	161	(3)
6.3 Competition	164	(7)
6.3.1 Competitive exclusion	164	(2)
6.3.2 Density dependence and competitive coexistence	166	(1)
6.3.3 Varying environments	167	(4)
6.4 Case studies	171	(8)
6.4.1 Stability and enrichment	171	(4)
6.4.2 Coexistence in a variable environment	175	(4)
6.5 Sources and suggested reading	179	(1)
6.6 Exercises and project	180	(3)
7 Ecosystems	183	(40)
7.1 Modelling ecosystems	183	(2)
7.1.1 The ecosystem paradigm	183	(1)
7.1.2 Formulating ecosystem models	184	(1)
7.2 Linear food-chains	185	(10)
7.2.1 Constant production: Linear functional response	185	(4)
7.2.2 Logistic primary production	189	(2)
7.2.3 Type II functional response	191	(4)
7.3 Material cycling	195	(5)
7.3.1 Linear trophic interactions	195	(3)
7.3.2 Type II trophic interactions	198	(2)
7.4 Ecosystem dynamics	200	(1)
7.5 Case study: A fjord ecosystem	201	(16)
7.5.1 Background	201	(2)
7.5.2 The model	203	(4)
7.5.3 Parameters and driving functions	207	(2)
7.5.4 Testing the model	209	(2)
7.5.5 Sea-loch dynamics	211	(6)
7.6 Sources and suggested further reading	217	(1)
7.7 Exercises and project	218	(5)
PART III FOCUS ON STRUCTURE	223	(97)
8 Physiologically Structured Populations	223	(47)
8.1 Modelling age-structured populations in discrete time	223	(6)
8.1.1 Balance equations	223	(1)
8.1.2 Ageing and recruitment	224	(2)
8.1.3 Exponentially growing populations	226	(1)
8.1.4 Control and stationary states	227	(2)
8.2 Modelling size-structured populations in discrete time	229	(8)
8.2.1 Fixed age-size relations	229	(3)
8.2.2 Models with dynamic growth	232	(5)
8.3 Modelling age-structured populations in continuous time	237	(9)
8.3.1 Balance equations	237	(2)
8.3.2 Exponentially growing populations	239	(1)
8.3.3 Stationary states	239	(1)
8.3.4 Local stability	240	(2)
8.3.5 Numerical realisation	242	(4)
8.4 Modelling size-structured populations in continuous time	246	(5)
8.4.1 Balance equations	246	(1)
8.4.2 Stationary states	246	(2)
8.4.3 Numerical realisation	248	(3)
8.5 Modelling stage-structured populations	251	(5)
8.5.1 Model formulation	251	(2)
8.5.2 An illustration	253	(3)
8.6 Case studies	256	(10)
8.6.1 Nicholson's blowflies	257	(5)
8.6.2 Barnacle population dynamics	262	(4)
8.7 Sources and suggested further reading	266	(1)
8.8 Exercises and project	267	(3)
9 Spatially Structured Populations	270	(50)
9.1 Modelling distributions in discrete time	271	(18)
9.1.1 Balance equations	271	(2)
9.1.2 Describing dispersal	273	(3)
9.1.3 Patterns of spread: Non-reproducing organisms	276	(3)
9.1.4 Patterns of spread: Reproducing organisms	279	(3)
9.1.5 Inhomogeneous environments	282	(3)
9.1.6 Interacting populations	285	(4)
9.2 Modelling distributions in continuous time	289	(6)
9.2.1 Describing dispersal	289	(2)
9.2.2 Growth and dispersal	291	(2)
9.2.3 Inhomogeneous environments	293	(2)
9.3 An overview of density distribution modelling	295	(1)
9.4 Exploiting structural features of the environment	296	(9)
9.4.1 A population and its environment	296	(3)
9.4.2 Patch dynamic models	299	(3)
9.4.3 Metapopulations	302	(3)
9.5 Open questions and unsolved problems	305	(3)
9.5.1 Formulation issues	305	(1)
9.5.2 Parameterisation and testing	306	(1)
9.5.3 Strategic questions	307	(1)
9.6 Case study: Foxes and rabies in Europe	308	(8)
9.6.1 Background	308	(1)
9.6.2 A first model	309	(2)
9.6.3 A model with a latent period	311	(1)
9.6.4 A numerical investigation	312	(4)
9.7 Sources and suggested further reading	316	(1)
9.8 Exercises and project	317	(3)
Bibliography	320	(9)
Index	329