Foreword ....................................................... xi
1 Introduction ................................................. 1
2 Ecological systems and their dynamics ........................ 5
2.1 Definition of ecological systems ........................ 5
2.2 Measurement of change in ecological systems ............. 8
2.3 Conceptual models of dynamic change .................... 10
2.4 Ecological theory and applications ..................... 15
3 Outline of modelling techniques and their
interrelationships .......................................... 17
3.1 Models ................................................. 17
3.2 Systems analysis ....................................... 19
3.3 Families of mathematical models ........................ 20
3.4 Interrelationships between model families .............. 25
3.5 Choice of models for dynamic change of ecosystems ...... 27
4 Systems analysis ............................................ 29
4.1 Introduction ........................................... 29
4.2 MAB concept of systems analysis ........................ 29
4.3 Later development of systems analysis and modelling .... 34
4.4 Sensitivity analysis ................................... 36
4.5 Verification and validation ............................ 38
4.6 The value of systems analysis .......................... 39
5 Dynamic models and sub-models ............................... 43
5.1 The origins and development of dynamic models .......... 43
5.2 Definitions and notation ............................... 45
5.3 Differential and difference equations .................. 47
5.4 Model types and applications ........................... 51
5.5 Computational solutions of dynamic models .............. 66
5.6 Case studies in dynamic modelling ...................... 67
6 Markov models and related procedures ........................ 71
6.1 Markov processes ....................................... 71
6.2 Transition matrices .................................... 72
6.3 Calculation of transition probabilities ................ 74
6.4 Powers of Markov transition matrices ................... 76
6.5 Classification of states and Markov chains ............. 76
6.6 Analysis of an ergodic Markov chain .................... 78
6.7 Analysis of an absorbing Markov chain .................. 80
6.8 Dependence, order and step length in Markov chains ..... 81
6.9 Discrete-state continuous time models .................. 82
6.10 Generating sequences of events from Markov chains ...... 83
6.11 Markov-type models, based on differential equations .... 83
6.12 Advantages and disadvantages of Markov-type models ..... 85
6.13 Case studies of Markov models .......................... 86
7 Multivariate models ......................................... 91
7.1 Origins and development of multivariate models ......... 91
7.2 Attributes, variables and variates ..................... 93
7.3 Notation ............................................... 95
7.4 Some essential stages in the analysis of multivariate
data ................................................... 95
7.5 Choice of method of analysis .......................... 105
7.6 Methods of multivariate analysis: introduction ........ 109
7.7 Ordination ............................................ 110
7.8 Discrimination ........................................ 133
7.9 Cluster analysis ...................................... 138
7.10 Fitting relationships between groups of variables ..... 146
References .................................................... 151
Appendix ...................................................... 161
Index ......................................................... 177
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