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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
A ground-up approach to explaining dynamic spatial modelling for an interdisciplinary audience.
Across broad areas of the environmental and social sciences, simulation models are an important way to study systems inaccessible to scientific experimental and observational methods, and also an essential complement to those more conventional approaches. The contemporary research literature is teeming with abstract simulation models whose presentation is mathematically demanding and requires a high level of knowledge of quantitative and computational methods and approaches. Furthermore, simulation models designed to represent specific systems and phenomena are often complicated, and, as a result, difficult to reconstruct from their descriptions in the literature. This book aims to provide a practical and accessible account of dynamic spatial modelling, while also equipping readers with a sound conceptual foundation in the subject, and a useful introduction to the wide-ranging literature.
Spatial Simulation: Exploring Pattern and Process is organised around the idea that a small number of spatial processes underlie the wide variety of dynamic spatial models. Its central focus on three ‘building-blocks’ of dynamic spatial models – forces of attraction and segregation, individual mobile entities, and processes of spread – guides the reader to an understanding of the basis of many of the complicated models found in the research literature. The three building block models are presented in their simplest form and are progressively elaborated and related to real world process that can be represented using them. Introductory chapters cover essential background topics, particularly the relationships between pattern, process and spatiotemporal scale. Additional chapters consider how time and space can be represented in more complicated models, and methods for the analysis and evaluation of models. Finally, the three building block models are woven together in a more elaborate example to show how a complicated model can be assembled from relatively simple components.
To aid understanding, more than 50 specific models described in the book are available online at patternandprocess.org for exploration in the freely available Netlogo platform. This book encourages readers to develop intuition for the abstract types of model that are likely to be appropriate for application in any specific context. Spatial Simulation: Exploring Pattern and Process will be of interest to undergraduate and graduate students taking courses in environmental, social, ecological and geographical disciplines. Researchers and professionals who require a non-specialist introduction will also find this book an invaluable guide to dynamic spatial simulation.
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Table of Contents
Title Page
Copyright
Dedication
Foreword
Preface
Acknowledgements
Introduction
Organisation of the book
Using the book
Using the example models
About the Companion Website
Chapter 1: Spatial Simulation Models: What? Why? How?
1.1 What are simulation models?
1.2 How do we use simulation models?
1.3 Why do we use simulation models?
1.4 Why dynamic and spatial models?
Chapter 2: Pattern, Process and Scale
2.1 Thinking about spatiotemporal patterns and processes
2.2 Using models to explore spatial patterns and processes
2.3 Conclusions
Chapter 3: Aggregation and Segregation
3.1 Background and motivating examples
3.2 Local averaging
3.3 Totalistic automata
3.4 A more general framework: interacting particle systems
3.5 Schelling models
3.6 Spatial partitioning
3.7 Applying these ideas: more complicated models
Chapter 4: Random Walks and Mobile Entities
4.1 Background and motivating examples
4.2 The random walk
4.3 Walking for a reason: foraging and search
4.4 Moving entities and landscape interaction
4.5 Flocking: entity–entity interaction
4.6 Applying the framework
Chapter 5: Percolation and Growth: Spread in Heterogeneous Spaces
5.1 Motivating examples
5.2 Percolation models
5.3 Growth (or aggregation) models
5.4 Applying the framework
5.5 Summary
Chapter 6: Representing Time and Space
6.1 Representing time
6.2 Basics of spatial representation
6.3 Spatial relationships: distance, neighbourhoods and networks
6.4 Coordinate space: finite, infinite and wrapped
6.5 Complicated spatial structure without spatial data structures
6.6 Temporal and spatial representations can make a difference
Chapter 7: Model Uncertainty and Evaluation
7.1 Introducing uncertainty
7.2 Coping with uncertainty
7.3 Assessing and quantifying model-related uncertainty
7.4 Confronting model predictions with observed data
7.5 Frameworks for selecting between competing models
7.6 Pattern-oriented modelling
7.7 More to models than prediction
Chapter 8: Weaving It All Together
8.1 Motivating example: island resource exploitation by hunter-gatherers
8.2 Model description
8.3 Model development and refinement
8.4 Model evaluation
8.5 Conclusions
Chapter 9: In Conclusion
9.1 On the usefulness of building-block models
9.2 On pattern and process
9.3 On the need for careful analysis
References
Index
Supplemental Images
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Library of Congress Cataloging-in-Publication Data
O'Sullivan, David, 1966–
Spatial simulation : exploring pattern and process / David O'Sullivan, George L.W. Perry.
pages cm
Includes bibliographical references and index.
ISBN 978-1-119-97080-4 (cloth) – ISBN 978-1-119-97079-8 (paper)
1. Spatial data infrastructures–Mathematical models. 2. Spatial analysis (Statistics) I. Perry, George L. W. II. Title.
QA402.O797 2013
003–dc23
2012043887
A catalogue record for this book is available from the British Library.
Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books.
Cover image: Photo is of Shinobazu Pond in the Ueno district, Tokyo, April 2012. Photo credit: David O'Sullivan.
Cover design by Nicky Perry.
To
Fintan & Malachy
Foreword
Space matters. To answer Douglas Adams' question about life, the universe and everything, we need to detect and understand spatial patterns at different scales: how do they emerge, and how do they change over time? For most spatial patterns in social and environmental systems, controlled experiments on real systems are not a feasible way to develop understanding, so we must use models; but analytical mathematical models that address all relevant scales, entities, and interactions are also rarely feasible.
The advent of fast computers provided a new way to address spatial patterns at multiple scales: it became possible to simulate spatial processes and check whether or not our assumptions about these processes are sufficient to explain the emergence and dynamics of observed patterns. But then, as when any new scientific tool appears, results piled up quickly, perhaps too quickly, produced by thousands of models that were not related in any coherent or systematic way. There is still no general ‘theory’ of how space matters. Spatial simulation is thus similar to chemistry before the discovery of the periodic table of elements: a plethora of unrelated observations and partial insights, but no big picture or coherent theory.
This book sets out to change the current situation. The authors group spatial simulation models into three broad categories: aggregation and segregation, random walk and mobile entities, and growth and percolation. For each category, they provide systematic overviews of simple, generic models that can be used as building blocks for more complex and specific models. These building blocks demonstrate fundamental spatial processes and principles; they have well-known properties and thus do not need to be justified and analysed from scratch.
Using this book, model developers can identify building blocks appropriate for their own models. They can use the principles of model building and analysis that the book's opening and closing chapters summarize with amazing clarity. The authors demonstrate how all this works in a case study, in which a moderately complex spatial simulation model of island resource exploitation by hunter-gatherers is developed and analysed.
To facilitate the re-use of building blocks, this book itself is based on building blocks, using the free software platforms NetLogo (Wilensky1999) and R (R Development Core Team2012, Thiele and Grimm2010, Thiele et al.2012), which are widely used. All the models and R scripts are available on the internet as a model zoo, or model kit, for the spatial modeller. There (unlike at real zoos) you are invited to play with the zoo's specimens, and even to change and combine them!
This book helps establish a new culture of model building and use by reminding us that, as scientists, we need to see the forest through the trees and, with spatial simulation, the patterns in our explanations of spatial patterns. This book was badly needed. It makes us think, and play.
Volker Grimm, Helmholtz Centre for Environmental Research – UFZ, Leipzig
Preface
This book had its genesis in three ideas.
The first, hatched at the 2006 Spatial Information Research Colloquium (or more precisely on the flight back from Dunedin to Auckland), is that for all their seeming variety, there are really only a limited number of truly different spatial processes and models of them. This modest proposal came up in conversation when we realised that we have both become good at anticipating what spatial models will do when they are described at conferences or workshops, and in the research literature. This perhaps debatable insight, followed by extended periods of omphaloscopy (often over a beer), eventually led us to the three broad categories of spatial model (aggregation, movement and spread) whose presentation forms the core of this book. As will become apparent, the dividing lines between these categories are hardly clear. Even so, we think the approach is a valuable one, and we have come to think of these as ‘building-block’ models. It is a central tenet of this book that understanding these will enable model builders at all levels of experience and expertise to develop simulations with more confidence and based on solid conceptual foundations. Belatedly, we have realised that the building-block model concept has much in common with the notion of ‘design patterns’ in computer programming and architecture.
The second insight, gleaned from several years' teaching a class where we require students to develop a spatial model on a topic that interests them, is that we (the authors) had picked up a lot of practical and usable knowledge about spatial models over the years, but that that knowledge is not easily accessible in one place (that we know of). This realisation took some time to dawn. It finally did, after the umpteenth occasion when a group of students seeking advice on how to get started with their model were stunned (and sometimes a little grumpy) when the seeming magic of a few lines of code in NetLogo (Wilenksy, 1999) or R got them a lot further than many hours of head scratching had. Examples par excellence are the code for a simple random walk in NetLogo:
to step ;; turtle procedure move-to one-of neighbors4 end
or for a voter model:
to update ;; patch procedure set pcolor [pcolor] of one-of neighbors4 end
It is easy to forget how much hard-earned knowledge is actually wrapped up in code fragments like these. Having realised it, it seemed a good idea to pass on this particular wisdom (if we can call it that) in a palatable form. The numerous example models at http://www.patternandprocess.org that accompany this book aim to do just that. A closely related motivation was the steady accumulation of fragments of NetLogo in a folder called ‘oddModels’ on one of our hard drives: ‘Surely’, we thought, ‘there is some use to which all these bits and pieces can be put?!’
Finally, while the building-block models that are our central focus are in some senses simple, they are deceptively so. In that most understated of mathematical phrases, these models may be simple, but they are ‘not trivial’. The thousands of papers published in the technically and mathematically demanding primary literature in mathematics, physics, statistics and allied fields attest to that fact. Unfortunately, this also means that students in fields where quantitative thinking is sometimes less emphasised—such as our own geography and ecology, but also in archaeology, architecture, planning, epidemiology, sociology and so on—can struggle to gain a foothold when trying to get to grips with these supposedly simple models. From this perspective we saw the value in presenting a more accessible point of entry to these models and their literature. That is what our book is intended to provide.
The jury remains out on just how many building-block models there are: our three categories are broad, but we are painfully aware that our coverage is necessarily incomplete. Reaction–diffusion systems and network models of one kind or another are significant omissions. The relatively demanding mathematics of reaction–diffusion models is the main reason for its absence. And because networks are about spatial structure, rather than spatial pattern per se, and to avoid doubling the size of an already rapidly growing book, we chose not to fill that gap, albeit with reservations. Perhaps as ‘network science’ continues to mature we can augment a future edition. At times, we also wondered if there might be only one spatial model (but which one?). In the end, we decided that there are already enough (near) incomprehensible mathematical texts staking claim to that terrain, and that our intended audience might not appreciate quite that degree of abstraction. Our more modest second and third ideas are, we hope, borne out by the book and its accompanying example models. Ultimately, how well we have delivered on these ideas is for readers to decide.
David O'Sullivan and George Perry School of Environment and School of Biological Sciences University of Auckland—Te Whare Wnanga o Tmaki Makaurau
August 2012
Acknowledgements
Any book is the product of its authors and a dense web of supporting interconnected people and institutions. Professionally we have benefited from a supportive environment at the University of Auckland. Research and study leave grants-in-aid in the first half of 2012 for both authors were vital to the timely completion of the manuscript.
David O'Sullivan is thankful to colleagues at the University of Tokyo who hosted a Visiting Professorship at the Center for Spatial Information Science from April to June 2012. He extends particular thanks to the Center's director Yasushi Asami; to Ryusoke Shibasaki, Yukio Sadahiro, Ikuho Yamada, Yuda Minori, Ryoko Tone and Atsu Okabe for making the visit such a rewarding one; and to Aya Matsushita for ensuring that all the administrative arrangements were handled so efficiently.
George Perry was fortunate enough to receive a Charles Bullard Fellowship, which enabled him to spend seven months working at Harvard Forest; this was an immensely rewarding time, both personally and professionally, and gave him time and space to think about and develop material in this book. Thanks to all the people at Harvard Forest who helped make his time there so productive and enjoyable. Over the last 15 years GP has spent considerable time working with colleagues at the Helmholtz Zentrum für Umweltforschung (UFZ) in Leipzig on various projects. Interactions with people there, especially Jürgen Groeneveld, have coloured his thinking on models and model-making. GP has also received funding from the Royal Society of New Zealand's Marsden fund and from the NSF (USA), ARC (Australia) and the NERC (UK)—the research that this funding enabled has contributed to his views on models and modelling.
We have been ably assisted at Wiley by Rachael Ballard, Jasmine Chang, Lucy Sayer and Fiona Seymour. We are both grateful for supportive noises and comments from many colleagues, and particularly to Mike Batty, Ben Davies, Steve Manson, James Millington and students in the ENVSCI 704 class of 2012 for insightful comments on late drafts of various parts of the manuscript. Iza Romanowska spotted what would have been an embarrassing error at a late stage, for which we are grateful. We are grateful to Volker Grimm for his kind words in the foreword. His work is a constant inspiration, and if this book delivers on even a few of the claims he makes on its behalf, we will consider it a roaring success! Conversations with many colleagues and students have improved the text at every turn. Any errors that remain are, of course, our own.
And finally, to those who have borne the brunt of it, our families: from David, heartfelt thanks to Gill, Fintan and Malachy for putting up with an often absent(-minded, and in body) husband and father for so long; and from George, to Nicky, Leo and Ash, for tolerating my peripatetic wanderings as I finished this book, thank you, arohanui, and I look forward to getting back to building hardware models with you!
Introduction
On the face of it, the literature on ‘spatial modelling’—that is models that represent the change in spatial patterns through time—is a morass of more or less idiosyncratic models and approaches. Likewise at first glance, the great diversity of observed spatial patterns calls for an equally wide range of processes to explain them. Ball (2009) provides a useful classification of the patterns in natural and social systems.
Our view, and the perspective of this book, is that just as there is a manageable number of spatial patterns, and it is useful to classify them, a relatively small suite of fundamental spatial process models are useful in exploring these patterns' origins. These models we consider to be ‘building-blocks’, which when thoughtfully combined can provide a point of departure for developing more complicated (and realistic) simulations of a wide variety of real-world phenomena. As Chesson (2000, page 343) notes, albeit in a different context, ‘The bewildering array of ideas can be tamed. Being tamed, they are better placed to be used.’ We aim to show how building-block models can help to accomplish this task in the context of spatial simulation.
Organisation of the book
Here we set out the general plan of this book to assist readers in making best use of it. Broadly, the material is organised into three parts as follows:
Finally, Chapter 9 concludes with a brief summary of the book's main themes.
Using the book
This book could form the basis for several courses with different emphases in several fields. Our own jointly taught course ‘Modelling of Environmental and Social Systems’ has been taken by students of geography, ecology, environmental science, environmental management, biology, bioinformatics, archaeology, transport and civil engineering, psychology, statistics and chemistry, among others. While we believe that building-block models have a broad and general applicability, not all of the ground that we cover will be suitable for all these disciplines. Nevertheless, we hope that even if it is not the core text this book will be a useful addition to reading lists in courses in all of these fields. We also hope that the book will be a useful resource for those researchers making their first steps in spatial modelling outside the confines of a traditional course.
There are multiple pathways through this book depending on the context in which it is being read, and the reader's background and interests. In some situations, it might make sense to fill in the background in a little more detail than Chapters 1 and 2 allow, and also to cover Chapter 6 before approaching the building blocks themselves. Alternatively, it may make sense to just dive in and postpone the ‘preliminaries’ until after some models have been sampled in Chapters 3 to 5. For some readers the context will make more sense after some examples have been absorbed. Last, but certainly not least, Chapters 7 and 8 will invariably make most sense with all the other material already absorbed. For some readers Chapter 7 may be rather more demanding than the earlier material but we firmly believe that there is more to spatial modelling than appealing animations. If we are to make robust inferences about real systems using spatial models then we need to evaluate them rigorously, and this is what the tools introduced in Chapter 7 allow.
The literature on each of the building-block model areas is massive and growing rapidly, and it was not our intention to exhaustively review it. In a book of this size in places our treatment is necessarily limited, but we hope that any chapter of the book can provide a good point of entry to the literature for graduate seminars, reading groups or individual study.
Using the example models
This book is accompanied by many freely downloadable NetLogo (Wilensky, 1999) implementations of the models described in the text. The models can be found at http://patternandprocess.org. All of these models are released under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. Most of the figures were directly generated from these models using the excellent NetLogo-R extension described by Thiele and Grimm (2010). The analyses we present were all conducted using the freely available R environment (R-Development-Core-Team, 2012), some taking advantage of the RNetlogo library (Thiele et al., 2012) which allows NetLogo to run within R and so takes advantage of the latter's analytical capabilities.
How these models are used is up to the reader. We learned a lot writing them, and we trust that experimenting with them and examining the code will be a useful adjunct to the main text, and one that helps circumvent the difficulty of conveying inherently dynamic things on a static page. The point at which each model is discussed in the text is identified by a marginal turtle icon. We suggest that readers download the model in question when they first encounter it, and experiment with its behaviour while reading the associated text. It should be possible to reproduce patterns similar to those shown in the figures that accompany the discussion of each model. Examination of the code should clarify any ambiguity over the definition of the model. It should also provide ideas for how to implement the model, and its variants, in NetLogo or other platforms.
About the Companion Website
This book is accompanied by a companion website:
The website includes:
Powerpoints of all figures from the book for downloading
PDFs of tables from the book
Chapter 1
Spatial Simulation Models: What? Why? How?
It is easy to see building and using models as a rather specialised process, but models are not mysterious or unusual things. We routinely use models in everyday life without giving them much thought, if any at all. Consider, for example, the word ‘tree’. We may not exactly have a ‘picture in our heads’ when we use the word, but we could certainly oblige if we were asked to draw a ‘tree’. The word is associated with some particular characteristics, and we all have some notion of the intended meaning when it is used. In effect, everyday language models the world, using concrete nouns, as a wide variety of categories of thing: cats, dogs, buses, trains, chairs, toothbrushes and so on. We do this because if we did not, the world would become an unfathomable mess of sensory inputs that would have to be continually and constantly untangled in order to accomplish even the most trivial tasks.
If you are reading this book, then you are already well-versed in using models in the language that you use everyday. We define scientific models as simplified representations of the world that are deliberately developed with the particular purpose of exploring aspects of the world around us. We are particularly concerned with spatial simulation models of real world systems and phenomena. Our aim in this book is to help you become as comfortable with consciously building and using such models as you are with the models you use in everyday language and life.
This aim requires us to address some basic questions about simulation models:
What are they?
Why do we need them and use them?
How can (or should) we use them?
It is clearly important in a book about simulation models and modelling to address these questions at the outset, and that is the purpose of this chapter.
The views we espouse are not held by every scientist or researcher who uses models in their work. In particular, we see models as primarily exploratory or heuristic learning tools, which we can use to clarify our thinking about the world, and to prompt further questions and further exploration. This view is somewhat removed from a more traditional perspective that has tended to see models as primarily predictive tools, although there is increasing realisation of the power of models as heuristic devices. As we will explain, our view is in large measure a product of the types of system and types of problem encountered in the social and environmental sciences. Nevertheless, as should become clear, this perspective is one that has relevance to simulation models as they are used across all the sciences, and becomes especially important when scientific models are used, as increasingly they are, to inform critical decisions in the policy arena.
After dealing with these foundational issues, we briefly introduce probability distributions. Our goal is to show that highly abstract models, which make no claim to realism, may nevertheless still be useful. It is also instructive to realise that probability distributions are actually models of a specific kind. Understanding the strengths and weaknesses of such models makes it easier to appreciate the role of more detailed models that take realism seriously and also the costs borne by this increased realism. Finally, we end the chapter by making a case for the more complicated dynamic, spatial simulation models that are the primary focus of this book.
1.1 What are simulation models?
You may already have noticed that we are using the word ‘model’ a great deal more than the word ‘simulation’. The reason for this will become clear shortly, but in essence it is because models are a more generic concept than simulations. We consider the specific notion of a simulation model in Section 1.1.5, but focus for now on what models are.
The term model is a difficult one to pin down. For many, the most familiar use of the word is probably with reference to architectural or engineering models of a new building or product design. Until relatively recently, most such models were three-dimensional representations constructed from paper, wood, clay or some other material, and they allowed the designer to explore the possibilities of a proposed new building or product before the expensive business of creating the real thing began. Such ‘design models’ are often built to scale, necessitating simplification of the full-size object so that the overall effect can be appreciated without the finer details becoming too distracting. Contemporary designers of all kinds generally build not only physical models but computer models, using computer-aided design (CAD) software to create virtual models that can be manipulated and explored interactively on screen. Design models then, are simplified representations of real objects that are used to improve our understanding of the things they represent. The underlying idea of model building of this kind is shown in Figure 1.1. An important idea is that more than one model is likely to beuseful.
Figure 1.1 Schematic illustration of the concept of models. Models simplify the real world, enabling manipulation, exploration and experimentation, from which we aim to learn about the real world. Photograph from authors' collection.
Scientific models perform a similar function—and follow the same general logic of Figure 1.1. Therefore, for our purposes, we define a scientific model as
a simplified representation of a system under study, which can be used to explore, to understand better or to predict the behaviour of the system it represents
The key term in this definition is ‘simplified’. In most scientific studies there are many details of the phenomena at hand that are irrelevant from the particular perspective under consideration. When we are tackling the transport problems of a city, we focus on aspects that matter, such as the relative allocation of resources for building roads relative to those for public transport infrastructure, the connectivity of the network and how to convince more people to car-pool. We do not concern ourselves with the colours of the cars, the logos on the buses or the upholstery on the subway seats. At the level at which we are approaching the system under study some components matter and others are irrelevant and may be safely ignored. The process of model development demands that we simplify from the often bewildering complexity of the real world by deciding what matters (and what does not) in the context of the current investigation. An important consequence of this simplification process, as George Box succinctly points out, is that, ‘[m]odels, of course, are never true’ (Box, 1979, page 2). Luckily, as Box goes on to say, ‘it is only necessary that they be useful’.
1.1.1 Conceptual models
The first step in any modelling exercise is the development of a conceptual model. All scientific models are conceptual models, and a particular conceptual model can be given more concrete expression as any of the distinct types discussed below. Thus, developing a conceptual model is fundamental to the development of any scientific model. Approaching the phenomenon under study from a particular theoretical perspective will bring a variety of abstract concepts into play, and these will inform how the system is broken down into its constituent elements in systems analysis.
In simple cases, a conceptual model might be expressible in words (‘if parking costs more, fewer people will drive’), but usually things are more complicated and we need to consider breaking the phenomenon down into simpler elements. Systems analysis is a method by which we simplify a phenomenon of interest by systematically breaking it down into more manageable elements to develop a conceptual model (see Figure 1.2). A critical issue is the desired level of detail. In the case shown, depending on our interests, a forest might be simplified or abstracted to a single value, its total biomass. A more detailed model might break this down into the biomass stored in trees and other plant species, with a single submodel representing how both categories function, the difference between trees and other plants being represented by differences in attribute values. A still more detailed analysis might consider individual species and develop submodels for each of them. The most appropriate model representation is not predetermined and will depend on the goals of the model-building exercise. In this case, a focus on carbon budgets may mean that the high-level ‘biomass only’ model is most appropriate. On the other hand, if we are concerned about the fate of a particular plant species faced with competition from invasive weeds, then a more detailed model may be required.
Figure 1.2 The systems analysis process. A real-world phenomenon is broken down into components, their attributes, how they interact with one another and how they change via process relationships. A particular phenomenon might be represented and analysed in a variety of ways, with the desired level of realism or, conversely, abstraction a key issue.
In the systems analysis process, we typically break a real-world phenomenon or system down into general elements, as follows:
Thus, a conceptual model of a system will consist of components, state variables, processes and interactions, and taken together these provide a simplified description of the phenomenon that the model represents.
A common way to represent a model is using ‘box and arrow’ diagrams, a format that will be familiar from numerous textbooks. Interactions between system components are represented as arrows linking boxes. We might add + or − signs to arrows to show whether the relationship between two components is positive or negative (as has been done in Figure 1.2). It is then only a short step from the conceptual model to a mathematical model where component states are represented by variables and the relationships between them by mathematical equations. As with design models, the advent of widely available and cheap computing has seen the migration of such mathematical models onto computers. The relationships and equations governing the behaviour of a model are captured in a computer model or simulation model. The simulation model can then be used to explore how the system changes when assumptions about how it works or the conditions in which it is set are altered. In practice the most appropriate way to represent a system will depend on the purpose of the modelling activity, and so there are many different model types. Although this book's focus is on spatially explicit mathematical and simulation models, it is important to recognise that many different approaches to modelling are possible. We consider a few of these in more detail in the sections that follow.
As we have already suggested, conceptual models can be represented in a variety of ways. Simple models may be described in words perfectly satisfactorily. Newton's three laws of motion provide a good example. The third law, for example, can be stated as: ‘for every action there is an equal and opposite reaction’. Even very complicated models can be described in words, although their interpretation may then become problematic, and it is debatable how sensible it is for such models to remain as solely verbal descriptions. Nevertheless, in many areas of the social sciences, verbal descriptions remain the primary mode of representation, and extremely elaborate conceptual models are routinely presented in words alone (give or take the occasional diagram), at book length. The work of political economists such as Karl Marx and Adam Smith provides good examples. Partly as a consequence, the interpretation of these theories remains in dispute, although it is important to acknowledge that the subsequent mathematisation of economic theory through the twentieth century has not greatly reduced the interpretative difficulties: however we represent them, complicated models remain complicated and open to interpretation.
Even so, verbal descriptions of complicated conceptual models have evident limitations. As a result many conceptual models are presented in graphical form, with accompanying explanation. As we have noted, it is a short step from graphical representation to the development of mathematical models, and the success since Newton's time of those physical sciences which adopted mathematical modelling as a tool has been a persuasive argument in other disciplines for the adoption of the approach.
1.1.2 Physical models
We began by briefly touching on the three-dimensional scale models often used by design professionals. Physical or hardware models are also occasionally used in the sciences, and in engineering. Wave tanks can be used to simulate coastal erosion and wind tunnels to investigate turbulence around aerofoils or the aerodynamics of vehicles. Hardware models can provide guidance about a system's behaviour when that system is not sufficiently understood for mathematical or computational models to provide reliable guidance. Careful scaling of the model system's properties or extrapolation from the model to the target system is necessary for this approach to work well. For example,the grain size of sand in a hardware model of a beach must be carefully considered in combination with the wave heights and speeds if the results from a flume are to be applicable to real beaches. Rice et al. (2010) provide a good summary of the potential value of this approach in the specific context of river science, where they show how it can be used to relate stream hydraulics to stream ecology.
A highly specific kind of ‘hardware’ model is the use of laboratory animals in medical research, where mice or rats or fruit flies are considered ‘model’ organisms for aspects of animal biology in general. Similar to flumes or wind tunnels, this use of models recognises that our ability to mathematically model whole organisms remains limited at present, and for the foreseeable future, and these models provide an alternative. Even setting ethical issues to one side, the difficulties of generalising from findings based on such models are apparent.
An interesting hardware model of a different kind is provided by the hydraulic model of a national economy built by the economist Bill Phillips while he was a student at the London School of Economics (Fortune Staff, 1952). The so-called MONIAC (MOnetary National Income Analogue Computer) used a system of reservoirs and pipes to represent flows of money circulating in a national economy. Flow rates in different pipes in the system were adjusted to represent factors such as the rate of income tax. Several MONIAC machines were built and working examples are maintained by the Science Museum in London and by the Reserve Bank of New Zealand (Phillips was a New Zealander). While this may seem a strange way to model an economy, Phillips would have been well aware that his hydraulic model was a representation of an underlying conceptual and mathematical model.
1.1.3 Mathematical models
The MONIAC example points us towards mathematical models, the most widely adopted approach to scientific modelling. In a mathematical model, the state of the system components is represented by the values of state variables with equations describing how the state variables change over time. Newton's Second Law of Motion is a straightforward example, where the equation
1.1
tells us that the velocity v of an object changes at a rate proportional to the net force on it, , and in inverse proportion to its mass, . Since Newton's time, many laws of physics governing the basic behaviour and structure of matter have been found to be well approximated by relatively simple mathematical equations not much more complicated than Newton's Second Law. Perhaps the best-known example is Einstein's celebrated concerning the relationship between energy, , mass, , and the speed of light, .
Such equations are simple mathematical models but taken in isolation they do not tell us much about the dynamic behaviour of systems. If we decompose a system into a number of interacting components, and equations representing the interactions can be established, then we have a mathematical model in the form of a system of simultaneous equations describing the system's state variables. This mathematical model can be used to explore how the state variables will change over time and through space, and how different factors affect overall system behaviour. How the necessary equations are determined depends on the nature of the system. The most productive approach over time has usually been the experimental method, where the relationships between different variables are determined by setting up laboratory experiments in which key system variables are carefully manipulated while others are held fixed, so that the independent effects of each can be determined. Experiments can be deliberately constructed to explore expected or hypothesised relationships between system variables. When the expected relationships are found not to hold, hypotheses are adjusted and new experiments designed, and over time a clear picture of the relationships between system variables emerges.
1.1.4 Empirical models
In an experiment, we artificially close the system under study so that only the single effect of interest is ‘in play’. However, many systems, such as ecosystems or social systems, cannot be experimentally closed. In these situations, classic experimental methods are problematic. An alternative approach is to make empirical observations of such systems and to use quantitative methods to construct an empirical model of the relationships among the system variables. Such models are generally statistical in nature, with regression models the most widely used technique. An example of this approach is hedonic price modelling of real estate markets, where the sale price of housing is modelled as an outcome of a collection of other variables, such as floor area, date of construction, number of bedrooms and so on (Malpezzi2008, provides a review of the approach). A statistical empirical model might show that other things being equal the sale price of larger houses is higher than that of smaller houses.
In empirical models, meaningful interpretation of observed statistical relationships can be challenging. In some cases, interpretations will be obvious and well-founded (for example larger houses attract higher prices becausepeople are happy to pay more for extra space) but in others the mechanisms will be less obvious and interpretation may be controversial. It is particularly challenging to handle interaction effects among variables. In the case of house prices, an interaction effect would be an association between proximity to the central city and land parcel sizes. This might make it appear that small parcels are more expensive than larger parcels, when it is actually the more central location of smaller parcels that leads to the observed relationship between parcel size and price.
There are many examples of empirical models where interpretation is problematic, particularly in the social sciences. For example, what are we to make of findings relating different rates of gun-ownership in various US states to crime rates? Many interpretations are possible (and are offered), and the observed empirical relationships can only be linked back to underlying processes via long chains of argument and inference, which are not as readily tested as is possible in the experimental sciences. Such concerns have led to considerable dissatisfaction with empirical models (see, for example, Sayer, 1992, pages 175–203). The root of the problem is that empirical models do not consider the mechanisms that give rise to the observed relationships.
Nevertheless, in cases where the causal mechanisms remain poorly understood, empirical models can provide useful starting points for the development of ideas. We have a more or less stable empirical relationship: the question is why? As a result, and also due to the numerous statistical tools available for their development, empirical models are the most common type of model across the sciences, other than the ubiquitous conceptual model.
1.1.5 Simulation models
Whether experimentally, empirically or theoretically derived, quantitative relationships among the state variables in a system can be used to build a simulation model. In a simulation model, a computer is programmed to iteratively recalculate the modelled system state as it changes over time in accordance with the relationships represented by the mathematical and other relationships that describe the system.
The most widely used simulation models are systems dynamics models. Systems dynamics models consist of essentially three types of variable: stocks, flows and parameters:
Systems dynamics models are effectively computer simulations of mathematical models consisting of interrelated differential equations, although they often also include empirically derived relationships and semi-quantitative ‘rules’. The predator–prey model in Figure 1.3 is a typical, albeit simple, example. Note that many of the probable relationships in a real predator–prey system are deliberately omitted from the model, for example the predator might have other potential food sources whose availability affects the level of predation. Phillips's MONIAC model referred to in Section 1.1.3 was a systems dynamics model of a national economy simulated using reservoirs and plumbing rather than a computer. The diagrammatic representation of systems dynamics models (see Figure 1.3) closely reflects the basis of such models in mathematical models of physical systems.
Figure 1.3 A simple systems dynamics model of the interaction between predator and prey species. Boxed variables are stocks, double-width arrows with ‘valve’ symbols are flows, clouds represent everything outside the system, and other named items are parameters. Arrows indicate where a relationship exists between variables.
While systems dynamic models are among the most widely used type of simulation model, many other model types and variations are possible. Of particular interest in this book are spatially explicit models, where we decide that representing distinct spatial elements and their relationships is important for a full understanding of the system. Thus, a spatially explicit model has elements representing individual regions of geographical space or individual enities located in space (such as trees, animals, humans, cities and so on). Each region and entity has its own set of state variables and interacts continuously through time with other regions and entities, typically interacting more strongly with those objects that are nearest to it. These interactions may be governed by mathematical equations, by logical rules or by other mechanisms, and they directly represent mechanisms that are thought to operate in the real-world system represented by the simulation.
The simplest way to think of the relationship between models and simulations is that simulations are implementations, usually in a computational setting, of an underlying conceptual or mathematical model. Simulation is often necessary because detailed analysis of the model is difficult or impossible, or because simulation allows convenient exploration of the implications of the model. Because any simulation implements an underlying model, most of the time in this book we discuss models rather than simulations. In each case discussion of the models and understanding of their properties is only possible because we have built a simulation of the model.*Winsberg (2009a) provides a useful account of the role of simulation in science that clarifies both the distinction and the close relationship between models and simulations.
1.2 How do we use simulation models?
Some of the reasons for using simulation models have already been mentioned in passing. Here we expand on these ideas and present the perspective on the role of simulation models in research in which this book is grounded. The critical issue is that not all models are created equal. Figure 1.4 shows in schematic form how two critical aspects of any phenomenon, the data we have available and how well we understand it, affect our ability to use simulation models for different purposes.
Figure 1.4 How data and understanding affect the use of models, with indicative fields of study (after Starfield and Bleloch, 1986). Note that the locations of different fields in the figure are suggestive only. See text for details.
Systems for which we have reliable, detailed data and whose underlying mechanisms we understand well are the ones most suitable for predictive modelling. Engineered systems such as bridges, cars, telephones and so on are good examples. We have a thorough understanding of how they work, and we have abundant and reliable data based on previous experience with using such systems. In this context, using models for prediction is worthwhile. However, in many cases we lack reliable, detailed observational data, even if we have a reasonable grasp of the underlying processes. For example, animal population dynamics are relatively well understood in general terms, but detailed rich datasets are scarce, especially for long-lived organisms. In this context, prediction is more problematic, and the best use for models may be to inform us about where critical data shortages lie. On the other hand, there are an increasing number of areas where we now have access to detailed data, but still have a poor understanding of how the system works, global financial markets being a prime example (May et al., 2008). Here, using models to help in developing theories may be appropriate. Finally, there are many fields where both the available data and current levels of understanding are poor. Here, the best prospect may be to use models as devices for learning, which may inform the development of theory and also steer us towards the areas of most pressing need for better data.
1.2.1 Using models for prediction
It is generally not long after a simulation model is presented to an interested audience before someone asks something like: ‘So what is Auckland going to look like 25 years from now?’ or ‘So are polar bears going to survive climate change?’ or any number of other questions about the future that are of interest. It is understandable that researchers, policy-makers and the public in general are interested in using simulation models to predict the future. After all, ‘real’ sciences make reliable predictions. Arguably, it was the advent of reliable predictions of the tides, seasons and planetary motion that began the human species' rise to dominance of life on Earth. Added to this, the ability of engineers to confidently predict the behaviour of the systems they design has enabled rapid technological progress over the last few centuries. Both kinds of prediction ultimately rely on scientific models. But there are good reasons to be wary of seeing models primarily as predictive tools.
We have already suggested that lack of data or of good understanding of the field in question are reasons for being cautious about prediction. If there are deficits in either dimension, it is quite likely that prediction will do more harm than good, although in such cases, it may not be prediction per se that is the problem. Placing unwarranted faith in inherently uncertain predictions is as likely to lead to ill-founded decision-making as having no predictive tools available at all. More circumspect approaches that consider alternative scenarios and possible responses to allow better-informed decision-making are usually a more appropriate way forward than blind faith in predictive models (see Coreau et al., 2009, Thompson et al., 2012). We consider aspects of the uncertainty around model outcomes in more detail in Chapter 7.
It is also important to be wary of the prospects for prediction in contexts where although individual elements are well understood, the aggregation of many interacting elements can lead to unexpected nonlinear effects. Perhaps the most important examples in this context are technological networks of various kinds. Here, individual system elements are designed objects, whose individual behaviour is well known. In many such networks, we also have good data on overall system usage and patterns. Nevertheless the nonlinear systems effects discussed in Section 1.3.2 have the capacity to surprise us, and there is an important role for modelling in improving our understanding of such systems (see, for example, O'Kelly et al., 2006).
1.2.2 Models as guides to data collection
Where the most pressing deficits in our knowledge of systems are empirical, so that we lack good observational data about actual behaviour, the most important role for models may be to help us decide which data are most critical to improving our understanding. Assuming that adequate models of the underlying processes in such situations can be developed, then we can perform sensitivity analysis (see Section 7.3.2) on the models to find out which parameters have the strongest effect on the likely outcomes. Once we know which data are most essential to improving our ability to forecast outcomes more reliably, we can direct our data collection energies more effectively.
Good examples of this sort of application of models are provided by animal conservation efforts. For endangered animals we may not have reliable data on their populations, but we do have good general frameworks for modelling population dynamics (for example Lande et al., 2003). Applying such models to endangered species with best guess estimates of critical parameters and the associated uncertainties may help conservation workers to target future data collection on the critical features of the system, and also to design improved management schemes. Unfortunately, population models applied to fisheries over recent decades provide depressing evidence of how important this is: arguably too much faith in the predictive capacity of models, and ignoring uncertainties in the models and the data used to inform them, has left many fisheries in a worse state than they may otherwise have been (see Clover, 2004, Pilkey and Pilkey-Jarvis, 2007).
1.2.3 Models as ‘tools to think with’
In some cases there is no shortage of empirical data, but we have limited understanding of how a system works. The advent of sensor technologies of various kinds—remote-sensing platforms being the most obvious, but more recently including phenomena such as volunteered geographic information (Haklay et al., 2008)—has created a situation where we may have vast amounts of empirical data (Hilbert and López, 2011), but no clear idea of what it tells us. While data-mining methods may offer some relief in these situations (Hilbert and López, 2011) and provide at least candidate ideas about what is going on, science without theory is an unsatisfactory approach.
In this situation, simulation models can become ‘tools for thought’ (Waddington, 1977). In this approach we use simulation models that represent whatever working hypotheses we have about the target system and then experiment on the model to see what the implications of those theories and hypotheses might be in the real world (see Dowling, 1999, Edmonds and Hales, 2005 and Morrison, 2009). This turns the traditional hypothetico-deductive approach to science on its head. In deductive science, we make observations of the world and then evaluate hypotheses that could explain those observations. We then make controlled experimental observations to decide if our hypotheses provide adequate explanations of the observations. When we experiment on models by simulation, we effectively explore what the implications of various possible hypotheses would be. Observation of model behaviours and comparison of those behaviours with real-world observations of the target system may then allow us to dismiss some hypotheses as implausible and so refine our theories. Some authors refer to this approach as science in silico (see, for example, Epstein and Axtell, 1996, Casti, 1997).
This is not an easy approach. In particular, it is beset by the equifinality problem, which refers to the fact that large numbers (in fact an infinite number) of possible models, including the same model with different input data, could produce behaviour consistent with observational data. In other words identifying the processes responsible for a given pattern, on the basis of that pattern alone, is problematic. This makes problems of model selection and inference acute for anyone adopting this approach. We consider some of these issues in more detail in Section 7.6, where we consider pattern-oriented modelling, which may be particularly suited to making inferences with spatially explicit models (Grimm et al., 2005, Grimm and Railsback, 2012).
In sum, the proper role of simulation models in advancing our understanding of the world and the consequent variety of their uses is complicated and heavily dependent on the nature of the systems under study and on the current state of empirical and theoretical knowledge about them. As is often the case, it is sensible to be flexible and pluralistic in outlook, using models as one tool among many in a mixed methods approach.
1.3 Why do we use simulation models?
Simulation models are a relatively recent addition to the scientific toolbox, and the reasons for their widespread adoption call for some explanation. Broadly speaking, we believe there are three reasons that scientific research based on simulation modelling has become so prevalent in recent decades. The first is obvious and quickly dealt with: simply that this approach has now become possible. Cheap, widely available computing, although it appears commonplace from the vantage point of the early twenty-first century, is a historically recent development. The electronic computer was invented towards the end of the Second World War, and the desktop personal computer only appeared towards the end of the 1970s, and was not widely available until a decade after that. In the same way that widely available computing power has changed society generally, we might also expect it to have changed aspects of scientific practice, and simulation modelling is an example of such change.
However, given the success of science before simulation models, a better answer to the question ‘Why use simulation models?’ than ‘Because we can!’ is surely necessary. This leads us to two further reasons: the difficulty of experimental science in many fields of enquiry and the realisation that many systems are nonlinear.
1.3.1 When experimental science is difficult (or impossible)
The experimental method of science has proved to be extremely successful at systematically extending our understanding of the world. However, it is not always recognised that the success of the experimental method relies on certain features of the systems under study.
Some systems of interest to social and environmental scientists are not amenable to experiment for rather prosaic reasons. Archaeologists, anthropologists and palaeontologists are interested in systems that no longer exist. Climate scientists are interested in a system that is effectively the whole of the terrestrial, atmospheric and oceanic system, and hence not controllable in any meaningful sense. In many fields, such as forest ecology or geology, the time horizons of interest are too long for experiments to be practical.
Other limitations to experiment relate to the nature of the systems themselves.The most obvious consideration is that experiments only produce conclusive evidence when they are closed systems
