Individual- or Agent-Based Models

Contents of this page

Introduction
Dynamic ecosystem models
Individual-based models
Agent-based models
Functional-structural models
Conclusion


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Introduction

The next three sections give an outline of the conceptual roots from which UIBM is grown.
This section opposes the ecosystem modeling paradigm to the individual-based or - more generally speaking - to the agent-based modeling paradigm. Moreover, it highlights how the ladder may overcome limitatons of the futher with respect to modeling biodiversity.
At the end of this section special attention is given to functional-structural models, which provide imortant concepts for dealing with competition in biodiversity models.


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Dynamic ecosystem models

Since the pioneering work of the US-American ecologists Eugene P. Odum (Odum EP 1959) and Howard T. Odum (Odum HT 1994) in quantifying ecosystem matter and energy flows, ecosystem ecology and, with it, dynamic ecosystem odels have developed into the mainstream of the ecological discipline.
To understand the key characteristics and major limitations of this kind of models, I think one has to go back to their roots, which lie in the "System Dynamics" of Jay W. Forrester (Forrester 1971, MIT System Dynamics Group) and, therefore, in economy rather than in ecology.
System dynamics (SD) is a process for modeling complex systems top-down and from aggregate components (Introduction to System Dynamics on the Introduction to System Dynamics on the System Dynamics Society webpage). Part of System Dynamics is an icon-based computer language for model construction from the building blocks of stocks, flows and others (original tool: DYNAMO; widely used successor software: STELLA).
To fill this definition with understanding it might be best to use an example: The SD model I chose for this purpose is Forrester's World_2 model (1971) in a NetLogo implementation done by Gilbert & Troitzsch (2005).
As usual in SD, the modeling process begins with a problem, in this case a serious problem scientists became aware of in the 1960s: To what kind of future world system dynamics leads the "paradoxon" of the current exponentially growing human population and the assumed limited resources of the future?
The problem, in the form I have stated it, includes already major assumptions and some of the aggregate components or, say, stocks Forrester used in building his world model, whose system diagram is shown in Figure 6.


Fig. 6: World_2 model. A NetLogo reimplementation of Forrester's model done by Nigel & Gilbert (2005)



In accordance with Forrester's severe warnings not to build too complex models World_2 is rather the essence of a "mental model" of the system and very simple, though. The state of the system is comprised of merely 5 stocks or, in other words, reservoirs: Population, Resources, Pollution, Capital Investment and Fraction of Capital Investment In Agriculture. All stocks have inflows and outflows except for Resources, which have only a consuming outflow under the given assumptions (see above).
As illustrated in Figure 7 using a simple STELLA example, the system diagram is internally translated into a system of differential equations, which the computer solves numerically by approximating them using finite difference equations of the kind "stock level (t) = stock level (t - delta_t) + input x delta_t - output x delta_t, where t = time".


Fig. 7: Example STELLA model. System diagram and its translation into procedural code with a system of finite difference equations



However, besides stocks and flows the World_2 model contains numerous converters (displayed as circles), holding auxilliary variables, and connectors, i.e. arrows indicating on which components the converters exert an influence. In principle, these elements glue the stocks/flows together to a whole system, thereby giving rise to feedback loops. Remarkably, the whole as well as the aggregated state variables are defined on the world level and no breakdown into regions with possibly distinct behavior has been performed.
Figure 8 displays a chart of a World_2 simulation run. Under the constraints of more and more limiting resources the world population is predicted to reach a maximum of 5,295,824,000 in the year 2020 - a development which will entail dramatic consequences (Meadows 1972).
However, the world population as of today (28th of December 2009, World population, Wikipedia) has already reached 6,792,800,000 and is projected to rise to 9,149,984,000 until 2050 in the medium variant of the UN World Population Prospects: The 2008 Revision.


Fig. 8: Historical chart of a World_2 model run. 



System Dynamics used to be very influential to ecosystem ecology as these examples suggest: Because of his interest in material and energy flows H.T. Odum & E.C. Odum (2000) have implemented a systems diagram language of their own in Extend: the energy systems diagram language (Odum HT 1994). R. Costanza, one of the founders of Ecological Economics, and A. Voinov have embedded the DYNAMO successor STELLA in their GIS-based landscape simulation environment (Costanza & Voinov 2004).
The SD modeling concepts, however, have actually penetrated all subdisciplines of ecology.


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Individual-based models

Individual-based models (IBM) simulate the life-cycle of individual plants. In their 1988 published paper "New computer models unify ecological theory" Huston, De Angelis & Post unveiled their vision of future individual-based modeling, which I will quote here:




The vision, in principle, pursues the bottom-up approach of IBMs and elegantly describes the consequences at each scale while moving upwards from the individual. This seems to be the most natural way of thinking about ecological processes to me, as well.
Indeed, the number of studies which applied individual-based models has rapidly increased since then. The original article as well as the book published four years later (DeAngelis & Gross 1992) already presented results of a large collection of case studies, which gave insights beyond traditional ecological knowledge. With the Across-Trophic-Level System Simulation (ATLSS) DeAngelis initiated a large research program ained at implementing IBMs to the Everglades.
Individual-based tree growth models of the JABOWA, FORET, SORTIE model family were the first to break through the Plant Functional Type threshold and reach the species level - an important step in biodiversity modeling. It was fascinating to watch shifts in species' abundances over 1,000 years of succession following a clear-cut (Deutschman et al. 1997).
But has IBM fulfilled the promise, metaphorically speaking, "that the broken soul of ecology will be remade by the individual-based formalism"?
Grimm (1999, cited in Grimm & Railsback 2005) adressed this question. As pointed out in "Individual-Based Modeling and Ecology" (Grimm & Railsback 2005, pp. 17-18, all citations are omitted) the conclusion is:




The first issue shall be discussed here using the SORTIE model (Deutschman et al. 1997) as an example.
SORTIE simulates growth and development of single trees in a mixed US forest stand by taking into account the competition among neighboring trees. Light is considered to exert the single-most important influence on competition, while competition for below-ground resources seemed negligible. The central drivers of the competition for light are the Gap Light Index and species-specific light extinction parameters, which were estimated empirically on the individual-level rather than mechanistically as the developers state (assuming mechanistic equals "based on lower scales"). The measurement protocol for the estimation, however, was developed prior to 1988 and measurements consisted of thousands of crown dimension measurements and analyses of hundreds of crown photographs were involved (Canham 1988, Canham 1989, Canham et al. 1994, Canham et al. 1999 in publications of SORTIE-ND). Moreover, allometric relationships between growth and local light availabilty were established with measured data (Deutschman et al. 1997).
This is in full agreement with the first issue of Grimm & Railsback (2005), i.e. that IBMs are too data-hungry, but it is more than that: There is a tendency for IBMs not to rely on parameters of lower scales, such as sturcture and function of organs, although this would be in line with Huston, DeAngelis & Post (1988). In fact, this factor hinders generality of SORTIE. Further, models that lack a mechanistic functional basis are inappropriate for climate change research. Actually, this makes an important difference to functional-structural models (see below).
In their book Grimm & Railsback (2005) were passionately committed to the second problematic issue by developing the theoretical and conceptual framework of Individual-Based Ecology (IBE). However, since they did rely in important ways on concepts of Agent-based Modeling (ABM) in their development, an introduction to ABM will be given in the next paragraph, while a more thorough discussion of IBE is reserved for the Outlook section. In fact, it was the ABM movement proposed by the science of complexity that finally made the closing expectation of Huston, DeAngelis & Post (1988) reality.


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Agent-baed models

Agent-Based Modeling (ABM) provides a general framework, that actually embodies IBM.
The first general-purpose ABM-platform SWARM was presented to the public in the mid 1990s (Minar, Burkhart, Langton & Askenazi 1996, SWARM Development Group Wiki). It had been developed by the artificial life group at the Santa Fe Institute to provide a general architecture for problems that arise in a wide variety of disciplines ranging from physics to biology to economics to social sciences to ecology. Around that time an ABM was built in each of the disciplines, each serving as a SWARM use case, namely Echo (Holland 1995) in complex adaptive systems sciences & biology, Santa Fe Institute Artificial Stock Market (Arthur et al. 1997) in economics, Mesa Verde Village (Village Ecodynamics Project) in social sciences, Arborscapes (Savage & Askenazi 1998) in ecology. All models were useful and provided facinating new insights. Most of these models became very popular, some famous and some gave even rise to the founding of new research areas or disciplines, respectively. ABM seemed to be most influential to social sciences and economics, but less so to ecology, at least until Grimm & Railsback (2005) published their book.
In principle, three major causes are responsible for the overall success of SWARM and other closely related, but later developed platforms (e.g. Repast, Ascape, MASON).
Figures 9-11 use the MASON platform along with broad UIBM concepts to elucidate those causes and show how ABM is usually carried out. All figures were modified from Stefansson (1999).
(1) The platforms provide a powerful conceptual framework for ABM (see Figure 9): A plant is modelled as a composite of agents, such as leaves, internodes and flowers. Agents, e.g. leaves, have state (mass, area, etc.) and behavior (photosynthesis, respiration, etc.). The simulation model holds a discrete-event scheduler that maintains a list of all agents together with the times they have to perform their action. When a leaf is scheduled to perform its action it is "animated" by the Scheduler and its public step method is called with the model's superclass SimState and its local environment therein. The rule-based step method then evaluates the condition "day" and conducts photosynthesis when the condition is true and respiration otherwise. The micro-scale behavior of the agent that resides in the virtual world is defined in code, whereas the macro-scale behavior at the canopy level rather emerges from the micrro-scale. This feature characterizes ABM as a bottom-up approach. The state of both, micro- and macro-scale, is accessible to analysis (compare Figure 11).
This all leads to the following ABM definition: Agent-based Modeling is a bottom-up method for object-oriented discrete-event simulation of agents, which are individual entities that exhibit state/behavior and interact with their local environment in a virtual world. In ABM the complex macro-level behavior emerges from encoded agent interactions on the micro-level and both are accessible to analysis.
(2) The platforms are libraries of object-oriented classes which contain powerful and flexible tools for the implementation of the ABM formalism: In MASON a model console GUI provides means to control the simulation. A 2d- and/or 3d-Display portray the agents and the environmental field that comprises the virtual world. Following the Model-View-Control design pattern the simulation model (subclass of SimState), and its visualization (extends GUIState, see right hand side of Figure 9) are decoupled so that the model can be run more efficiently without visualization. The Inspector is the third major tool. An Inspector is activated by clicking on an agent or an envirornmental field in the Display. It allows the user to ultimately monitor the state and behavior of the object either graphically or by saving the data to a file.


Fig. 9: UIBM within the 3d-Platform MASON The internal working of the UIBM model and the main tools for 3d-visualization and inspection of the UIBM model.



As Figure 10 shows the inspection mechanism tackles the final frontier of ABM in ecology: Virtual Ecology - doing field experiments in virtual worlds.
As in other more traditional models users are able to manipulate the reference atmospheric environment in UIBM as well.
But, besides that, a host of additional experiments is available to the virtual ecologist in UIBM.
The atmospheric environment of a single plant or leaf is accesible to experimental manipulation thereby emulating real world gas exchange experiments in virtual reality. In principle, the inspection mechanism allows to study how the effects of the manipulation propagate through the various scales.
UIBM further opens up the possiblity to conduct bio-manipulation experiments, which are prohibited in real world monitoring programs. You may conduct either species removal experiments or turn on or off specific functions of a certain species in order to compute a dynamic interaction network for the function under study.
In contrast to real world experiments, where data collection is very time-consuming and the "data faucet is merely dripping", virtual experiments are done with a "streaming data facucet" due to UIBM's inspection mechanism (compare left-hand side of Figure 10).


Fig. 10: The final Frontier - Virtual Ecology 



(3) The implementation of the models itself relies also on the object-oriented programming (OOP) paradigm: By this means ABM is transformed into a special case of object-oriented software engineering thereby making available all advanced techniques for mastering complexity that were developed in the software sector. In OOP encapsulation, inheritance and polymorphism (see Figure 11) have replaced the time-consuming and error-prone system of calling subroutines on shared data as done in procedural programming. A more radical paradigm shift is almost inconceivable. Ultimately, it has lead to code that is much more flexible, modular and reusable.


Fig. 11: The three principles of OOP 



The advancement of the tools available for OOP affects ABM actually in three ways:
(a) Code writing: For example we used the 21st century integrated development environment Eclipse and all its wizardry (incremental Java compiler, J-Unit, debugger, profiler, Suhclipse SVN tool) for writing Java code instead of the editor that was used as all-in-one tool for writing code in the old days.
(b) Software design: The high-level design of the software architecture is often accomplished domain-driven (Evans 2004). Below that level GOF design patterns are commonly used as building blocks (Gamma et al. 1995). Overall object-oriented developers adhere to an evolutionary design cycle with frequent refactoring of the system (Fowler & Beck 1999, Kerievsky 2005).
(c) Software documentation/communication: Since 1997 a standard set of UML diagrams is accepted for graphical representation of the structural and behavioral relationships among software components. In contrast to the old times when code was based on methematics and therefore almost cryptic well-written object-oriented code is likely to be expressive, self-explanatory and very readable. A web-based SVN repository of the open-source code is therefore considered to be the best documentation of an ABM. A description of the underlying domain concepts on an adjoining webpage best communicates an ABM project.


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Functional-structural models

The term "Functional-Structural (Tree) Models" was first introduced 1996 at a workshop of the same title held in Helsinki (Silva Fennica Vol. 31(3), 1997).
At that time, however, the main foundations to this area of research were already layed:
The theoretical framework and algorithms for developing plant architecture in the computer using a grammar of string-based L-systems had been tested (Prusinkiewicz & Lindenmayer 1990) and software platforms for its measurement, analysis and simulation had been available for some time (L-Studio, AMAPmod, GROGRA). Actually, the use of computer graphics enabled the tools to produce realistic and aesthetically appealing visualizations of plant structures. This was very stimulating to me.
However, the field is most inspiring because of the underlying idea that the plant form implicitly contains the history of the functions that have molded such a form (modified from Prusinkiewicz & Lindenmayer 1990). In this case validation of physiological process parametrizations should be possible simply by visual comparison of models with real structures.
Since then, the highly interdisciplinary field has received growing interest by researchers studying botanical themes as diverse as biomechanics, carbon source/sink strength and hormonal regulation of development.
But functional-structural models offer advantages to ecologists, as well. A biodiversity model, for instance, will explicitly consider how competition for light among multiple species varies with contrasting plant architectures and physiological processes. Plant architecture or location of meristems, in particular, exerts a significant influence on a species' ability to regrow after management events, such as mowing or grazing.


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Conclusion

Individual-based models entered the scientific "landscape" with a great vision and a paradigm that contrasts that of dynamic ecosystem models. The huge data requirements and a lack of a conceptual framework hindered IBM to make the envisioned progress. Concepts of functional-structural models are envisaged here to help with reduction of data requierments in IBMs. Agent-based modeling is considered to provide a perfect and most general conceptual framework for the implementation of IBMs.
Hence, UIBM shall be an individual-based model with a functional-structural basis. It shall be designed using ABM concepts. The implementation shall be done with the 3d--platform MASON.
The daunting question remains where we can get the information about the life-cycle of thousands of species that would be required for the construction of an individual-based biodiversity model. This question will be adressed in the next two sections.


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Copyright Dec. 2009 Dr. U. Grueters



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