Complexity, Modelling & Plants

Teodor GhetiuNSC Group, CoSMoS project

Supervisors: Dr Fiona Polack and Dr Jim Bown1

1 University of Abertay Dundee

Complexity, Modelling & Plants Etymology: 14th century Latin expression

complexus• ‘embracing or comprehending several elements‘

[Simpson1989]

Types [Manson2001]: Algorithmic: information theory Deterministic: chaos and catastrophe theory Aggregate: complexity theory, complex systems

Definitions: 32 definitions of complexity [Lloyd2006]

Complex Systems

Definitions: A whole that is greater than the sum of its parts

[Aristotle350BC]

Cilliers finds 10 properties [Cilliers1998]: Large number of elements Rich, non-linear, local and recurrent interactions Have history React based on local knowledge Usually open, far-from-equilibrium

A system defined by: agent-based, dynamic, heterogeneous, feedback, organisation, emergence [Santa Fe CSCS]

Complex Systems

Features - Hierarchy theory [Simon1962] Scale: have multiple layers of description Emergence: high-level behaviours based on low-level

interactions Environment: influenced by and influencing their environment

Paradox (1) Natural (complex) systems: robust, adaptive, self-* properties Complexity: ‘A word problem and not a word solution’

[Morin1990]

Challenge: to improve the way we study and construct such systems Scientifically engineer, model, simulate, analyse

Complexity, Modelling & Plants Modelling motivations [Grim1999]

Pragmatic: tools for solving problems Paradigmatic: tools that facilitate a better understanding

Paradigms Mathematical modelling

Equation Based Modelling (EBM)

Computational modelling Cellular Automata (CA) Agent Based Modelling (ABM)

Individual Based Modelling (IBM) Process Oriented Modelling (POM)

Mathematical Modelling

Lotka-Volterra predator-prey model [Lotka1925] prey's numbers: own growth minus rate at which it is

preyed upon predator population: own growth minus natural death.

Mathematical modelling

Benefits Integrated view on populations [Kaiser1979] Explicit mathematical treatment, analytic truths

[Bryden2006]

Shortcomings Limits understanding of system properties [Kaiser1979] Scalability problems [Huston1988] Strong assumptions [Bullock1994] Centralised systems, physical laws dynamics

[Parunak1998]

Cellular Automata

Large sets of identical, finite-state automata [VonNeumann1955]

Simple but capable of generating complex behaviours

Benefits [Hogeweg1988] Extendability Observability Spatial representation [Durrett1993]

Shortcomings Synchrony Space-orientedness

Conway’s Game of Life

Agent-Based Modelling

Source www.esourceagent.com

Extending CA’s Autonomy Reactivity Proactivity Sociability

Agent-Based Modelling

Benefits Prediction of outcomes under novel conditions [Kaiser1979] Simpler and more accurate than mathematical models

[Huston1988] Relaxed assumptions [Bullock1994] Localised, distributed, information processing dynamics

[Parunak1998] Integrating many levels of description [Bousquet2004]

Shortcomings Performance, providing synthetic truths [Bryden2006] Oriented on social systems [Andrews2008] Time, space and component-quantity aspects [Andrews2008] Dependence on MAS platforms [Sudeikat2005]

Process Oriented Modelling

Benefits [Ritson2007] Finer granularity Plasticity, dynamism Simulations at larger scales Mapping to natural processes

Shortcomings Lower granularity: harder to model macro-entities Recent interdisciplinary tool

Process composition[Ritson2007]

Occoids simulation [Sampson2008] POP based Continuous space Scalable architecture Large scale simulations

Process Oriented Modelling

Models and simulations are generally used in [Andrews2008]: ‘Improving scientific understanding of (natural) systems’ ‘Constructing or exploring alternative realities’

Scientific use raises issues of: Realism, Precision and Generality trade-off [Holling1964] Analysis [Braitenberg1984] Transparency [DiPaolo2000] Validity [Sargent1987]

‘Scientific validity, like engineering validity, means that it must be possible to demonstrate, with evidence, how models express the scientific realities’ [Andrews 2008]

Scientific Modelling

Scientific Modelling

Paradox (2) Objective: to model complex systems Means: complexity features not addressed

thoroughly

Questions: How to construct (engineer) complex

systems? How to validate their behaviour?

Methodologies

Sargent’s process for developing simulation models [Sargent1981]

Methodologies

The CoSMoS process [Garnett2008]

Plant ecologies

Plant ecologies

Ecology: ‘Scientific study of the interactions between organisms

and their environment’ [Begon2006]

Ecology’s Holy Grail: General rules relating environment conditions, species

traits and community composition [Lavorel2002; Reineking2006]

Plant ecologies are complex systems [Huston1988] Scale: Individual, patch, population, community,

ecosystem Emergence: Patterns emerge from processes [Wu1994] Environment: Direct interdependence [Fornara2008]

Modelling ecologies

Mathematical models Matrix life-cycle models

Individual Based Models Simple representations: [Sebert-Cuvillier2007],

[Arii2006] homogeneous populations, non-spatial

Detailed representations: [Wu2007], [Evers2007] Complicated, Composite models

Modelling ecologies

Intraspecific variation through traits trade-off [Tilman2000] Detailed models: [Marks2006] one plant, 34 traits, no

reproduction

Addressing the “Holy Grail” Time and space heterogeneity matters

[Reineking2006]: 24 common traits, 4 species specific, spatial model

Intra and interspecific variation united [Bown2007a]: 12 traits, spatial “Individuals that are too similar cannot coexist”

Importance of diversity at the individual scale [Bown2007b]: community productivity related to

individual traits and environment

Summary Complexity and Complex Systems Approaches to modelling complex systems Scientific validation Plant ecologies

References 1 [Andrews 2008] Andrews, P., Polack, F., Sampson, A., Timmis, J., Scott, Coles, (2008), Simulating biology:

towards understanding what the simulation shows, CoSMoS workshop 2008 [Arii2006] Arii, K., Parrott, L. (2006) – Examining the colonization process of exotic species varying in

competitive abilities using a cellular automaton model, Ecological Modelling, Vol. 199, No. 3., pp. 219-228.

[Aristotle350BC] Aristotle, Metaphysics, volume book H (VIII). 350 BC., Translation fromW. D. Ross, Aristotle’s metaphysics, 2 vols, Oxford University Press, 1924

[Begon2006] Begon, M.; Townsend, C. R., Harper, J. L. (2006). Ecology: From individuals to ecosystems. (4th ed.), Blackwell.

[Bousquet2004] F Bousquet, C Le Page, Multi-agent simulations and ecosystem management: a review, Ecological Modelling, Vol. 176, No. 3-4. (1 September 2004), pp. 313-332.

[Bown 2007a] Bown, L., Pachepsky, E., Eberst, A., Bausenwein, U., Millard, P., Squire, R., Crawford, J., Consequences of intraspecific variation for the structure and function of ecological communities Part 1: Linking diversity and function, Ecological Modelling, Vol. 207, No. 2-4. (10 October 2007), pp. 264-276.

[Bown 2007b] Bown, L., Pachepsky, E., Eberst, A., Bausenwein, U., Millard, P., Squire, R., Crawford, J., Consequences of intraspecific variation for the structure and function of ecological communities Part 2: Linking diversity and function, Ecological Modelling, Vol. 207, No. 2-4. (10 October 2007), pp. 277-285.

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Seventh International Conference on Artificial Life (2000), pp. 497-506. [Durrett1993] Durette, The importance of being discrete (and spatial), Theoretical population biology, vol

46, 363-394 [Evers2007] – J Evers, J Vos, C Fournier, B Andrieu, M Chelle, P Struik, An architectural model of spring

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allocation trade-offs maintain species diversity in a process-based model of succulent plant communities, Ecological Modelling, Vol. 199, No. 4., pp. 486-504

[Ritson2007] A Process-Oriented Architecture for Complex System Modelling, Concurrent Systems Engineering, Vol. 65 (July 2007), pp. 249-266.

[Sampson2008] Adam T. Sampson, John Markus Bjørndalen and Paul S. Andrews, Birds on the Wall: Distributing a Process-Oriented Simulation, CEC 2009, awaiting publication

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Any questions?