Complexity, Modelling & Plants

1. Complexity, Modelling & Plants Teodor Ghetiu NSC Group, CoSMoS project Supervisors: Dr Fiona Polack and Dr Jim Bown1 1University of Abertay Dundee

2. Complexity • Etymology: 14th century Latin expression complexus • ‘embracing or comprehending several elements‘ • ‘plaited together, interwoven’ [Simpson1989] • Types [Manson2001]: • Algorithmic: information theory • Deterministic: chaos and catastrophe theory • Aggregate: complexity theory, complex systems • Definitions: 32 definitions of complexity [Lloyd2006]

3. 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 recurrentinteractions • 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]

4. 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 • 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

5. Modelling • 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)

6. 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.

7. 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]

8. Cellular Automata • Large sets of identical, finite-state automata [VonNeumann1966] • Simple but capable of generating complex behaviours • Benefits [Hogeweg1988] • Extendability • Observability • Spatial representation [Durrett1993] • Shortcomings • Synchrony • Space-orientedness Conway’s Game of Life

9. Agent-Based Modelling • Extending CA’s • Autonomy • Reactivity • Proactivity • Sociability Source www.esourceagent.com

10. 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]

11. 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]

12. Process Oriented Modelling • Occoids simulation [Sampson2008] • POP based • Continuous space • Scalable architecture • Large scale simulations

13. Scientific 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]

14. Scientific Modelling • Paradox • Objective: to model complex systems • Means: complexity features not addressed thoroughly • Questions: • How to construct (engineer) complex systems? • How to validate their behaviour?

15. Methodologies • Sargent’s process for developing simulation models [Sargent1981]

16. Methodologies • The CoSMoS process [Garnett2008]

17. Plant ecologies

18. 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]

19. Plant ecology [Reineking2006] Modelling ecologies • Mathematical models • Individual Based Models • Simple representations: • [Arii2006], [Sebert-Cuvillier2007] • homogeneous populations • non-spatial • Detailed representations: • [Wu2007], [Evers2007] • Complicated, Composite models

20. Modelling ecologies • Traits as building blocks of individual [Tilman2000] • Addressing the “Holy Grail” • Time and space heterogeneity matters • [Reineking2006]:24 common traits, 4 species specific, spatial model • Intra and interspecific variation combined • [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

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

22. 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. • [Braitenberg1984] Braitenberg V (1984) Vehicles, Experiments in Synthetic Psychology. The MIT Press. • [Bryden2006] Bryden, J., Noble, J. (2006), Computational modelling, explicit mathematical treatments and scientific explanation, Artificial Life X: Proceedings of the Tenth International Conference on Artificial Life, pp. 520-526. • [Cilliers 1998] Cilliers (1998), Complexity and Postmodernism: Understanding Complex Systems • [DiPaolo2000] Di Paolo, E., Noble, J., Bullock, S., Simulation models as opaque thought experiments, 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 wheat: Evaluation of the effects of population density and shading on model parameterization and performance , Ecological Modelling, Vol. 200, No. 3-4. (24 January 2007), pp. 308-320 • [Fornara2008] Fornara, Tilman, Plant functional composition influences rates of soil carbon and nitrogen accumulation, Journal of Ecology, Vol. 96, No. 2. (2008), pp. 314-322.

23. References 2 • [Garnett2008] Garnett, P., Stepney, S., Leyser, O., Towards an Executable Model of Auxin Transport Canalisation, CoSMoS Workshop 2008 • [Grim1999] Grimm, V., Ten years of individual-based modelling in ecology: what have we learned and what could we learn in the future?, Ecological Modelling, Vol. 115, No. 2-3. (15 February 1999), pp. 129-148. • [Hogeweg1988] Hogeweg, P. Cellular automata as a paradigm for ecological modeling, Appl. Math. Comput., Vol. 27, No. 1. (1988), pp. 81-100. • [Holling1964] The Analysis of Complex Population Processes, Can. Entomol., 96, 335-347 • [Huston1988] Huston, M., DeAngelis, D., Post, W., 1988. New computer models unify ecological theory. BioScience 38, 682-691 • [Kaiser1979] Kaiser, H., 1979, The dynamics of population as result of the properties of individual animals, Fortschr. Zool, 25., 109-136 • [Manson2001] Manson, S. (2001), Simplifying complexity: a review of complexity theory, Geoforum, Vol. 32, No. 3., pp. 405-414. • [Lavorel2002] Lavorel, S., Garnier. E (2002), Predicting changes in community composition and ecosystem functioning from plant traits: revisiting the Holy Grail, Functional Ecology, Vol. 16, No. 5., pp. 545-556. • [Lloyd, S. 2006] Lloyd, S, (2006) Programming the Universe: From the Big Bang to Quantum Computers, Knopf • [Lotka1925] Lotka, A. J. 1925. Elements of physical biology. Baltimore: Williams & Wilkins Co. • [Manson2001] Manson, S., Simplifying complexity: a review of complexity theory, Geoforum, Vol. 32, No. 3. (August 2001), pp. 405-414. • [Marks2006] Marks, C, Lechowicz, M., A holistic tree seedling model for the investigation of functional trait diversity, Ecological Modelling, Vol. 193, No. 3-4. (15 March 2006), pp. 141-181. • [Morin1990] Morin, E. (1990), Introduction a la Pensee Complexe, (Paris, ESF) • [Parunak1998] Parunak Van Dyke, Savit, R., Riolo, R.L., (1998), Agent-Based Modeling vs. Equation-Based Modeling: A Case Study and Users’ Guide, Multi-Agent Systems and Agent-Based Simulation, pp. 10-25

24. References 3 • [Polack2005b] Polack, F., Stepney, S. (2005), Emergent properties do not refine • [Polack2005a] Polack F, (2005) An Architecture for Modelling Emergence in CA-Like Systems, • [Reineking2006] B Reineking, M Veste, C Wissel, A Huth, (2006), Environmental variability and 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 • [Santa Fe CSCS] Santa Fe Center for Study of Complex Systems • [Sargent1987] Sargent, R.G. (1987), An overview of verification and validation of simulation models, pp. 33-39 • [Sebert-Cuvillier2007] E Sebert-Cuvillier, F Paccaut, O Chabrerie, P Endels, O Goubet, G Decocq, – Local population dynamics of an invasive tree species with a complex life-history cycle: A stochastic matrix model, Ecological Modelling, Vol. 201, No. 2. (24 February 2007), pp. 127-143. • [Simon1962] Simon, H.A., The architecture of complexity, Proceedings of the American Philosophical Society, Vol. 106 (1962), pp. 467-482. • [Simpson1989] Simpson, J. et al (1989/2005) Oxford English Dictionary Online (2ndedn) [Electronic resource] (Oxford, Oxford University Press)‏ • [Sommerville2006] Sommerville, I., (2006), Software Engineering • [Squire1990] Squire, G.R., 1990. The Physiology of Tropical Crop Production., CAB International. • [Stepney2005] Stepney, S., Polack, F, Turner, H. (2005), Engineering Emergence, Proceedings of the 11th IEEE International Conference on Engineering of Complex Computer Systems, 89-97 • [Sudeikat2005] Sudeikat, J., Braubach, L., Pokahr, A., Lamersdorf, W., Evaluation of Agent–Oriented Software Methodologies – Examination of the Gap Between Modeling and Platform, Agent-Oriented Software Engineering V (2005), pp. 126-141.

25. References 4 • [Tilman2000] Tilman,D., Causes, consequences and ethics of biodiversity.,Nature 405, 208–211. • [VonNeumann1966] J. Von Neumann, Theory of Selfreproducing Automata (edited and completed by A. W. Burks), Univ. of Illinois Press, 1966, 388 pp • [Wu1994] J Wu, SA Levin, A spatial patch dynamic modeling approach to pattern and process in an annual grassland, Ecological monographs, Vol. 64, No. 4. (1994), pp. 447-464. • [Wu2007] Wu, J. (2006), – SPACSYS: Integration of a 3D root architecture component to carbon, nitrogen and water cycling—Model description, Ecological Modelling, Vol. 200, No. 3-4. (24 January 2007), pp. 343-359. Any questions?