An introduction to Simulation Modelling Scientific Enquiry in Biology and the Environmental Sciences Modelling Session 1 Mathew Williams Introduce myself; education, history, interests What I expect from the students: 100% attendance class participation by all assignments on time and double-checked before submission What students can expect from me: a thorough grounding in the principles of modelling examples of applications from my expertise a willingness to focus on individual or class interests opportunities for research with me in summer jobs or post-graduate positions availability outside class for discussion office: Darwin 115, email: mat.williams@ed.ac.uk

Seminar 1 outline Why model? What are models? Decoding model jargon How are models developed, structured, applied and tested? Develop skills and explore modelling concepts with practical modelling exercises What are some examples of systems? Populations of interacting individuals Multiple interacting populations an ecosystem the atmosphere a lake the earth What are the component objects in these systems? Identify the concept of scale Modelling is a fundamental activity between humans – we use models to communicate a view of the world. Model construction is a somewhat arbitrary procedure, and modelling conventions may be a matter of convenience.

What are models? A model is a description of a system and its relations to its surroundings A system is any collection of interrelated objects An object is some elemental unit upon which observations can be made What are some examples of systems? Populations of interacting individuals Multiple interacting populations an ecosystem the atmosphere a lake the earth What are the component objects in these systems? Identify the concept of scale Modelling is a fundamental activity between humans – we use models to communicate a view of the world. Model construction is a somewhat arbitrary procedure, and modelling conventions may be a matter of convenience.

Why do we model? Understanding - of either a real physical system or a system of logic Prediction - of the future or of some state that is currently unknown Control - to constrain or manipulate a system to produce a desirable condition

Examples of models Global Climate – IPCC Weather forecast Flood planning Pest Control - coypu Conservation Planning - beaver Disease Control – Foot and mouth What are some examples of systems? Populations of interacting individuals Multiple interacting populations an ecosystem the atmosphere a lake the earth What are the component objects in these systems? Identify the concept of scale Modelling is a fundamental activity between humans – we use models to communicate a view of the world. Model construction is a somewhat arbitrary procedure, and modelling conventions may be a matter of convenience.

Forms of model Conceptual or verbal Diagrammatic; graphical representations of objects and relations Physical; a real, physical mock-up – e.g. plane in wind-tunnel Formal; mathematical, using algebraic or differential equations What are the advantages and disadvantages of each approach?

Types of model Empirical/phenomenological versus process-based/mechanistic; e.g. linear regression (e) and numerical weather-forecasting (m) Deterministic versus stochastic; e.g. atmospheric model (d) and fire model (s) Static versus dynamic; e.g. residence time model (s) and dynamic simulation (d) Time: Continuous versus discrete; chemical kinetics (c) and annual population models (d) Space: Homogenous or heterogeneous (continuous versus discrete); simple population equation vs. cellular population model

Components of a model State variables – time varying components of the system Fluxes - flows of matter/energy Parameters – rate constants on fluxes Driving variables - forcing/excitation Output - predictions

Differential equations State variable x inflow outflow 1st Law of Thermodynamics: Conservation of matter

Modelling exercises A population model A hydrological model Used for epidemiology, population control, conservation studies A hydrological model Used for crop management, land surface for climate/BGC models, flood management www.geos.ed.ac.uk/homes/mwilliam/SE.html

Population growth State variable = n, population number Births (b) Deaths (d) State variable = n, population number Fluxes = births and deaths dn/dt = b - d

Modelling questions 1. What value must the fluxes take when a steady state exists? 2. What factors might determine a carrying capacity and growth rate in a natural population? 3. Are growth rate and carrying capacity likely to be constants in reality? 4. How would you determine parameter values for a natural population? 5. What time-step should the model run on? 6. What problems are there in using a single state variable for a population? 7. What external factors might be important and how would you add these to the model?

Understanding forest hydrology p W d State variable = W Fluxes = p, e, d dW/dt =p – e – d

Review Physical laws (e.g., conservation of mass) can guide system trajectories Models should be constructed in the context of the science objective or question Determine model parameters and their errors from independent data Use of residual analysis and sensitivity analysis to probe model outputs.

Tutorials Based on a peer-reviewed description, we discuss a model that has been used to address a practical problem in biological or ecological science. Critical questions to address include: What were the strengths and successes of the modelling approach? What were the weaknesses and limitations of the approach? What are some examples of systems? Populations of interacting individuals Multiple interacting populations an ecosystem the atmosphere a lake the earth What are the component objects in these systems? Identify the concept of scale Modelling is a fundamental activity between humans – we use models to communicate a view of the world. Model construction is a somewhat arbitrary procedure, and modelling conventions may be a matter of convenience.