1. 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,

2. 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.

3. 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.

4. 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

5. 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.

6. 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?

7. 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

8. 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

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

10. 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

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

12. 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?

13. Understanding forest hydrologyp W d
State variable = W
Fluxes = p, e, d
dW/dt =p – e – d

14. 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.

15. 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.