Quantitative Reasoning Project: Mathematical Modelling

Introduction and objectives -

The objective of this project is to show you how to develop a mathematical model of a real system, implementing it in R, running through all stages of the mathematical modelling process. To remind you, those stages are:

1. State your problem

2. Using your knowledge of scientific theory, translate the problem into mathematical form. This will always involve making a number of simplifying assumptions. You need to clearly state those assumptions and use your scientific knowledge to evaluate the extent to which they are valid in this situation. It will often be helpful to draw a diagram to help in this stage.

3. Solve the mathematical problem identified in the step above

4. Plot or otherwise display the results of your mathematical modeling

5. Compare the results of your mathematical model with observed data or information about your real world system

6. If necessary, modify your simplifying assumptions and repeat from stage two.

An important part of this process is to conduct sensitivity analysis, which is the process of investigating how the results of your mathematical modelling depend on the values of the input parameters and also how the results may change if you modify some of your simplifying assumptions.

Report and assessment criteria -

Introduction: Describe the system you have chosen to model. Identify the scientific questions you will seek to answer with your model. This will likely require referring to some scientific literature, although referring to websites may also be acceptable.

Methods and model structure: Here, you should describe how you have decided to model the system. You should outline the simplifying assumptions you have chosen to make and describe why those simplifications have been made. As part of the methods, you should present your model is a flowchart or diagram. As an appendix to your report, include the R code you have used, with appropriate annotations (use the # commenting facility).

Results: Describe, in words, the results of your modelling exercise. You should include some graphs here, but there should also be interpretation in words (for example, "figure 1 shows that..."). Each of your graphs should have an informative legend.

Discussion: This is the essential step of relating your modelling findings back to the original problem. To what extent does your model answer the original question? How do the results depend on the values of the parameters you have used in your model? Which of the assumptions you have made do you think may be particularly problematical? How do your mathematical findings relate to the biology of the original problem?

Within each section, marks will be awarded for presentation, clarity and logical structure.

Suggested Projects - Some suggestions for projects follow. It may also be possible to do something different, but check with your tutor to make sure your idea is suitable.

I have chosen to do the turtle project.

This project is based on the following scientific paper, which you should download and read before you attempt this project.

Crouse, D. T., L. B. Crowder, and H. Caswell. 1987. A stage-based population model for loggerhead sea turtles and implications for conservation. Ecology 68:1412-1423.

Formatting & Referencing: APA

Attachment:- Assignment Files.rar