This workshop will introduce participants to the logic behind modeling in biology, focusing on developing equations, finding equilibria, analyzing stability, and running simulations.Techniques will be illustrated with the software tools, Mathematica and Maxima. This workshop was held in two parts: January 14 and January 16, 2020.

Technical

EN

Author

Sarah P. Otto

University of British Columbia

Published

January 14, 2020

In this workshop, I introduce various modelling techniques, using mostly ecological and evolutionary examples, with a focus on how computer software programs can help biologists analyze such models.

Content

Part 1: Classic one-variable models in ecology and evolution Part 2: Equilibria and their stability Part 3: Beyond equilibria Part 4: Example of building a model from scratch Part 5: Extending to models with more than one variable Part 6: Another example of building a model from scratch

Software

In my research, I primarily use Mathematica, which is a powerful software package to organize and conduct analytical modelling, but it is not free (at UBC, we have some licenses available). I will also show some example code and provide translation of most of what I present in a free software package called Maxima.

Mathematica installation

There is a free trial version that you can use for 15 days, if you don’t have a copy (click here to access), or you can buy a student version online. If you want to make sure that all is working, copy the code below, put your cursor over each of the following lines and press enter (on some computers, “enter” is a separate button, on others, press “shift” and “return” at the same time):

You should see (a) \(3x^2\), (b) a plot of a line, (c) \({{x[t]->A^t x0}}\), and (d) \(\frac{e^\frac{-x^2}{2}}{\sqrt{2\pi }}\).

Maxima installation:

On a Mac, install using the instructions here. For other file systems, download here.

Maxima testing

When you first open Maxima, it will give you a choice of GUIs, chose wxMaxima. Once wxMaxima is launched type this command and hit return to see if it answers 4:

2+2;

If it doesn’t, then scan the installation document for the error that you run into.

If it does return 4, then type in and enter these commands:

This PDF was generated from the Mathematica notebook linked above. It doesn’t include dynamic plots, but it’s a good alternative if you want to print out or have a quick reference at hand.

Other resources

An Introduction to Mathematical Modeling in Ecology and Evolution(Otto and Day 2007).

Niki Love and Gil Henriques did a great job of translating the code into wxMaxima, with limited help from me. Thanks, Niki and Gil!!

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References

Otto, Sarah P, and Troy Day. 2007. A Biologist’s Guide to Mathematical Modeling in Ecology and Evolution. Vol. 13. Princeton University Press.

Citation

BibTeX citation:

@online{p.otto2020,
author = {Sarah P. Otto},
title = {Mathematical {Modeling} in {Ecology} and {Evolution}},
date = {2020-01-14},
url = {https://bios2.github.io/posts/2020-01-14-mathematical-modeling-in-ecology-and-evolution},
langid = {en}
}