Essential Models in Ecology
Preface and Syllabus
Welcome!
If you’re reading this message, this means these lectures are far from complete. However, I’m hoping to add more soon – so you eager ecologists have something to look forward to!
Learning/teaching strategy
Lecture format
I love yapping and telling people about things I’m passionate about.
However, I often notice a glaze crossing over people’s eyes unless I actively engage with them by asking questions. (This doesn’t stop me from yapping if I’m feeling self-indulgent, but it’s an inefficient way of communicating information).
In these lectures, I strive to present information in the form of questions as much as possible. Instead of merely “providing” information, I frame it as questions that emphasize key concepts. All the information is still given to you, but it encourages you to think critically throughout the lectures. This approach has practical utility—if you’re ever tested on this information, it’s beneficial to get in the habit of applying what you’ve learned to various situations. The philosophy is, more or less, to “give you enough to make something of the ideas, but not enough to fool you into thinking that you can learn them by passively reading.”
Additionally, these lectures emphasize recalling key concepts in a “mixed up” manner. That is, the key concepts will appear throughout the lectures in somewhat different ways. To this end, questions are formulated to be somewhat challenging so that you will likely make errors (if you don’t, then you’re cleverer than I am). The key point is to continually test your knowledge—there will probably be gaps that this lecture structure aims to fill. This structure is loosely based on empirically supported learning strategies (e.g. see Brown, Roediger, and McDaniel 2014).
Who is this for?
My goal is to teach you key concepts in ecological models (well, ecological models and some key models from evolutionary biology and population genetics). Emphasis on the word concepts – math is a tool in these lectures, not the point.
It is my hope that these lectures will (1) help you appreciate the profound utility of classic models in ecology and evolutionary biology and (2) encourage you to start thinking about creating models of your own when addressing questions in the biological sciences (or, with a bit of luck, everyday life).
These lectures are not for mathematicians, meaning I will not present rigorous mathematical justifications or proofs of the models. Rather, I want to get you thinking about the utility of specific models in ecology, which will benefit both mathematicians and the “math-phobic” among you alike.
To those of you who are a bit “math-phobic”:
Even if you don’t like math, I believe you will benefit from these lectures. Ideally, this will serve as a starting point for you to think more quantitatively and engage with theory. In particular, I want you to think deeply about the assumptions that go into the models—you don’t need to have a degree in mathematics (or much competency in math at all) to understand what a mathematical model is “doing.” Quantitative reasoning (often expressed in mathematical terms) should make things easier to understand. This applies even if you don’t want to build theoretical models yourself.
To the mathematically inclined:
A decent amount of the math we will deal with here is simple in that it will not require a lot of tricky algebra. You might think this simple math is too easy on a technical level. However, conceptually wrapping your head around how a particular mathematical model is profound and/or useful in the biological sciences is very different from being able to solve integrals, differential equations, and juggle difficult algebra. In fact, I find students with a mathematical background often have some difficulty with the key concepts, despite their formidable technical skills. These lectures, I hope, will move you in the direction of emphasizing the concepts first and the technical aspects second (although both are indispensable).
Course structure
These lectures will cover some of the key models in ecology (with some overlap with evolutionary biology / population genetics). The idea is to build from the simplest models, emphasizing the why rather than the how.
Also, if you’re reading this, it means the lecture notes are still under construction. Therefore, several (many?) of the below topics still must be added and may be modified.
| Topic | Key concepts | Modules | Related papers |
|---|---|---|---|
| Simple density-independent growth | TBA | TBA | TBA |
| Density-independent growth in variable environments | TBA | TBA | TBA |
| Stochastic density-independent growth | TBA | TBA | TBA |
| Density-dependence part I: simple models | TBA | TBA | TBA |
| Predator-prey interactions: why does war favor sharks? | TBA | TBA | TBA |
| Consumer-resource interactions: mind the assumptions | TBA | TBA | TBA |
| Density-dependence part II: adding (some) biology | TBA | TBA | TBA |
| Competition: the basics | TBA | TBA | TBA |
| Competition: resource competition | TBA | TBA | TBA |
| Competition and predation: toward realistic models | TBA | TBA | TBA |
| Mutualisms and cooperation: on working together | TBA | TBA | TBA |
| Scaling up part I: large Complex systems, mathematicans, and random zoos | TBA | TBA | TBA |
| Scaling up part II: island biogeography and neutral theory | TBA | TBA | TBA |
| Scaling up part III: niches, neutrality, modern coexistence theory, and more | TBA | TBA | TBA |