If I'm on the committee for your general knowledge exam, below are some topics we might cover. They are just kickoff points. This is not a comprehensive list.
1. Define density-dependent growth. How can it be identified from data?
2. Write an equation for a population with density-dependent growth. Analyze its stability analytically. Sketch a time series. Describe methods for numerical integration.
3. What is chaos and where can we find it?
4. Define discrete-time and continuous-time models, autonomous and non-autonomous rates.
5. Why is diversity highest in the tropics? Define diversity.
6. What is demographic stochasticity and when is it important? What about process and environmental noise?
7. What makes communities stable?
8. Describe different sources of cyclic behavior, including at least two that are endogenous (i.e., that do not rely on interaction with another species or external forcing).
9. How can species interactions be inferred from experiment and observation?
1. What is a p-value? How should we interpret it? How is it commonly misinterpreted?
2. Define Bayes' theorem. Provide a quantitative example of Bayesian reasoning.
3. When should we trust a model? How should we decide between models?
4. What are credible intervals and confidence intervals, and how are they calculated?
5. How should we handle multiple hypothesis testing?
6. Can causality be inferred from observational data, and if so, how?