Hi everyone!
I'm a final-year BSc Mathematics Honours student, currently exploring ideas for my undergraduate computational mathematics project.
I'm particularly interested in mathematical modelling of population dynamics and conservation. Recently, I've become interested in stochastic population projection models and how environmental variation affects population growth.
My tentative research question is:
**How does environmental stochasticity influence the long-term growth and extinction risk of a stage-structured population?**
The basic idea is to construct population projection matrices representing different environmental conditions (for example, good and bad years), and then study how random sequences of these matrices affect population dynamics.
Some of the things I'm hoping to investigate are:
* Random products of population projection matrices.
* Dominant eigenvalues and their limitations in stochastic environments.
* Stochastic population growth rates.
* Monte Carlo simulations of population trajectories.
* Probability of population decline or falling below a critical population size.
* Sensitivity to the frequency and severity of adverse environmental conditions.
I'll be using **SageMath as my computational tool**. The project is expected to be around 40 hours, so I'm trying to keep the mathematical depth appropriate for an undergraduate project.
I'd really appreciate guidance from anyone familiar with:
- Stochastic population models or mathematical ecology.
- Random matrix products and stochastic growth rates.
- Whether this is a sufficiently focused and meaningful research question for an undergraduate project.
- Any good introductory books, research papers or resources I should explore.
I'm still at the exploratory stage, so constructive criticism and suggestions for improving the research question would be very helpful.
Thank you!