To conserve species in disturbed natural environments, we need to use mathematical models to predict the consequences of different interventions. Unfortunately, these models are based on partial information of complex systems, and the systems themselves are subject to substantial observational and process noise.
We often use ordinary differential equations to describe ecosystems, like the classic logistic growth model:
- dn/dt = r n (1 - n / k)
However, these models are deterministic, and they assume we know the values of the key parameters (r and k). Unfortunately, these are bad assumptions, and they make a big difference to our predictions. There is real impetus to develop more complex models that account for this uncertainty.
In this project, we're going to develop these more complex models. We're going to extend the simple ODE models to include stochasticity, and then we're going to apply them to timeseries data from experimental microcosm ecosystems (that is, ecosystems of tiny animals living in buckets).
You will start by understanding how the simple ODE models work, and how they’re applied to real ecosystems. You’ll then extend these models into a stochastic ecosystem model, and fit this model to synthetic data (i.e., data we made up on a computer), and real microcosm time-series data.
This work is numerical, not analytic. That is, you won't be sitting with pencil and paper, you'll be writing and adapting computer code that answers these questions. Source code for many of the essential algorithms required for this work will be provided. However, you will need to modify and combine these code bases are the project develops.
This project will provide important insights into the role of stochastic modelling for conservation decision making. In particular, the incorporation of intrinsic system noise has the potential to substantially improve the way decisions are assessed and monitored after management actions commence.
Put simply, the models that we currently use aren’t working, and the conservation scientists who use them know it. As a result, too many fish are being caught, too much forest is being cleared, and too few invasive species are being controlled. If we can create mathematical tools which admit that ecosystems are fluctuating and uncertain, we can help to save more species from extinction.
Skills and experience
Familiarity with dynamical systems, simple stochastic process modelling, and parameter estimation (either frequentist or Bayesian perspectives). Experience in computational statistical methods is useful, but not essential.
Contact the supervisor for more information.