Project Level: Winter

Project Duration:

4 weeks – 20-36 hours per week. Applicant will be required on-site for the project.


Accurately estimating trends in population abundance is critical for developing ecological theory, performing environmental assessments, and advising natural resource management. While the error and power of statistical methods for detecting population declines and recoveries are well-studied, they rarely consider the issue of density dependence. If population size time series data occurs in an area where the species is abundant, density dependence may cause the over-prediction of a population decline. In this project, we will provide simple analytic formulae for the probability of misestimating population growth rates above or below a specified threshold. We will then use the formulae in two applied contexts (1) the probability of falsely predicting a threatened species is declining or recovering and (2) the use of linear population models for predicting species occurrence. In the latter case, we will derive simple rules of thumb for the critical population abundance, in relation to carrying capacity, after which density dependence interferes with accurate predictions of persistence. The critical abundance can be used as a guideline for when it may be appropriate to use linear population process models to predict species occurrence in a density-dependent world. The outcomes of the project can inform conservation planning from reserve design to invasive and threatened species management

Expected Outcomes:

Scholars may gain skills in natural resource mathematics, data visualisation and have an opportunity to generate publications from their research. 

Suitable for:

This project is open to applications from students with a background in 2nd/3rd year applied mathematics or statistics. Having taken Math 3070 – Natural Resource Mathematics is highly desirable but not required.

Some background in either dynamic models (difference equations or ODEs) or statistical modelling is required, but not necessarily both.

Further information:

Please contact Dr Matthew Holden to discuss the project.

Project members

Dr Matthew Holden

School of Mathematics and Physics