Applications of Mathematics in Ecology

Talk details

Daniel Bearup – Modelling the effects of habitat destruction on communities of species.

Habitat destruction reduces both the habitat available to species and the connectivity of the landscape. These two modes of habitat destruction have differing effects on species depending on their dispersal capabilities. Meta-population modelling provides a convenient framework in which to investigate the responses of communities of species to these pressures and thus identify the types of species that are at most risk.

James Bentham – Bayesian modelling of population-level height

Although an individual’s height is strongly influenced by genetics, at the population level there are strong environmental effects. I will discuss a Bayesian hierarchical model that we fitted to data on height from countries around the world, and will also provide some of the key results. I will then discuss future work using Bayesian nonparametric models.

Diana Cole – Inference with non-identifiable models

The ideal model for a complex ecological process may be non-identifiable, so that regardless of the amount of data collected it is not possible to estimate all the parameters.  Here we discuss methods of overcoming non- identifiability, which includes reparameterisation, constraints, robust design, covariates, integrated models and priors.

Natalia Petrovskaya – TBC

Management of pest populations requires, first, knowledge of the population distribution and, second, how a given intervention might influence that popuation distribution. Techniques from numerical analysis provide a structure in which to interpret trap count data and develop management strategies.

Jonathan Potts – TBC

Mathematical models of spatial population dynamics typically focus on the interplay between dispersal and reproduction. However, for many animal communities, significant arrangement in space can occur on short timescales where births and deaths are negligible. The spatial patterns in population distributions that emerge from complex movement behaviours have been largely neglected until now.

Dave Roberts – Conserving Schrödinger’s Cat: When is a species extinct?

Knowing if a species is extinct is critical for conservation not just in terms of active conservation interventions but our understanding of species decline and extinction. Often the last sighting of s species is used as an extinction date however species can persist unseen for many years before becoming extinct. Sighting-based methods have been developed to infer extinction but even then there are issue as to the reliability of sightings of rare and elusive species. In recent years attempts have been made to incorporate sighting uncertainty into these methods of extinction inference, however it still remains a challenge.