Research Priorities 2007

• Spatially explicit population models - can we explain why population persistence is affected by different habitat disturbance regimes?
• Marine reserve networks - what is the optimal spacing of reserves that maximises species viability?
• The spread of HIV - can we model the spread of HIV in mobile heterosexual populations?
• Gene duplicates - can we estimate the probability that eventually every chromosome in a population is a descendant of the one which initially carried the duplicate?
• Population networks - can ensemble behaviour be deduced from models for the behaviour of individuals?

Researchers

• Chief Investigator: Phil Pollett
• Research Fellow: Martin O'Hely
• PhD student : Fionnuala Buckley
• PhD student : Thomas Taimre

Sub-themes

• Genetic models
• Population networks (metapoulations)
• Models for the spread of infection

Research Outcomes

• Diffusion approximation techniques were derived to estimate the probability of "preservation", the event that eventually every chromosome in a population is a descendant of the one which initially carried the duplicate.
• A simple model was proposed that gives the likelihood of of map change, namely the loss of functional copies of a gene at its original locus, as we well as the time taken for a map change.
• Markovian models for population processes in continuous time were studied and questions concerning the behaviour of ensembles of individuals were addressed, and in particular what can be deduced from models for individual behaviour (equilibrium, quasi-equilibrium and time-dependent behaviour).
• The problem of estimating arrival and service rates in a network was addressed, in particular, when queue length data was collected at successive, but not necessarily equally spaced, time points. The estimation procedure made use of an Ornstein-Uhlenbeck diffusion approximation to the Markov process description of the queues.
• Several stochastic models for the spread of HIV in a heterosexual mobile population were proposed. Deterministic and diffusion analogues of these models were derived to assess stability and equilibrium behaviour.
• A stochastic spatially explicit model that includes population and habitat dynamics was used to explain why persistence is affected by different habitat disturbance regimes, and the way in which disturbances spread, when populations are compact or elongated. It was discovered that the risk of population extinction is larger for spatially aggregated disturbances than for spatially random disturbances.
• Using a simple discrete-time Markov chain model for the presence or absence of a species, the optimal spacing between marine reserves was obtained for maximising the viability of a species occupying a reserve network.

Awards and Achievements

• Phil Pollett held the 2007 Alan David Richards Visiting Fellowship in Mathematics, Grey College Durham (UK)

Industry Collaborators

• CSIRO Marine and Atmospheric Research

Collaborating Researchers

• Dirk P. Kroese (University of Queensland)
• Hugh P. Possingham (University of Queensland)
• Joshua V. Ross (University of Cambridge)
• Asrul Sani (University of Queensland)
• Severine Vuilleumier (University of Bern)
• Liam D. Wagner (University of Queensland)
• Chris Wilcox (CSIRO Marine and Atmospheric Research)
• Lisa Wockner (University of Queensland)

Highlight Publications

• O'Hely, M. (2007) A diffusion model for the fate of tandem gene duplicates in diploids. Theoretical Population Biology 71, 491-501.
• Sani, A., Kroese, D.P. and P.K. Pollett (2007) Stochastic models for the spread of HIV in a mobile heterosexual population. Mathematical Biosciences 208, 98-124.