Research Priorities

• Population models - how do we efficiently calibrate Markovian models from discrete-sampled abundance data?
• Marine ecology - how do we estimate animal movements using information contained in family trees?

Researchers

• Chief Investigator: Phil Pollett
• Research Fellow: Ross McVinish
• PhD student: Robert Cope
• PhD student: Daniel Pagendam
• PhD student: Nimmy Thaliath
• Vacation scholar: Trent Spears

Collaborating Researchers

• Prof. Anyue Chen, Department of Mathematical Sciences, University of Liverpool, UK
• Dr Janet Lanyon, School of Biological Sciences, University of Queensland
• Prof. Junping Li, School of Mathematical Science and Computing Technology, Central South University Changsha, China
• Dr Joshua Ross, King's College, University of Cambridge, UK
• Dr Jennifer Seddon, School of Veterinary Science, University of Queensland
• Prof. Hanjun Zhang, School of Mathematics and Computational Science, Xiangtan University, China

Selected Research Projects

• General Stochastic Models for Branching Phenomena

  Project leader: Phil Pollett (UQ)
  Researchers: Anyue Chen (University of Liverpool), Junping Li (Central South University Changsha) and Hanjun Zhang (Xiangtan University)

  A common feature of branching models is that particles or individuals behave independently producing descendants according to the same rule. However, since particles may interact, through collision or some other mechanism, this branching property may be lost and thus more general branching models are needed. We are studying a particularly interesting class, which we call the weighted (or non-linear) Markov branching processes. We are examining questions concerning the existence and uniqueness of such processes, and criteria for extinction and explosivity. Our methods have led to advances in the theory of bulk queues, where individuals can arrive or be served in batches.

  Research outputs

  • Chen, A., Pollett, P.K., Li, J. and H. Zhang (2010) Markovian bulk-arrival and bulk-service queues with state-dependent control. Queueing Systems 64, 267-304.
  • Chen, A., Pollett, P.K., Li, J. and H. Zhang (2010) Uniqueness, extinction and explosivity of generalised Markov branching processes with pairwise interaction. Methodology and Computing in Applied Probability 12, 511-531.
• Design and Inference for Population Models

  Project leader: Phil Pollett (UQ)
  Researchers: Anthony Dooley (UNSW), Daniel Pagendam (UQ) and Joshua Ross (University of Cambridge)

  Statistical inference for discretely observed stochastic models is an active and challenging area of research. However, whilst much attention has been given to methodologies for parameter estimation, little work has been done to find optimal schedules for observing these processes. We have addressed the topic of optimal experimental design for density dependent Markovian models, which are routinely encountered in ecology and epidemiology, with a view to improving the manner in which data is collected for both controlled and natural experiments.

  Research outputs

  • Pagendam, D.E. and P.K. Pollett (2010) Locally optimal designs for the simple death process. Journal of Statistical Planning and Inference 140, 3096-3105.
  • Pagendam, D.E. and P.K. Pollett (2010) Robust optimal observation of a metapopulation. Ecological Modelling 221, 2521-2525.
  • Pollett, P.K., Dooley, A.H. and J.V. Ross (2010) Modelling population processes with random initial conditions. Mathematical Biosciences 223, 142-150.

• Animal Movement Between Populations Deduced from Family Trees

  Project leader: Phil Pollett (UQ)
  Researchers: Robert Cope (UQ), Janet Lanyon (UQ) and Jennifer Seddon (UQ)

  Our aim is to develop new methods for estimating animal movements using information contained in family trees. Movement estimates are essential to population models that assist natural resource managers to plan species recovery and to predict the effect of future challenges, such as human-mediated activities and climate change. We have evaluated several methods for constructing family trees from genetic data and developed a statistic that describes animal movement between populations which is based on the families whose members were sampled in more than one population; empirical data has been sourced from a long-term mark-recapture study of dugongs in Moreton Bay, and new samples from two adjacent populations.

  Research outputs

  • This work will be presented at the 19th Biennial Conference of the Society for Marine Mammalogy (Tampa, USA, November 27-December 2, 2011)

Awards and Achievements

• Trent Spears was awarded an AMSI Vacation Scholarship for a project titled "Probability with Martingales for Economics and Finance" (November 2010)
• Daniel Pagendam completed his PhD degree (awarded November 2010) at the University of Queensland: thesis title "Experimental Design and Inference for Population Models"