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Report on MASCOS Workshop on Metapopulations

The University of Queensland
Thursday 2nd September 2004



General   A metapopulation is a population that occupies several geographically separated habitat patches. Although the individual patches may become empty through local extinction, they may be recolonized through migration from other patches. There is considerable empirical evidence which suggests that a balance between migration and extinction is reached that enables metapopulations to persist for long periods and there has been considerable interest in developing methods which account for the persistence of these populations and which provide an effective means of studying their long-term behaviour before extinction occurs.

This workshop, sponsored by the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems (MASCOS), brought together ecologists and mathematicians to examine recent developments in metapopulation modelling.

Invited speakers

  • Andrew Barbour (University of Zürich)
  • Michael Bode (University of Queensland)
  • Ben Cairns (University of Queensland)
  • Jo-anne Holley (Department of Primary Industries and Fisheries)
  • Phil Pollett (University of Queensland)
  • Hugh Possingham (University of Queensland)
  • Tracey Regan (University of Queensland)
  • Joshua Ross (University of Queensland)
  • Severine Vuilleumier (University of Queensland)

[There were no contributed papers]

Venue   Riverview Room, Emmanuel College, St Lucia Campus, University of Queensland

Organizers   Ben Cairns and Phil Pollett (MASCOS, University of Queensland)

Programme  

  09:30  Opening
  09:40  Hugh Possingham  "What is a metapopulation and why should I care?"
  10:30  --Break-- [Refeshments provided]
  11:00  Tracey Regan   "An application of spatially structured metapopulation modelling to forest planning"
  11:30  Phil Pollett  "Limiting conditional distributions for stochastic metapopulation models"
  12:00  Ben Cairns  "Limit theorems for metapopulation processes subject to catastrophes"
  12:30  --Lunch Break-- [Lunch provided]
  13:30  Andrew Barbour  "Asymptotic behaviour of a metapopulation"
  14:30  Severine Vuilleumier   "Cognitive ability affects connectivity in metapopulations: A simulation approach"
  15:00  --Break-- [Refeshments provided]
  15:30  Jo-anne Holley   "Red Imported Fire Ant: an Australian experience"
  16:00  Joshua Ross  "Diffusion approximation for a structured metapopulation model"
  16:30  Michael Bode  "Understanding the effects of complex migration in metapopulations"
  17:00  Close

Abstracts

  • Andrew Barbour

    Asymptotic behaviour of a metapopulation

    Abstract: A simple metapopulation model consists of N identical patches. Within each patch, the population evolves as a logistic birth and death process, but it is also subject to random catastrophes. Recolonization occurs because of random migration between patches. For large N, the stochastic evolution can be approximated by the solution of an infinite system of ODEs; we are interested in its equilibria. One such is that all patches are empty, but we show that there may be another, corresponding to a stochastic `quasi-equilibrium', which then attracts most solutions of the system. Our method of proof involves stochastic comparison arguments, based on couplings of the birth and death processes describing individual patch dynamics. (Joint work with A. Pugliese)

  • Michael Bode

    Understanding the effects of complex migration in metapopulations

    Abstract: A metapopulation's dynamics are defined in part by migration between the separate habitat patches. When migrating individuals interact with the heterogeneous landscape between these patches, the resulting patterns can differ significantly from well-mixed or distance-based migration assumptions. Analysing metapopulations as complex networks can accurately predict the effect of these migration patterns on the metapopulation dynamics, and help to more directly understand the roles of migration.

    [talk]

  • Ben Cairns

    Limit theorems for metapopulation processes subject to catastrophes

    Abstract: Of particular interest in metapopulation modelling are those processes with a fixed maximum number of patches, N. However, this maximum may be relatively large, and if the metapopulation process is multidimensional then its state space may be very large indeed. We present the problem of approximating such processes as N becomes large. In particular, we consider a model with dynamics in the suitability of habitat patches, driven by catastrophic events arriving at a constant rate and with binomial size. With appropriate scaling, the process has a piecewise-deterministic limit, consisting of deterministic trajectories that are interrupted by linear, downward jumps at the catastrophe times. We also consider a functional central limit theorem for the process, which yields an approximation consisting of a diffusion that evolves between Normal catastrophes with a linear mean size.

    [talk]

  • Jo-anne Holley

    Red Imported Fire Ant: an Australian experience

    Abstract: The Red Imported Fire Ant (Solenopsis invicta Buren) was formally recognised in Brisbane, Australia in 2001 and two subpopulations identified. Genetic studies suggest the USA as the most likely origin of the Brisbane infestation. In this presentation we consider some of the factors at work in the early stage of a fire ant infestation. This invasion appears to have been: assisted by a number of anthropomorphic practices, such as movements of material and land use changes; and hindered by the presence of a substantial number of the polygyne colonies, a decade of hotter and drier years than normal and interactions with local ant fauna.

    [talk]

  • Phil Pollett

    Limiting conditional distributions for stochastic metapopulation models

    Abstract: We consider a Markovian model proposed by Gyllenberg and Silvestrov [J. Math. Biol. 33, 35-70, 1994] for studying the long-term behaviour of a metapopulation. There is considerable empirical evidence reported in the work of Hanski and Gilpin which suggests that a balance between migration and extinction is obtained which enables these populations to persist for long periods. For this reason, there has been considerable interest in developing methods which account for the persistence of these populations and which provide an effective means of studying the long-term behaviour before extinction occurs. We propose a method, based on work of Jacka and Roberts [J. Appl. Probab. 32, 902-916, 1995] on weak convergence of conditioned Markov processes. We compare and contrast this with the methods of Gyllenberg and Silvestrov (quasi-stationary and pseudo-stationary distributions) as well as those of Day and Possingham [Theoret. Pop. Biol. 48, 333-360, 1995], which are based on the classical notion of a quasi-stationary distribution.

    [talk]

  • Hugh Possingham

    What is a metapopulation and why should I care?

    Abstract: I will discuss the concept of a metapopulation. Specifically I will:

    1. introduce some of the pros and cons of the metapopulation approach
    2. illustrate this with biological examples
    3. raise the issue of habitat dynamics
    4. briefly talk about the suite of modelling options
    5. mention the idea of metapopulation control (and provide an example)

    [talk]

  • Tracey Regan

    An application of spatially structured metapopulation modelling to forest planning

    Abstract: The use of Australia's forests for competing demands of timber production and the conservation of biological diversity gives rise to questions regarding the implications of anthropogenic disturbance on species persistence. Such activities have the potential to result in reductions in the habitat available to sensitive species as well as decreased probabilities of dispersal and persistence through fragmentation of suitable habitat. We apply spatially structured metapopulation models to forest sensitive species that describes the dynamics of each population with structured demographic models and incorporates spatial dynamics by modeling dispersal and habitat dynamics. The aim is to investigate alternative spatial and temporal management options that provides timely feedback to managers about the sustainability of current and alternative forest management options, and to support the development of better-targeted and more relevant forest planning.

    [talk]

  • Joshua Ross

    Diffusion approximation for a spatially realistic structured metapopulation model

    Abstract: We consider a stochastic metapopulation model for the number of individuals at each patch in a network of k patches. Local population dynamics are governed by a stochastic logistic model and spatial structure is incorporated through a density-dependent migration term, which allows migration to be dependent upon the distance between patches. A suitably scaled version of our model converges, uniformly in probability over finite time intervals, to a system of k differential equations. The fluctuations about the equilibrium point of this system can be accurately described by a k-dimensional normal approximation.

    [talk]

  • Severine Vuilleumier

    Cognitive ability affects connectivity in metapopulations: A simulation approach

    Abstract: Connectivity among demes in a metapopulation depends on both the landscape's and the focal organism's properties (including its mobility and cognitive abilities). Using individually-based simulations, we contrast the consequences of three different cognitive strategies on several measures of metapopulation connectivity. Model animals search suitable habitat patches while dispersing through a model landscape made of cells varying in size, shape, attractiveness and friction. Our results point to the important effect of cognitive ability of dispersers on the connectivity, genetics and dynamics of metapopulations.

    [talk]

Participants  

  Name Email Affiliation
       
  Andrew Barbour adb at amath.unizh.ch Institute of Mathematics, University of Zürich
  Shaun Belward shaun.belward at jcu.edu.au School of Mathematical and Physical Sciences, James Cook University
  Michael Bode mbode at maths.uq.edu.au Department of Mathematics, University of Queensland
  Michael Bulmer mrb at maths.uq.edu.au Department of Mathematics, University of Queensland
  Ben Cairns bjc at maths.uq.edu.au MASCOS, University of Queensland
  Luke Connelly l.connelly at uq.edu.au Centre of National Research on Disability and Rehabilitation Medicine, University of Queensland
  Jemery Day Jemery.Day at csiro.au CSIRO Marine Research
  Valerie Debuse valerie.debuse at dpi.qld.gov.au Department of Primary Industries and Fisheries, Queensland State Government
  Nick Ellis Nick.Ellis at csiro.au CSIRO Marine Research
  Jo-anne Holley Jo-anne.Holley at dpi.qld.gov.au Department of Primary Industries and Fisheries, Queensland State Government
  Liana Joseph l.joseph at zen.uq.edu.au The Ecology Centre, University of Queensland
  Dirk Kroese kroese at maths.uq.edu.au Department of Mathematics, University of Queensland
  Dharma Lesmono dlesmono at maths.uq.edu.au Department of Mathematics, University of Queensland
  Andrew Lowe a.lowe at uq.edu.au School of Life Sciences, University of Queensland
  Sharon Marsden Sharon.Marsden at dpi.qld.gov.au Department of Primary Industries and Fisheries, Queensland State Government
  Alana Moore a.moore at epsa.uq.edu.au Sustainable Minerals Institute, University of Queensland
  Justine Murray j.murray at sols.uq.edu.au School of Life Sciences, University of Queensland
  Jeremy O'Reilly jor at maths.uq.edu.au Department of Mathematics, University of Queensland
  David Pavlacky d.pavlacky at uq.edu.au School of Life Sciences, University of Queensland
  Ben Petschel b.petschel at uq.edu.au Department of Mathematics, University of Queensland
  Phil Pollett pkp at maths.uq.edu.au MASCOS, University of Queensland
  Hugh Possingham hpossingham at zen.uq.edu.au The Ecology Centre, University of Queensland
  Tracey Regan t.regan at uq.edu.au The Ecology Centre, University of Queensland
  Jonathan Rhodes j.rhodes at uq.edu.au School of Geography, Planning and Architecture and The Ecology Centre, University of Queensland
  Joshua Ross jvr at maths.uq.edu.au MASCOS, University of Queensland
  Mark Seeto mbs at maths.uq.edu.au Department of Mathematics, University of Queensland
  David Sirl dsirl at maths.uq.edu.au Department of Mathematics, University of Queensland
  Antony Stace aws at maths.uq.edu.au MASCOS, University of Queensland
  Thomas Taimre ttaimre at maths.uq.edu.au MASCOS, University of Queensland
  Tianhai Tian tian at maths.uq.edu.au ACMC, University of Queensland
  Severine Vuilleumier severine.vuilleumier at epfl.ch The Ecology Centre, University of Queensland
  Liam Wagner ldw at maths.uq.edu.au Department of Mathematics, University of Queensland
  Kerrie Wilson k.wilson2 at uq.edu.au The Ecology Centre, University of Queensland
  Hanjun Zhang hjz at maths.uq.edu.au MASCOS, University of Queensland
  Justin Xi Zhu j.zhu at imb.uq.edu.au IMB, University of Queensland

The Centre of Excellence for Mathematics and Statistics
of Complex Systems is funded by the Australian Research
Council, with additional support from the Queensland
State Government and the University of Queensland