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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
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09:30 |
Opening
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09:40 |
Hugh Possingham |
"What is a metapopulation and why should I care?" |
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10:30 |
--Break-- |
[Refeshments provided] |
|
11:00 |
Tracey Regan |
"An application of spatially structured metapopulation
modelling to forest planning" |
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11:30 |
Phil Pollett |
"Limiting conditional distributions for stochastic
metapopulation models" |
|
12:00 |
Ben Cairns |
"Limit theorems for metapopulation processes subject to
catastrophes" |
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12:30 |
--Lunch Break-- |
[Lunch provided] |
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13:30 |
Andrew Barbour |
"Asymptotic behaviour of a metapopulation" |
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14:30 |
Severine Vuilleumier |
"Cognitive ability affects connectivity in
metapopulations: A simulation approach" |
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15:00 |
--Break-- |
[Refeshments provided] |
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15:30 |
Jo-anne Holley
|
"Red Imported Fire Ant: an Australian experience" |
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16:00 |
Joshua Ross |
"Diffusion approximation for a structured
metapopulation model" |
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16:30 |
Michael Bode |
"Understanding the effects of complex migration in
metapopulations" |
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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:
- introduce some of the pros and cons of the
metapopulation approach
- illustrate this with biological examples
- raise the issue of habitat dynamics
- briefly talk about the suite of modelling options
- 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
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Name |
Email |
Affiliation |
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Andrew Barbour |
adb at amath.unizh.ch
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Institute of Mathematics, University of Zürich
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Shaun Belward |
shaun.belward at jcu.edu.au
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School of Mathematical and Physical Sciences,
James Cook University
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Michael Bode |
mbode at maths.uq.edu.au
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Department of Mathematics,
University of Queensland
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Michael Bulmer
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mrb at maths.uq.edu.au
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Department of Mathematics,
University of Queensland
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Ben Cairns |
bjc at maths.uq.edu.au
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MASCOS, University of Queensland
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Luke Connelly |
l.connelly at uq.edu.au
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Centre of National Research on Disability and Rehabilitation Medicine,
University of Queensland
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Jemery Day
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Jemery.Day at csiro.au
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CSIRO Marine Research
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Valerie Debuse |
valerie.debuse at dpi.qld.gov.au
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Department of Primary Industries and Fisheries,
Queensland State Government
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Nick Ellis |
Nick.Ellis at csiro.au
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CSIRO Marine Research
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Jo-anne Holley
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Jo-anne.Holley at dpi.qld.gov.au
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Department of Primary Industries and Fisheries,
Queensland State Government
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Liana Joseph |
l.joseph at zen.uq.edu.au
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The Ecology Centre, University of Queensland
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Dirk Kroese
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kroese at maths.uq.edu.au
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Department of Mathematics, University of Queensland
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Dharma Lesmono |
dlesmono at maths.uq.edu.au
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Department of Mathematics,
University of Queensland
|
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Andrew Lowe
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a.lowe at uq.edu.au
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School of Life Sciences,
University of Queensland
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Sharon Marsden
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Sharon.Marsden at dpi.qld.gov.au
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Department of Primary Industries and Fisheries,
Queensland State Government
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Alana Moore
|
a.moore at epsa.uq.edu.au
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Sustainable Minerals Institute,
University of Queensland
|
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Justine Murray
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j.murray at sols.uq.edu.au
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School of Life Sciences,
University of Queensland
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Jeremy O'Reilly
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jor at maths.uq.edu.au
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Department of Mathematics,
University of Queensland
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David Pavlacky
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d.pavlacky at uq.edu.au
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School of Life Sciences,
University of Queensland
|
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Ben Petschel |
b.petschel at uq.edu.au
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Department of Mathematics,
University of Queensland
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Phil Pollett
|
pkp at maths.uq.edu.au
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MASCOS, University of Queensland
|
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Hugh Possingham
|
hpossingham at zen.uq.edu.au
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The Ecology Centre, University of Queensland
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Tracey Regan
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t.regan at uq.edu.au
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The Ecology Centre, University of Queensland
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Jonathan Rhodes
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j.rhodes at uq.edu.au
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School of Geography, Planning and Architecture and
The Ecology Centre, University of Queensland
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Joshua Ross
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jvr at maths.uq.edu.au
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MASCOS, University of Queensland
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Mark Seeto
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mbs at maths.uq.edu.au
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Department of Mathematics,
University of Queensland
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David Sirl
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dsirl at maths.uq.edu.au
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Department of Mathematics,
University of Queensland
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Antony Stace
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aws at maths.uq.edu.au
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MASCOS, University of Queensland
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Thomas Taimre
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ttaimre at maths.uq.edu.au
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MASCOS, University of Queensland
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Tianhai Tian
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tian at maths.uq.edu.au
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ACMC, University of Queensland
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Severine Vuilleumier
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severine.vuilleumier at epfl.ch
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The Ecology Centre, University of Queensland
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Liam Wagner
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ldw at maths.uq.edu.au
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Department of Mathematics,
University of Queensland
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Kerrie Wilson
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k.wilson2 at uq.edu.au
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The Ecology Centre, University of Queensland
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Hanjun Zhang
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hjz at maths.uq.edu.au
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MASCOS, University of Queensland
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Justin Xi Zhu
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j.zhu at imb.uq.edu.au
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IMB, University of Queensland
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