What is a metapopulation? And why should I care?

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What is a metapopulation? And why should I care?

• Hugh Possingham and friends

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How to manage a metapopulationProblem 1

• Michael Westphal (UC Berkeley),
• Drew Tyre (U Nebraska), Scott Field (UQ)
• Can we make metapopulation theory useful?

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Specifically how to reconstruct habitat for a
small metapopulation

• Part of general problem of optimal landscape
  design the dynamics of how to reconstruct
  landscapes
• Minimising the extinction probability of one part
  of the Mount Lofty Ranges Emu-wren population.
• Metapopulation dynamics based on Stochastoc Patch
  Occupancy Model (SPOM) of Day and Possingham
  (1995)
• Optimisation using Stochastic Dynamic Programming
  (SDP) see Possingham (1996)

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The Mount Lofty Ranges, South Australia
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MLR Southern Emu Wren

• Small passerine (Australian malurid)
• Very weak flyer
• Restricted to swamps/fens
• Listed as Critically Endangered subspecies
• About 450 left hard to see or hear
• Has a recovery team (flagship)

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The Cleland Gully Metapopulation basically
isolated Figure shows options Where should we
revegetate now, and in the future? Does it
depend on the state of the metapopulation?
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Stochastic Patch Occupancy Model(Day and
Possingham, 1995)
State at time, t, (0,1,0,0,1,0)
Intermediate states
Extinction process
(0,1,0,0,1,0)
(0,1,0,0,0,0)
(0,0,0,0,1,0)
Colonization process
State at time, t1, (0,1,1,0,1,0)
Plus fire
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The SPOM

• A lot of population states, 2n, where n is the
  number of patches. The transition matrix is 2n
  by 2n in size (128 by 128 in this case).
• A chain binomial model SPOM has recolonisation
  and local extinction where functional forms and
  parameterization follow Moilanen and Hanski
• Overall transition matrix, a combination of
  extinction and recolonization, depends on the
  landscape state, a consequence of past
  restoration activities

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Decision theory steps

• Set objective (minimize extinction prob)
• Define state variables (population and landscape
  states) and control variables (options for
  restoration)
• Describe state dynamics the SPOM
• Set constraints (one action per 5 years)
• Solve in this case SDP

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Control options (one per 5 years, about 1ha
reveg) E5 largest patch bigger, can do 6
times E2 most connected patch bigger, 6
times C5 connect largest patch C2 connect
patches1,2,3 E7 make new patch DN do nothing
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Management trajectories1 only largest patch
occupied
C5
E5
E5
E5
E5
E5
E5
E7
DN
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Management trajectories2 all patches occupied
E5
E5
E2
E2
C5
C2
E5
E2
E5
E5
E7
DN
E5
E5
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Take home message

• Metapopulation state matters
• Actions justifiable but no clear sweeping
  generalisation, no simple rule of thumb!
• Previous work has assumed that landscape and
  population dynamics are uncoupled. This paper
  represents the first spatially explicit optimal
  landscape design for a threatened species.

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Other issues

• Computational problems
• Problems, models and algorithms what are they?

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Optimal translocation strategiesProblem 2
Brigitte Tenhumberg, Drew Tyre (U Nebraska),
Katriona Shea (Penn State)

• Consider the Arabian Oryx Oryx leucoryx if we
  know how many are in the wild, and in a zoo, and
  we know birth and death rates in the zoo and the
  wild, how many should we translocate to or from
  the wild to maximise persistence of the wild
  population

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Oryx problem
Growth rate R 0.85 Capacity 50
Growth rate R 1.3 Capacity 20
??
Zoo Population
Wild Population
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Result base parameters
R release, mainly when population in zoo is
near capacity C capture, mainly when zoo
population small, capture entire wild population
when this would roughly fill the zoo
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If zoo growth rate changes, results change but
for a new species we wont know R in the zoo
Enter active adaptive management, Management
with a plan for learning
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Metapopulaton dynamics in a dynamic landscape

• What do mussels, Leadbeaters possum and annual
  herbs have in common? Empirical conversations
  over a long time

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Eradicate, Exploit, Conserve

Decision Theory
Pure Ecological Theory