What is a metapopulation? And why should I care?

Hugh Possingham and friends

How to manage a metapopulationProblem 1

Michael Westphal (UC Berkeley),Drew Tyre (U Nebraska), Scott Field (UQ)

Can we make metapopulation theory useful?

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)

The Mount Lofty Ranges, South Australia

Hugh’s birthplace

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)

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?

Stochastic Patch Occupancy Model(Day and Possingham, 1995)

State at time, t, (0,1,0,0,1,0)

Intermediate states

State at time, t+1, (0,1,1,0,1,0)

(0,0,0,0,1,0)

Extinction process

Colonization process

(0,1,0,0,1,0)

(0,1,0,0,0,0)

Plus fire

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

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

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

E5E5E5E5E5

Management trajectories:1 – only largest patch occupied

C5

E5

E7

DN

E5E5E5E5

Management trajectories:2 – all patches occupied

C2E2

E7DNE5

E5E5E2 C5

E2

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.

Other issues

• Computational problems• Problems, models and algorithms – what

are they?

Optimal translocation strategiesProblem 2

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

Brigitte Tenhumberg, Drew Tyre (U Nebraska), Katriona Shea (Penn State)

Oryx problem

Zoo Population

Growth rate R = 1.3 Capacity = 20

Wild Population

??

Growth rate R = 0.85 Capacity = 50

Result – base parameters

Captive Population

Wild

Pop

ulat

ion

C

R

Captive Population

Wild

Pop

ulat

ion

C

R

R = release, mainly when population in zoo is near capacityC = capture, mainly when zoo population small, capture entire wild population when this would roughly fill the zoo

If zoo growth rate changes, results change – but for a “new” species we

won’t know R in the zoo

Enter – active adaptive management,Management with a plan for learning

Metapopulaton dynamics in a dynamic landscape

What do mussels, Leadbeater’s possum and annual herbs have in common? Empirical conversations over a long time

Eradicate, Exploit, Conserve

Decision TheoryPure Ecological Theory

Applied

Theoretical

Ecology

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