What is a metapopulation? And why should I care? Hugh Possingham and friends

How to manage a metapopulation Problem 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, 2 n, where n is the number of patches. The transition matrix is 2 n by 2 n 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

E5 Management trajectories: 1 – only largest patch occupied C5 E5 E7 DN

E5 Management trajectories: 2 – all patches occupied C2 E2 E7DN E5 E2 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 strategies Problem 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 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

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 + =