# Decision Theory for Conservation Biology

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 Hughs 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 Extinction process (0,1,0,0,1,0) (0,1,0,0,0,0) (0,0,0,0,1,0)

Plus fire Colonization process State at time, t+1, (0,1,1,0,1,0) 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 Management trajectories: 1 only largest patch occupied C5 E5 E5 E5 E5

E5 E5 E7 DN Management trajectories: 2 all patches occupied E2 DN

C2 E5 E5 E2 C5 E7 E5

E5 E5 E5 E5 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 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 Oryx problem

Growth rate R = 0.85 Capacity = 50 Growth rate R = 1.3 Capacity = 20 ?? Zoo Population Wild Population

Wild Population Result base parameters R C Captive Population 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 wont know R in the zoo Enter active adaptive management,

Management with a plan for learning Metapopulaton dynamics in a dynamic landscape What do mussels, Leadbeaters possum and annual herbs have in common? Empirical conversations over a long time Eradicate, Exploit, Conserve Pure Ecological Theory

+ = Applied Theoretical Ecology Decision Theory

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