1. Rescuing an Endangered Species with Monte Carlo AI Tom Dietterich based on work by Dan Sheldon et al. 1

2. Overview Collaborative project to develop optimal conservation strategies for Red-Cockaded Woodpecker (RCW) – Institute for Computational Sustainability (Cornell and OSU): Daniel Sheldon, Bistra Dilkina, Adam Elmachtoub, Ryan Finseth, Ashish Sabharwal, Jon Conrad, Carla P. Gomes, David Shmoys – The Conservation Fund: Will Allen, Ole Amundsen, Buck Vaughan Recent paper: Maximizing the Spread of Cascades Using Network Design, UAI 2010 2

3. Red-Cockaded Woodpecker Originally wide-spread species in S. US Population now shrunken to 1% of original size 5000 breeding groups ~12,000 birds Federally-listed endangered species Lifestyle: – nests in holes in 80yo+ Longleaf pine trees – sap from the trees defends the nest – takes several years to excavate the hole Will colonize man-made holes Wikipedia 3

4. Spatial Conservation Planning What is the best land acquisition and management strategy to support the recovery of the Red-Cockaded Woodpecker (RCW)? 4

5. Problem Setup Given limited budget, what parcels should we conserve to maximize the expected number of occupied patches in T years? Conserved parcels Available parcels Current patches Potential patches 5

6. Metapopulation Model Population dynamics in fragmented landscape Stochastic patch occupancy model (SPOM) – Patches = occupied / unoccupied – Colonization – Local extinction 6

7. SPOM: Stochastic Patch Occupancy Model – Patches are either occupied or unoccupied – Two types of stochastic events: Local extinction: occupied  unoccupied Colonization: unoccupied  occupied (from neighbor) – Independence among all events Time 1 Time 2 7

8. Network Cascades Models for diffusion in (social) networks – Spread of information, behavior, disease, etc. – E.g.: suppose each individual passes rumor to friends independently with probability ½ Note: “activated” nodes are those reachable by red edges 8

9. SPOM Probability Model k j j i i j p ij 1-β j p lj l l i k l 9

10. Monte Carlo Simulation of a SPOM Key idea: a metapopulation model is a cascade in the layered graph representing patches over time a b c d e a b c d e a b c d e a b c d e a b c d e 12345 Colonization Non-extinction Patches Time 10

11. Metapopulation = Cascade Key idea: a metapopulation model is a cascade in the layered graph representing patches over time a b c d e a b c d e a b c d e a b c d e a b c d e 12345 Patches Time 11

12. Metapopulation = Cascade Key idea: a metapopulation model is a cascade in the layered graph representing patches over time a b c d e a b c d e a b c d e a b c d e a b c d e 12345 Patches Time 12

13. Metapopulation = Cascade Key idea: a metapopulation model is a cascade in the layered graph representing patches over time a b c d e a b c d e a b c d e a b c d e a b c d e 12345 Patches Time 13

14. Metapopulation = Cascade Key idea: a metapopulation model is a cascade in the layered graph representing patches over time a b c d e a b c d e a b c d e a b c d e a b c d e 12345 Patches 14

15. Monte Carlo Simulations Each simulation can produce a different cascade a b c d e a b c d e a b c d e a b c d e a b c d e 12345 Patches 15

16. Insight #1: Objective as Network Connectivity Conservation objective: maximize expected # occupied patches at time T Cascade objective: maximize expected # of target nodes reachable by live edges i j k l m i j k l m i j k l m i j k l m i j k l m targets Live edges 16

17. Insight #2: Management as Network Building Conserving parcels adds nodes and (stochastic) edges to the network Parcel 1 Parcel 2 Initial network 17

18. Insight #2: Management as Network Building Conserving parcels adds nodes to the network Parcel 1 Parcel 2 Initial network 18

19. Insight #2: Management as Network Building Conserving parcels adds nodes to the network Parcel 1 Parcel 2 Initial network 19

20. Monte Carlo Evaluation of a Proposed Purchase Plan 20

21. Research Question 21

22. Evaluating a Purchase Plan Plan 1: Purchase nothing Initial network Parcel 1 Parcel 2 22

23. Plan 2: Purchase Parcel #1 Initial network Parcel 1 Parcel 2 23

24. Plan 3: Purchase Parcels 1 and 2 Initial network Parcel 1 Parcel 2 24

25. 25

26. Solution Strategy (aka Sample Average Approximation) 26

27. Solving the Deterministic Problem CPLEX commercial optimization package (sold by IBM; free to universities) Applies a method known as Branch and Bound NP-Hard, so can take a long time but often finds a solution if the problem isn’t too big or too hard 27

28. Experiments 443 available parcels 2500 territories 63 initially occupied 100 years Population model is parameterized based (loosely) on RCW ecology Short-range colonizations (<3km) within the foraging radius of the RCW are much more likely than long-range colonizations 28

29. Greedy Baselines Adapted from previous work on influence maximization Start with empty set, add actions until exhaust budget – Greedy-uc – choose action that results in biggest immediate increase in objective [Kempe et al. 2003] – Greedy-cb – use ratio of benefit to cost [Leskovec et al. 2007] These heuristics lack performance guarantees! 29

30. Results M = 50, N = 10, N test = 500 Upper bound! 30

31. Results M = 50, N = 10, N test = 500 Upper bound! 31

32. Results Conservation Reservoir Initial population M = 50, N = 10, N test = 500 Upper bound! 32

33. Conservation Strategies 33 Both approaches build outward from source – Greedy buys best patches next to currently-owned patches – Optimal solution builds toward areas of high conservation potential In this case, the two strategies are very similar Conservation Reservoir Source population

34. A Harder Instance Move the conservation reservoir so it is more remote. 34

35. Conservation Strategies Greedy Baseline SAA Optimum (our approach) $150M$260M$320M Build outward from sources Path-building (goal-setting) 35

36. Shortcomings of the Method 36

37. Status The Conservation Fund is making purchasing decisions based (partially) on the plans computed using this model Alan Fern, Shan Xue, and Dan Sheldon have developed an extension that proposes a schedule for purchasing the parcels 37