Rocky Mountain Population Sandhill Cranes

Transcription

1 Rocky Mountain Population Sandhill Cranes

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3 RMP Crane Monitoring Programs Annual Population Count (index) Recruitment survey in Fall stopover (very good) Hunter harvest survey (very good) Historic banding/recovery/resight data

4 Modeling Age-Structure? N t,1 ɸ t1 N t+1,1 ɸ n1 N T,1 N t,2 ɸ t2 N t+1,2 ɸ n2 N T,2 N t,3 ɸ t3 N t+1,3 ɸ n3 N T,3 N t,4 λ 5,t ɸ t4 N t+1,4 λ 5,T ɸ n4 N T,4 N t,5 λ 6,t ɸ t5 N t+1,5 λ 6,T ɸ n5 N T,5 N t,6 ɸ t6 N t+1,6 ɸ n6 N T,6 N t,7 λ 7,t ɸ t7 N t+1,7 λ 7,T ɸ t7 N T,7 Brian D. Gerber, William L. Kendall, and Mevin B. Hooten Integrated Population Modeling and Harvest Decisions of Sandhill Cranes

5 Juvenile λ t Adult N J1t Summer Breeding Area Summer Breeding Area N A1t φ 12 φ A4 φ A2 Fall N J2t San Luis Valley Spring N A4(t+1) San Luis Valley Fall N A2t φ A3 Wintering Area t Observed N.1 = N J1t +N A1t P t = N J2t N J2t +NA 2t

6 Population Dynamics and Management of Cackling Geese Perry J. Williams 1,2 Craig R. Ely 3 William L. Kendall 4 Mevin B. Hooten 4,2 Joel A. Schmutz 3 1 Colorado Cooperative Fish and Wildlife Research Unit Department of Fish, Wildlife, and Conservation Biology Colorado State University 2 Department of Statistics Colorado State University 3 U.S. Geological Survey Alaska Science Center 4 U.S. Geological Survey Colorado Cooperative Fish and Wildlife Research Unit Department of Fish, Wildlife, and Conservation Biology Colorado State University Williams et al. Cackling goose management October 28, / 26

7 Background and Motivation Williams et al. Cackling goose management October 28, / 26

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10 Photo: Chris Nicolai Williams et al. Cackling goose management October 28, / 26

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12 Objective: Develop a decision tool for managing cackling goose abundance. Williams et al. Cackling goose management October 28, / 26

13 Objective: Develop a decision tool for managing cackling goose abundance. Objective function for multiple management objectives. Model population dynamics. Predict response of population dynamics to management actions. Identify optimal management policy. Williams et al. Cackling goose management October 28, / 26

14 Population Model Williams et al. Cackling goose management October 28, / 26

15 Data Annual aerial surveys Photo: USFWS Mark-resight data Photo: Andre Breault Williams et al. Cackling goose management October 28, / 26

16 Aerial survey Count of geese during nesting period on Yukon-Kuskokwim Delta present. y t = n 2(single birds i +paired birds i )+birds in flocks i i=1 surv.area i. y t is estimate of relative abundance. U.S. Fish and Wildlife Service estimates total abundance using: 3.35 y t. Set management frameworks based on 3-year average of 3.35 y t. Williams et al. Cackling goose management October 28, / 26

17 Mark-Resight Neck-collared geese Resighted birds 6 times throughout the year Alaska, California, Oregon, Washington 5,044 birds first caught as juveniles Williams et al. Cackling goose management October 28, / 26

18 Observation model Aerial Survey: y t Normal(N tot,t, σ 2 y ) Mark-Resight Data m i,t σ 2 y = 5, { 0, z i,t = 0 Bern(p season,t ), z i,t = 1 Williams et al. Cackling goose management October 28, / 26

19 Observation model Aerial Survey: Mark-Resight Data m i,t y t Normal(N tot,t, σ 2 y ) σ 2 y = 5, { 0, z i,t = 0 Bern(p season,t ), z i,t = 1 Process model (survival) { 0, z i,t 1 = 0 z i,t Bern(φ season,age,sex,t,mgmt ), z i,t 1 = 1 Williams et al. Cackling goose management October 28, / 26

20 Process model (abundance) N tot,t = N sub,t + N ad,t N sub,t Normal(µ sub,t, σ 2 sub ) µ sub,t = N ad,t 1 fec φ juv,t 1 2 N ad,t = q t + w t Williams et al. Cackling goose management October 28, / 26

21 Process model (abundance) N tot,t = N sub,t + N ad,t N sub,t Normal(µ sub,t, σ 2 sub ) µ sub,t = N ad,t 1 fec φ juv,t 1 2 N ad,t = q t + w t q t Normal(N ad,t 1 φ ad,t 1, σ 2 q) w t Normal(N sub,t 1 φ sub,t 1, σ 2 w ) Williams et al. Cackling goose management October 28, / 26

22 Process model (abundance) N tot,t = N sub,t + N ad,t N sub,t Normal(µ sub,t, σ 2 sub ) µ sub,t = N ad,t 1 fec φ juv,t 1 2 N ad,t = q t + w t q t Normal(N ad,t 1 φ ad,t 1, σ 2 q) w t Normal(N sub,t 1 φ sub,t 1, σ 2 w ) logit(φ) = X φ β φ logit(p) = X p β p Williams et al. Cackling goose management October 28, / 26

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24 Results Williams et al. Cackling goose management October 28, / 26

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28 Estimating true abundance: c = 1 T T t=1 MarkResight t 1 T T t=1 y t c = 3.35 Williams et al. Cackling goose management October 28, / 26

29 Estimating true abundance: c = 1 T T t=1 MarkResight t 1 T T t=1 y t c = 3.35 c = 1 T 1 T T t=1 MarkResight t T t=1 E[N.tot t y t, m t ]. Williams et al. Cackling goose management October 28, / 26

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35 Survival during years of hunting and no hunting: Williams et al. Cackling goose management October 28, / 26

36 Discussion Williams et al. Cackling goose management October 28, / 26

37 Incorporate population model in Markov Decision Process: H π = argmax π E[ R t (S t, A t, S t+1 ) π]. t=0 Williams et al. Cackling goose management October 28, / 26

38 N tot {1000, 2000,..., } simulate probability of transition from N tot,t to N tot,t+1 using management specific posterior distributions from model. Williams et al. Cackling goose management October 28, / 26

39 Hunting Transition Probability Non-Hunting Transition Probability Williams et al. Cackling goose management October 28, / 26

40 Optimal Policy, given reward function and transition probabilities: Williams et al. Cackling goose management October 28, / 26

41 Acknowledgments U.S. Geological Survey, Alaska Science Center. Association of Village Council Presidents. Oregon Farm Bureau. Eric Taylor, Division of Migratory Bird Management, U.S. Fish and Wildlife Service. Brandon Reishus, Oregon Dept of Fish and Wildlife. Don Kraege, Washington Dept of Fish and Wildlife. Todd Sanders, Division of Migratory Bird Management, U.S. Fish and Wildlife Service. Dan Rosenberg, Alaska Dept of Fish and Game. Julian Fischer, U.S. Fish and Wildlife Service. Biometrics Working Group Williams et al. Cackling goose management October 28, / 26

42 Thank You!!! Williams et al. Cackling goose management October 28, / 26

43 Full conditional distribution of φ [β.] [Z β] [x N ad, β, σ2] x [w N sub, β, σ2 w ] [N sub N ad, fec, β, σn.sub 2 ] [β] logit(φ) = X β y t = N sub,t + x t + w t Williams et al. Cackling goose management October 28, / 26

44 Raveling, D. G., J. D. Nichols, J. E. Hines, D. S. Zezulak, J. G. Silveira, J. C. Johnson, T. W. Aldrich, and J. A. Weldon Survival of cackling Canada geese. Journal of Wildlife Management 56: Williams et al. Cackling goose management October 28, / 26

45 Priors fec Gamma(1, 1) β j Normal(0, ) α j Normal(0, ) σ 2 y = 5, σ 2 x = 5, σ 2 w = 5, σ 2 n.sub = 5, 0002 Williams et al. Cackling goose management October 28, / 26

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