Michael J. Conroy
� Background and motivation (brief) � Background and motivation (brief) � ASDP and other approaches for optimal � ASDP and other approaches for optimal harvest management � Use of heuristic methods for harvest optimization p � Some thoughts on the future
� Most NR decision problems involve dynamic, � Most NR decision problems involve dynamic, stochastic systems with sequential controls � Attractiveness H-J-B (DP) � Adaptation/ Adaptive management Some downsides �
� Most NR decision problems involve dynamic, � Most NR decision problems involve dynamic, stochastic systems with sequential controls � Attractiveness of H-J-B (DP) � Adaptation/ Adaptive management Some downsides �
� Forest harvest scheduling � Forest harvest scheduling � Optimal wildlife and fisheries harvest � Optimal wildlife and fisheries harvest � Stocking translocations re introductions � Stocking, translocations, re-introductions � Regulations of dams on rivers � Regulations of dams on rivers � Impoundment management I d t t
� Most NR decision problems involve dynamic, � Most NR decision problems involve dynamic, stochastic systems with sequential controls � Attractiveness of H-J-B (DP) � Adaptation/ Adaptive management Some downsides �
� Guarantees a globally optimal strategy for � Guarantees a globally optimal strategy for control � Provides closed-loop feedback � Provides closed loop feedback � Future resource opportunities “anticipated”
� Most NR decision problems involve dynamic, � Most NR decision problems involve dynamic, stochastic systems with sequential controls � Attractiveness of H-J-B (DP) � Adaptation/ Adaptive management Some downsides �
� Environmental stochasticity � Environmental stochasticity � Partial controllability � Partial controllability � Partial observability � Partial observability � Structural uncertainty � Structural uncertainty
� Accounts for structural uncertainty in DM y � Model-specific transitions � Model-specific information weights (model probabilities) � Explicitly treats information weights as another system state � Current decision making “anticipates” future reward to objective of learning
� Most NR decision problems involve dynamic, � Most NR decision problems involve dynamic, stochastic systems with sequential controls � Attractiveness of H-J-B (DP) � Adaptation/ Adaptive management Some downsides �
� The Curse of Dimensionality � The Curse of Dimensionality � High-dimensioned problems difficult or intractable to solve with DP � In our community � Issues of software accessibility and support � Relative complexity for the end users � Still a relatively small user group Still l ti l ll
� Maximum long-term total harvest … but � Maximum long term total harvest … but � Constraints for achieving population goals � Allocation (parity) sub objective � Allocation (parity) sub-objective � Canada vs. US
t US Harvest Utility of U U Proportion of harvest in US
� Harvest regulations g � Canada and US set these independently at present � Regulations in US can differ by flyways or portions of flyways � Can result in up to 6 combinations of spatially-stratified regulations � 3 zones in Canada � 3 in US 3 i US � 7 6 = 117,649 decision combinations � For now assuming regulations are homogenous within US and Canada US and Canada � For now assuming fixed harvest rate levels � Regulations perfectly control harvest rates � 7 harvest rate levels/ nation = 49 decision combinations 7 harvest rate levels/ nation 49 decision combinations
� State variables � Spring population size of black ducks (60 discrete levels) � Spring population size of mallards (a competitor; 60 discrete levels) � Dynamics � Black ducks � Density impacts on reproduction (presumed resource limitation) y p p (p ) � Competition impacts from mallards (absent under alternative H) � Survival impacts from harvest (absent under alternative H) � Generalized stochastic effects (estimated) ( ) � Mallards � Simply Markovian growth (stationary) � Generalized stochastic effects (estimated (
τ m M t τ , ) 1 / 3 ( A M A , M non hss , ) 2 / 3 t ( A M non t M A , M t Winter N A , M pm Fall t t J , M Fall t t pm , ) t 2 / 3 + ( ( J M ) non non 1 t J J , M M t t Winter ~ 0.5 J , M hss t t N + 1 t 0.5 , ) 2 / 3 ( J F AR non N J , F J , F t Fall Winter t t t t J , F hss t − 1 p pm + + 1 1 , ) , ) t t 1 1 / / 3 3 2 2 / / 3 3 ( A A F F A , F ( A A F F non non hss F t A , F A , F t Fall Winter N − t 1 pm t t t + 1 t , , c c c c c c c c 0 , 1 2 3
� Environmental stochasticity � Represented by estimated random effect on black duck and mallard dynamics � Discrete lognormal distribution (14 levels) � Partial controllability P ti l t ll bilit � Assume for now that specific harvest rates can be achieved � Further work needed to characterize stochastic relationship of regulations to harvest outcomes regulations to harvest outcomes � Partial observability � Incorporated into state-space mode � Ignored in optimization Ignored in optimization � Structural uncertainty � 4 alternative process models � Harvest effects X Mallard competition p
� State-decision- RV space p � 60 2 X 7 2 X 14 2 = 3.5 X 10 7 � Stationarity issues � Most model/ objective scenario combinations did not converge on stationary solution in 200 iterations not converge on stationary solution in 200 iterations � Reported stationary state-specific strategy (if found) or iteration 200 strategy � Simulation of “optimal” strategies � Initial conditions 570K black ducks 470L mallards � 100 simulations of 200 years 100 i l ti f 200
Black ducks Black ducks Additive + Compete Additive + No Compete No Harvest No Harvest 1100 1300 1200 1000 1100 900 1000 Bpop p Bpop 800 900 800 700 700 600 600 500 500 0 50 100 150 200 250 0 50 100 150 200 250 Year Year Additive, no competition Additive, competition
HN HS Additive + Compete Additive + Compete Pop Slope= -10, Pop Goal= 640, Parity Slope= -10, Parity Goal= 0.6 Pop Slope= -10, Pop Goal= 640, Parity Slope= -10, Parity Goal= 0.6 3000 3000 2500 2500 2000 2000 Mallards Mallards 1500 1500 1000 1000 1000 0.00 0.00 500 0.05 0.05 500 0.10 0.10 0.15 0.15 0.20 0.20 0 25 0.25 0.25 0 0.30 0 0.30 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Blackducks Blackducks Canada US
Black ducks Black ducks Additive + Compete Pop Slope= -10, Pop Goal= 640, Parity Slope= -10, Parity Goal= 0.6 800 800 750 700 650 Bpop 600 550 500 450 0 50 100 150 200 250 Year
HS HN Additive + No Compete Additive + No Compete Pop Slope= -10, Pop Goal= 640, Parity Slope= -10, Parity Goal= 0.6 Pop Slope= -10, Pop Goal= 640, Parity Slope= -10, Parity Goal= 0.6 3000 3000 2500 2500 2000 2000 Mallards Mallards 1500 1500 1000 1000 500 500 0.00 0.00 0.05 0.05 0.10 0.10 0.15 0.15 0.20 0.20 0 0 0 0 0.25 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 0.30 Blackducks Blackducks Canada US
Black ducks Black ducks Additive + No Compete Pop Slope= -10, Pop Goal= 640, Parity Slope= -10, Parity Goal= 0.6 900 900 850 800 750 Bpop 700 650 600 550 0 50 100 150 200 250 Year
� Incorporation of partial controllability p p y � 14 random harvest rate outcomes per harvest decision (4- 5 levels) � Spatial stratification � Spatial stratification � 3 breeding populations � 6 harvest zones � State – decision- RV dimensions (independent populations and harvest zones) � 60 6 X 5 6 X14 9 =1 5 X 10 25 60 X 5 X14 1.5 X 10 � Haven’t done this! � Still trying to get buy-in on single population, 2 – harvest international strategy international strategy
� Mallard AHM based (c. 2005) on single stock ( ) g (“Midcontinent Population”) � Pacific Flyway mallards � Derive much of harvestable population from coastal and trans-Rockies west � However substantial intermixing with midcontinent However substantial intermixing with midcontinent population � Work explored feasibility of western AHM � 2-stock “virtual model” � Independent stochastic effects and dynamics � Independent harvest regulations Independent harvest regulations
� Equal or less complexity than MCP q p y � Take state space = D 2 � Harvest decisions and population states independently determined of similar dimension to independently determined, of similar dimension to MCP � Could reduce dimension by linkage � No current model of population interaction � Assume independent for now � Interaction structure potentially reduces dimension � Interaction structure potentially reduces dimension � Stochastic variation � Assumed independent for now � Covariance structure would reduce dimension
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