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Dynamic programming

Dynamic programming. A gentle introduction using zooplankton behaviour as an example. Outline. Lecture 1: A gentle introduction to Dynamic Programming: Behavioural and life-history decisions in zooplankton as an example (Øyvind Fiksen)

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Dynamic programming

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  1. Dynamic programming A gentle introduction using zooplankton behaviour as an example

  2. Outline • Lecture 1: A gentle introduction to Dynamic Programming: Behavioural and life-history decisions in zooplankton as an example (Øyvind Fiksen) • Lecture 2: An advanced application of dynamic programming: Life history evolution in cod (Christian Jørgensen)

  3. Fish feeding efficiency Growth Depth Light (risky) + + ÷ Dark (safe) ÷ Pelagic vertical gradients: a classical dilemma

  4. Diel vertical migration

  5. Size-structured patterns of distribution Increasing size Increasing depth

  6. Multiple predators – complicates the trade-off.. Large zooplankton Fish Small zooplankton

  7. Pseudocalanus in Dabob Bay Ohman 1990

  8. Predator regimes in shallow and deep areas Ohman 1990

  9. Flexible DVM behaviour in Pseudocalanus Ohman 1990

  10. An experiment with Daphnia magna Loose & Dawidowicz 1994

  11. Mass gained in time interval New body mass New body mass - alternative notation Reproduction State dynamics in discrete time

  12. Optimal habitat selection and allocation of energy Risk Growth Backward iteration * * Eggs *

  13. Computer pseudo-code DEFINE TERMINAL FITNESS(STATE,H) DO TIME = H-1, 1, -1 DO STATE = MINSTATE, MAXSTATE DO HABITAT = 1,N_HABITATS DO ALLOCATION = 1, N_ALLOCATION Find NEW_STATE(HABITAT, ALLOCATION) Find REPRODUCTION(HABITAT, ALLOCATION) Find SURVIVAL(HABITAT,ALLOCATION) Find FITNESS=SURVIVAL*[FITNESS(NEW_STATE,T+1) + REPRODUCTION] IF(FITNESS>MAX_FITNESS) THEN STORE HABITAT*(STATE,TIME) STORE ALLOCATION*(STATE,TIME) ENDIF ENDDO ALLOCATION ENDDO HABITAT ENDDO STATE ENDDO TIME Loops State dynamics (physiology) & mechanics Evaluate consequences of actions in terms of fitness

  14. The dynamic programming equation Maximise fitness = find the behavioural and life history decision that maximises the sum of current and expected future reproduction: Fitness (size, time) Survival Eggs Future fitness (new state, time)

  15. Optimal behaviour and life history Optimal strategy depending on environment, body mass, time and implicitly, expectations of future conditions These matrixes of the best strategy can be applied in forward projections with IBMs or state-structured population models

  16. Optimal depth selection: data and model Data from Loose & Dawidowicz 1994 Model

  17. Behaviour and life-history decisions interact Low fish density 0.01 fish/L with DVM 0.01 fish/L restricted from DVM High fish density

  18. Real dilemma: when access to safety is restricted.. Sakwinska & Dawidowicz 2005 L&O

  19. ..decrease size at first reproduction! Sakwinska & Dawidowicz 2005 L&O

  20. Conclusions • Dynamic programming is excellent in clarifying the role of state in behavioural ecology and life history theory • It is good at • integrating proximate constraints, physiology, ecological mechanics and physics with evolutionary theory • asking ‘What if’-questions and make predictions • It is not suitable for density- or frequency-dependent traits

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