2. DYNAMIC FOREST GROWTH MODEL CONTROLS (CUTTING AND PLANTING) OUTCOME SCENARIOS (BIOMASS AND SIZE- DISTRIBUTION) OBJECTIVE FUNCTIONS (ECONOMIC BENEFIT AND ECOLOGICAL COST)

3. Sub-task 1: Perfect Plasticity Approximation (PPA) model: analytical solution Sub-task 2: Optimization for periodic cuts Sub-task 3: Optimization for constant cutting rates

5. ,, forest growth equation recruitment of new plants initial size-distribution of forest

6. actual shading gradient PPA Light determines growth: high growth in full light and low growth in shade

7. ,, transport equation boundary condition threshold initial condition

8. Method of characteristics Solution is defined by two differential equations with delays

10. . Controls: number of cuts number of cuts planting rate planting rate the share of cut biomass the share of cut biomass the harvest threshold the harvest threshold

11. ECONOMY ECOLOGY ?

12. Economic benefit discounting timber price biomass cut biomass remained Ecological cost vs. undisturbed state number of cuts harvestthreshold planting rate share of cut biomass

13. Problem 1: two-criteria optimization Problem 2: economic benefit for a given cost

15. PPA model Time-independent dynamics Constant planting and harvesting (controls)

16. ,, B = economic benefit c = cutting rate p = planting rate

17. ,, C = ecological benefit c = cutting rate p = planting rate

18. ,, maximum U = weighted sum of economic benefit and ecological cost c = cutting rate p = planting rate U U

21. Continuous at Continuous at For any there exists Continuous at

22. Solution is defined by and Two conditions – the boundary condition and the threshold condition define and Two differential equations with delays => sequence of equations to derive and

23. Arbitrary values Controls: cutting rate planting rate

24. ,,

25. ,,