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

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

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

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

,, transport equation boundary condition threshold initial condition

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

. 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

ECONOMY ECOLOGY ?

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

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

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

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

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

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

Continuous at Continuous at For any there exists Continuous at

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

Arbitrary values Controls: cutting rate planting rate

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