Introducing a Non-Stationary Matrix Model for Stand-Level Optimization, an Even-Aged Pine (<em>Pinus Sylvestris</em> L.) Stand in Finland

In general, matrix models are commonly applied to predict tree growth for size-structured tree populations, whereas empirical–statistical models are designed to predict tree growth based on a vast amount of field observations. From the theoretical point of view, matrix models can be considered to be more generic since their dependency on ad hoc growth conditions is far less prevalent than that of empirical–statistical models. On the other hand, the main pitfall of matrix models is their inability to include variation among the individuals within a size class, occasionally resulting in less accurate predictions of tree growth compared to empirical–statistical models. Thus, the relevant question is whether a matrix model can capture essential tree-growth dynamics/characteristics so that the model produces accurate stand projections which can further be applied in practical decision-making. Such a dynamic characteristic in our model is the basal area of trees, which causes nonlinearity in time. Therefore, our matrix model is a nonlinear model. The empirical data for models was based on 20 sample plots representing 8360 tree records. Further, according to the model, stand projections were produced for three Scots pine (Pinus sylvestris L.) sapling stands (age of 25 years, stand density fluctuating from 850 to 1400 stems ha - 1). Then, (even-aged) stand management was optimized by applying sequential quadratic programming (SQP) among those growth predictions. The objective function of the optimization task was to maximize the net present value (NPV) of the ongoing rotation. The stands were located in Northern Ostrobothnia, Finland, on nutrient-poor soil type. The results indicated that initial stand density had an effect on optimal solutions—optimal stand management varied with respect to thinnings (timing and intensity) as well as to optimal rotation. Further, an increasing discount rate shortened considerably the optimal rotation period, and relaxing the minimum thinning removal to 30 m 3 ha - 1 resulted in an increase both in number of thinnings and in the maximum net present value.