Annika Kangas

Comparison of percentile based prediction methods and the Weibull distribution in describing the diameter distribution of heterogeneous Scots pine stands.

Abstract The goal of this study was to compare percentile based distribution methods and the Weibull distribution method in predicting the stand characteristics of forests with great variability in their diameter distribution. Stand structure characteristics were compared between thinned and unthinned stands dominated by Scots pine. The thinned forests were located in eastern Finland, while the unthinned natural forests were located in Republic of Karelia and Leningrad district, Russian Federation. Each data sets included 49 stands. The diameter distributions were more heterogeneous in the unthinned stands. Most of the thinned stands formed unimodal distributions. Among the unthinned stands, decreasing, multi-modal and irregular forms of diameter distributions were also found. In these data, percentile based distribution methods proved to be considerably more effective in predicting the diameter distribution than the Weibull distribution method. With the percentile based distribution method it was also possible to reproduce considerably varying shapes of diameter distributions.

On the prediction bias and variance in long-term growth projections

Abstract Forest growth is often projected for several subsequent periods. This being the case, the independent variables of a growth model will contain error due to prediction errors in the preceding periods, which cumulate through the simulation process. Thus, the accuracy of growth predictions depends on the number of growth periods. In this paper, the effect of cumulating errors is considered by conducting a simulation study using models estimated from thinning experiments carried out in Finland. The aim of the study is to estimate the prediction bias and the precision of long-term growth projections due to sequential use of growth models. The study demonstrates that it is important to take the residual variation of the models into account in long-term projections in order to reduce the prediction bias.

On the bias and variance in tree volume predictions due to model and measurement errors

The effect of errors in independent variables on the prediction of tree volume is studied. These errors may be either measurement errors, sampling errors, prediction errors or grouping errors. If the model is linear, errors with zero means do not cause bias in predictions, although they do affect the prediction variance. However, if the model is non‐linear, errors with zero means cause bias to the predictions. Taylor series expansion, Monte Carlo simulation and recursive modelling are compared in this paper with regard to bias reduction in a simulation experiment. Reasonable bias corrections were obtained with each method. However, if the assumptions about the models do not hold, the corrections may not improve the estimates. The methods selected differ in regard to the assumptions required and the nature of the information used. Thus, the selection of the most preferable method depends on the situation.

Application of nearest‐neighbour regression for generalizing sample tree information

Nearest‐neighbour regression was tested for generalizing sample tree information in data from the national forest inventory of Finland. The following variables were found to be good regressors: stem diameter, mean diameter, density and age of growing stock, and plot location. The nearest‐neighbour estimator appears to maintain the natural variation of the variables to be estimated well. Reliable volume and height estimates can be obtained even when using only one nearest neighbour. Increasing the number of neighbours improves the accuracy of estimates.

Effect of errors-in-variables on coefficients of a growth model and on prediction of growth

If the data set used for estimating the growth model coefficients contains random measurement errors, the estimated coefficients are biased. This bias makes interpretation of the models difficult, since even the sign of the coefficients may change due to measurement errors. Also, the statistical tests of the coefficients may be invalid. In this study, the biases in diameter growth model coefficients are studied under different assumptions of errors in the estimation data. An example of adjusting the model coefficients for the bias using the SIMulation EXtrapolation (SIMEX) algorithm is given. The effect of biased model coefficients on the prediction of forest growth under different situations is also discussed. If the prediction data set has the same population parameters as the estimation data set, the predictions are generally unbiased. If, however, the effect of some of the independent variables is studied, while the other variables remain constant, the biases in the coefficients may cause invalid inferences.

Uncertainty in growth and yield projections due to annual variation of diameter growth

The growth models used for predictions are usually built to predict growth under average weather conditions. The annual variation in diameter growth may, however, be quite large. Since the annual variation affects the growth of each tree in the same direction, it does not cancel out in larger areas. The aim of this study is to analyze the uncertainty in stand growth and yield projections due to annual variation in tree diameter growth. The annual variation is described with an ARIMA model fitted to a series of growth indices. The diameter growth variation increases the coefficient of variation (CV) of stand volume growth markedly. The CV of stand volume also increases unless the stand is too dense: in a dense forest stand the variation of stand volume is restricted by the predicted self-thinning in the stand. The effect of annual variation on the accuracy of growth predictions is important, especially in short-term predictions. In long-term predictions other components of uncertainty may be more important.

HERO: Heuristic Optimisation for Multi-Criteria Forestry Decision Analysis

A heuristic optimisation method (HERO) has been developed for tactical forest planning at the area, or forest holding, levels. In such an approach, the planning area consists of many forest stands, each having several alternative treatment schedules. The idea is to find for each forest stand, or compartment, a treatment schedule that is optimal at the level of the entire planning area. HERO includes both a method for eliciting value judgements and a solution algorithm. It consists of two main phases: estimating a utility model (i.e. analysing and modelling objectives and preferences) and maximising the utility model. Variables in the utility model can be selected from parameters that are associated with the whole forest area, such as drain, costs, income, or qualities of the growing stock. An initial version of HERO used an additive utility model consisting of partial utilities that are determined using so-called sub-priority functions. There are no preconditions on the form of a sub-priority function. Pairwise comparisons among the variables and eigenvalue preference estimation can be used to derive the sub-priority functions and the relative importance of decision criteria. Since 1993, several applications of the initial method have been published. More recent versions of HERO contain extensions, such as multiplicative components in the utility model, which are described in this article.

Forest Management Planning for Maintaining the Viability of Wildlife Populations

Ecological information about the impacts of forestry on wildlife populations have rarely been used in calculations of forest management planning. Some applications exist, where models predicting sizes of some wildlife populations have been used in optimisation calculations. When such models are used, it is important to take the inherent uncertainty into account. It is essential to know the probability that the size of the population of interest would fall below presumably critical limits. One useful tool in decision-making concerning wildlife populations is risk analysis. In risk analysis, viability of the populations is assessed by a stochastic population dynamics model. The population viability may, for instance, be expressed as the probability of the population surviving the next 1000 years. To make use of risk analysis in forest management planning, viability needs to be expressed as a function of forest-based characters. It may also be necessaty to sort out the risk due to different factors, such as initial population size and changes in the environment. In this paper, the possibility of using information about wildlife populations in forest management planning is considered. Special attention is given to the handling of uncertainty inherent in most ecological information.