Models for individual tree mortality in Norway

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Abstract

Logistic models predicting probability of survival for individual trees were developed, respectively, for Norway spruce (Picea abies (L.) Karst.), Scots pine (Pinus sylvestris L.), birch (Betula spp.), and for other broadleaved trees. The models were based on data from one remeasurement of a nation-wide grid of permanent sample plots recorded by the Norwegian National Forest Inventory. The data comprised 4506 sample plots with 46107 individual trees. Approximately 80% of the observations were used for model development and 20% for validation. The models were designed to be used in large scale forestry scenario models for even-aged and uneven-aged forests, as well as for forests with mixed and pure species composition. The explicatory variables in the models were the inverse of diameter at breast height, a competition index for individual trees, site index, and the proportion of basal area for the respective tree species. All parameter estimates were found highly significant (P<0.001) in predicting mortality except site index in the model for Norway spruce (P<0.05) and the inverse of diameter in the model for birch (P<0.01). Although the phenomenon of mortality is a stochastic, rare and irregular event, the model fit and validation tests were fairly good. Given the general uncertainty related to large scale forestry scenario analyses, and the uncertainty related to mortality as a phenomenon, the mortality models presented in this paper were considered to have an appropriate level of reliability.

Introduction

Large scale forestry scenario models and long-term timber production analyses in Norway have traditionally been based on an even-aged management regime of the forest areas, thus area-based recruitment-, growth-, and mortality models have been developed and applied. Recent developments with respect to environmentally oriented practices in forestry involve different selective cutting techniques. The natural step to adapt large scale forestry scenario models to such treatments, and to enhance the description of the forest dynamics and the accuracy of predicted economical parameters, is to apply models for individual trees.

Until recently, no growth models for individual trees had been developed in Norway. Holte and Solberg (1989) tested a growth model developed for Swedish conditions (Söderberg, 1986) and found it suitable for Norwegian conditions. At the Norwegian Forest Research Institute (NFRI) there is an ongoing project that aims at developing models for individual recruitment and growth for all tree species of interest for Norwegian conditions. The model development is based on permanent sample plots recorded by the National Forest Inventory (NFI) in Norway. The models are supposed to work under even-aged as well as uneven-aged conditions.

Braastad (1982) and Øyen (2000) developed area-based mortality models for Norwegian conditions using experimental permanent sample plots from NFRI. Preliminary mortality models for individual trees based on a nation-wide permanent sample plot grid from the Norwegian NFI were developed by Tuhus (1997). The data of this study comprised approximately 40% of all sample plots of current interest.

Internationally, there is a wide range of mortality models adapted to individual tree growth predictions (see e.g. Vanclay, 1994). However, most models do not sufficiently meet the requirements of large scale forestry scenario analyses applied to a country or to country-wide analyses on the property level. Some models are based on locally relevant, or insufficiently representative data, others are adapted to certain treatments, e.g. only unthinned stands, and some account for only one, or a few, out of all tree species of interest. For nation-wide analyses the data should reflect the full range of variability with respect to treatments, sites, forest structures, and tree species. To use data from a NFI with permanent sample plots is probably the best way to meet these requirements. Few models for individual tree mortality based on such data exist. One example is the models developed by Monserud and Sterba (1999) for Austria.

The preliminary models developed by Tuhus (1997) were applicable to all forest structures and tree species of interest in Norway. The models were based on permanent sample plots from the Norwegian NFI. The plots comprised approximately 40% of all sample plots of current interest. Since 1997 the remaining 60% of the permanent sample plots have been remeasured. The aim of the present study was to develop models for individual tree mortality based on the entire population of permanent sample plots. The models should include regular mortality (mortality due to suppression and competition) and irregular mortality (mortality due to wind, snow, diseases, etc.). The models should be applicable to even-aged and uneven-aged forest as well as forest with mixed and pure species composition. Since the mortality models also should be applicable to large scale forestry scenario analyses in practical management planning, the modelling was restricted to include only explicatory variables that directly or indirectly are available from practical inventories.

Section snippets

Data collection and data preparation

The NFI established permanent sample plots from 1986 to 1993, and remeasured them from 1994 to 1998; data from one remeasurement were available for the present study. The sample plots cover the forest area of Norway (Finnmark county excluded) in a systematic 3km×3 km grid (Norsk Institutt for jord-og skogkartlegging, 1998). Each plot had an area of 100 m2. The time periods between the measurements varied from 1 to 12 years, with an average of 5.6 years.

Sample plots used for model development and

Results

For all species, except birch, d−1 was highly significant (P<0.001) in predicting tree survival (Table 4). For birch the level of significance was lower (P<0.01) for d−1. The probability of survival for all species increased when diameter increased (negative parameter estimates), thus mortality rate decreased as diameter increased. For all species, except birch, the summarised basal area for all trees greater than the subject tree (BAL) was highly significant in predicting survival (i.e. the

Model development

Mortality of individual trees is a stochastic, rare, and irregular phenomenon. Many mortality models for individual trees include three or fewer explicatory variables (e.g. Monserud, 1976, Buchman et al., 1983, Ojansuu et al., 1991, Avila and Burkhart, 1992, Monserud and Sterba, 1999). Thus, it was as expected when several candidate variables of the hypothesised survival model were excluded when it came to the final models (Table 4).

For all tree species d−1 was significant in predicting

Conclusions

Logistic models for prediction of mortality for individual trees, designed for use in large scale forestry scenario models and analyses, have been developed. The models were developed from a substantial data set representing the entire dispersion of conditions and treatments of the Norwegian productive forest area. Although mortality as a phenomenon is complicated to model, and in spite of several uncertain topics revealed from the work, the model fit and the validation tests turned out

Acknowledgements

This work was financially supported by the Norwegian Research Council as a part of research project no. 107889/111. We are also grateful to Stein Tomter, Norwegian Institute of Land Inventory, who made the Norwegian National Forest Inventory data available, and to Heidi Asbjørnsen and Erik Næsset, Agricultural University of Norway, and two anonymous referees for comments on the manuscript.

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