Jouni Siipilehto. (2006). Height distributions of Scots pine sapling stands affected by retained tree and edge stand competition. Silva Fennica vol. 40 no. 3 article id 331. https://doi.org/10.14214/sf.331

Keywords: Pinus sylvestris; retention; height distribution; Weibull function; percentile prediction; edge effect

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The paper focused on the height structure of Scots pine saplings affected by (1) retained solitary pine trees or (2) a pine-dominated edge stand. The study material in (1) and (2) consisted of ten separate regeneration areas in southern Finland. In (1) 2-m radius study plots were located at 1, 3, 6 and 10 m distances from 10 systematically selected, solitary retained trees in each stand. In (2) the study plots were systematically located within 20 m from the edge stand. Competition of the individual trees was modelled using ecological field theory. The 24th and 93rd sample percentiles were used for estimating the height distribution using the two-parameter Weibull function. The models incorporated the effect of varying advanced tree competition on the predicted percentiles. Competition free dominant height was used as a driving variable for the developmental phase. Competition resulted in retarded height development within a radius of about 6 m from the retained tree, while it extended up to roughly half of the dominant height of the edge stand. The height distribution without external competition was relatively symmetrical, but increasing competition resulted in a more peaked and skewed distribution. Slight differences were found between northern sunny and southern shaded stand edges, while the least retarded height occurred at the north-western edge receiving morning sunlight. Kolmogorov-Smirnov goodness-of-fit tests showed acceptable and equal fit for both data sets; 2% and 8% of the distributions did not pass the test at the alpha 0.1 level when the Weibull distribution was estimated with the observed or predicted percentiles, respectively.

Siipilehto, Finnish Forest Research Institute, P.O. Box 18, FI-01301 Vantaa, Finland E-mail: jouni.siipilehto@metla.fi

article id 594, category Research article

Walter Zucchini, Matthias Schmidt, Klaus von Gadow. (2001). A model for the diameter-height distribution in an uneven-aged beech forest and a method to assess the fit of such models. Silva Fennica vol. 35 no. 2 article id 594. https://doi.org/10.14214/sf.594

Keywords: diameter-height distribution; mixture models; bivariate normal distribution; SBB distribution; goodness-of-fit; pseudo-residuals; beech forest

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This paper illustrates the application of a mixture model to describe the bivariate diameter-height distribution of trees growing in a pure, uneven-aged beech forest. A mixture of two bivariate normal distributions is considered but the methodology is applicable to mixtures of other distributions. The model was fitted to diameter-height observations for 1242 beech trees in the protected forest Dreyberg (Solling, Germany). A considerable advantage of the model, apart from the fact that it happens to fit this large data set unusually well, is that the individual parameters all have familiar interpretations. The bivariate Johnson SBB distribution was also fitted to the data for the purpose of comparing the fits. A second issue discussed in this paper is concerned with the general question of assessing the fit of models for bivariate data. We show how a device called ‘pseudo-residual’ enables one to investigate the fit of a bivariate model in new ways and in considerable detail. Attractive features of pseudo-residuals include the fact that they are not difficult to interpret; they can be computed using generally available statistical software and, most important of all, they enable one to examine the fit of a model by means of simple graphs.

Zucchini, Georg-August-Universität Göttingen, Institute for Statistics and Econometrics E-mail: zucchini@wi-wiss.uni-goettingen.de
Schmidt, Forest Research Station of Lower Saxony E-mail: ms@nn.de
Gadow, Georg-August-Universität Göttingen, Institute for Forest Management and Yield Sciences E-mail: kvg@nn.de

article id 617, category Research article

Jouni Siipilehto. (2000). A comparison of two parameter prediction methods for stand structure in Finland. Silva Fennica vol. 34 no. 4 article id 617. https://doi.org/10.14214/sf.617

Keywords: Pinus sylvestris; Picea abies; parameter prediction; dbh and height distribution; Johnson’s SBB distribution; Näslund’s height curve

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The objective of this paper was to predict a model for describing stand structure of tree heights (h) and diameters at breast height (dbh). The research material consisted of data collected from 64 stands of Norway spruce (Picea abies Karst.) and 91 stands of Scots pine (Pinus sylvestris L.) located in southern Finland. Both stand types contained birch (Betula pendula Roth and B. pubescent Ehrh.) admixtures. The traditional univariate approach (Model I) of using the dbh distribution (Johnson’s SB) together with a height curve (Näslund’s function) was compared against the bivariate approaches, Johnson’s SBB distribution (Model II) and Model Ie. In Model Ie within-dbh-class h-variation was included by transforming a normally distributed homogenous error of linearized Näslund’s function to concern real heights. Basal-area-weighted distributions were estimated using the maximum likelihood (ML) method. Species-specific prediction models were derived using linear regression analysis. The models were compared with Kolmogorov-Smirnov tests for marginal distributions, accuracy of stand variables and the dbh-h relationship of individual trees. The differences in the stand characteristics between the models were marginal. Model I gave a slightly better fit for spruce, but Model II was better for pine stands. The univariate Model I resulted in clearly too narrow marginal h-distribution for pine. It is recommended applying of a constrained ML method for reasonable dbh-h relationship instead of using a pure ML method when fitting the SBB model.

Siipilehto, Finnish Forest Research Institute, Vantaa Research Centre, P.O. Box 18, FIN-01301 Vantaa, Finland E-mail: jouni.siipilehto@metla.fi

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