Distance-independent Competition Indices Research Articles

Modelos de crescimento em diâmetro de árvores individuais de <i>Araucaria angustifolia</i> (Bertol.) Kuntze em Floresta Ombrófila Mista

Este trabalho objetivou modelar o crescimento em diâmetro para árvores individuais de Araucaria angustifolia, ocorrentes na Floresta Ombrófila Mista no nordeste do Rio Grande do Sul. Para tanto, foram utilizadas remedições em intervalo de 7 anos de 251 indivíduos de araucária ocorrentes nas parcelas permanentes do Projeto PELD/CNPq. Foi construído um modelo de produção, tendo como variável dependente o diâmetro futuro, utilizando regressão e análise de covariância. Como variáveis independentes, foram utilizadas as características dimensionais e sociológicas dos indivíduos e os índices de concorrência independentes de distância. A variável mais correlacionada com o diâmetro futuro foi o diâmetro atual. Os índices de concorrência apresentaram alta correlação com a variável dependente, representando a pressão competitiva exercida sobre a árvore, mas não foram selecionados no modelo de regressão. Somente o diâmetro atual, multiplicado por um coeficiente, acrescido de um valor constante o qual diferiu de acordo com a posição sociológica do indivíduo, foi eficiente para predizer o diâmetro futuro. Foram construídos três variações do modelo de produção. Esses modelos apresentaram melhores estimativas para indivíduos de Araucaria angustifolia emergentes, no entanto, o seu emprego na prognose de crescimento de árvores individuais deve ser cauteloso por causa da magnitude dos erros de predição que apresentou.

Effects of red alder and paper birch competition on juvenile growth of three conifer species in southwestern British Columbia

We examined the effects of competition from red alder ( Alnus rubra Bong.) and paper birch ( Betula papyrifera Marsh.) on the growth of western redcedar ( Thuja plicata Donn), western hemlock ( Tsuga heterophylla Sarg.), and Douglas-fir ( Pseudotsuga menziesii Franco) at a site near Maple Ridge, British Columbia, Canada. At this site, the three coniferous species and two broadleaf species had been planted in 1999 as part of a long-term experiment examining effects of broadleaf density on conifer growth. Red alder and paper birch were planted alone and as a 50:50 mixture at four densities (0, 277, 556, and 1150 stems ha −1). Red alder density was positively correlated with total available nitrogen in soil measured using ion-exchange membranes whereas density of paper birch was not. For Douglas-fir only, foliar N concentration was positively related to red alder density. Relationships between stem volume increment and competition indices varied between the three conifer species: (1) For Douglas-fir the highest correlations were obtained using a distance-independent competition index based on broadleaf crown surface area and diffuse transmittance (DIFN) measured using LAI-2000 plant canopy analyzers had the lowest R 2 of the competition measures tested; (2) for western redcedar the highest correlations were with DIFN and the second best competition measures were distance-dependent indices; (3) for western hemlock broadleaf competition did not have significant effects on growth. Height of each species at the time of measurement and crown surface area appear to be more important than shade tolerance in affecting conifer growth. At this site, significant reductions in stem volume (30%) of Douglas-fir and western redcedar occurred when red alder density exceeded 500 stems ha −1 while paper birch was not detrimental to western redcedar growth until densities exceeded 1000 stems ha −1 and birch density did not significantly affect Douglas-fir. The influence of red alder on soil N and foliar N of Douglas-fir may be leading to a weaker relationship between growth and DIFN for Douglas-fir compared to that for western redcedar.

An empirical ecological-type model for predicting stone pine ( Pinus pinea L.) cone production in the Northern Plateau (Spain)

Data from a 10 year series of cone production taken from 755 trees were used to model individual cone production in stone pine ( Pinus pinea L.) stands in the Northern Inland Plateau of Spain following three different approaches. The first step was the construction of a silvicultural model, including typical forest growth covariates as tree size, stand density, site index and distance independent competition indices. Remaining between-plot variability was related with ecological attributes, as winter rainfall and altitude, resulting in a hybrid model. The third approach attempted to develop an ecological-type based model by considering a previous stratification of stone pine forests based on altitude, soil, geology and climate characteristics. The best model in terms of likelihood, bias and accuracy on predictions was the ecological-type one, producing unbiased marginal estimates for the main part of the territory with an efficiency reaching up to 39%. Due to the hierarchical structure of data set, proposed model was formulated as a multilevel mixed model. Stochastic formulation allows simulating cone production under different changing scenarios and describing real distribution of cone production within a given stand. Developed model constitutes the cone yield module for PINEA2, an integrated single tree model for the management of stone pine stands within the northern Plateau of Spain.

Stand and tree-level variability on stem form and tree volume in Pinus pinea L.: A multilevel random components approach

Stem analysis data from 536 sampled trees located in 36 permanent sample plots were used to develop a taper function which allows flexible end products volume estimation for stone pine (Pinus pinea L.) in Spain. To alleviate inference problems derived from high correlation among observations a multilevel linear mixed approach, including random coefficients varying at both plot and tree levels, was used. The proposed taper function expresses the section diameter as a function of breast height diameter and relative height of the section, showing a logical behaviour at both breast and total height. Between and within plot stem form variability was explained by including explanatory covariates as basal area or distance independent competition indices. Mixed models allow calibration of the model for new locations, by predicting random coefficients if additional stem form measurements are available. Several alternatives of calibration, considering section diameters measured at different heights in a variable number of trees per plot, were compared between them, and with the basic marginal model and the marginal model including covariates. The best calibration alternative was to use additional section diameter measurements taken at 0.5 m height above ground. This model results in substantial improvement in stem form and single tree volume predictive ability over previously existing volume functions for the species, allowing size end-use classification for timber products.

The effect of competition on individual tree basal area growth in mature stands of Pinus cooperi Blanco in Durango (Mexico)

In this paper, we evaluated how well-selected distance-dependent and distance-independent competition indices explain individual tree basal area growth of trees, growing in mature and even-aged stands of Pinus cooperi Blanco. A total of 18 competition measures were analyzed of which six do not need tree location (distance-independent) and 12 that utilize tree location (distance-dependent). The competition situation of a stand and/or an individual tree was studied using 11 different competitor selection methods. The mean square error reduction relative to no-competition was used to judge the performance of each competition index. It was found that the best distance-independent competition indices performed as well as the best distance-dependent competition indices. It was concluded that the BALMOD-index would be a good competition index to be incorporated into further individual tree basal area growth models for the study area.

Multilevel linear mixed model for tree diameter increment in stone pine (Pinus pinea): a calibrating approach

Diameter increment for stone pine (Pinus pinea L.) is described using a multilevel linear mixed model, where stochastic variability is broken down among period, plot, tree and within-tree components. Covariates acting at tree and stand level, as breast height diameter, density, dominant height or site index are included in the model as fixed effects in order to explain residual random variability. The effect of competition on diameter increment is expressed by including distance independent competition indices. The entrance of regional effects within the model is tested to determine whether a single model is sufficient to explain stone pine diameter increment in Spain, or if, on the contrary, regional models are needed. Diameter increment model can be calibrated by predicting random components using data from past growth measurements taken in a complementary sample of trees. Calibration is carried out by using the best linear unbiased predictor (BLUP) theory. Both the fixed effects model and the calibrated model mean a substantial improvement when compared with the classical approach, widely used in forest management, of assuming constancy in diameter increment for a short projection period.

Predicting basal area increment in a spatially explicit, individual tree model: a test of competition measures with black spruce

A current trend in the development of forest stand models is to use spatially explicit, individual-tree information to simulate forest dynamics with increased accuracy. By adding spatial information, such as tree coordinates, crown shape, and size, it is hypothesized that the computation of the model's driving function is improved over traditional competition indices, especially when simulating multistoried stands. In this paper, we want to test whether computationally demanding competition indices outperform traditional indices in predicting mean basal area increment. The study was undertaken in old, uneven-aged black spruce (Picea mariana (Mill.) BSP) stands in northeastern Quebec, Canada. The predictability of individual tree growth rates was related to crown dimensions and other stand and tree variables measured in the field. Data were collected from 90 trees coming from stands of varying site quality (range 9.6–16.5 m height at 50 years, age taken at 1 m) and age (range 66–257 years). Hegyis's distance-dependent competition index was found to be the most strongly correlated competition measure (r = 0.57) with mean basal area growth of the last 20 years. This value, 12% higher than the value obtained from the best distance-independent competition index (r = 0.45), clearly shows that precision gains can be achieved when estimating basal area increment with spatial indices in black spruce stands. Using indices computed from virtual hemispherical images did not prove superior to simpler distance-dependent indices based on their individual correlations with basal area increment. When included in a basal area increment model for the last 20 years of growth, however, the gains in precision were comparable to Hegyi's competition index. This indicates that indices derived from a hemispherical approach have some value in spatially explicit forest simulations models but that further tests using younger stands are needed to confirm this result in black spruce stands.

An age-independent basal area increment model for maritime pine trees in northwestern Spain

An individual tree basal area increment model for pure stands of maritime pine ( Pinus pinaster Ait.) is presented. The data used to fit the model were collected from 67 temporary 0.05 ha plots installed in regularly stocked, even- and uneven-aged stands located in Galicia (northwestern Spain). Explanatory variables used to predict the basal area increment are breast-height diameter outside bark, a diameter-squared term, a distance-independent competition index, crown spread ratio, and effective soil depth. Age and site index are intentionally omitted to obtain generality for a wide range of even- and uneven-aged stand conditions. The resulting model explains more than 78% of the total growth variation, corresponds to current hypotheses about tree growth, and is expected to provide reliable site-specific predictions for most of the pure maritime pine stands found in the study area.

Testing a new competition index for Maritime pine in northwestern Spain

A distance-independent competition index is derived from the basal area in larger trees (BAL) index combining individual tree's basal area percentiles with a relative-spacing stand-density measure. Empirical increment data from Maritime pine trees (Pinus pinaster Ait.) sampled from regular, naturally regenerated stands in the province of Pontevedra, northwestern Spain, are used to compare the performance of the two competition indices in the context of basal area growth modelling. The basal area increment of individual trees was first predicted exclusively as a response to competition using a two-parameter exponential function and then as a function of potential growth reduced by competition. For the criteria evaluated in this paper, the new competition index has shown superior qualities. The main improvement over BAL is the incorporation of the relative spacing measure.

Evaluation of simple competition indices for the prediction of volume increment of young jack pine and trembling aspen trees

Seven simple competition indices were evaluated for their ability to predict the 1983 volume increment of an 8-year-old jack pine ( Pinus banksiana Lamb.) and trembling aspen ( Populus tremuloides Michx.) trees. A total of 298 subject trees (two subsets of 149 subject trees for each species) were sampled. Each subset was randomly subsampled 48 times with replacement. Each of the 48 subsamples was separately analysed by calculating of Spearman rank correlations between the 1983 volume increment of the subject tree and the competition indices. The distance-dependent competition index (Daniels' 1976 competition index — dc1) based on all competitors selected by the horizontal sampling method was more correlated with the 1983 volume increment. dc1 was followed by distance-independent competition indices (Lorimer's 1983 competition index — lc1) based on trees only equal or in a higher height class than the height class of the subject tree. Also, competition indices based on only competitors of higher height class than the height class of the subject tree performed better than the modified Spurr's point density (Spurr's 1962). Although limited in scope because only one stand was studied, the results of this study suggest that evaluation of stand competition by means of competition indices in young shade-intolerant jack-pine/aspen mixed stands should take into account both the competitor size and inter-tree distances between subject trees and all selected competitors.