Characterising the diameter distribution of Sal plantations by comparing normal,lognormal and Weibull distributions at Tilagarh Eco-park,Bangladesh

For many years foresters have been using statistical probability density functions to describe and characterise stand structure. Predicting the current and future yields of a stand is essential for successful stand and timber management. Implicit prediction of current yield is accomplished by using diameter distribution methods. All diameter distribution yield systems predict the number of trees per unit area by diameter class. In this study, the normal, lognormal and the three-parameter Weibull probability density function were compared to characterise the diameter distributions of Sal (Shorea robusta) plantations grown at Tilagarh Eco-park, Bangladesh. Data from 70 plots, established in three plantations, were used for this study. The Weibull parameters were estimated by the maximum likelihood and moments estimator methods. A one-sample Kolmogorov–Smirnov test was used for the goodness of fit for all models. The Kolmogorov–Smirnov test results showed that both lognormal and Weibull distributions were suitable to characterise the diameter distributions of Sal plantations in the study area and may be applicable for other Sal forests in Bangladesh.     

An allometric equation for estimating stem biomass of Acacia auriculiformis in the north-eastern region of Bangladesh

Tree biomass plays an important role in sustainable management and in estimating forest carbon stocks. The objective of this study was to select the best model for measuring stem biomass of Acacia auriculiformis in the study area. Data from five hillocks and 120 individual trees from each hillock were used in this study. Twelve different forms of linear, power and exponential equations were compared in this study to select the best model. Two models (VI and XI) were selected based on R ², adjusted R ², the Akaike information criterion, F-statistics and the five assumptions of linear regression. Model VI was discarded based on the Durbin-Watson value of autocorrelation of the residuals, then the ARIMA (2, 0, 1) model was used to remove the autocorrelation from the model and the final bias-corrected model XI was derived. The model was validated with a test data set having the same range of DBH and stem height of the training data set on the basis of linear regression, Morisita's similarity index, and t-test for mean difference between predicted and expected biomass. A comparison between the best logarithmic and non-linear allometric model shows that the non-linear model produces systematic biases and overestimates stem biomass for larger trees. The overall results showed that the bias-corrected logarithmic model XI can be used efficiently for estimating stem biomass of A. auriculiformis in the northeastern region of Bangladesh.     

Fitting irregular diameter distributions of forest stands by Weibull, modified Weibull, and mixture Weibull models

Irregular diameter frequency distributions of forest stands include multimodal structure of mixed-species stands, highly skewed and highly irregular shapes of uneven-aged stands, and rotated sigmoid form of old-growth stands. In this study, a traditional two-parameter Weibull model, a modified two-parameter Weibull model, and a finite mixture of two-parameter Weibull models were used to fit four artificial example plots. The model fitting and comparison results indicate that the mixture Weibull model is more flexible to fit various irregular diameter distributions, while the traditional Weibull model fails in every case to adequately describe these frequency distributions. The modified Weibull model is a good choice for fitting the “rotated-sigmoid” diameter distribution of an uneven-aged old-growth stand. However, it may not be sufficient when a diameter frequency distribution is multimodal or highly irregular in shape.     

Growth and yield prediction models for Acacia mangium grown in the plantations of the central region of Bangladesh

Acacia mangium is a very fast growing species belonging to the family Leguminosae that has been introduced in the plantations in Bangladesh for its faster growth and wide range of adaptability. The present study aimed at development of growth and yield prediction models for the species using simultaneous equation method. Models were selected for the species to estimate stand dominant height, stand diameter, stand basal area per hectare and total volume yield per hectare. Paired t-test, 45-degree line test, percent absolute deviation and biological principle of stand development were used for the validation of chosen models. The results suggest that the models derived were statistically and biologically acceptable and could be satisfactorily used for stands of Acacia mangium of ages 4–7 yrs based on a base age of 6 yr.     

Predicting and calibrating diameter distributions of Eucalyptus grandis (Hill) Maiden plantations in Zimbabwe

Diameter distribution models for even-aged Eucalyptus grandis plantations in Zimbabwe were developed using the two-parameter Weibull function. The analysis was based on data from Correlated Curve Trend (CCT) experiments replicated on four different sites. Parameters of the Weibull distribution were predicted using stand characteristics as regressors. Two sets of parameter models were estimated: a set with and one without stand basal area as a predictor. Stand variables such as dominant height, age, site index and number of stems were used in both sets. The models were further calibrated to result in a given number of stems and stand basal area simultaneously. The usability of constructed models was tested both in prediction of yield in a stand inventory situation and in simulation of growth in connection with different growth models. The results indicated that models not including stand basal area produce considerably less precise stand volume estimates compared to models including also stand basal area. Calibration improved the accuracy of diameter distribution models. In growth simulation diameter distribution models can be connected both to single tree growth models and to stand projection models. The usability of calibration in growth simulation depends on the accuracy of the prediction of stand characteristics.     

Tree improvement effects on tree size distributions for Picea glauca and Picea mariana in New Brunswick,Canada

Abstract

Height and diameter distributions between improved and unimproved (checklot) seedlots for white spruce [Picea glauca (Moench) Voss] and black spruce [Picea mariana (Mill.) BSP] were compared using the two-parameter Weibull function. Individual tree height at age 5–15 years and diameter at breast height at age 15 years that were collected from two series of large-plot realized gain tests were used for this purpose. For both species, improved seedlots did not significantly (α=0.05) change the shape parameter of the distributions relative to their checklots, suggesting that an overall shape value will be adequate to predict tree size distributions of various improved seedlots. The most important finding was that seedlot influenced the scale parameter (related to the range of the distribution) significantly, but from a practical viewpoint, only those scale values of the higher rated seedlots (i.e. seedlots collected from a rogued seed orchard or superior families) were significantly higher (α=0.05) than those of the respective unimproved seedlot. The changes in scale value of the alternative improved seedlots relative to the checklot (Δ_Scale) were comparable in magnitude to the respective realized genetic gains, suggesting that tree improvement effects on the scale value can be adjusted by realized genetic gains. The results also suggest that site and age significantly affected the scale value; in general, Δ_Scale became larger at earlier ages or on better sites. The findings reported here will be used in the development of yield functions for genetically improved white and black spruce in New Brunswick.     

Comparison of beta,Johnson’s SB,Weibull and truncated Weibull functions for modeling the diameter distribution of forest stands in Catalonia (north-east of Spain)

The purpose of this study was to compare the beta, Johnson SB, Weibull and truncated Weibull functions in describing the diameter distributions of forest stands in Catalonia. The data consisted of permanent sample plots from the Spanish National Forest Inventory in Catalonia. The empirical data represent left-truncated distributions, as the smallest diameter measured in the field was 7.5 cm. A total of 1,242 plots were used to fit the functions and analyze their performance. The distribution functions were fitted to the diameter distributions of the number of stems (DD_N) and stand basal area (DD_G). The performance of the candidate functions was compared by means of their bias and RMSE for different diameter sums measuring the difference between the empirical and fitted distributions. The leftmost part (from 0 to 7.5 cm) of the non-truncated functions was ignored in this analysis. Sensitivity analyses were conducted to check whether the results depended on the number of trees measured in the stand, or the main species of the stand. The truncated Weibull function for the diameter distribution of stand basal area appeared to be in all cases the most accurate and consistent function. Generally, functions describing the distribution of stand basal area performed better than functions that described the distribution of the number of trees. Of the basal area distributions, beta and Johnson’s SB were the second best and nearly equally good with each other. The order of precision of the tested functions was: truncated Weibull for DD_G, truncated Weibull for DD_N, Johnson’s SB for DD_G, beta for DD_G, beta for DD_N and Weibull for DD_G, Weibull for DD_N, and Johnson’s SB for DD_N.