Modeling The Probability Of Individual Tree Mortality

Author : Chung-Muh Chen
Publisher :
ISBN 13 :
Total Pages : 236 pages
Book Rating : 4.:/5 (319 download)

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Download or read book Dynamics of an Even-aged Stand : Structure, Mortality, Competition and Growth written by Chung-Muh Chen and published by . This book was released on 1976 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of three components - stand structure, competition and growth, and mortality. Data from an unthinned even-aged red pine stand were used for the analysis. Stand structure was described by diameter and height distributions. The red pine diameters over time were assumed to follow a Weibull distribution. The hypotheses were accepted at the 95% confidence level both by Chi-Square and K-S tests. The Weibull parameters were estimated bu the Maximum Likelihood method (MLE). The normal equations resulting from the MLE can be solved by iteration based on order statistics (see Nailey and Dell 1973). For this study, Newton-Raphson iteration was introduced for solving the normal equations. The initial value for the iteration was based on Menon's (1963) estimator of the Weibull shape parameter. The efficiency of this approach was demonstrated by the fast convergence of parameter estimates. Parameters of te diameter distribution were related to stand age, number of trees per aacre and average dominant height by Clutter and Bennet (1965), as well as Burkhart and Strub (1974). Only poor correlations were obtained in their studies. Inthis study, the Weibull parameters were found to be highly correlated with stand age, number of trees per acre, mean diameter and standard deviation of diameter respectively. The tree height probability distribution was estimated from the diameter distribution (the Weibull function) based on height-diametr relationships, a new approach in forestry. The hypothesis was accepted at the 95% confidence Iewel by the K-S test. This concept is not applicable to any situation where tree height and diameter are poorly correlated as would be the case for trees growing in uneven-aged stands. However, the method may be applicable for deriving distributions of crown width (of open-grown trees), functional crown surface or any other tree variable related to tree diameter. In the second component, existing individual tree competition indexes were classified and critically evaluated. The relative tree size concept of these indexes was explored. Currently the zone count competition index has received the greatest attention. In this phase of the study, a set of reasonable factors was presented for modifying and improving the zone zount approach. A strong correlation between the basal area growth and the index was noted for young stands when using the relative basal area as the weighting factor. For older stand ages, the relative live crown ratio was found to be a better weighting factor than the relative basal area. The highest correlation was noted when using the relative current diameter increment as the weighting factor for young and old stands. For future study, it is instructive to use relative functional crown surface and tree size as the weighting factor because crown ratio may not be applicable in many cases. For individual tree competition in uneven-aged stands of mixed species, one should also consider relative species tolerance and other factors in deriving a weighting factor. The existing tree size growth models (open-grown tree and empirical growth models) were discussed in detail. The open-grown tree approach is useful for describing tree size increment of dominant trees. However, it may not predict well the growth behavior of trees in lower crown classes after release. Further-more, lack of information on potential growth of open-grown trees will limit its application. Wxisting empirical growth functions are numerous. A major disadvantage of these models is that they can not explain logically the relationship between the dependent variables. In this second phase of the study, the existing open-grown tree model was modified for taking species tolerance into account. In addition to the open-grown tree approach, a set of nonlinear biological growth models was formulated and tested. For a given site and species in an even-aged stand, the individual tree basal area increment was assumed directly related to the tree initial basal area and inversely related to the tree competition index. A strong multiple correlation (R2=.81 to .85) of this model was noted for two sample plots (site index 65 and ages 32-37). The growth parameters were insensitive between plots. However, for a wider range of stand density, these parameters would be expected to vary density decause the growth parameters are generally related to site; density and age for a given species. The growth model was modified for trees growing in uneven-aged stands. Factors affecting tree-size growth in uneven-aged stands were also discused. In the third component, factors affecting tree mortality in even-aged and uneven-aged standswere cited. Similar to Dale's (1975) method, tree mortality was grouped by increment class and then the mortality in each class was simulated according to a binomial probability distribution. This study tested the approach for each growth period. Simulated mortality was close to the observed data. Tree mortality in each diameter class and each growth period was simulated in the same fashion. The results were also satisfactory. For a specific growth period, mortality proportions were highly related to diameter for each diameter class. Tree mortality was also grouped by stand age classes. Stochastic processes new to forestry were then introduced for estimating the survival probability and death rate over time. The results were consistent with the trend of the observed data over four growth periods. Furthermore, life length probability distributions of individual trees were presented and tested by assuming two mortality rate functions, again a new concept in forestry. The hypotheses were accepted by the K-S test and the 95% confidence level. When applying the above components for individual tree growth prediction, it is instructive to use the nonlinear basal area growth models (equations 21 and 22). For growth period t, deltaBc=f(Cstst-1, Bc-1, Cc-1) for a given site (54) and a given species. Then the basal area growth of individual trees in the next growth period t=1 can be predicted by using the equation deltaBc=f(Cst, Bc, Ct) ... (55) where deltaBt, deltaBc=1 = the basal area growth of a sample tree during the growth period t and t=1 respectively. Cst-1, Cst=the funtional crown surface of the sample tree at the beginning of growth period t and t=1 respectively. Bt-1, Bc = the basal area of the sample tree at the beginning of period t and t=1 respectively. Ct-1, Ct=the competiton index of the sample tree at the beginning of the growth period t and t=1 respectively. The parameters of equation (54) may be fixed for the parameters of equation (55) if observations on Bc=1 are not available for each tree in the model, and if the basal area growth rate will not change greatly from period from period t to period t=1. If information on Bc=1 is available, one would estimate the parameters of model (55) from these data and more reliable results could be expected. Stand structure at the beginning of the period t=1 can be described by the diameter distribution (the Weibull function) and the height distribution (the modified Weibull function) if height data is also available. Tree mortality in each diameter or increment class of period t=1 can be simulated according to the binominal probability.