Faculty of Agriculture, Shimane University

ISSN:0370-940X

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Bulletin of the Faculty of Agriculture, Shimane University 15

1981-12-15 発行

Relation between "Gentan Probability" and "Diameter Growth"(1) : Derivation of new "Gentan Probability" Models

Yamamoto, Mitsuo

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1. "Gentan probability" q(j) is the probability that a initial forest will be reserved till j age-class and will be cut in the same j age-class. The probability q(j) is the life span distribution of forest stands in a district. In almost all countries, at present, each individual owner of forests is treating his forests of his own will. So q(j) is considered as a kind of waiting time up to the first replacement. Now we assume that a forest stand will be harvested when the mean diameter is k mm wide. q(j) is considered as the probability that the tree becames k mm across at j age-class. And it imparts a new meaning to q(j), as a waiting time untill the tree becames k mm across. Therefore, we can interpret "diameter growth" and "Gentan probability" in the same model, such as Fig. 1.

2. Applying the Markov Chain theories, the auther derived two formulas which give the life span distribution of forest stands as well as Suzuki's one*.

* F_k(t)=(M<(Mt)>^^^<k-1>)/((k-1)!) exp[-Mt]

F_k(t)=(N<(1-e^<-ct>)>^^^<k-1>/((k-1)!) exp[-N(1-e^<-ct>)]Nce^<-ct>

F_k(t)=(N!c)/(k-1)!(N-k)i <(e^<-ct>)>^^^<N-k+1><(1-e^<-ct>)>^^^<k-1>

2. Applying the Markov Chain theories, the auther derived two formulas which give the life span distribution of forest stands as well as Suzuki's one*.

* F_k(t)=(M<(Mt)>^^^<k-1>)/((k-1)!) exp[-Mt]

F_k(t)=(N<(1-e^<-ct>)>^^^<k-1>/((k-1)!) exp[-N(1-e^<-ct>)]Nce^<-ct>

F_k(t)=(N!c)/(k-1)!(N-k)i <(e^<-ct>)>^^^<N-k+1><(1-e^<-ct>)>^^^<k-1>

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