島根大学農学部
島根大学農学部研究報告

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島根大学農学部研究報告 Volume 15
published_at 1981-12-15

減反率と直径生長の関係 : 第1報 新しい減反率モデルの誘導

Relation between "Gentan Probability" and "Diameter Growth"(1) : Derivation of new "Gentan Probability" Models
Yamamoto Mitsuo
full_text_file
d0030015n007.pdf ( 1.01 MB )
Descriptions
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>