混合マルコフ過程を応用した択伐林直径分布モデル

The auther proposed a new diameter distribution model for selection forests, and examined its applicability. Applying the Markov Chain theories, the auther derived the diameter distribution model for selection forest stands. The assumptions for this derivation are that a forest tree will be cutted when the cumulative cutting condition for the tree counts k times, and that each tree of the stand will increases its condition M times in average for a unit diameter increasing interval. Under these assumptions, the auther derived the probability functions

f_k(x) = (<(Mx)>^^^k)/(k!)･exp [-Mx]

F_k(x) = (M<(Mx)>^^^<k-1>)/((k-1)!)･exp[-Mx]

where fk(x) is the probability function which the cutting condition for a tree counts k times across during its diameter becoming x. Fk(x) is the probability function which the cutting condition for a tree counts k times at exactly its diameter being x. This Fk(x) gives the tree-cutting distribution. According to this tree-cutting distribution, the auther derived the probability function

r(d) = ∫^∞_d(M<(Mx)>^^^<k-1>)/((k-1)!)･exp [-Mx] dx

where r(d) is the probability which a tree will remain its diameter is over d The applicability of this model was examined by appled it to six observed diameter distributions of Ate (Thujopsis dolabrata SIEB. et ZUCC var. hondai MAKINO) at Noto district, Ishikawa. This model shown good fits and reliablity and could be recognized as the diameter distribution model in addition to the following ordinary eqution, MEYER equation

g(d)=a exp(-bd),

where g(d) is a number of trees, d is diameter, a, constants.