@article{oai:mie-u.repo.nii.ac.jp:00006415,
 author = {林, 拙郎 and Hayashi, Setsuo},
 journal = {三重大學農學部學術報告 = The bulletin of the Faculty of Agriculture, Mie University},
 month = {Dec},
 note = {application/pdf, 筆者のρ-logistic生長方程式中の目標値Wを一定と仮定とすることによって，3/2乗則線の一つが理論的に導かれた。その理論解は，森林が生長を終える段階までを含んでおり，次式で表される。(w/w₀f)[(ρ/ρ₀f)∧β+δ]=1, δ=w₀f/Wc ここに，ｗ:平均個体重，w₀f:その初期値，ρ:個体密度，ρ₀f:その初期値，β:3/2乗則線のベキ係数，Wc:wの目標値である。上式を拡張3/2乗則と呼ぶ。ここで，δ→0とすれば，従来の3/2乗則線が得られる。一方，この場合のw(t)式は従来の3/2乗則線に既報のρ(t)式を代入することによって次式のように表される。w=w₀f exp(β(ｔ-to)∧m/α) ここに，t₀，m，α は定数，w₀fは3/2乗則線上でのwの初期値である。次に，この拡張3/2乗則線を新たにρ-logistic生長方程式の目標値Wとすることにより，全生長過程を表現するｗ～ρ曲線を導いた。この曲線をSPURR等のデータにあてはめたところ結果は良好であった(式中の∧はベキ乗を表す)。, In the previous paper, the ρ-logistic equation was given as the growth equation under natural decrease on stand density. In the present paper, one of 3/2th power laws is derived theoretically based on the assumption that growth goal (W) in this ρ-logistic growth quation is constant. This theoretical solution includes all growth stages of the plant stand regarding the full-density curve, and gives (w/w₀{(ρ/ρ₀)∧β+δ}=1, δ=w₀/Wc. Here, w is the mean plant weight, w₀ is the initial value of w, ρ is the stand density, ρ₀ is the initial stand density, Wc is the goal value of w and β is the power of the 3/2th power law. This equation is called the axpanding 3/2th power low. If we assume δ→0 in this equation. We obtained the normal formula for the 3/2th power law, and w(t) equation for the 3/2th power law is solved by substituting the ρ(t) formula of the previous paper into the nomal formula for the 3/2th power law. This equation is as follows: w=w₀f exp(β(t-t₀)∧m/α). Here w₀f is the initial value of w for the 3/2th power law, and t₀, m and α are the constants. On the other hand, the expanding formula for w in the previous paper again yielded the same way by use of this expanding 3/2th power law as growth goal (W). Furthermore, This w can be used as new growth goal (W) in the ρ-logistic growth equation, and the solution of the ρ-logistic equation under this new growth goal represents the w-ρ curve for all growth process in the plant stands. A result which supports the assumption obtained by fitting this solution of the growth equation to SPURR et al., data. (the symbol ｚ∧x/a represent zx/a in the above formulas.)},
 pages = {39--52},
 title = {同種同齢林の全生長過程に関する一考察},
 volume = {75},
 year = {1987}
}