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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. 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同種同齢林の全生長過程に関する一考察
http://hdl.handle.net/10076/6863
http://hdl.handle.net/10076/68636a481585-67ba-4b9f-a6a1-ec6d18afef04
名前 / ファイル | ライセンス | アクション |
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AN002343370007503.pdf (812.1 kB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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公開日 | 2007-08-27 | |||||
タイトル | ||||||
言語 | ja | |||||
タイトル | 同種同齢林の全生長過程に関する一考察 | |||||
言語 | ||||||
言語 | jpn | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
資源タイプ | departmental bulletin paper | |||||
著者 |
林, 拙郎
× 林, 拙郎 |
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抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | 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)。 | |||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | 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.) | |||||
書誌情報 |
三重大學農學部學術報告 = The bulletin of the Faculty of Agriculture, Mie University 巻 75, p. 39-52, 発行日 1987-12-01 |
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ISSN | ||||||
収録物識別子タイプ | PISSN | |||||
収録物識別子 | 0462-4408 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AN00234337 | |||||
フォーマット | ||||||
内容記述タイプ | Other | |||||
内容記述 | application/pdf | |||||
著者版フラグ | ||||||
出版タイプ | VoR | |||||
出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||
その他のタイトル | ||||||
en | ||||||
A Study on the All Growth Process of Even-Aged Pure Stand | ||||||
出版者 | ||||||
出版者 | 三重大学農学部 | |||||
ノート | ||||||
Agropedia提供データ | ||||||
資源タイプ(三重大) | ||||||
Departmental Bulletin Paper / 紀要論文 |