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Title Transcription
セチョウ キョクセン ノ ケントウ ダイ2ホウ テイラー キュウスウ テンカイ ト CROZIER シキ
Title Alternative (English)
Analysis of Growth Curve(2) : Taylor Series and the Crozier Equation
File
language
jpn
Author
Yamamoto, Mitsuo
Yasui, Hitoshi
Description
The system of growth can be defined mathematically in various ways. Assuming that the system consists of only one measure y, the system is reduced to the single differential equation :
(dy)/(dt) = f(y)
where f(y) is the function of y. Let us assume that f(y) can be developed into Taylor series :
f(y) = a_0 + a_1y + a_2y_2 + a_3y_3 + . . . ..
Retaining three trems, we have :
(dy)/(dt) = a_0 + a_1y + a_2y_2 .
This equation is almost the same as the Crozier (Crozier, 1926). Moreover, this equation comes to the Mitscherlich (when a_2 = 0) and the Logistic (when a_0 = 0).
Denoting the Crozier by
(dy)/(dt) = (K_1 + K_2y)(A - y),
the solution of the Crozier is :
y =( AB exp[(K_1 + K_2A)t] - K_1)/(B exp[(K_1 + K_2A)t] + K_2)
where A. B. K_1 and K_2 are constants. To examine the applicability of the Crozier equation, it was applied to the observed height growth. The Crozier showed a good fit to the growth not only with a clear inflection but also without one, as compared with the Mitscherlich, the Logistic and the Gompertz. The applicability of the Crozier equation in the growthcurve- fitting was recognized.
Journal Title
Bulletin of the Faculty of Agriculture, Shimane University
Volume
17
Start Page
34
End Page
38
ISSN
0370940X
Published Date
1983-12-20
NCID
AN00108015
Publisher
島根大学農学部
Publisher Aalternative
Shimane University, Faculty of Agriculture
NII Type
Departmental Bulletin Paper
OAI-PMH Set
Faculty of Life and Environmental Science
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