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Title  :  A Note on the Fundamental Equation of SelfThinning in the Logistic Theory of Plant Growth 
Authors  :  Hagihara, Akio 
Authors alternative  :  萩原, 秋男 
Issue Date  :  Sep1997 
Abstract  :  The fundamental equation of selfthinning, which was proposed in the logistic theory of
plant growth for describing the density effect in selfthinning populations, is based on
the following two fundamental assumptions: one is that the growth of mean phytomass w
follows a general logistic equation; the other is that the final yield Y(t), which is pre
scribed as the product of the asymptote of mean phytomass W(t) and density P , becomes
constant irrespective of P , i.e. the law of constant final yield is assumed. In the light
of the basic principle of selfthinning that the relative growth rate of mean phytomass
(l/u>) (dw/dt) is given by the sum of the relative growth rate of yield (1/y) (dy/dt) and
the relative mortality (1/P) (dP/dt), the first assumption brings to the conclusion that the
final yield Y(t) is not prescribed by W{t) P , but is prescribed by(ltn/A (t))W(t) P
(ro, relative mortality; A (f), coefficient of growth), whose value depends on density P
except for the special case where both Wit) P and m are independent of P. This inevitable
consequence is in conflict with the prescription referring to the final yield Y(t) in the
second assumption of the logistic theory of plant growth. As a result, it is suggested
that an alternative theory for the density effect in selfthinning populations should be
newly constructed to harmonize the assumption referring to the growth of mean phytomass
with the assumption referring to the law of constant final yield. 
Type Local  :  紀要論文 
ISSN  :  02869640 
Publisher  :  琉球大学理学部 
URI  :  http://hdl.handle.net/20.500.12000/11819 
Citation  :  琉球大学理学部紀要 = Bulletin of the College of Science. University of the Ryukyus no.64 p.69 76 
Appears in Collections  :  No.64 (1997/9)

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