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Theoretical considerations on the C‐D effect in self‐thinning plant populations
Author(s) -
Hagihara Akio
Publication year - 1999
Publication title -
population ecology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.819
H-Index - 59
eISSN - 1438-390X
pISSN - 1438-3896
DOI - 10.1007/s101440050017
Subject(s) - reciprocal , thinning , population , density dependence , logistic function , constant (computer programming) , statistical physics , statistics , population density , mathematics , biology , physics , ecology , demography , philosophy , linguistics , sociology , computer science , programming language
A model for describing the competition–density (C‐D) effect in self‐thinning populations was developed on the basis of the following three basic assumptions: (1) the growth of mean phytomass follows a general logistic equation; (2) final yield is independent of initial population density; and (3) there exists a functional relationship between actual and initial population densities at any given time. The resultant equation takes the same reciprocal form as the reciprocal equation of the C‐D effect derived from Shinozaki–Kira's theory (i.e., the logistic theory of the C‐D effect), which deals with the density effect in nonself‐thinning populations. However, one of the two time‐dependent coefficients is quite different in mathematical interpretation between the two reciprocal equations. The reciprocal equation for self‐thinning populations is essentially the same as the reciprocal equation assumed in the derivation of the functional relationship between actual and initial population densities. The establishment of the reciprocal equation is supported by the empirical facts that the reciprocal relationship between mean phytomass and population density is discernible in not only nonself‐thinning populations but also in self‐thinning populations. The present model is expected to systematically interpret underlying mechanisms between the C‐D effect, which is observed at a time constant among populations with various initial densities, and self‐thinning, which is observed along a time continuum in a given population.