@article{oai:u-ryukyu.repo.nii.ac.jp:02004812,
 author = {Hagihara, Akio and 萩原, 秋男},
 issue = {66},
 journal = {琉球大学理学部紀要, Bulletin of the College of Science. University of the Ryukyus},
 month = {Sep},
 note = {A mathematical model for describing the density effect occurring in self-thinning\npopulations is developed on the basis of the following three basic assumptions: (1)\nthe growth of yield follows the general logistic equation; (2) final yield becomes\nconstant irrespective of initial density; and (3) there exists a functional relationship\nbetween actual and initial densities. The resultant equation takes the same reciprocal form as the reciprocal equation derived from Shinozaki-Kira's theory, i.e., the\nlogistic theory of the C-D effect, which deals with the density effect occurring in nonself-thinning populations. It is, however, recognized that one of the two coefficients is quite different in mathematical interpretation between the two reciprocal\nequations based on the present theory and the logistic theory of the C-D effect, respectively. The present conclusion is consistent with the empirical facts that the reciprocal relationship between yield (or mean phytomass) and density is discernible\nin not only nonself-thinning populations, but also self-thinning populations. The\npresent model is expected to systematically interpret underlying mechanisms be\ntween the density effect, which is observed at a time constant among populations\nvarying in initial density, and self-thinning, which is observed along a time continuum in any given population., 紀要論文},
 pages = {71--79},
 title = {Mathematical and Biological Considerations on Yield- and Competition-Density Effects in Self-thinning Plant Populations},
 year = {1998}
}