Connection between Growth/Development and Mathematical Function

Abstract

To investigate universal principles of growth and development, theauthor examined the questions of when mathematical functions canbe applied to growth curves, what type of functions can be used,and, from a consideration of the historical background, the contextfor application and validity of such mathematical functions. Examinationsof this issue have developed along two main lines: the establishmentof logistic models as sigmoid curves showing the proliferation processof living organisms, and the establishment of polynomial systems(spline functions) that describe smoothing of the growth curve andfluctuations in the process. The conceptual prescriptions of fittingfunctions for the former are structural models, and those for thelatter are nonstructural models. The fundamental thinking is that,similar to proliferation of organisms, growth phenomena can be describedand explained with the use of differential equations. However, changesin aspects of growth curves are produced with differences in measurementintervals: waves are seen in growth phenomena as measurement intervalsbecome shorter. Thus, a mathematical function is needed that candescribe the changes in growth phenomena using a scaling concepton the time axis. To do this it is necessary to separate growth phenomenafrom biology and develop mathematical functions derived from an independentconceptual framework. In this context, the author has proposed uniquewavelets. Herein, the author discusses the historical and theoreticalbackgrounds of mathematical fitting functions and their validity.The author also examine the interface of these functions with growthstudy, and its theoretical background.