In lieu of an abstract, here is a brief excerpt of the content:

RELATIVE-GROWTH LAW WITH A THRESHOLD GEORGE M. ANGLETON* and DAVID PETTUSf Even before Huxley [i] formulated the relative-growth law, it was undoubtedly a matter of common observation that the relative growth of individuals and populations was frequently proportional to the relative time over which such measurements were made. The growth law is a solution to the differential equation dM/dt= ßM/t. The variables Mand (represent mass and time, respectively; ß is theproportionality constant which characterizes the mass growth being described by the law. The equation may alternately be put in the form dM/M= ßdt/t; that is, the relative-growth law states that the relative change in the mass is proportional to the relative change in time. The relative-growth law, and thus the solution to this differential equation, is M = at0, a being the value ofM at a time t equal to one. According to this model, the mass at time t equal to zero also has to be zero. The estimation ofthe two parameters in the model is facilitated ifit is assumed that the observations have a log-normal distribution [2]. This type ofvariation is frequently observed in biological studies; namely, the variations ofthe observations are proportional to their mean or expected value. When this occurs, maximum-likelihood estimates ofthe parameters can be obtained, and tests ofhypotheses can be conducted using analysisof -variance techniques. Estimates ofthe parameters may be obtained using the following computational formulas where ? is the number of observations,M¿ is the observed mass ofthe ith observation corresponding to the z'th value oft. * Departments ofRadiology and Radiation Biology, Mathematics and Statistics, Colorado State University, Fort Collins. I Department ofZoology, Colorado State University, Fort Collins. 42I Xi=In(U); Fi = In(Mi). ? = ^X' . ? — 5_í_i ? ' ? Sxv = 2XiYi-nXY. Sxx = S?] - nX* . S ß = estimate of ß = -^ . O ?? A = Y — ß?; à = estímate of a = exp( A ) . The computational formulas for obtaining the confidence limits on the estimates ofthe parameters are as follows: „ S(G?-?-;3?;)2 c¿ rr ----------------------------------- ¦ (n-2) ß-


Additional Information

Print ISSN
pp. 421-424
Launched on MUSE
Open Access
Back To Top

This website uses cookies to ensure you get the best experience on our website. Without cookies your experience may not be seamless.