A new generalized logistic sigmoid growth equation compared with the Richards growth equation

A new sigmoid growth equation is presented for curve-fitting, analysis and simulation of growth curves. Like the logistic growth equation, it increase s monotonically, with bath upper and lower asymptotes. Like the Richards gr owth equation, it can have its maximum slope at any value between its minim um and maximum. The new sigmoid equation is unique because it always tends towards exponential growth at small sizes or low densities, unlike the Rich ards equation, which only has this characteristic in part of its range. The new sigmoid equation is therefore uniquely suitable for circumstances in w hich growth at small sizes or low densities is expected to be approximately exponential, and the maximum slope of the growth curve can be at any value . Eleven widely different sigmoid curves were constructed with an exponenti al form at low values, using an independent algorithm. Sets of 100 variatio ns of sequences of 20 points along each curve were created by adding random errors. In general, the new sigmoid equation fitted the sequences of point s as closely as the original curves that they were generated from. The new sigmoid equation always gave closer fits and more accurate estimates of the characteristics of the 11 original sigmoid curves than the Richards equati on. The Richards equation could not estimate the maximum intrinsic rate of increase (relative growth rate) of several of the curves. Both equations te nded to estimate that points of inflexion were closer to half the maximum s ize than was actually the case; the Richards equation underestimated asymme try by more than the new sigmoid equation. When the two equations were comp ared by fitting to the example dataset that was used in the original presen tation of the Richards growth equation, both equations gave good fits. The Richards equation is sometimes suitable for growth processes that may or ma y not be close to exponential during initial growth. The new sigmoid is mor e suitable when initial growth is believed to be generally close to exponen tial, when estimates of maximum relative growth rate are required, or for g eneric: growth simulations. (C) 1999 Annals of Botany Company.