An open-ended logistic-based growth function

The logistic equation as usually formulated and applied to organism growth has a prescribed asymptote. Some applications require an asymptote depending on conditions during growth such as nutrition, temperature or irradiance. A logistic-based growth equation which fulfils this requirement has not, to-date, been available. A direct dependence of asymptote on growth conditions would be ineffective as well as scientifically incorrect. An indirect method of achieving the objective is suggested. The usual logistic asymptote becomes a state variable which can decrease, depending on degree of growth limitation, current organism mass and an additional parameter, D, representing development or differentiation. Early limitation has greater effect than late limitation. Duration of limitation is also important. The proposed modification of the logistic also moves mass at the inflexion point closer to asymptotic final mass; this could be valuable for many applications. An open-ended logistic-like growth model extends the range of applications of this valuable equation in the animal, plant and ecological sciences.