The Gompertz Function as a Model for Cotton Hypocotyl Elongation1

Abstract

AbstractSuccessful modeling of cotton (Gossypium hirsutum L.) seedling emergence requires a model capable of simulating hypocotyl growth under a wide range of soil environments. A previous model used an autocatalytic growth equation which was satisfactory for relatively favorable soil environments. We report here the use of the Gompertz equation as a hypocotyl elongation model which should have adaptability to greater environmental extremes than the autocatalytic model. A three parameter form of the Gompertz equation was applied to a comprehensive set of cotton hypocotyl elongation data, obtained over a range of steady‐state soil environments. The form used was y = A exp {—exp [b(c—t]} where y is hypocotyl length at time t, A is maximum (potential) hypocotyl length under prevailing soil conditions, b is the weighted mean relative growth rate, and c is the time at which maximum growth rate is attained. This function describes an asymmetrical sigmoid curve in which all parameters can be assigned physiological meaning. Best‐fit estimates of the Gompertz parameters were derived for hypocotyl elongation in each environment by a non‐linear least squares program. Multiple linear regression analyses of the estimated Gompertz parameters (in ) with soil temperature, physical impedance, and moisture were used to examine the influence of soil environment on the parameters. Each of the three Gompertz parameters were adequately described by a cubic regression model involving these soil factors. The regression models were used to develop a Gompertz model in which each parameter was responsive to fluctuating changes in soil environment. The model should be adaptable to simulating cotton hypocotyl elongation under a wide range of soil conditions, including those resulting in seedling stress.