The Gompertz Function as a Model for Cotton Hypocotyl Elongation¹

Abstract

Successful 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 normalA∘, normalb∘, and normalc∘) 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.

Dry matter accumulation of winter wheat and barley at different sowing dates

“…The WMAGR and DUR were calculated according to Pagelow Jr. et al (1977) and Munakamwe et al (2014):Data were subjected to a combined analysis of variance, treating the sowing date as the main plot and the species as the sub-plot. The cultivars were nested within species.…”

Quantitative characterization of five cover crop species

“…The ground cover was calculated as the number of pixels of the layer divided by the total number of pixels that constitute the image of the marked surface (Ramirez-Garcia et al 2012). Ground cover data before the first frost were adjusted to the Gompertz function, which assumed a sigmoid growth until an asymptotic maximum value (Pegelow et al 1977;Bodner et al 2010):…”

Variation in intra‐annual wood formation, and foliage and shoot development of three major Canadian boreal tree species

“…Xylem cell formation, shoot extension, and foliage growth of individual tree were fit using the commonly used Gompertz sigmoidal growth function (Gompertz, 1825). The function has been previously used to describe intra‐annual diameter growth of trees (Deslauriers et al, 2003a; Rossi et al, 2006b) and other intra‐annual growth processes like cotton hypocotyl ( Gossypium hirsutum L.) elongation (Pegelow et al, 1977). All analyses were conducted using the SigmaPlot statistical package (version 10, Systat, San Jose, California, USA).…”