A mathematical model of conidial germination and appressorial formation for Colletotrichum graminicola

Abstract

A mathematical model, which is a modification of the Gompertz equation, can determine the number of germinations and the number of appressorial formations in a population of conidia of Colletotrichum graminicola. It will determine both the maximum proportion of conidia which will germinate or which will form appressoria and the time for these events to occur. The equation parameters, which are functions of biotic and abiotic conditions, are determined using a nonlinear regression programme. The data used to test the model show that continuous light on the parent fungal colony reduces subsequent conidial germination but does not change the time taken to reach this maximum.

Adopting adequate leaching requirement for practical response models of basil to salinity

“…van Genuchten and Hoffman (1984), Steppuhen et al (1996), and Wang et al (2002) used the bi-exponential function to describe the yield response of perennial ryegrass (Lolium perenne L.), wheat (Triticum aestivum L.), and elephant grass (Pennisetum purpureum Schum), respectively. According to Lapp and Skoropad (1976), to predict human mortality during long periods, it is possible to use a form of the equation proposed by Gompertz (1825). The same equation in various forms has been applied in botany to model germination (Tipton, 1984), emergence (Gan et al, 1992), and growth (Baker et al, 1975).…”

Quantification of Allelopathic Potential of Sorghum Residues by Novel Indexing of Richards' Function Fitted to Cumulative Cress Seed Germination Curves

“…Plant growth analysis was used to quantify the simple bioassay response of cumulative seed germination. Despite its advantages, this functional approach to plant growth analysis has been applied to cumulative germination data in only a few instances (15,23 Aqueous Extract Preparation. A crude extract was prepared by stirring 10 g of ground sorghum material with 100 ml of H20 overnight at 4°C.…”

“…Using the strategy of Lapp and Skoropad (15) by a significant F value (0.05 level) for the interaction of extract potency and harvest date (Fig. 1).…”

Physiological and ultrastructural investigations of caryopsis dormancy in Setaria lutescens (Gramineae)

“…Many modeling strategies have been used such as polynomial regres sion (Goodchild and Walker, 1971), normal distribution function (Janssen, 1973), autocatalytic function (Hageseth, 1974), Gompertz equation (Lapp and Skoropad, 1976), and logistic function (Schimpf, Flint, and Falmblad, 1977). Although each procedure has its advantages, it is clear that whichever modeling procedure is chosen, it should not be based on predetermined assumptions about the shape of the germination curve.…”

“…Schimpf et al (1977) did report the maximum germination achieved, which is of course biologically significant, but they derived this value directly from their observations rather than from the equations of their fitted curves. In contrast, Lapp and Skoropad (1976) derived both the maximum germination percentage achieved and the time to achieve it from the Gompertz regression equation. However, neither of these investigators attempted to incorporate several biolog ically significant germination parameters into a single index that was amenable to statistical analysis.…”