Applying the Richards function in freezing tolerance determination with electrolyte and phenolic leakage techniques

Abstract

The purpose of the present study was to apply the Richards function to fit electrolyte and phenolic leakage data for several taxa of woody plants subjected to freezing stress and to determine how the curve inflection point relates to the lethal temperature range. The lowest survival temperature of Fraxinus americana, Lagerstroemia cv. Natchez, Magnolia grandiflora, Rhododendron cv. Red Ruffle and Zelkova serrata was determined based on visual evaluation of oxidative browning facilitated by a modified regrowth test and differential thermal analysis. Lethal injury occurred in all cases within a range of 3°C below lowest survival temperature. Using the Richards function inflection point as an estimate of lethal temperature led to an overestimation of freezing tolerance in most taxa. This overestimation was greater for stems than leaves, and was greater in winter than in summer. The lethal temperature range generally coincided with the initial increase in leakage caused by freezing. The lethal temperature range also was determined by using a point of interception of the lower asymptote of a curve with a line tangential to the inflection point. In most taxa tested estimated lethal temperature based on the point of interception provided an improvement over the estimate based on the point of inflection.

Relating Freeze-induced Electrolyte Leakage Measurements to Lethal Temperature in Red Raspberry

“…The lethal temperatures were also determined by further manipulating the Richards and Gompertz functions with two correction methods ( Table 1). The first one, suggested by Anisko and Lindstrom (1995), determines the corrected lethal-temperature value by using the first-order approximation of Taylor series. To approximate the percentage-adjusted injury (I) value at the inflection point, we define I at zero temperature (I T (0)) as I T (0) ≈ I max + (dI/dT) max (0 -T max ), where I max and T max are percentage-adjusted injury and temperature at the inflection point of the appropriate function.…”

“…The correction method of Anisko and Lindstrom (1995), described above, will most often generate a hardiness index value that is higher (warmer temperature) than that given by the original inflection point. In addition, the correction may often be too large.…”

“…In most of our data sets, the T max estimations by the logistic curve were in close agreement with visual evaluations. The main drawback in using the logistic function is its symmetry; an asymmetric model is considered more appropriate for describing plant response to temperature stress in terms of physical and physiological mechanisms (Anisko and Lindstrom, 1995;Lim et al, 1998;von Fircks and Verwijst, 1993). Fitting an asymmetric curve to EL data has yielded varying results.…”

“…Therefore, the authors developed a correction method for interpreting leakage vs. temperature curves: they determined the lethal-temperature range by a point of interception of the lower asymptote with a line tangential to the inflection point of a fitted curve. The procedure is based on the assumption that the transition from the living to the dead state coincides with the initial increase rather than the highest rate in EL (Anisko and Lindstrom, 1995). Recently, Lim et al (1998) compared two asymmetric sigmoid models, Richards and Gompertz functions, to estimate the freezing tolerance of rhododendron (Rhododendron L.…”

“…Presently, there are only a few reports on applying asymmetric functions to fit EL data, probably due to the complexity of the curvefitting process. To our knowledge, the report by Anisko and Lindstrom (1995) is the only one where leakage response for woody stem samples is described using an asymmetric function. Therefore, the following research was undertaken to compare the graphic and parametric curve-fitting methods of relating EL data from woody stems to lethal temperature.…”