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A. Maaike Wubs, Yun T. Ma, Ep Heuvelink, Lia Hemerik, and Leo F.M. Marcelis

., 2003 ; Daymond and Hadley, 2008 ; Garriz et al., 2005 ; Marcelis, 1992 ; Tadesse et al., 2002 ). However, these functions have different properties with respect to their shapes. Comparison of different sigmoid functions and model selection should be

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Leena Lindén, Pauliina Palonen, and Mikael Lindén

Seasonal cold hardiness of red raspberry (Rubus idaeus L.) canes was measured by freeze-induced electrolyte leakage test and visual rating of injury. Leakage data were transformed to percentage-adjusted injury values and related to lethal temperature by graphical interpolation and by the midpoint (T50) and inflection point (Tmax) estimates derived from three sigmoid (the logistic, Richards, and Gompertz) functions. Tmax estimates produced by Richards and Gompertz functions were corrected further using two different procedures. The 10 leakage-based hardiness indices, thus derived, were compared to lethal-temperature estimates based on visual rating. Graphical interpolation and Tmax of the logistic or T50 of the Gompertz function yielded lethal-temperature estimates closest to those obtained visually. Also, Tmax values of the Gompertz function were well correlated with visual hardiness indices. The Richards function yielded hardiness estimates deviating largely from visual rating. In addition, the Richards function displayed a considerable lack of fit in several data sets. The Gompertz function was preferred to the logistic one as it allows for asymmetry in leakage response. Percentage-adjusted injury data transformation facilitated curve-fitting and enabled calculation of T50 estimates.

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Michael H. Hagemann, Malte G. Roemer, Julian Kofler, Martin Hegele, and Jens N. Wünsche

regression analysis, normality and variance homogeneity, were checked. The seasonal curves of FPP were best described with a four-parametric sigmoid function: where x is the dependent variable DAFB. The parameter y 0 is diverging to positive infinity

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Chon C. Lim, Rajeev Arora, and Edwin C. Townsend

Seasonal patterns in freezing tolerance of five Rhododendron cultivars that vary in feezing tolerance were estimated. Electrolyte leakage was used, and raw leakage data were transformed to percent leakage, percent injury, and percent adjusted injury. These data were compared with visual estimates of injury. Percent adjusted injury was highly correlated (0.753) to visual estimates. Two asymmetric sigmoid functions—Richards and Gompertz—were fitted to the seasonal percent adjusted injury data for all cultivars. Two quantitative measures of leaf freezing tolerance—Lt50 and Tmax (temperature at maximum rate of injury)—were estimated from the fitted sigmoidal curves. When compared to the General Linear Model, the Gompertz function had a better fit (lower mean error sum of squares) than Richards function. Correlation analysis of all freezing tolerance estimates made by Gompertz and Richards functions with visual LT50 revealed similar closeness (0.77 to 0.79). However, the Gompertz function and Tmax were selected as the criteria for comparing relative freezing tolerance among cultivars due to the better data fitting of Gompertz function (than Richards) and more descriptive physiological representation of Tmax (than LT50). Based on the Tmax (°C) values at maximum cold acclimation of respective cultivars, we ranked `Autumn Gold' and `Grumpy Yellow' in the relatively tender group, `Vulcan's Flame' in intermediate group, and `Chionoides' and `Roseum Elegans' in the hardy group. These relative rankings are consistent with midwinter bud hardiness values reported by nurseries.

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Majken Pagter, Karen K. Petersen, Fulai Liu, and Christian R. Jensen

estimate the temperature representing 50% injury (LT 50 ), data for all four (stems) or five (roots) replicates per treatment were fitted by regression analysis (PROC NLIN), to the sigmoid function y = y 0 + a /{1 + exp[−( x − x 0 )/ b ]}, where

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James E. Altland, James S. Owen Jr, and William C. Fonteno

): where θ s is water content at saturation, θ r is residual water content, x 0 is an estimated parameter that represents the value of h where the sigmoid function transitions from convex to concave in shape, and n and m are estimated parameters

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Ali Akbar Ghasemi Soloklui, Ahmad Ershadi, and Esmaeil Fallahi

hardiness was expressed as LT 50 (lethal temperature at which 50% of the total ion leakage occurs; or, in the case of TST, the lethal temperature at which 50% of the tissues are dead) by fitting response curves with the following logistic sigmoid function

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Orlanda Cristina Barros Moreira, José Martins, Luís Silva, and Mónica Moura

fraction of the data. A Tukey honestly significant difference test was used as a multiple comparison procedure. In relevant cases, namely the best treatments, variation in germination was displayed with germination curves and the Gompertz sigmoid function

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Smita Barkataky, Robert C. Ebel, Kelly T. Morgan, and Keri Dansereau

. Fla. State Hort. Soc. 97 33 36 Yin, X. Goudrian, J. Lantinga, E.A. Vos, J. Spiertz, H.J. 2003 A flexible sigmoid function of determinate growth Ann. Bot. (Lond.) 91 361 371 Young, R. 1970 Induction of dormancy and cold hardiness in citrus HortScience 5

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Ali Akbar Ghasemi Soloklui, Ali Gharaghani, Nnadozie Oraguzie, and Armin Saed-Moucheshi

logistic sigmoid function ( Ghasemi Soloklui et al., 2012 ): where x = treatment temperature; b = slope at inflection point; and c , a , and d determine the asymptotes of the function. Statistical analyses. The diallele crosses were analyzed