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\hypersetup{pdftitle={Using Non"=linear Models to Predict Flowering Time in Three Millet Species Based on Thermal Time Concept},pdfauthor={Morteza Eshraghi Nejad, Behnam Kamkar, Afshin Soltani},pdfsubject={Tropentag 2010: Abstract},pdfkeywords={Cardinal temperatures, critical photoperiod, flowering, millet, non-linear fitting, thermal time},pdfpagemode=None,colorlinks=true}
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\parbox[b]{13.4cm}{\centering \large{\textbf{Tropentag, September 14-16, 2010, Zurich}}\\[1ex] \Large{``World Food System  ---\\A Contribution from Europe''\\[2ex]}}
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\begin{center}
\Large{\textbf{Using Non"=linear Models to Predict Flowering Time in Three Millet Species Based on Thermal Time Concept\footnote{\textbf{Contact Address:} Behnam Kamkar, Gorgan University of Agricultural Sciences and Natural Resources, Dept. of Agronomy, Basij Square, Gorgan, Iran, \mbox{e-mail}: \email{bkamkar@yahoo.com}}\\[0.8ex]}}
\normalsize{\textsc{Morteza Eshraghi Nejad, Behnam Kamkar, Afshin Soltani}}
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\begin{itemize*}
\item[]{\small{\textit{Gorgan University of Agricultural Sciences and Natural Resources, Department of Agronomy, Iran}}}
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\index[author]{Eshraghi Nejad, Morteza}
\index[author]{Kamkar, Behnam}
\index[author]{Soltani, Afshin}
\begin{center}
\vspace{1.1cm}
\textbf{Abstract}
\begin{abstract}
\normalsize{
This study aimed to quantify the response of flowering rate to temperature and photoperiod (PP) in three millet species (Common millet (\textit{panicum miliaceum}), pearl millet (\textit{Pennisetum glaucum}) and foxtail millet (\textit{Setaria italica})). We aimed to formulate and validate mathematical functions that can be used to determine the cardinal temperatures and photoperiod"=related parameters. Also biological days required from planting to flowering of each species was calculated. In this case, eight non"=linear regression models (including  flat (F), logistic (L), cubic (C), dent"=like (D), segmented (SE), curvilinear (C), quadratic (Q), sigmoidal (SI), beta (B) and quadratic (Q)) were used to quantify temperature function and three non"=linear regression models (including negative exponential (NE), segmented (SE) and quadratic (Q)) were applied to quantify the photoperiod function. Root Mean Square of Errors (RMSE), Mean Absolute Error (MAE), Relative Mean Absolute Error (RMAE), The intercept and slope of regression line between observed against predicted flowering rate (a and b) and coefficient of determination of predicted versus observed values were used to find the appropriate combined model. Results show that Logistic Quadratic (L-Q) (R$^{2}$ = 0.98, a = 0.0006, b = 0.97) and Quadratic Quadratic (Q-Q) (R$^{2}$ = 0.90, a = 0.002, b = 0.91) were   both the best combined models to predict flowering rate of common millet, while Beta Quadratic (B-Q) (R$^{2}$ = 0.88, a = 0.001, b = 0.97) and Quadratic Quadratic (Q-Q) (R$^{2}$ = 0.86, a = 0.002, b = 0.87) models were selected as the best models to predict flowering rate of foxtail millet. For the pearl millet only Beta Quadratic model was appropriate (B-Q) (R$^{2}$ = 0.89, a = 0.001, b = 0.98) . Base on selected models, the base, the optimum and the ceiling temperatures varied between 7--9, 35--40.5, and 45--47.10\&\#9702;C, respectively. The thermal time required to flowering for common, foxtail and pearl millet were determined as 706.8, 963.12 and 807.9, respectively. Model predictions of the time required for flowering agreed reasonably well with the observed times. These functions and parameters can be used in millet simulation models to predict planting to flowering duration based on a photothermal time concept.}

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\end{abstract}
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\noindent \textbf{Keywords:} Cardinal temperatures, critical photoperiod, flowering, millet, non"=linear fitting, thermal time
\index[key]{Cardinal temperatures}
\index[key]{Critical photoperiod}
\index[key]{Flowering}
\index[key]{Millet}
\index[key]{Non"=linear fitting}
\index[key]{Thermal time}
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