Soybean [Glycine max (L.) Merr.] growth and yield models depend on good predictions of phenological events such as flowering. Parameters for predicting flowering date of 12 cultivars were estimated for various development‐rate models. Date of flowering is predicted by accumulating a daily rate of development, which depends on night length and temperature, until a threshold is reached. Daily development rate is computed by a multiplicative relationship containing two functions: one for describing the variation in development rate with night length under optimal temperature and the other describing variation with temperature under optimal night length. There were 39 to 115 year‐location‐sowing date combinations for each cultivar, covering latitudes from 18°03′ to 45°25′ N lat. The downhill simplex method was used to estimate phenological parameters for each cultivar by minimizing the error sum of squares between observed and simulated flowering dates. Many formulations of the development‐rate model were compared. Linear‐plateau functions for both night length and temperature effects provided the best fit and yielded the most consistent results. The root mean squarerror between observed and simulated dates of flowering ranged from 3.45 to 5.28 d. Correlation coefficients between observed and simulated days from sowing to flowering varied from 0.987 to 0.841, with a decreasing trend from late toward early‐maturity cultivars. There was a clear difference among cultivars with respect to night‐length sensitivity, but a similaresponse to temperature.

Soybean growth and yield models require good predictions of vegetative and reproductive development stages, as a function of specific environmental variables. Parameters for predicting R5 (beginning of seed growth) and R7 (physiological maturity) dates of four soybean cultivars were estimated for a development rate model. R5 is predicted by accumulating a daily rate of development, which depends on night length and temperature, starting at Rl (flowering) until a threshold is reached. Daily development rate is computed by a multiplicative relationship containing two linear‐plateau functions: one for describing the variation in development rate with night length under optimal temperature and the other describing variation with temperature under optimal night length. The downhill simplex method was used to estimate phenological parameters for each cultivar, minimizing the error sum of squares between observed and simulated dates of R5 occurrence. The same type of model and methodology was used to estimate parameters for R7 prediction, but beginning at R5 until a threshold is reached. The results indicate that as plants develop from V1 (first true leaf) to R7 they become more responsive to photoperiod and less sensitive to temperature. Differences among cultivars with respect to optimal night length tend to diminish as the plants approach physiological maturity; with respect to temperature, the reverse happens. The optimal temperature for reproductive development varied between 25 and 29 °C, without great differences among cultivars of differing maturity, but with a slight increasing trend from V1 toward R7.

Unbiased prediction of plant growth stages is essential for accurate simulation of stage‐specific responses to environmental factors. The phenology model in SOYGRO V5.42 was compared with the phenology model in CROPGRO V3.0 for prediction of flowering and maturity date. Data came from 17 sources in North America and covered a wide range of maturity groups. An additional large‐scale data set from the U.S. Soybean Uniform Tests was used to evaluate predictions of maturity date. Parameters of the phenology models were estimated with an optimization procedure in which the downhill simplex method determined the direction of the search. While the optimization procedure was valuable to estimate the parameters, additional criteria were required to obtain realistic values. Based on the root mean square error (RMSE) criterion between predicted and observed dates, SOYGRO and CROPGRO predicted flowering equally well. Development rate after flowering was underpredicted by SOYGRO in cool environments so that in some years, maturity was predicted very late. CROPGRO has a separate temperature function after beginning seedfill, which decreased the RMSE for prediction of maturity date compared with SOYGRO, especially for early maturity cultivars. Allowing the critical short day length to increase after flowering date in the CROPGRO model consistently decreased the RMSE for prediction of beginning seedfill and maturity. CROPGRO was superior to SOYGRO for prediction of maturity date.

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