Response of flowering to the time of transfer
Plants of the two parents and the 94 RILs tested in the greenhouse experiment flowered in all treatments. As expected, plotting the thermal days from sowing to flowering as a function of the thermal days from sowing to transfer indicated that the photoperiod-sensitive phase was flanked by two insensitive phases. Results for the two parents are shown in Fig. 1. The pattern of the relationship represents well the theoretically expected one (Ellis et al., 1992
; Yin et al., 1997a), with the two sets of broken linear segments as described by equation (4).
Duration of photoperiod-sensitive and insensitive phasesEstimation of the length for photoperiodically sensitive and insensitive phases of each genotype on the basis of
equation (4) involves an iterative regression procedure. For all genotypes, iterations, based on data of either actual days to flowering or thermal days, converged to reach the definite estimate of the phases. Use of data in thermal days resulted in a more stable parameter estimation than the use of data in days (results not shown), as the confounding effect of diurnal and seasonal temperature fluctuations during the experimental period could effectively be removed using thermal days. Estimated values for the duration of the phases are therefore all based on thermal days.
Equation (4) fitted well to the total of 30 observations of each genotype, with
r2 ranging from 0.67 to 0.94. The average value of estimated
I1,
I2I,
I2N, and
I3 was 27.7, 25.2, 42.7, and 16.6 thermal days, respectively. The estimated value of each parameter differed little between the two parents (
Table 1). However, there were significant variations among the 94 RILs for each of these four estimates (
Table 1), indicating a transgressive segregation in this population.
Prediction of flowering under field conditions
To enable the phenology model, equations (1–3), to be used for prediction, the four input parameters of the model were calculated for each genotype from the estimated value of I1, I2I, I2N, and I3. Again, transgressive segregation existed for each of these four input parameters (Table 2).
The model captured 37% to 67% of the phenotypic variation in flowering time observed in a field environment (Table 3). The linear regression for predicted days against observed days all had a positive intercept value and a slope of less than one, indicating that the model tended to over-predict the lower end and to under-predict the higher end of observed flowering dates in each of these eight field environments. Therefore, the range of predicted values is less than that of the observed values. The narrower range of the predicted values is an expected general phenomenon: the observed variations are partly due to structure and partly due to random noise, whereas a model always represents the structure. Consequently, the contribution of noise to extreme observations on the low and high ends will be greater than the contribution of noise to intermediate values. Therefore, compared with intermediate values, extreme observed values will appear to be shrunken back more to a common line through the cloud of predicted versus observed points. This reasoning is supported by the fact that the field environments for which the model performed poorly coincide with those for which identified QTL explained little phenotypic variation of observed days to flowering, as revealed in the subsequent analysis (Yin et al., 2005).
Overall, the model predicted well the average flowering dates across the eight environments (Fig. 2A), whereby the random noise is at least partly removed via averaging the eight observations. Further, the model satisfactorily predicted variation in the mean flowering time across the 96 genotypes among the eight environments (Fig. 2B). When all observations for the 96 genotypes in the eight environments are pooled, the model predicted 81% of the total observed variation (Fig. 3).
Sensitivity analysis to determine the importance of four model parametersAn important application of an ecophysiological model is to conduct sensitivity analysis to test which model-input traits are most important in determining the trait under study (Hammer
et al., 2002
). Yin
et al. (2000)
made such an analysis by fixing one parameter at a time at its across-genotype averaged value and found that only two of the six model-input traits were important for grain yield determination among the RILs of the ‘ApexxPrisma’ population. Here, the same approach was used to examine if the four input parameters (
fo,
1,
2, and
) of the phenology model,
equations (1–
3), are important for determining the flowering time.
Use of across-genotype averaged value of each model-input parameter resulted in a reduced model-explained percentage of variation in across-environment mean flowering times of genotypes (Table 4), indicating that all the four parameters are important for determining flowering time. The extent to which the explained variation was reduced varied among the four parameters; use of averaged fo even resulted in a negative slope value in the linear regression between predicted and observed values (Table 4). However, as expected, use of across-genotype averaged parameter values did not change the model performance in predicting environment mean (result not shown). As a consequence, the model-explained percentage of overall variation, when all the observations for 96 genotypes in the eight environments were pooled (Table 4), was higher than the explained variation in genotype mean flowering times. It can be seen, in terms of explained variation either in genotype mean flowering time or in all observations for 96x8 genotype environment combinations, that the parameters contributed most to the determination of flowering time in the order of fo, , 1, and 2.
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