Time to flowering is an elementary, important trait for predicting crop yields, as in many crops (cereals in particular), the maximum yield in a growing season is determined during the preflowering period (Slafer, 2003). Therefore, time to flowering has been an important trait for improving crop productivity and adaptation (Lawn et al., 1995).
As for any typical quantitative trait, phenotypic variation of time to flowering is controlled both by genetic characteristics and by environmental variables. Temperature and photoperiod are two major environmental factors that affect time to flowering (Loomis and Connor, 1992). Crop modellers have developed ecophysiological quantitative equations for describing the photothermal responses of phenology, in order to predict flowering times of crop genotypes under a range of environmental conditions, or to provide the temporal framework for modelling a number of processes in a general crop growth model. Yin et al. (1997c) evaluated four popular phenology models of different complexities, and found that all of them were able of capturing flowering responses to a wide range of photothermal environments albeit with varying levels of accuracy.
A common feature of such models is that an index variable, development stage (), is defined as a state variable, having a dimensionless value of 0 at sowing and 1 at flowering. The value of at any day between sowing and flowering is the accumulation over time of daily development rate (i), which has a unit of d–1. The value of i is calculated by:
) is the daily temperature response function, h
) is the daily photoperiod response function, fo
is the minimum number of days from sowing to flowering when both temperature and photoperiod are at their optimum, representing the genotype's intrinsic earliness of flowering, 1
are the development stages for the start and the end of photoperiod-sensitive phase, respectively. Equation (1)
recognizes the fact that, unlike temperature, photoperiod has an impact on developmental rate only during a certain part of the preflowering period (Ellis et al
; Yin et al
). Several studies (Slafer and Rawson, 1995
; Adams et al
) have emphasized the importance of accurately specifying the timing of the photoperiod-sensitive phase in phenology prediction models.
The temperature effect function, g(T), in equation (1) is best defined by a bell-shaped function using three-cardinal temperatures (Yin et al., 1995; Yan and Hunt, 1999):
, and Tc
are the base, the optimum, and the ceiling temperature for phenological development [i.e. g
)=0 if TTb
The photoperiod function during the photoperiod-sensitive phase (when is between 1 and 2), h(P), in equation (1) can be defined as having a value between 0 and 1 simply with (Loomis and Connor, 1992):
is the maximum optimum photoperiod for a short-day crop or the minimum optimum photoperiod for a long-day crop,
is the photoperiod-sensitivity parameter, being positive for long-day crops and negative for short-day crops.
Ecophysiological phenology models have so far been used only for predicting flowering (or maturity) time of distinct cultivars within a crop species. There is a growing awareness that in order to predict phenotypes of complex traits for any plant or crop genotypes under any environmental scenarios using increasingly available genomic information, integration of ecophysiological modelling with genetics and molecular biology is required (Tardieu, 2003; Yin et al., 2003). For a successful interfacing of physiological modelling with genetics, there is a need to work with a relevant genetic population (Yin et al., 2000). The present study aims to predict environment-dependent flowering time in individual genotypes of a genetic population, with emphasis on the parameterization and independent testing of the above phenology model.