Model analysis of flowering phenology in recombinant inbred lines of barley

Abstract

RESEARCH PAPER

Model analysis of flowering phenology in recombinant inbred lines of barley

Xinyou Yin^1,2,*, Paul C. Struik², Jianjun Tang¹, Changhan Qi¹and Taoju Liu¹

¹College of Agriculture, Jiangxi Agricultural University, Nanchang 330045, PR China
²Crop and Weed Ecology Group, Wageningen University, PO Box 430, 6700 AK Wageningen, The Netherlands

^* To whom correspondence should be addressed at Wageningen. Fax: +31 317 485572. E-mail: [email protected]

Received 24 August 2004; Accepted 22 November 2004

Abstract 

A generic model for flowering phenology as a function of daily temperature and photoperiod was applied to predict differences of flowering times among 96 individuals (including the two parents) of a recombinant inbred line population in barley (Hordeum vulgare L.). Because of the large number of individuals to study, there is a need for simple ways to derive model parameters for each genotype. Therefore the number of genotype-specific parameters was reduced to four, namely f_o (the minimum number of days to flowering at the optimum temperature and photoperiod), ₁ and ₂ (the development stages for the start and the end of the photoperiod-sensitive phase, respectively), and (the photoperiod sensitivity). Values of these parameters were estimated using a newly described methodological framework based on data from a photoperiod-controlled experiment where plants were mutually transferred between long-day and short-day environments at regular intervals. This modelling approach was tested in eight independent field environments of different sowing dates in two growing seasons. The four-parameter model predicted 37–67% of observed phenotypic variation in an environment, 76% of variation in across-environment mean days to flowering among the genotypes, and 96% of variation in across-genotype mean among the eight environments. When all the observations of the 96 genotypes across the eight environments were pooled, the model explained 81% of the total variation. Sensitivity analysis showed that all four model parameters were important for predicting differences in flowering time among the genotypes; but their relative importance differed and the ranking was in the order of f_o, , ₁, and ₂. This study highlighted the potential of using ecophysiological models to assist the genetic analysis of quantitative crop traits whose phenotype is often environment-dependent.

Key words: Daylength, ecophysiological modelling, flowering, genotype-by-environment interaction, Hordeum vulgare, phenology, photoperiod, temperature

Journal of Experimental Botany 2005 56(413):959-965. Published by Oxford University Press [on behalf of the Society for Experimental Biology].

Introduction

 

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:

(1)

where g(T) is the daily temperature response function, h(P) is the daily photoperiod response function, f_o 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 and ₂ 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., 1992; Yin et al., 1997a). Several studies (Slafer and Rawson, 1995; Adams et al., 2001) 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):

(2)

where T_b, T_o, and T_c are the base, the optimum, and the ceiling temperature for phenological development [i.e. g(T)=0 if TT_b or T_c].

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):

(3)

where P_o 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.

Materials and methods

 

Recombinant inbred line population
The same recombinant inbred line (RIL) population used in a previous study (Yin et al., 2000) was used in the present study. The population consists of 94 RILs, produced by eight generations of single seed descent from a cross of the two-row spring barley cultivars ‘Apex’ and ‘Prisma’. The two parents differ in yielding ability, morphological characteristics, and phenological traits. Plants of ‘Apex’ usually flower earlier than those of ‘Prisma’.

Greenhouse and field experiments
A greenhouse experiment was conducted at Jiangxi Agricultural University, China. Seeds of each RIL were sown on 8 November 2002 in pots arranged on mobile trolleys. The trolleys stayed in the greenhouse between 07.00 h and 17.00 h, after which they were moved into darkrooms attached to the greenhouse. The darkrooms were programmed to create the required photoperiods. There were two photoperiod conditions: long-day (LD) and short-day (SD), which were set to 15 h and 10 h, respectively. The LD photoperiod was created by providing the darkroom with 10 µmol m^–2 s^–1 supplementary light of 2 h in the morning (05.00–07.00 h) and 3 h in the evening (17.00–20.00 h) of each day. Temperature both in the greenhouse and in the darkrooms was monitored over the experimental period. Initially, half of the pots for each RIL were placed in SD, half in LD. Starting from 17 d after sowing, plants were simultaneously transferred, one pot at a time for each RIL, from one photoperiod to the other, at an interval of 10 d. Once a plant was transferred, it was grown in the new photoperiod until flowering. In total, 14 transfers were implemented. The control plants grown continuously in SD or LD are equivalent to those transferred at 0 d after sowing. The two series of transfer, with 15 transfer times for each series (14 real transfers plus 1 control plant), gave a total of 30 observations for each RIL.

Field experiments were conducted over two growing seasons on the experimental farm of Jiangxi Agricultural University (latitude 28.7° N). In the first season, seeds were sown five times (month/date: 10/25, 11/5, 11/16, 11/25, and 12/4) in 2001. In the second season, there were three sowing dates (10/25, 11/10, and 11/25 in 2002). This created a total of eight field environments. Flowering time was recorded for each RIL of each environment. Daily maximum and minimum temperature over the seasons was obtained from a nearby weather station.

Because some RILs did not flower due to the incomplete appearance of ears from the flag-leaf sheath, the date of awn appearance was considered as the flowering time for all RILs in both greenhouse and field experiments. The greenhouse experiment was used to estimate model parameters. These parameters were then applied to predict flowering time of individual RILs in the two-season field experiments.

Specifying model parameters
The greenhouse experiment does not allow temperature response-related model parameters to be specified for each RIL. Nevertheless, it is a general rule that within a crop species, the genetic difference in temperature sensitivity of phenology is small, compared with the genotypic difference in photoperiod sensitivity (Ellis et al., 1990). Therefore, the same parameter value involving temperature response for all the RILs and parents was assumed. They are determined as: T_b=0, T_o=21 and T_c=35 °C, based on data of Ellis et al. (1988), Cao and Moss (1989), and Tamaki et al. (2002) for barley. Sensitivity analysis showed that a change in the value of these three cardinal temperatures had only small impact on final model predictions. For photoperiod response, genotypic difference in P_o is also small, compared with that in , ₁, and ₂ (Yin et al., 1997b). It was assumed that all RILs have the same P_o of 17 h (Ellis et al., 1988). Thus, the above model has four parameters (f_o, ₁, ₂, and ) to be estimated.

Analysis of data from the greenhouse experiment
Because temperature fluctuated both diurnally and seasonally under these experimental conditions, any impact of these fluctuations should be accounted for in order to obtain an accurate estimate of the four parameters. Equation (2) was used to convert observed days to flowering in the greenhouse experiment to thermal days. A thermal day is equivalent to an actual day only if temperature at any moment of that day is at the optimum value (i.e. 21 °C). g(T) was estimated on an hourly basis and hourly g(T) values were averaged to obtain a daily value. When plants remained in the darkrooms, the hourly temperature was obtained from monitored room temperatures. The hourly temperature outside the darkroom was estimated from the observed daily maximum and minimum temperatures by a sine function assuming the daily maximum occurs at 14.00 h each day (Matthews and Hunt, 1994). Accumulated daily g(T) from sowing to the day when an RIL flowered is the total thermal days for that RIL. Using the calculated thermal days, the model parameter values were estimated.

The time interval from sowing to flowering (f) of each RIL from the SD–LD mutual transfer experiment can be quantified by the following summary relations (Yin et al., 1997a):

(4)

where t is the time interval from sowing to each transfer, I₁ is the duration of the juvenile phase when plants are not yet responsive to photoperiod, I_2I and I_2N are the durations of the photoperiod-sensitive phase under the inductive and non-inductive photoperiod conditions, respectively (15 h and 10 h, respectively, in this experiment), I₃ is the duration of post-photoperiod-sensitive phase, Z₀ and Z₁ are dummy variables: Z₀=0 and Z₁=1 refers to transfers from inductive to non-inductive photoperiods, and Z₀=1 and Z₁=0 refers to transfers from non-inductive to inductive photoperiods. Readers are recommended to refer to an earlier work (Yin et al., 1997a) for details of equation (4). With this model, I₁, I_2I, I_2N, and I₃ can then be estimated using the iterative procedure of the PROC NLIN of the Statistical Analysis Systems (SAS Institute Inc.). The advantage of such an approach is that data from both sets of transfers (LD to SD and SD to LD) can be combined in one single analysis (Adams et al., 2001).

Conversion of I₁, I_2I, I_2N, and I₃ into the four model parameters f_o, ₁, ₂, and
Equations are derived here for the conversion of I₁, I_2I, I_2N, and I₃ into f_o, ₁, ₂, and , according to whether or not the inductive photoperiod (P_I) in the experiment agrees with the optimum photoperiod P_o.

If P_I equals P_o or is above P_o for long-day plants and below P_o for short-day plants, then f_o, ₁, and ₂ can be straightforwardly calculated by:

(5a)

(5b)

(5c)

where I_2o is the minimum duration of photoperiod-sensitive phase, equivalent to I_2I in the case. The photoperiod sensitivity parameter in equation (3) can be estimated by:

(6)

where P_N is the non-inductive photoperiod used in the transfer experiment. Equation (6) is derived by considering the accumulation of daily development rate over the photoperiod-sensitive phase at the optimum temperature condition. First, in terms of definition of the phenology model, equation (1), this accumulation for the case of non-inductive photoperiod gives:

(7)

where I_2o/f_o is the result by substituting equation (5b, c) for ₁ and ₂. Equation (7) means that

(8)

Secondly, the accumulation for the case of the optimum photoperiod is:

(9)

Equation (9) means that

(10)

Because h(P_o)=1, the ratio of equation (8) to equation (10) results in:

(11)

Substituting equation (11) into equation (3) and solving for results in equation (6).

If P_I is below P_o for long-day plants and above P_o for short-day plants, equation (5a–c) is still valid; but first, I_2o in these equations has to become known. The ratio of I_2I to I_2N can be formulated as:

(12)

On the basis of equation (3) and equation (11), equation (12) can be further written as:

(13)

Solving for from equation (13) gives the photoperiod sensitivity parameter :

(14)

The value of I_2o can then be estimated by either of the following two:

(15a)

(15b)

where is calculated by equation (14).

For the present greenhouse experiment, P_I is 15 h, less than the pre-set P_o (=17 h). Therefore, equation (14) and equation (15) are used first to obtain and I_2o, respectively. Equation (5a– c) is then applied to obtain the estimates for f_o, ₁, and ₂.

Predicting flowering dates of field experiments
On the basis of the four parameters f_o, ₁, ₂, and , equations (1– 3) were used to predict the flowering dates obtained from field experiments with eight sowing dates of the two growing seasons. The calculation used hourly temperatures, with the approach mentioned earlier. The photoperiod required for each day under field conditions of the growing seasons was the astronomic daylength calculated from the equation presented by Goudriaan and van Laar (1994). For each genotype grown in each environment, calculated daily development rates were accumulated to obtain the value of development stage ; the day at which is 1.0 is the predicted date of flowering for that genotype grown in that particular environment.

Results and discussion

 

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).  

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, I_2I, I_2N, 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 parameters
An 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 (f_o, 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 f_o 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 f_o, , ₁, and ₂.

Concluding remarks

 

This study explored the ability of a simple phenology model to explain differences in flowering time among individuals in an RIL population of spring barley. The model was parameterized for each RIL from a well-established reciprocal transfer greenhouse experiment where plants were transferred between LD and SD photoperiods at regular intervals throughout development. The reciprocal transfer experiment has long been shown to be a powerful tool in quantifying the length of the photoperiodically sensitive phase and the photoperiod sensitivity of distinct cultivars of a crop species (Chandraratna, 1948; Kiniry et al., 1983; Ellis et al., 1992; Mozley and Thomas, 1995; Yin et al., 1997a; Adams et al., 1998). As far as is known, the present study is the first one where this type of experiment was applied to individual genotypes of an entire segregating genetic population.

The model with parameter values estimated from the reciprocal transfer experiment was then used for predicting flowering times of the same individual RIL in independent multiple field environments. Although the parameterization and validation experiments were completely independent and the model ignores any genetic difference in responsiveness to temperature, the model yielded a reasonable prediction of differences in flowering time across genotypes and across environments (Fig. 3). The prediction of genetic difference among genotypes within a single specific environment remains a challenge, despite the possibility that the model performance in this respect would be associated with random noise during experimentation. The resolution of the model would be improved by considering (i) genetic difference in temperature response, and (ii) low temperature requirement for vernalization during the early development phase (Loomis and Connor, 1992). Such a consideration would need more expensive, temperature-controlled experimentation for model parameterization than the one used in the current study.

Ecophysiological models separate different aspects of responses of the trait under study to environmental variables and dissect a phenotype into elementary traits known as model-input parameters (Yin et al., 2000). These parameters represent certain genetic characteristics, and are sometimes called ‘genetic coefficients’ (Boote et al., 2003). They are genetically determined and are not altered by environment, but predict the expression of a genotype under a wide range of environments. Ecophysiological models could thus be a powerful tool for predicting genotype–phenotype relationships (Hammer et al., 2002; Slafer, 2003; Yin et al., 2003). Based on similar lines of reasoning, Reymond et al. (2003) demonstrated a potential value of combining ecophysiological modelling and genetic mapping in predicting genotypexenvironment interaction, using maize (Zea mays L.) leaf elongation rate as the example. Demonstration of the role of ecophysiological modelling in assisting the genetic unravelling of genotypexenvironment interaction for time to flowering is the subject of our next paper.

Acknowledgements

This research was funded by the National Natural Science Foundation of China (contract No. 30060036). We thank Hui Li and Peilian Zhang for their assistance in managing the experiments.

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