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AOBPreview originally published online on July 15, 2008
Annals of Botany 2008 102(4):561-569; doi:10.1093/aob/mcn115
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Published by Oxford University Press on behalf of the Annals of Botany Company 2008

Simulating the Influence of Vernalization, Photoperiod and Optimum Temperature on Wheat Developmental Rates

Gregory S. McMaster1,*, Jeffrey W. White2, L. A. Hunt3, P. D. Jamieson4, S. S. Dhillon5 and J. I. Ortiz-Monasterio6

1 USDA-ARS, Agricultural Systems Research, 2150 Centre Avenue, Building D, Suite 200, Fort Collins, CO 80526, USA
2 USDA-ARS, Plant Physiology and Genetics Research Unit, US Arid Land Agricultural Research Center, 21881 North Cardon Lane, Maricopa, AZ 85239, USA
3 Department of Plant Agriculture, University of Guelph, Guelph, Ontario N1G 1K1, Canada
4 New Zealand Institute for Crop & Food Research, Ltd, New Zealand
5 Punjab Agricultural University, Department of Plant Breeding, Ludhiana, Punjab, India
6 CIMMYT, Apdo. Postal 6–641, 06600 Mexico, D.F., Mexico

* For correspondence. E-mail Greg.McMaster{at}ars.usda.gov

Received: 21 February 2008    Returned for revision: 8 April 2008    Accepted: 12 June 2008    Published electronically: 15 July 2008


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 LITERATURE CITED
 

Background and Aims: Accurately representing development is essential for applying crop simulations to investigate the effects of climate, genotypes or crop management. Development in wheat (Triticum aestivum, T. durum) is primarily driven by temperature, but affected by vernalization and photoperiod, and is often simulated by reducing thermal-time accumulation using vernalization or photoperiod factors or limiting accumulation when a lower optimum temperature (Toptl) is exceeded. In this study Toptl and methods for representing effects of vernalization and photoperiod on anthesis were examined using a range of planting dates and genotypes.

Methods: An examination was made of Toptl values of 15, 20, 25 and 50 °C, and either the most limiting or the multiplicative value of the vernalization and photoperiod development rate factors for simulating anthesis. Field data were from replicated trials at Ludhiana, Punjab, India with July through to December planting dates and seven cultivars varying in vernalization response.

Key Results: Simulations of anthesis were similar for Toptl values of 20, 25 and 50 °C, but a Toptl of 15 °C resulted in a consistent bias towards predicting anthesis late for early planting dates. Results for Toptl above 15 °C may have occurred because mean temperatures rarely exceeded 20 °C before anthesis for many planting dates. For cultivars having a strong vernalization response, anthesis was more accurately simulated when vernalization and photoperiod factors were multiplied rather than using the most limiting of the two factors.

Conclusions: Setting Toptl to a high value (30 °C) and multiplying the vernalization and photoperiod factors resulted in accurately simulating anthesis for a wide range of planting dates and genotypes. However, for environments where average temperatures exceed 20 °C for much of the pre-anthesis period, a lower Toptl (23 °C) might be appropriate. These results highlight the value of testing a model over a wide range of environments.

Key words: Wheat, Triticum aestivum, T. durum, air temperature, thermal time, shoot apex, phenology, growth stages, anthesis, flowering


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 LITERATURE CITED
 
Accurate representation of phenology is essential when using crop simulation models to explore the consequences of changes in climate or management practices (e.g. planting date, cultivar selection or irrigation scheduling). Unfortunately, the timing of phenological stages is not always well simulated when models are used in environments or cultural practice regimes differing significantly from those for which they were developed (White et al., 2003).

Flowering in wheat (Triticum aestivum L., T. durum Desf.) occurs after all main-stem leaves have appeared and are fully expanded. Therefore, at the whole-plant level, the time to flowering can be considered to be the consequence of the rate of leaf appearance (i.e. the phyllochron) and the final number of main-stem leaves, although flowering is controlled at a deeper level of organization through responses to temperature and photoperiod. Leaf appearance rate is controlled mostly by the temperature of the apical meristem and leaf expansion zones (Jamieson et al., 1995; McMaster et al., 2003). Final leaf number is largely controlled by responses to vernalization and photoperiod (Brooking, 1996; Mahfoozi et al., 2001; Brooking and Jamieson, 2002). Thermal time intervals between flag leaf ligule appearance and anthesis and from sowing to emergence are much more constant among genotypes and environments than time from emergence to flowering (Jamieson et al., 1998a). The substantial variation in thermal time from emergence to flowering is the result of large variation in the number of phyllochrons between emergence and flag leaf ligule appearance, which varies from about eight to as much as 24 or more (Wang et al., 1995; although such high leaf numbers are seldom produced in conventional sowings). These processes are handled explicitly in the Sirius model (Jamieson et al., 1998b), but in many models, including version 4·0 of CERES-Wheat, a different approach is used. In these models, thermal time is accumulated through various phases between events on the shoot apex, with developmental factors for vernalization and photoperiod reducing the rate of accumulation. The adjusted thermal time between emergence and anthesis (which corresponds to a physiological time influenced by photoperiod, vernalization and temperature) is assumed to be constant, but the rate of accumulation is slowed when the development factors are less than unity. Thus, the effective thermal time can vary substantially, resulting in variation in final leaf number. This approach improves on earlier efforts to incorporate the role of photoperiod in predicting phenology by using photothermal time calculated by multiplying the thermal time by the photoperiod (e.g. Robertson, 1968; Bauer et al., 1988). In the approach of accumulating thermal time through developmental phases, both the calculation of thermal time and the manner of incorporating vernalization and photoperiod factors are important, and apparent contradictions in alternative approaches have been reconciled (Jamieson et al., 2007).

The photoperiod factor in CERES-Wheat is calculated using a quadratic function of the difference between the current photoperiod and a saturating photoperiod, above which development rate is assumed to be at a maximum. The vernalization factor is based on the ratio of the current degree of vernalization (i.e. portion of vernalization requirement completed) compared to the total vernalization requirement. The vernalization or photoperiod factor with the lowest value is used to proportionally reduce the daily rate of development (Ritchie, 1991). In contrast, models such as ARCWHEAT1 (Weir et al., 1984) use the product of the two factors to slow development. There is evidence that in most circumstances non-vernalized wheat plants have little response to photoperiod, although the temperature response of vernalization may change in long days as compared with short days (Mahfoozi et al., 2001; Brooking and Jamieson, 2002). The results from these two studies strongly suggests that photoperiod and vernalization factors should be applied either simultaneously, as multiplicative factors, or sequentially. In the latter case, a day length factor would not be applied until vernalization was complete.

In the context of a developmental model, thermal time is the time integral of the temperature response function that is accumulated over time. Characterizing the temperature response function has proven problematic. Typical assumptions are that temperature response is linear between some base temperature (Tbase; see Table 1 for a list of abbreviations), below which development ceases, and a lower optimal temperature (Toptl), at which development rate is maximal. Maximum development rate is maintained for temperatures from Toptl to an upper optimum temperature (Toptu). At temperatures above Toptu, the temperature response declines linearly until development again ceases at an upper threshold temperature (Tmax). When daily temperatures lie between any pair of these cardinal temperatures, calculation of the daily increment of thermal time is straightforward; for example, between the base and optimum temperatures the daily increment in thermal time is the difference between the average daily temperature and Tbase. Differences occur amongst implementations in circumstances where the daily temperature range spans a cardinal temperature (McMaster and Wilhelm, 1997).


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  		TABLE 1. Abbreviations used in the text

 
For temperate cereal crops, there is uncertainty regarding whether the base temperature varies among genotypes or changes during the life cycle (Angus et al., 1981; Weir et al., 1984; McMaster and Smika, 1988; Slafer and Rawson, 1995a, b). Indeed, it is difficult to ascertain whether development has ceased and whether the end-point, Tbase, is the same for all developmental processes (French and Hodges, 1985; McMaster and Smika, 1988). Similar uncertainty applies to considerations of optimum and maximum temperatures, but generally this has received less attention and is often confounded by water availability. Given the uncertainty, a value of 0 °C is often assumed for Tbase and maintained over the entire life cycle (Slafer and Rawson, 1994; McMaster, 1997).

Modelling the phenology of spring wheat genotypes has largely involved data sets from temperate regions where early development occurs under low soil and air temperatures and lengthening photoperiod. Under such conditions, vernalization and photoperiod effects proceed straightforwardly. Errors in modelling the two processes are difficult to detect, and known genotypic differences (e.g. Laurie et al., 2004; van Beem et al., 2005) are minimized. In contrast, for spring wheat sown in the autumn in warm climates (October to December in the northern hemisphere for regions such as the Southern Great Plains, USA, or India), warmer temperatures and a shortening photoperiod mean cultivars differing in vernalization response or photoperiod sensitivity will respond very differently; these locations provide ideal conditions for examining the interacting effects of these two processes on development in order to improve model assumptions and to obtain more robust calibrations of cultivars.

The objectives of this study were to evaluate the phenological responses (as represented by the time to anthesis) of wheat to temperature and photoperiod over a wide range of planting dates with genotypes varying in vernalization response and photoperiod sensitivity by examining (1) alterations in the cardinal temperature related to maximum development rate (Toptl) in the thermal time calculations, and (2) different approaches for incorporating vernalization and photoperiod influences in altering developmental rates.


   METHODS
TOP
 ABSTRACT
 INTRODUCTION
 METHODS
RESULTS AND DISCUSSION
 CONCLUSIONS
 LITERATURE CITED
 
Experimental data set
Data for days to heading (approx. growth stage 55; Zadoks et al., 1974) vs. sowing date for spring wheat cultivars varying in vernalization response and photoperiod sensitivity were obtained for 1989–1990 from a series of genotype-by-sowing-date experiments conducted from 1985 to 1992 at Punjab Agricultural University, Ludhiana, India (30·93 °N, 75·87 °E, 247 m a.s.l.). The treatment design was a factorial combination of sowing dates as main plots and cultivars as subplots in a split-plot design. The main plots were arranged in three randomized blocks.

Soil was classified as a Fatehpur series soil (coarse-loamy, mixed, hyperthermic Typic Ustochrept). The soil pH was about 8·5, and the top 15 cm soil layer was considered medium in fertility. Rainfall in the wheat-growing season at the site averages 143 mm from October to April. Nutrient and water management were aimed to achieve non-limiting conditions: fertilizer rates of 120 kg N, 26 kg P and 25 kg K ha–1 and four or five flood irrigations were applied each growing season. Grain yields for November plantings were typically from 4000 to 5500 kg ha–1 (Dhillon and Ortiz-Monasterio, 1993; Ortiz-Monasterio et al., 1994), which supports the assertion that growing conditions were adequate to permit normal phenological development exclusive of effects of temperature and photoperiod.

Eight sowing dates from October to January were used. Plots were sown after summer fallow with a seeding density of 100 kg ha–1, which was intended to provide a population of approximately 180 plants m–2. Broadleaf and grass weeds were controlled by hand-hoeing and diseases with fungicides. Each plot area consisted of eight rows spaced 23 cm apart by 8 m long. Further experimental details are given in Dhillon and Ortiz-Monasterio (1993) and Ortiz-Monasterio et al. (1994).

The environment at the site of data collection is characterized by hot summers and warm winters (Table 2). Wheat is grown as part of a rice (Oryza sativa L.)–wheat rotation. Normally, wheat is sown in November or December after rice has been harvested, and is harvested in May. Late-maturing cultivars usually suffer a yield penalty, attributed by Ortiz-Monasterio et al. (1994) to rising temperatures. An important feature of the environment is that it is marginal in providing conditions for vernalization. Indeed, wheat varieties with strong vernalization responses (i.e. facultative and winter types) are unlikely to produce much grain because very late flowering would result in grain fill occurring under high temperatures. The intermediate latitude of the experiment site means that photoperiods from November to May are between 11 and 13 h.


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  		TABLE 2. Monthly temperature summary data from 1989–90 for Ludhiana, Punjab, India data set. Data within parentheses are means from 1985 to 1991

 
The bread (Triticum aestivum L.) and durum (T. durum Desf.) wheat cultivars chosen for this study were seven spring wheats (Table 3), which were thought to vary in response to vernalization. In particular, ‘HD 2329’ was reported by van Beem et al. (2005) as having dominant alleles at four Vrn loci, giving it an exceptionally low response to vernalization.


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  		TABLE 3. Wheat lines examined, together with type and pedigree as reported in the Global Wheat Information System (http://mendel.lafs.uq.edu.au:8080/ICIS5) and the vernalization (P1V) and photoperiod coefficients (P1D) used in the model

 
Simulation model
The CROPSIM/CERES-Wheat version 4·0 model was used as the framework into which the various assumptions under examination were introduced. This model is based on CERES-Wheat (Ritchie, 1991), but with the code extensively rewritten so that physiological parameters are read from external files instead of being specified in the software code. Additional simplifications were made but had minimal effects on simulation of reproductive development. The plant growth module of this model is incorporated in the Cropping Systems Model (Hunt and Pararajasingham, 1995; Jones et al., 2003) distributed in DSSAT 4·0 (Hoogenboom et al., 2004).

Temperature response functions were tested using the CROPSIM/CERES-Wheat module, as distributed in DSSAT 4·0 (Hoogenboom et al., 2004). Key developmental events represented in CROPSIM/CERES-Wheat are germination, seedling emergence, terminal spikelet initiation, flag leaf lamina growth completion, end of spike growth, beginning of grain fill and physiological maturity, with anthesis being positioned by input parameters in the phase following the end of ear growth. The rate of development varies with temperature per se, vernalization and photoperiod.

Developmental stages are simulated when the accumulation of thermal development units (TDU) reaches pre-determined levels as specified by coefficients defined either for groups of similar cultivars (‘ecotypes’) or for individual cultivars. Daily TDUs are calculated as:


Formula 115M1

(1)
where DTT (degree days, °Cd) is the daily thermal time, VF (0–1) is a vernalization factor and DF (0–1) is a day length/photoperiod factor. Terminal spikelet is reached when TDU reaches 400 °Cd. The duration from terminal spikelet formation to anthesis is assumed to be affected only by temperature, with the TDU requirement being provided as an input parameter in a file of ecotype characteristics. The default TDU requirement we used was to assume the equivalent of 5 phyllochrons (3 to end of leaf growth and 2 to more to anthesis), equivalent to 425 °Cd when the phyllochron is 85 °Cd per leaf.

The daily increment of thermal time (DTT) is calculated by comparing the mean daily temperature (Tavg ) with cardinal temperatures, and reducing DTT by a 0 to 1 factor if Tavg is outside the optimal range of temperatures (Fig. 1). CROPSIM/CERES-Wheat calculates Tavg as the sum of the daily maximum and minimum temperature divided by 2, with a modification for using crown temperature when snow cover is present. In this respect, the model differs from CERES-Wheat, in which a diurnal temperature cycle based on a sinusoidal function is interpolated from daily maximum and minimum temperatures, with adjustment for day length. Four cardinal temperatures are recognized, a base temperature (Tbase), a lower optimum temperature (Toptl), an upper optimum (Toptu), and a maximum temperature (Tmax) above which development ceases. Values of the cardinal temperatures are input through a file of species' parameters.


Figure 1
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  		FIG. 1. Adjusting the daily increment of thermal time by comparing daily average temperature to cardinal temperatures. The daily average temperature is multiplied by the 0–1 DTT factor, giving the daily thermal time in °Cd.

 
Further rate modifiers of accumulated thermal development time (TDU) are calculated to incorporate vernalization and photoperiod responses (eqn 1). The vernalization factor (VF) is calculated as the relative development rate when unvernalized (VF0) plus the ratio of the accumulated vernalization-days (CUMVD) to required vernalization-days (P1V):


Formula 115M2

(2)
where VF0 is calculated as:


Formula 115M3

(3)
P1V is cultivar-specific and input through a file containing cultivar parameters. Values of P1V are currently determined through model calibration whereby different values are tested (in conjunction with other parameters), seeking values whereby the differences between simulated and observed phenology are minimized for a given cultivar and set of field observations. We note, however, that attempts to estimate P1V and other parameters based on cultivar genotypes show promise (White et al., 2008). Values of P1V for cultivars used in this study are presented in Table 3. Accumulation of vernalization time begins at germination and proceeds until floral initiation begins (i.e. terminal spikelet initiation) or the required number of vernalization-days has been reached (i.e. the vernalization requirement has been satisfied). Accumulation of vernalization-days is calculated by determining the effectiveness of the average daily temperature (Tavg) in satisfying the vernalization requirements. Vernalization is assumed to occur at temperatures between –5 °C to 15 °C (Fig. 2). Up to one vernalization-day can be accumulated each day (based on the relationship shown in Fig. 2), and adds incrementally to the total vernalization-days (VD) to date. If the vernalization process has not been completed, de-vernalization may occur when less than 10 vernalization-days have accumulated and the maximum daily temperature exceeds 30 °C. In CERES-Wheat (Ritchie, 1991), for each day that maximum daily temperature exceeds 30 °C, 1 vernalization-day is subtracted from the accumulated vernalization-days. In CROPSIM/CERES-Wheat, this approach was slightly modified to be equal to 0·05(Tdailymax – 30), where Tdailymax is the daily maximum temperature. However, for our particular data set de-vernalization was not a factor as only a few days in October had Tdailymax > 30 °C (and Tavg was always less than 30 °C; Table 2) and vernalization would not have begun.


Figure 2
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  		FIG. 2. Daily increment of vernalization-days based on daily average temperature. Each daily average temperature will accumulate between 0 and 1 vernalization-days dependent on the effectiveness of the temperature on vernalization response. See text for explanation of conditions of de-vernalization when daily average temperatures are >30 °C.

 
After seedling emergence, photoperiods shorter than 20 h (calculated using civil twilight) slow development through a day length factor (DF) that decreases from 1 to 0 as photoperiods shorten (Fig. 3):


Formula 115M4

(4)
where P1D is cultivar sensitivity to photoperiod, input from a cultivar parameter file (values for cultivars used in this study are presented in Table 3), and PP (h) is the photoperiod. DF affects development from emergence to terminal spikelet. As with P1V, the value of P1D is determined empirically, although efforts are underway to estimate it based on genetic data (White et al., 2008). A file of ecotype parameters is also used to specify minor differences among groups of bread and durum wheat (e.g. for reference grain nitrogen concentration).


Figure 3
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  		FIG. 3. Day length factor for two cultivars differing in photoperiod sensitivity. A relatively low photoperiod sensitivity (P1D) of 25 is represented by cultivar ‘PDW 220’ and a relatively high photoperiod sensitivity of 65 is represented by ‘HD 2329’.

 
Simulation methods
In simulating anthesis, we used the default value of 0 °C for Tbase, but tested the model with different values of Toptl of 15, 20, 25 and 50 °C (which is the equivalent of no Toptl or upper threshold). Toptu was set to 50 °C and Tmax to 60 °C (see Fig. 1). In addition, two methods (minimum value vs. the product) of using the vernalization and photoperiod factors were evaluated. For all evaluations, the photoperiod and vernalization parameters were estimated using an updated version of the Gencalc calibration program (Hunt et al., 1993, and available with the DSSAT V4·5 system; Hoogenboom et al., 2008). This tool allows users to specify a range of parameter values to test, runs the model for those values, and then identifies which combination of parameter values results in simulated values that show the least deviations from observed values of a specified trait using root-mean-square error (RMSE) as the main criterion. The default values for cardinal temperatures were used in the parameter estimation (e.g. Tbase = 0 °C, Toptl = 50 °C). Usually 1989–90 data were used both for cultivar parameterization and validation. Use of the temperatures should not influence the validity of the overall conclusions, merely the absolute value of the predictions.

Because CROPSIM/CERES-Wheat predicts anthesis (Zadoks stage 65) date rather than heading date (our observed data), anthesis date was estimated as occurring 7 d after heading (based on McMaster and Smika, 1988; McMaster and Wilhelm, 2003; G. S. McMaster, unpubl. data). Although the interval from heading to anthesis can vary slightly for several reasons, errors should be small.

To assist in interpreting the results, RMSE and sum of the residuals (SRES) were calculated. RMSE and SRES were determined as:


Formula 115M5

(5)


Formula 115M6

(6)
where OBSi is the observed day of year and SIMi is the simulated day of year for the phenological growth stage. The SRES estimates model bias, whereby if SRES is large and positive, then the model is biased towards predicting the developmental stage earlier than observed, and if SRES is large and negative the model tends to predict the developmental stage later than observed.


   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS AND DISCUSSION
CONCLUSIONS
 LITERATURE CITED
 
The influence of different optimum temperature values (Toptl) on development rates was examined for seven cultivars over a range of planting dates (Figs 4 and 5, Table 4). Little difference in RMSE was noted among Toptl values of 20, 25 and 50 °C, and there was no apparent bias in predictions. For five of the seven cultivars (excluding ‘PBW 222’ and ‘PBW 34'), a Toptl of 20 °C had a very slightly lower RMSE than 25 or 50 °C (which were identical). However, the Toptl of 15 °C had a much higher RMSE than any other Toptl, with a consistent bias for predicting anthesis later than observed (negative SRES), especially for the three earliest planting dates. Other work has shown similar results; for instance, McMaster and Smika (1988) found that an upper threshold of 20 °C also had a slightly smaller RMSE than 25 or 30 °C (which were also identical). These studies and our results indicate a slight shift in developmental rates occurs between 20 and 25 °C, although there is minimal benefit over setting Toptl up to 50 °C (i.e. not having an optimal temperature). Slafer and Rawson (1995b) also found similar results when examining the role of Toptl for four varieties of wheat under controlled environments using constant daily temperatures. Two varieties showed a linear relationship to temperature between base and optimum temperatures and two showed a curvilinear relationship. All four varieties showed an increase in both base and optimum temperatures for emergence to terminal spikelet initiation, terminal spikelet initiation to heading, and heading to anthesis, with optimum temperatures pooled for the four cultivars of <22, 25 and >25 °C, respectively. Importantly, individual cultivars varied considerably from the mean of all cultivars. As noted in the Introduction, the possibility exists that the base and optimum temperatures increase through the life cycle, which would suggest that Toptl for the entire period should be at least 20 °C, similar to our finding.


Figure 4
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  		FIG. 4. Simulated and observed dates (as days after planting, DAP) of estimated (from heading date) time of anthesis for different planting dates (day of year, DOY) for four cultivars not having a vernalization requirement. Simulated results are presented for 15, 20, 25 and 50 °C lower optimal temperatures (Toptl). All simulated results multiplied the vernalization and photoperiod factors, except for the ‘25 °C Toptl (min)’ simulation that used the most limiting of the two factors. However, since the cultivars had no vernalization requirement, the vernalization factor was set to 1, so no difference existed between the two approaches for incorporating vernalization and photoperiod. Genotype x date s.e. = 1·03; Table 4 presents the RMSE results.

 


Figure 5
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  		FIG. 5. Simulated and observed dates (as days after planting, DAP) of estimated (from heading date) time of anthesis for different planting dates (day of year, DOY) for four cultivars having a vernalization requirement. Simulated results are presented for 15, 20, 25 and 50 °C lower optimal temperatures (Toptl). All simulated results multiplied the vernalization and photoperiod factors, except for the ‘25 °C Toptl (min)’ simulation that used the most limiting of the two factors. Genotype x date s.e. = 1·03; Table 4 presents the RMSE results.

 


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  		TABLE 4. Root-mean-square error (RMSE, d) and sum of the residuals (SRES, d) for different lower optimal temperatures (Toptl). All results multiplied the vernalization and photoperiod factors except for ‘25(min)’, which used the most limiting (i.e. minimum) of the vernalization and photoperiod factors

 
Many controlled environment and some field studies have shown that development rates for many processes (both phenology and others such as leaf appearance) above some Toptu are decreased, and the response is often curvilinear (e.g. Friend et al., 1962; Cao and Moss, 1989; Masle et al., 1989a, b). While the response to temperature and photoperiod over a broad range is probably curvilinear, often there is a fairly linear relationship up to Toptl, and clearly there seems to be slowing of developmental rates above some Toptu.

Consideration of the temperature environment, both diurnally and over the growing season suggest, however, that there may be little need for precisely determining Toptu when applying the model to most field conditions where wheat is normally grown. For the earliest planting dates, temperatures at our location were relatively warm (Table 2) and photoperiod was shortening. Yet, monthly average temperatures approached 28 °C only at the end of the growing season. Maximum and minimum temperatures bracket this average, and much of the diurnal temperature is well within the portion of the response curve where the developmental rate increases linearly with temperature (Friend et al., 1962; Cao and Moss, 1989; McMaster, 2005). Further, air temperature usually differs from shoot apex or canopy temperature based on soil water available for transpiration. Given that this experiment was irrigated, it is likely that day-time canopy temperatures were lower than air temperatures, further reducing the occurrence of canopy temperatures exceeding 25 or 30 °C.

We also examined two approaches for using the photoperiod and vernalization factors to modify thermal development rates (Figs 4 and 5, Table 4). The most-limiting factor approach used a Toptl value of 25 °C, whereas the multiplication approach used all Toptl values (e.g. 15, 20, 25 and 50 °C). For the four cultivars with the lowest response to vernalization (Table 3), the vernalization response factor, VF, was set to 1·0, therefore making the two approaches tested equivalent because only the photoperiod factor, DF, would be used. Thus, the planting date response of anthesis and associated RMSE using the minimum or multiplicative effects of vernalization and photoperiod factors were identical (Fig. 4, Table 4). However, for those cultivars responding to vernalization (0 < VF < 1), using the minimum of the two factors clearly did not predict the earliest planting dates accurately, particularly in comparison to the multiplicative approach (Table 4, Fig. 5). Presumably for later planting dates, both vernalization and photoperiod requirements were satisfied, suggesting both approaches were similarly accurate.

CROPSIM/CERES-Wheat has adopted a multiplicative approach to incorporating vernalization and photoperiod factors. Choosing this approach was based on the results reported here, which indicate that the multiplicative approach improves the robustness of the model for situations where wheat is sown in the autumn or early winter, as happens in many mid-latitude regions with winter growing seasons. Implicit in the alternative minimum factor approach is the assumption that effects of vernalization and photoperiod are closely coupled at the process level. Conceptual models based on evidence from molecular studies, however, suggest that the vernalization and photoperiod systems operate independently (Laurie et al., 2004; Beales et al., 2007), which again supports the use of a multiplicative approach. We recognize, however, that there are various issues that remain to be resolved. A key step is to determine how well P1V and P1D, as well as parameters affecting earliness per se (assumed constant in this paper), relate to the cultivar differences in the Vrn and Ppd loci. Initial efforts to estimate P1V and P1D from genetic information confirmed this promise (White et al., 2008) but were constrained by the availability of genetic data for individual cultivars. There would also be value in comparisons of cultivar parameters used in CERES with parameters of other models that assume somewhat different responses for temperature, vernalization and photoperiod.

This work demonstrates that simulation modelling that tests hypotheses concerning individual traits or processes can provide information that support findings from seemingly distant research endeavours such as functional genomics. The role of hypothesis testing to promote understanding was emphasized early by modellers such as R. S. Loomis and R. Rabbinge (Loomis et al., 1979), but in recent years seems to have lost attention in the face of demand for quantitative predictions for growers, farm advisers and policy makers, among others.


   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
LITERATURE CITED
 
Simulations of days-to-anthesis were examined in order to determine whether predictions could be improved across a broad range of planting dates and genotypes in environments that differed substantially from those usually considered in developing wheat models. Varying Toptl rarely altered anthesis predictions for values greater than 20 °C. In part, this may be due to the low frequency of daily mean temperatures above 20 °C. For cultivars having a large vernalization response, anthesis was more accurately simulated over a broad range of planting dates when multiplying vernalization and photoperiod factors to influence development rates than when using only the most limiting of the vernalization and photoperiod factors. Both suggested improvements emphasize the value of ensuring that models are tested over a broad range of temperature and photoperiod regimes, even including non-commercial planting dates or locations that maximize expression of key processes.


   LITERATURE CITED
TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 LITERATURE CITED
 

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