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Crop Science 41:415-423 (2001)
© 2001 Crop Science Society of America

CROP ECOLOGY, PRODUCTION & MANAGEMENT

Incorporating Radiation and Nitrogen Nutrition into a Model of Kernel Number in Wheat

Sabine Demotes-Mainardb and Marie-Hélène Jeuffroya

a UMR d'Agronomie INRA-INA PG, BP 01, 78850 Thiverval-Grignon, France
b INRA, UMR SAGAH INRA/INH/Université d'Angers, 42 rue Georges Morel, BP 57, 49071 Beaucouzé cedex, France

Corresponding author (jeuffroy{at}bcgn.grignon.inra.fr)


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Wheat (Triticum aestivum L.) kernel number per square meter (KN) depends on radiation, temperature, and crop N nutrition. Some models of KN using climatic data or N nutrition characteristics as input variables account for variations either in radiation and temperature or in N nutrition, but not for both. Our objective was to produce a model of KN that accounts simultaneously for variations due to radiation, temperature, and crop N nutrition, and that has input variables that are simple to measure or to simulate. Field experiments were conducted over 3 yr with ‘Trémie’ winter wheat. Treatments involved the application of N fertilizer at different dates and rates to achieve various N deficiencies and the use of shading nets for various periods during spike growth to reduce incident radiation. Crop N status was assessed by determining N nutrition index (NNI) at anthesis. The KN was counted, it ranged from 9420 to 31 036 kernels m-2. Two characteristics of N nutrition (NNI at anthesis and IDD, the duration of deficiency before anthesis multiplied by its intensity) and three characteristics of radiation and temperature (photothermal quotient calculated from 45 d before anthesis to anthesis, from 30 d before anthesis to anthesis and from 20 d before anthesis to 10 d after anthesis) were used as input variables. Six relationships combining one characteristic of N nutrition and the photothermal quotient over one period were estimated. The best fit was obtained for a relationship between KN and the logarithm of NNI at anthesis and photothermal quotient over the 45 d preceding anthesis (R2 = 0.883, n = 19). This relationship could be useful for estimating KN in crop models, as its input variables are simple to simulate.

Abbreviations: DM, dry matter • IDD, intensity of deficiency before anthesis multiplied by duration of deficiency before anthesis • KN, kernel number per square meter • Nc, critical N concentration • NNI, nitrogen nutrition index • PAR, photosynthetically active radiation • Q, photothermal quotient • Q20+10, photothermal quotient from 20 d before anthesis to 10 d after anthesis • Q30, photothermal quotient from 30 d before anthesis to anthesis • Q45, photothermal quotient from 45 d before anthesis to anthesis


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
IN WHEAT CROPS, kernel number per square meter (KN) is the component most explicative of yield variations (Midmore et al., 1984; Slafer and Andrade, 1993). The KN depends on weather conditions and increases in response to higher levels of radiation during the spike growth period (Caldiz and Sarandon, 1988; Evans, 1978; Fischer, 1975). Conversely, an increase in mean temperature during the spike growth period in the range 13 to 22°C causes KN to decrease (Fischer, 1985; Fischer and Mauer, 1976; Midmore et al., 1984). The KN is also strongly influenced by crop N nutrition, with deficiencies before anthesis causing KN to decrease (Darwinkel, 1983; Fischer, 1993; Singh et al., 1997). The stage of development at which the various components of KN respond to N stress agrees globally with the timing of organ initiation. Thus, an early deficiency before Zadoks' stage 13 (Zadoks et al., 1974) reduces tillering, whereas the number of spikelets per spike responds to N until terminal spikelet formation, about Zadoks' stage 16 (Fischer, 1993). However, the competition between components, the overlap of the phases of determination of various components, and the lack of accurate assessment of the periods of deficiency in most studies, make complex the determination of the stages of sensitivity to N of individual components of KN. In temperate climates, N is still a major limiting factor for wheat (Boiffin et al., 1981; Frederick and Marshall, 1985; Mascianica and Walden, 1986). The N deficiencies generally affect crops grown with low rates of N fertilizer or on organic farms (David, 1997). The N deficiencies can also affect crops grown conventionally, if N is applied after the optimum date (Aubry, 1995; Meynard, 1985; Meynard et al., 1988), or if the N fertilizer is not available to the plant. Environmental constraints may also lead to the application of low rates of N fertilizer to reduce the risk of leaching (MacDonald et al., 1989), thereby increasing the risk of N deficiency.

To simulate KN in wheat crops models managed under N-limited conditions, wheat models need to account for variations in KN due to both weather conditions (particularly radiation and temperature) and N nutrition. For crops grown with no water or nutrient limitations, KN and the photothermal quotient (Q), the ratio of mean daily incident radiation to mean daily temperature minus base temperature, are linearly related (Fischer, 1985; Midmore et al., 1984). Both these authors calculated this ratio over the 30 d immediately preceding anthesis. The relationship was strengthened by replacing incident radiation with intercepted radiation. Abbate et al. (1995) also observed a linear relationship between KN and Q (calculated from 20 d before anthesis to 10 d after anthesis) with crops not deficient in N. However, crops supplied with low levels of N fertilizer did not fit this relationship, with KN dropping below the regression line between KN and Q established for crops that were not deficient in N. Simple models simulating the decrease in KN due to N deficiency were proposed by Jeuffroy and Bouchard (1999) and Justes et al. (1997). These models did not estimate KN itself. Instead, they estimated relative kernel number, defined as the ratio of the KN of the deficient crop to the KN of a control crop grown under the same weather conditions. Relative kernel number is linearly related to the logarithm of the N nutrition index (NNI) at anthesis (Justes et al., 1997) and to the variable IDD, defined as the intensity of N deficiency before anthesis multiplied by the duration of deficiency before anthesis (Jeuffroy and Bouchard, 1999). In both studies, N deficiencies were defined in terms of NNI (Lemaire and Gastal, 1997), the ratio of the observed N concentration of the aerial parts to the critical N concentration. The critical N concentration corresponds to the minimum N concentration of the aerial parts required to ensure maximal growth. If NNI is equal to or higher than 1, then crop N status is not limiting for growth. If NNI is lower than 1, then the crop is N deficient and the lower the NNI, the more severe the deficiency. This indicator has already been successfully used both for analyzing the effect of N deficiency on various agronomic variables and for crop management studies (Bélanger et al., 1992; Jeuffroy and Bouchard, 1999; Justes et al., 1997; Lemaire and Meynard, 1997).

The objective of our study was to develop a model of KN that accounts for variations due to radiation, temperature, and crop N nutrition, and that has input variables that are simple to measure or to simulate, so that the model is easy to use. We focused on the input variables used in existing models estimating KN for crops not deficient in N (variable Q calculated over various periods, Abbate et al., 1995; Fischer, 1985; Midmore et al., 1984) and in models estimating the decrease in KN for N-deficient crops relative to a non-deficient reference (variable NNI at anthesis, Justes et al., 1997; variable IDD, Jeuffroy and Bouchard, 1999). We investigated whether these variables could be combined in a single model accounting for combined variations in radiation, temperature, and N nutrition status.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Crop Growth Conditions and Experimental Treatments
The winter wheat cultivar Trémie was grown in the field at Grignon (near Paris, France, 48°60'N, 1°54'E) for 3 yr. Seed was sown on 19 October 1995 (Exp. 1), 22 October 1996 (Exp. 2), and 21 October 1998 (Exp. 3), at a density of 300 grains/m2 on a clay loam soil (Hapludalf). The preceding crop in each of the 3 yr was maize (Zea mays, L.). Weeds, diseases, and insects were controlled by pesticide applications. Plots were irrigated whenever soil water potential reached -30 103 Pa at a depth of 0.4 m to ensure that no water deficit occurred during the crop cycle.

We attempted to create a diversity of N nutrition conditions and of incident radiation during spike growth. In Exp. 1 and 2, some plots were shaded with nets intercepting 45% of the incident photosynthetically active radiation (PAR) for various periods during spike growth (Table 1). The nets consisted of black polyethylene. The percentage of radiation intercepted by the nets did not vary with wavelength in the range 400 to 1100 nm. Air temperature under the shade cloth was not measured. In each of the three experiments, the experimental treatments involved the application of various rates of N fertilizer (ammonium nitrate) on several dates (Table 1). In each experiment, the fertilization pattern of some treatments was managed such that the crop would be well fertilized (Treatments CC, CT, TC, and TT in Exp. 1; Treatments A and I in Exp. 2; Treatment T3 in Exp. 3). For other treatments, the amount of N fertilizer applied was suboptimal from various dates onwards, creating N deficiencies starting at various dates and continuing to the end of the experiment (Treatments NN, TN and T(NC) in Exp. 1; Treatments C and J in Exp. 2 and Treatments T0, T1, and T2 in Exp. 3). Finally, for some treatments, the amount of fertilizer applied was suboptimal, but N fertilizer was applied later creating temporary deficiencies (Treatment NT in Exp. 1; Treatments E and H in Exp. 2; Treatment T0L in Exp. 3). There were eight, six and five treatments in Exp. 1, 2, and 3, respectively. The treatments were arranged in a complete randomized block design with three blocks. The plots were 30 m long and 1.75 m wide. Each plot contained nine rows, and the two border rows on each side were avoided when sampling to minimize edge effects.


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  		Table 1. Experimental treatments: dates and amounts of N fertilizer application and dates of beginning and end of shading. The mean date for the main phenological stages are given for each experiment, using Zadoks' scale (Zadoks et al., 1974)

 
Plant and Climatic Condition Measurements
From the end of winter until anthesis, two subplots, each 0.175 m2, were sampled per block and per treatment once per week for Exp. 1 and 2 and once per fortnight for Exp. 3. The aerial parts of the plants were dried for 48 h at 80°C and weighed. They were ground, and the N concentration of the aerial dry matter (DM) was determined according to the Dumas method (Dumas, 1831). This involves the combustion of dehydrated and ground plant tissue at about 1800°C, the reduction of nitrogen oxide by reduced Cu at 600°C, and N2 determination by catharometry (NA 1500 analyzer, Fisons Instruments, Cheshire, UK). This method enabled us to measure the total N content of the plant, including nitrate. To assess kernel number in Exp. 1 and 2, two subplots, each 0.175 m2, were sampled per block and per treatment. The number of plants was counted, and a subsample of 40 plants that was typical of the populations of the two subplots in terms of the number of tillers per plant was taken. The spikes of these 40 plants were threshed, and all kernels were counted. The kernel number per square meter (KN) was estimated as the number of kernels per plant multiplied by the number of plants per square meter, counted on the subplots. In Exp. 3, KN was estimated using four subplots per block and per treatment, each 0.175 m2. All spikes were threshed and all kernels were counted. Mean daily air temperature and mean daily global radiation were recorded 400 m from the experimental field using a platinum resistor for temperature and a thermopile sensor with a black and white type thermocouple for global radiation. Photosynthetically active radiation (PAR) was calculated from global radiation using the equation PAR = 0.48 x global radiation, with PAR and global radiation expressed in MJ m-2 d-1 (Varlet-Grancher et al., 1982). Climatic data from sowing to anthesis are presented for each experiment in Table 2. Photothermal quotient was calculated as the ratio of cumulative PAR to cumulative temperature (base 0°C) over three periods: (i) from 45 d before anthesis to anthesis (Q45), (ii) from 30 d before anthesis to anthesis (Q30), (iii) from 20 d before anthesis to 10 d after anthesis (Q20+10). Statistical analyses were performed by the REG and CORR procedures of the SAS software package (SAS Institute, 1987).


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  		Table 2. Mean temperature and photosynthetically active radiation from sowing to anthesis, at Grignon, France

 
Assessment of the N Status of the Crop
The N status of the crop was assessed by determining the N nutrition index (NNI), from the end of winter to anthesis. The NNI was calculated as the ratio between the measured concentration of N in the aerial DM and the critical N concentration (Nc) determined from the DM by the equation proposed by Justes et al. (1994): if DM < 1.55 x 103 kg ha-1, Nc = 4.4%; if DM >= 1.55 x 103 kg ha-1, Nc = 5.35 DM-0.442, with DM expressed in tonnes per ha. NNI at anthesis was determined either on the exact date of anthesis or by linear interpolation between two dates, one just before and the other just after anthesis.

The variable IDD, defined by Jeuffroy and Bouchard (1999), was calculated by multiplying the intensity of the deficiency before anthesis by its duration before anthesis. The duration of deficiency, expressed in degree days base 0°C, was defined as the time before anthesis during which the NNI was below 0.90, as in Jeuffroy and Bouchard (1999). The exact dates at which this threshold value was reached were determined by linear interpolation with values on either side of 0.90. If there was no deficiency before anthesis, the duration of deficiency was 0.00 degree days. The intensity of deficiency was defined as the difference between 1.00 and the minimum value of NNI for each treatment between the end of winter and anthesis. Thus, if the treatment was never N-deficient, IDD was 0.00 and the higher IDD, the more severe (long or intense) the deficiency.


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Characterization of the Treatments in Terms of N Nutrition and Photothermal Quotient
The N fertilizer was applied on 12 June 1996, 9 d after anthesis, for the purpose of another study. This application had no effect on NNI until anthesis or on KN. The various fertilization regimes created a wide diversity of patterns of change in NNI over time (Fig. 1) . Treatments TT, TC, CT, CC, and T(NC) in Exp. 1 and Treatment T3 in Exp. 3 had non-limiting N nutrition because NNI did not fall significantly below 1.00 (5% level of significance). All other treatments involved a period of deficiency. If no N fertilizer was applied after the deficiency had begun, NNI continually decreased until anthesis (e.g., NN, C, and T2), whereas if N fertilizer was applied after the deficiency had begun, it was possible to increase NNI (e.g., NT, E, and T0L). The date on which the deficiency began differed for the various treatments. The deficiency began between 13 March (T0 in Exp. 3) and 23 May (TN in Exp. 1), corresponding to various developmental stages between mid-tillering and mid stem extension (Table 1). The effect of shading on crop N status was negligible, except for treatment T(NC). Treatment T(NC), that was shaded, was fertilized exactly as in Treatment TN, that was not shaded. In contrast to TN, T(NC) presented a NNI that did not fall significantly below 1.00. For the treatments involving N deficiency, the intensity of deficiency was between 0.17 and 0.70 and its duration before anthesis was between 158 and 861 degree days. The differences between treatments in terms of changes in NNI over time resulted in a large range of IDD (between 0 and 604) and of NNI values at anthesis (between 0.30 and 1.12) (Table 3).



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  		Fig. 1. Nitrogen nutrition index (NNI) over time for wheat grown under N and radiation treatments in the three experiments

 

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  		Table 3. Characteristics of N nutrition, photothermal quotient, kernel number per square meter, spike number per square meter, and kernel number per spike for each treatment

 
For treatments involving shading, the plots were shaded for the whole spike growth period (Treatment CC), or the first (CT) or second parts [TC, T(NC), I and J] of the spike growth period only. Photothermal quotient depended on shading and on differences in radiation and temperature among years. For each of the three periods over which the photothermal quotient was calculated, Q differed substantially among treatments (Table 3).

Table 4 shows the coefficients for the correlation between N nutrition characteristics and Q calculated over the three periods. The NNI at anthesis, the logarithm of NNI at anthesis and IDD were correlated. The photothermal quotients Q45, Q30, and Q20+10 were correlated. However, NNI at anthesis, the logarithm of NNI at anthesis and IDD were not correlated with Q, except for a significant but weak correlation between IDD and Q45. This indicates that there was no association between the characteristics of N nutrition and weather conditions in our treatments.


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  		Table 4. Correlation coefficient (r) between the characteristics of N nutrition, the photothermal quotient and kernel number per square meter

 
Relationships among Kernel Number, N nutrition Characteristics and Photothermal Quotient
The treatments resulted in a wide diversity in KN, with the highest and lowest KN values differing by a factor of 3 (Table 3). These variations in KN came from variations in both spikes per square meter and kernels per spike. Kernel number per square meter was correlated with NNI at anthesis and with IDD, but was not correlated with Q calculated over any of the three periods (Table 4). To identify which of the characteristics of N nutrition (NNI at anthesis or IDD), when combined with one of the characteristics of photothermal quotient (Q45, Q30, or Q20+10), was the most explicative of KN variations, we estimated six models of regression (Table 5). According to Justes et al. (1997), the relationship between the KN loss due to N deficiency and NNI at anthesis is logarithmic rather than linear. The correlation between KN and the logarithm of NNI at anthesis was higher than the correlation between KN and NNI at anthesis (Table 4). We therefore used the logarithm of NNI at anthesis as the input variable. All models were significant at the 0.1% significance level, except Models 5 and 6, which were significant at the 1% level. In all models, both dependent variables were significant at the 5% level (data not shown). The intercept was only significant in Model 3. The signs of the parameters were consistent with the well-known effects of a deficiency (the more intense or the longer the deficiency, the lower KN) and with the effects of the equilibrium between radiation and temperature (the lower the ratio of radiation to temperature, the lower KN). Thus, IDD had a negative sign (high IDD corresponds to a long and intense deficiency), whereas the logarithm of NNI at anthesis had a positive sign (high NNI corresponds to non-limiting N nutrition), and Q had a positive sign (high Q corresponds to high incident PAR per unit of thermal time, and thus favorable growth conditions during the period considered).


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  		Table 5. Estimation of models simulating kernel number per square meter according to N nutrition characteristics and photothermal quotient

 
Model 1 accounted for 88% of the variability in KN and was the best of the six models, as shown by the values for R2 and the square root of the mean square error (Table 5). Figure 2 shows the relationship between the observed KN and the simulated values. The points are distributed evenly near the line y = x, and the figure shows a high fitting value, with no tendency to overestimate or to underestimate, according to whether or not the treatment involved N deficiency and shading. In Model 1, the intercept was not significantly different from zero, ln(NNI at anthesis) and Q45 were both significant at the 0.01% level. Each of the two variables accounted for a major part of the variability, as Model 1 was better than models based on ln(NNI at anthesis) or Q45 alone (Table 4). The low r2 for the regression between KN and ln(NNI at anthesis) results from KN being lower for shaded treatments than for unshaded treatments for similar values of NNI at anthesis (Fig. 3) . Conversely, for similar Q45, KN was lower for treatments involving N deficiency than for non-deficient treatments (Fig. 4) . However, for treatments involving N deficiency with recovery at anthesis (NNI at anthesis greater than 1), KN was as high as expected for the same value of Q45 without deficiency. This explains why ln(NNI at anthesis) was a better predictor of KN than IDD. Thus, Model 1 accounted for variations in KN due to variations in N nutrition, radiation, and temperature, whereas neither of its two input variables alone could account for such variation.



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  		Fig. 2. Relationship between observed and simulated values of kernel number per square meter (KN) for all treatments classified according to nitrogen deficiency and shading. No D, No S = no deficiency, no shade; No D, S = no deficiency, shade; D, No S = deficiency, no shade; D, S = deficiency, shade

 


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  		Fig. 3. Relationship between nitrogen nutrition index (NNI) at anthesis and kernel number per square meter (KN) for all treatments classified according to shading

 


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  		Fig. 4. Relationship between photothermal quotient over the 45 d preceding anthesis (Q45) and kernel number per square meter (KN) for all treatments classified according to nitrogen deficiency between the end of winter and anthesis, and nitrogen nutrition index (NNI) at anthesis. No D = no deficiency. D, NNIa<1 = deficiency and NNI at anthesis <1. D, NNIa>1 = deficiency and NNI at anthesis >1

 
We evaluated Model 1 using the "leave-one-out cross validation" method (Linhart and Zucchini, 1986). This involves (i) eliminating one observation, i, from the original data set; (ii) estimating the parameters of the model on the n - 1 = 18 observations left; (iii) simulating KN for the observation, i, using the parameters estimated on the 18 other observations, and (iv) performing steps (i), (ii), and (iii) for each of the n = 19 observations. The square root of the mean square error of prediction (square root of MSEP) calculated with the values predicted by the cross validation method was 2187. The linear regression between the values predicted by the cross validation method and the observed values was:

This regression was not significantly different from y = x, confirming that Model 1 predicts KN in various conditions of N nutrition, radiation, and temperature.

Model 1 was also tested on the data of Jeuffroy and Bouchard (1999) obtained with the cultivar Soissons. The data were collected in two sites over several years. The KN and NNI at anthesis were indicated in their paper, and values of Q45 were calculated from climatic data and the dates of anthesis given in the paper. The data covered large ranges of KN (from 6812 to 28 835 kernels per m2), and of N nutrition (NNI at anthesis was from 0.31–1.10), but Q values varied less than in our experiment (from 0.64–0.77 MJ °C-1). When Model 1 was used to simulate KN using the data of Jeuffroy and Bouchard (1999), the square root of the mean square error of prediction (square root of MSEP) was 2361. The linear regression between simulated and observed KN was:

This regression was not significantly different from y = x (Fig. 5) . Consequently, Model 1 was adequate to simulate KN on the data of Jeuffroy and Bouchard (1999).



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  		Fig. 5. Relationship between observed and simulated values of kernel number per square meter (KN) obtained with Model 1 on the data of Jeuffroy and Bouchard (1999)

 

   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
CONCLUSIONS
 REFERENCES
 
Large variation in KN existed among the experimental treatments. These treatments differed on the dynamics of crop N nutrition and on weather conditions. Our results (Fig. 4) confirm those of Abbate et al. (1995) showing that the regression between KN and Q for crops not deficient in N cannot be used for N-deficient crops, which have a lower KN for similar values of Q. Conversely, the relationship between KN and the logarithm of NNI at anthesis proposed in the study of Justes et al. (1997) cannot account for variations in KN in crops with low Q (Fig. 3). However, variations in KN were well explained by the combination of one variable characterizing crop N nutrition and one variable characterizing temperature and radiation variations. The best of the six models tested was Model 1, which related KN to the logarithm of NNI at anthesis and to Q calculated over the 45-d period preceding anthesis. Model 1 accounted for 88% of the variability of KN.

Model 1 could probably be improved by calculating Q with intercepted PAR rather than incident PAR. A model with Q calculated with the intercepted PAR would involve additional measurements for the input variables, such as leaf area index or radiation interception efficiency over the period considered. The N deficiencies can reduce tillering (Masle, 1981a,b) and leaf area index (Bélanger et al., 1992; Justes et al., 1997), thereby decreasing the fraction of incident PAR intercepted by the crop (Bélanger et al., 1992; Garcia et al., 1988). Incident PAR and intercepted PAR should differ most in treatments subjected to severe N deficiency. The square of the difference between simulated and observed KN shows how well individual data points fitted the model. The square root of the mean square difference between simulated and observed KN was 8.2% of the average KN for non deficient treatments whereas it was 9.9% for N-deficient treatments. Thus, data points from treatments with no deficiency fitted Model 1 better than those from N-deficient treatments. This is understandable, considering that Model 1 uses incident and not intercepted PAR. However, data points from N-deficient treatments fitted Model 1 well enough for the model to be adequate, since no individual data point deviated notably (Fig. 2) and since the R2 of the model was 0.88. Model 1 accounted for a percentage of variability in KN similar to that for the models based on KN and Q proposed by Abbate et al. (1995), Fischer (1985), and Midmore et al. (1984) for crops with no N deficiency, in which Q was calculated from intercepted PAR. The percentage of variability in KN accounted for by Model 1 was similar to that for the model proposed by Justes et al. (1997) and lower than that for the model of Jeuffroy and Bouchard (1999) (r2 = 0.93). Model 1 has a larger domain of validity than models accounting for variations in radiation and temperature only or for variations in N nutrition only. This is of great value if such a model is to be integrated into a general crop model (e.g., Brisson et al., 1998; Ritchie and Otter, 1984).

The range of variation explored by our treatments involving differences in Q was wide, similar to that covered by Abbate et al. (1995). The shading nets intercepted 45% of the solar PAR. The shading nets may have modified the air temperature, which is used in the calculation of Q, but the temperature below the nets was not measured. In another field experiment, the difference between mean air temperature above and below a shading net intercepting 70% of radiation was 0.1°C (Pellerin, 1991). Thus, we can assume that if shading affected Q through variations in temperature, these variations (which were omitted in our calculation of Q) were small compared to the variations of Q due to the effect of shading on radiation. In the field, variations in Q during spike growth are caused by variations in radiation and in temperature, the relative part of each factor depending on the location (Fischer, 1985; Midmore et al., 1982). Our results and those of Abbate et al. (1995) were obtained with variations of Q mainly due to shading. Fischer (1985) and Midmore et al. (1984) obtained large ranges of Q, due to large ranges of both radiation and temperature, by varying the site, year of experiment, and sowing date. The consistency of all these results suggests that the relationship between KN and Q is similar if Q varies because of shading, or because of variations in solar radiation or in temperature.

The various N fertilization patterns created a wide range of NNI dynamics. These dynamics can be classified into three types: Type 1 (no deficiency), Type 2 (permanent deficiency, i.e., no fertilizer applied after the onset of deficiency, with deficiency lasting until anthesis), and Type 3 (temporary deficiency, i.e., N fertilizer was applied to the crop at some time after the start of the deficiency, increasing NNI, which reached one or remained below one). It was important to represent these three types of situations in our data because they all exist in agricultural practice. Type 1 corresponds to intensive farming with a fertilization insurance strategy, the farmer supplying the crop with enough fertilizer to ensure maximal growth and to prevent N deficiency throughout the crop cycle. Type 2 corresponds to crops grown with low rates of N fertilizer or organic crops (David, 1997). Type 3 is observed on conventional farms, either when N fertilizer application is postponed beyond the optimal date, generally due to work organization constraints or unfavorable weather (Aubry, 1995; Aubry et al., 1998; Meynard, 1985; Meynard et al., 1988) or when N fertilizer is not available to the plant. Model 1 was established with the winter wheat cultivar Trémie. It proved to be adapted to simulate KN of cultivar Soissons, as shown by its evaluation on the data of Jeuffroy and Bouchard (1999). The adaptation of Model 1 to other cultivars should be studied. If the parameters depend on the genotype, they should be easy to estimate. The Q depends only on climatic variables, and NNI assessment requires to dry and weigh the above-ground biomass at anthesis and to determine its concentration in N, an analysis routinely performed by many laboratories at a reasonable price.

Comparison of the six models showed that the logarithm of NNI at anthesis used as an explicative variable always gave a better fit than that did IDD, regardless of the period covered by Q. Jeuffroy and Bouchard (1999) found that the characteristic of N deficiency that was most explicative of the lower KN for deficient crops than for non-deficient crops was IDD, but they used NNI at anthesis rather than its logarithm. With their data, the correlation coefficient between the loss of KN due to N deficiency and the logarithm of NNI at anthesis was r = 0.95, which is very close to the correlation coefficient between the loss of KN and IDD (r = 0.96), and higher than the correlation coefficient between the loss of KN and NNI at anthesis (r = 0.92). There is no obvious explanation to why in the study of Jeuffroy and Bouchard (1999) the correlation between the loss of KN and the logarithm of NNI at anthesis was nearly as high as the correlation between the loss of KN and IDD, whereas in our experiment the models with the logarithm of NNI at anthesis were better than those with IDD. The results of the study of Justes et al. (1997), of the data of Jeuffroy and Bouchard (1999), and of this study (Fig. 3 and Table 4) suggest that the relationship between KN and NNI at anthesis is not linear but logarithmic.

For the six models tested, the relationship was always better if Q45 was used rather than Q30, and Q30 gave a better relationship than Q20+10. The bad results obtained for Q20+10 could be due to the fact that KN is fixed within a few days after anthesis, definitely before the tenth day following anthesis (Armstrong et al., 1987). In non-limiting N conditions, KN depends on spike growth (Fischer and Stockman, 1980). We can assume that there is a strong relationship between KN and Q because spike growth depends on the radiation intercepted by the crop during the spike growth period (Abbate et al., 1997), and because the length of the spike growth period, expressed in days, is influenced by temperature (Rahman and Wilson, 1978). The authors who studied the relationship between KN and Q calculated Q over various periods of times, depending on which showed the best correlation between KN and Q, but they did not define the spike growth period in their studies (Abbate et al., 1995; Fischer, 1985; Midmore et al., 1984; our work). To test the assumption that Q should cover the spike growth period, it would be necessary to determine which definition of the spike growth period is best adapted (from spike initiation to anthesis (Fischer, 1985) or from the time the spike accumulated 5% of its final dry weight to 7 d after anthesis (Abbate et al., 1997)). If such a study concluded that Q should be calculated only over the spike growth period, a model predicting the beginning and end of spike growth would be necessary.


   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
REFERENCES
 
These results show that variations in the KN of winter wheat due to variations in crop N nutrition and weather conditions (radiation and temperature) are successfully accounted for by two variables, the logarithm of NNI at anthesis and the photothermal quotient over the 45 d preceding anthesis. This relationship could be useful for estimating KN in crop models. The NNI at anthesis is easy to simulate, as most crop models simulate aerial growth and N accumulation in the aerial parts of the crop (Brisson et al., 1998; de Willigen, 1991; O'Leary and Connor, 1996; Ritchie and Otter, 1984; van Keulen and Seligman, 1987; Weir et al., 1984). The Q, at least as used here, is easily calculated in crop models, as it depends only on climatic variables, which are input variables in all crop models. Our model could probably be improved by replacing incident PAR by intercepted PAR in the calculation of Q. This change would not complicate the model very much, because intercepted radiation can be calculated from incident radiation and leaf area index, a variable often simulated in crop models.


   ACKNOWLEDGMENTS
 
We thank C. Bouchard, A. Demilly, G. Durandet, E. Fovart, F. Lafouge, J. Lanzere, M. Le Barrier, B. Le Fouillen, S. Leliévre, and the team of the Unité Expérimentale of INRA Grignon for technical assistance.

Received for publication February 10, 2000.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 





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