Optimizing the nitrogen rate in the rice crop in relation to soil mineralized nitrogen with anaerobic incubation without shaking to different times and temperatures

Nitrogen fertilization in rice crop are based on crop needs and the capacity of the soil to supply it. In this study six rice soils of central Chile were fertilized with 0, 80 and 160 kg N ha -1 and incubated in anaerobic conditions for time periods from 0 to 28 days at 20 and 40°C. Field experiments were conducted in the same soils with equal N rates. Nitrogen mineralization showed a quadratic response that was directly proportional to incubation time, N rate used, and increase in incubation temperature. At the same time, mineralized N exhibited patterns of different magnitude, including in soils of the same order; therefore, this N supply capacity indicator is soil-dependent. The yield was maximized with 80 kg N ha -1 and the N uptake was highly correlated with the N mineralized for both 21 days at 20°C and 7 days at 40oC. The optimum N rate to apply was represented using a lineal model that associates the yield with the crop N needs, the N soil supply through mineralization and the supplement that must be supplied by the N fertilization.


INTRODUCTION
Rice, Oryza sativa L., is very important in the diet of the world's population because of its nutritional value (Juliano, 1993) and low price.In the year 2008, the world area cultivated with rice was approximately 155 million ha with yields of 661 million tons (Kögel-Knabner et al., 2010), with the greatest cultivated area being in Asia (Bouman et al., 2007;Jing et al., 2008;Kögel-Knabner et al., 2010).Worldwide, cultivated paddy rice soils belong to five taxonomic orders: Entisols, Inceptisols, Alfisols, 2006;Wilson et al., 1994a), showed that the use of deficient or excessive N rates generate alterations in the crop cycle which affects the length of the vegetative and reproductive cycles, with negative effects on crop productivity (Hirzel et al., 2011a;Ortega, 2007).
To optimize N fertilizer supply to rice crop, it is important to know of the amount of N supplied by the soil mineralization (Angus et al., 1994;Sainz et al., 2008) since crop N uptake derives mainly from soil reserves (organic matter (OM) mineralization, microbial biomass turnover, and N-NH 4 + fixed in clay) (Jokela and Randall, 1997;Jensen et al., 2000;Sainz et al., 2004;Sahrawat, 2006), and N fertilization (Wienhold, 2007).A small fraction is derived from irrigation water and other environmental and biotic sources.Soil N supply or the quantity of available mineral N for plant uptake is variable and difficult to estimate, and represents only a very small fraction of total soil N (Scott et al., 2005;Wienhold, 2007).Since mineralization can substantially contribute to plant available N, it is necessary to have adequate methods for its quantification (Angus et al., 1994;Bushong et al., 2007;Soon et al., 2007).Several authors have proven that anaerobic incubation is a good method for assessing potentially mineralized N because the initially available soil N is scarce, and a continuous N supply to the rice crop depends on mineralized ammonium from labile organic N in flooded soil (Angus et al., 1994;Bushong et al., 2007;Rodriguez et al., 2008;Soon et al., 2007;Waring and Bremner, 1964;Wilson et al., 1994a).Additionally, Angus et al. (1994) suggested that mineralized N that is measured in flooded soil during rice growth is a very good indicator of potential N uptake by the crop.
Previous investigations have studied the effects of incubation time and temperature on N mineralization (Angus et al., 1994;Bushong et al., 2007;Wilson et al., 1994a).Shorter incubation time (7 d at 40°C) generally measures the contribution of microbial biomass and soluble N sources, whereas long incubations can measure the whole active fraction of OM (Scott et al., 2005), and the choice of a given method should be based on the correlation between the N uptake and the N mineralized (Wilson et al., 1994b).Moreover, field experiments carried out in Chile indicated that soil N supply in paddy rice soil is higher than that indicated using a short time of anaerobic incubation (Hirzel et al., 2011a), so both time and temperature of soil incubation will be selected in relationship with the N uptake obtained in field experiments.Sahrawat andNarteh (2001, 2003) indicated that mineralizable N under anaerobic incubation is controlled by the contents of OM and reducible iron (Fe).In a previous study, soils of different orders (Alfisols, Entisols, Inceptisols, Mollisols, Ultisols and Vertisols) had diverse rates of mineralized N-NH 4 + using anaerobic incubation at 40ºC for 14 days or acid oxidation (Bushong et al., 2007), which could suggest that the N mineralized in the soils may depend on the soil order and the associated clay type, as well as the fraction of residual N that is fixed on to the clays (Jensen et al., 2000).Since OM is an important source for available N in paddy rice soil, the quantity of OM is very important for potential crop yields (Olk et al., 1999).Reichardt et al. (1999) also state that the formation and mineralization of soil OM depend on C and N biogeochemical pathways that are governed by soil enzymes, and the size of the pool of microbial biomass (normally only 2 to 4% of total C), which is the most labile of soil OM.Moreover, the chemical environment of flooded soils affects OM quality, especially the proportion of organic N fractions and dominant chemical structures of specific soil OM pools that contribute to N mineralization (Sahrawat, 2006).Olk and Senesi (1999) point out that soil OM seems to play a significant role in crop nutrient uptake in intensively cropped lowland rice soils, but more research is needed to learn how submerged conditions of this unique cropping system affect soil OM and potential nutrient cycling and uptake by plants.Functions of soil biota related to N immobilization and mineralization are influenced by organic C content and fertilizer inputs, as well as soil redox potential that is influenced by irrigation (Kögel-Knabner et al., 2010;Reichardt et al., 1999).
The supply of N in soil plays an important role in the overall N nutrition of wetland rice because one half to two-thirds of total N uptake, even in paddies with N fertilization, comes from the soil N pool (Sahrawat, 1983).Based on this information, the soil type (taxonomical order and chemical or physical properties) and soil incubation method (time and temperature) could affect the amount of mineralized N. Additionally, applying N to soil could also affect the amount of mineralized N and the subsequent relationship between N uptake and mineralized N, because N fertilization affects microbial activity in soil (Jensen et al., 2000).
Considering that Chile has a variety of rice paddy soils with different N supply capacity and potential for yields, and in order to find out the optimum N rate in the rice crop associate to a method of soil incubation as predictor of the N supply, the objectives of this investigation were; (i) determinate the N mineralized in laboratory incubations in anaerobic conditions for different times and temperatures in six Chilean paddy soils and determine its relationship with the N uptake by the rice crop in field conditions, and (ii) adjust mathematically the N rate to use in the rice crop that will optimize the yield in different soil conditions in relation to its N need and the N soil supply through of the mineralization.(CIREN, 1997).The investigation was conducted under both controlled laboratory conditions for soil incubations (soil without plants) to measure N mineralization, and field conditions (crop in the field) to measure the amount of N extracted from soil by rice in both seasons.Soil samples were collected in cores of 0 to 20 cm depth before crop establishment in both seasons; which were air-dried and subsequently characterized for physical and chemical properties (Table 1).Soils were fertilized in both experimental conditions (lab and field) with three N rates of 0, 80, and 160 kg ha -1 as urea, 60 kg P2O5, and 60 kg K2O as triple super phosphate and potassium chloride, respectively.Before initiating the laboratory incubation procedure, the N, P, and K rates were adjusted accordingly with regard to bulk density of the soils (Table 1).The N rates were chosen because in previous experiments in the same study area they had been verified to produce a range of crop responses (Hirzel et al., 2011a, b;Ortega, 2007).The analytical procedures to characterize the soils were carried out in the laboratory of the Instituto de Investigaciones Agropecuarias (INIA), Chile using standard methodologies (Sadzawka et al., 2006).All samples were air-dried and ground to pass a 2 mm sieve.Soil pH was determined in 1:2.5 soil:water extracts using a pH meter; electrical conductivity was measured using a conductivity cell (soil:water ratio 1:5); organic C and total N by a total elemental analyzer (Vario MAX CNS, Elementar, Hanau, Germany); soilextractable P was determined in 0.5 M NaHCO3 (Olsen-P) using the molybdate-ascorbic acid method; soil available K, Ca, Mg, and Na were determined by 1 M NH4OAc extraction followed by flame emission spectrometry (K and Na) and atomic absorption (Ca and Mg).Soil-extractable S-SO4 was determinated with 0.01 M calcium phosphate and turbidimeter; soil micronutrient and trace element concentrations were determined in a DTPA (diethylentriamine pentaacetic acid) extract (Lindsay and Norvell, 1978) by atomic absorption spectrometry.The concentration of B was determined by extraction in hot water with azometine-H.For the laboratory experiment, soil samples were incubated in controlled conditions with anaerobic incubation without shaking for 7, 14, 21, and 28 days at 20 and 40ºC using a CARBOLITE model PIC 200 incubator.As previously stated, shorter incubation times generally measure microbial biomass and soluble N sources, whereas longer incubation times can measure potentially mineralized N from the whole active fraction of OM (Scott et al., 2005;Hirzel et al., 2011a) and indicate more precisely the soil N supply capacity.The effects of the incubations at different times and temperatures were compared to N mineralization in field conditions of both seasons (N uptake by the control without N).
The field experiments also included N uptake as determined in whole-plant analysis and grain yield adjusted to 14.5% of moisture content.
The anaerobic incubation methods to estimate N mineralization as N-NH4 + were carried out as follows: Five gram of soil and 12.5 mL of distilled water were placed in a test tube, sealed with a stopper, and incubated anaerobically for 7, 14, 21 and 28 days at 20 and 40ºC without shaking.In addition, the initial N-NH4 + , without incubation (0 days), was determined.To measure the mineralized N, extracts of ammonium from soil were obtained by adding 12.5 mL 2M KCl to the soil-tubes, and the mixture shaken for 1 h (Mulnavey, 1996), filtered, and N-NH4 + was measured with a Skalar auto-analyzer.
For the field experiments, all plots were cultivated under traditional management to optimize crop growth in accordance with standard agronomic practices for rice crops in central Chile.Nitrogen (urea) was applied three times: 33% the day prior to sowing, 33% at tillering, and 34% at initial panicle (Hirzel et al., 2011b).The seed dose was 160 kg ha -1 in all experimental locations, and the cultivar used in the experiment was Zafiro-INIA (the second main variety used in Chile).The seed had been pregerminated two days before sowing.After emergence, weed control consisted of a combination of herbicides of Penoxsulam (Ricer 240 g L -1 ), MCPA (MCPA 750 SL 750 g L -1 ), and Bentazon (Basagran 480 g L -1 ) at rates of 0.03, 0.19, and 0.72 kg a.i.ha -1 , respectively.The crop was harvested at grain maturity (at 20% moisture content of grain), and grain moisture content was measured with a Satake model SS-5 moisture meter.Whole-plant dry matter and N concentration were determined with tissue samples collected at harvest time.In addition, the grain yield at 14.5% moisture content was calculated for the crop.Dried subsamples (2 g) were ground in a mill, passed through a 2 mm sieve, and analyzed for total N as determined by the macro-Kjeldahl procedure (Sadzawka et al., 2006).The total N extraction for the crop was calculated by multiplying the total dry matter by its N concentration.

Experimental design
The experimental design for soil incubation at two temperatures (20 and 40ºC) and three N rates (0, 80, and 160 kg ha -1 ), was a splitsplit-split-split plot where the main plot was the season, the split plot was the temperature, the split-split plot the soils (three orders), the split-split-split plot incubation time (0, 7, 14, 21, and 28 days), and the split-split-split-split plot the N-rates.Experiments consisted of four replicates per treatment.
For the field experiment the experimental design was split-split plot where the main plot was the season (2), the split plot was the soil (three orders), and the split-split plot was the N rates.Experiments consisted of four replicates per treatment.
Results were analyzed with ANOVA and the Tukey test (P = 0.05) by the SAS general model procedure (SAS Institute, 1989).When there was interaction between sources of variations, its effects were compared by orthogonal contrasts.
The relationships between mineralized N in incubations without shaking for 7, 14, 21, and 28 days at two temperatures and N uptake by the crop was determined for each soil and evaluated with a linear mathematical model (Wilson et al., 1994b;Sahrawat, 2006;Hirzel et al., 2011b), using the SAS procedure for simple regression.At the same time, the relation between the grain yield of rice and the mineralized N in incubations for the times previously indicated was determined with a linear mathematical model.

Model of optimizing of the nitrogen rate
The model to be used is a linear equation where N uptake is associated with a range of grain yield per unit area, which is obtained during both experimental seasons and is the simple sum of N uptake from soil supply and N uptake as complementary fertilization expressed in Equation (1).
N uptake = N uptake from soil supply + N uptake as complementary fertilization (kg ha -1 ) (kg ha -1 ) (kg ha -1 ) (1) Grain yields (GY) in the present study were associated with crop N uptake (Nupt), which was associated with mineralized N in each soil (Nsoil mineralized) and the complementary effect of N applied as fertilizer (N rate).In this way, applied N was calculated as the difference between Nupt and Nsoil mineralized with specific values for each soil where Nsoil mineralized was determined by a linear regression model that associates N uptake with Nsoil mineralized.Given that GY varies within an agronomic range for each study condition (Artacho et al., 2009;Hirzel et al., 2011a, b;Ortega, 2007), the need for N uptake was related to GY by using the maximum yield value obtained at each study site and expressed as an N uptake index in the rice crop (NUI-Rice) (kg N Mg grain -1 ).The effect of N fertilization increases crop N uptake that is lower than the applied quantity because of the dynamic processes affecting N applied as fertilizer (Jensen et al., 2000;Scott et al., 2005;Wienhold, 2007).Therefore, the need to apply N to increase N uptake was expressed as the Index of the relationship between N applied and N uptake by the rice crop (IRNN) (kg N applied to kg N uptake -1 ).The simple model that allows optimizing the N rate in the rice crop with regard to Nsoil mineralized is shown in Equation 2.
Then, N rate, N to applied through of the fertilization, corresponding to the N uptake as complementary fertilization (kg ha -1 ); GY, grain yield (Mg grain ha -1 ); NUI-Rice, N uptake index in the rice crop (kg N Mg grain -1 ); Nsoil mineralized (kg ha -1 ), soil supply of N through mineralization in incubation conditions without shaking at 20ºC for 21-days or 40ºC for 7-days IRNN, Index of the relationship between N applied and N uptake by the rice crop (kg N applied to kg N uptake -1 ) as effect of the N fertilization (determinate as the difference of N uptake between the treatment fertilized and the control without N fertilization)

RESULTS AND DISCUSSION
Soil physical and chemical properties (Table 1) mainly indicated that no limitations exist for rice crop production, with the exception of P concentration in the Inceptisol in both of the evaluated seasons and B concentration in all the soils and both evaluated seasons in accordance with the critical levels that have been established by the Instituto de Investigaciones Agropecuarias for the rice zone in Chile.Although the exchangeable K concentration can be a limiting factor in the Inceptisol for the second season and in the Vertisol for the first season that was evaluated (Table 1), applying this element in field experiments allowed the correction of these limitations in accordance with the reference rate used in the zone under study (Ortega, 2007).
The statistical analysis of mineralized N in incubated soils (Table 2) indicated there were differences between seasons (p<0.01),incubation temperatures (p<0.01),soils (p<0.01),incubation times (p<0.01),and interactions between most of the combinations of the sources of variation (p<0.01);there was no interaction between temperature and N rate (p>0.05) and between soils and N rate (p>0.05).The contrasts of different incubation times indicated a difference for most of the times (Table 2), with the exception of the comparison between 14 and 28 d since mineralized N exhibited a quadratic behavior with a maximum on day 21 and a generalized decrease in mineralized N when time was increased from 21 to 28 days, independently of temperature and N rate (Figure 1a to f).The contrasts between N rates (Table 2) indicated differences in mineralized N for the three N rates being used, which showed that mineralized N tends to be directly proportional to the N rate being used (Figure 1a to f).The differences in mineralized N between both evaluated seasons are mainly related to the differences in chemical properties of each soil (Table 1) since mineralized N is associated with OM content and reducible Fe (Sahrawat andNarteh, 2001, 2003).Meanwhile, differences in mineralized N obtained at both incubation temperatures (Table 2, Figure 1a to f) suggest that the correlation to be performed between N uptake and mineralized N must be adjusted for each incubation temperature and also take into account differences between soils and incubation times given the interactions that were obtained between these sources of variation and the incubation temperature (p<0.01).In addition, for future soil incubations with the objective of standarized the N supply capacity to rice crop by soil type, would selected the incubation temperature between both evaluated in this experiment (20 and 40°C).
Mineralized N in the Inceptisol1 soil (first evaluated season) with three applied N rates had values fluctuating between 7 and 88 mg N-NH 4 + kg -1 and between 10 and 134 N-NH 4 + kg -1 for temperatures of 20 and 40°C,  and 40ºC) and three N rates (0, 80 and 160 kg ha -1 ) during a period of 28 days.The quadratic model for each temperature and N rates were: Y = -14.61+ 22.05*X -2.641*X 2 , R 2 = 0.98 for 20ºC and N-0 kg ha -1 ; Y = -21.30+ 31.66*X-3.823*X 2 , R 2 = 0.98 for 20ºC and N-80 kg ha -1 ; Y = -30.72 + 43.05*X -5.496*X 2 , R 2 = 0.99 for 20ºC and N-160 kg ha -1 ; Y = -42.61+ 60.60*X -7.178*X 2 , R 2 = 0.98 for 40ºC and N-0 kg ha -1 ; Y = -49.47+ 71.89*X -9.041*X 2 , R 2 = 0.96 for 40ºC and N-80 kg ha -1 ; Y = -60.37+ 87.57*X -11.20*X 2 , R 2 = 0.95 for 40ºC and N-160 kg ha -1 .respectively (Figure 1a).For the Inceptisol2 soil (second evaluated season), mineralized N with three applied N rates fluctuated between 4 and 35 mg N-NH 4 + kg -1 and between 4 and 46 mg N-NH 4 + kg -1 for temperatures of 20 and 40°C, respectively (Figure 1b).Differential mean values in mineralized N for the 80 and 160 kg N ha -1 rates compared with the control in the Inceptisol1 soil were 9 and 26 mg N-NH 4 + kg -1 (incubation at 20°C), and 18 and 27 mg N-NH 4 + kg -1 (incubation at 40°C) (Figure 1a), whereas the Inceptisol2 soil, showed different mean values compared with the control of 10 and 17 mg N-NH 4 + kg -1 (incubation at 20°C) and 8 and 16 mg N-NH 4 + kg -1 (incubation at 40°C) (Figure 1b) for the 80 and 160 kg N ha -1 rates compared with the control, respectively.The differences in magnitude that were obtained in mineralized N for the Inceptisol order and at the same incubation temperature (Figure 1a and b) suggest that it is not possible to find a general correlation between N uptake in the rice crop and mineralized N for this soil order; work with must be done with soil-specific correlations, which is also indicated by the interaction obtained between soil and incubation temperature (Table 2).
For soils of the Alfisol order, mineralized N in the Alfisol1 soil exhibited values fluctuating between 18 and 152 mg N-NH 4 + kg -1 and between 33 and 199 N-NH 4 + kg -1 at temperatures of 20 and 40°C, respectively (Figure 1c).Mineralized N in the Inceptisol2 soil (second evaluated season) fluctuated between 24 and 94 mg N-NH 4 + kg -1 and between 20 and 200 mg N-NH 4 + kg -1 at temperatures of 20 and 40ºC, respectively (Figure 1d).Different mineralized N mean values for rates of 80 and 160 kg N ha -1 compared with the control for the Alfisol1 soil (Figure 1c) were 21 and 32 and 11 and 27 mg N-NH 4 + kg -1 at temperatures of 20 and 40°C, respectively.For the Alfisol2 soil, different mineralized N mean values for the 80 and 160 kg N ha -1 rates compared with the control were 9 and 17 mg N-NH 4 + kg -1 (incubation at 20°C) and 15 and 27 mg N-NH 4 + kg -1 (incubation at 40°C), respectively (Figure 1d).Just as it was found for the Inceptisol order, variations in magnitude of mineralized N for the Alfisol order soils at the same incubation temperature (Figure 1c and d) suggest that correlations between N uptake for the rice crop and mineralized N for soils used in the present study are soil-specific and cannot be generalized for this soil order.
For soils of the Vertisol order, mineralized N exhibited values fluctuating between 8 and 90 mg N-NH 4 + kg -1 and between 14 and 77 N-NH 4 + kg -1 at temperatures of 20 and 40°C, respectively, in the Vertisol1 soil (Figure 1e).In Vertisol2, mineralized N values fluctuated between 5 and 55 mg N-NH 4 + kg -1 and between 8 and 107 N-NH 4 + kg -1 at temperatures of 20 and 40°C, respectively (Figure 1f).Different mineralized N mean values in for the 80 and 160 kg N ha -1 rates compared with the control for Vertisol1 (Figure 1e) were 16 and 32, and 6 and 12 mg N-NH 4 + kg -1 at temperatures of 20 and 40°C, respectively.For the Vertisol2 soil, the different mineralized N means for the 80 and 160 kg N ha -1 rates compared with the control were 9 and 15 mg N-NH 4 + kg -1 (incubation at 20°C) and 7 and 19 mg N-NH 4 + kg -1 (incubation at 40°C) (Figure 1d), respectively.Likewise for the Inceptisol and Alfisol soils, variations of magnitude obtained in mineralized N for soils of the Vertisol order with the same incubation temperature (Figure 1e and f) suggest that correlations between N uptake for the rice crop and mineralized N in the soils of the Vertisol order used in the present study are soil-specific and cannot be generalized for this soil order.For the three soils orders evaluates in the two seasons, both the N mineralization and the correlations soil-specific with N uptake, could response to the chemical properties as reducible Fe and OM content (Sahrawat andNarteh, 2001, 2003), and the variations of yield between seasons (Figure 2a and b).
Grain yield for the field experiment for the Inceptisols fluctuated between 5.1 and 7.7 Mg ha -1 (season 1) and between 7.8 and 11.8 Mg ha -1 (season 2) (Figure 2a and b), while that for the Alfisols fluctuated between 6.4 and 9.1 Mg ha -1 (season 1) and between 8.7 and 11.3 Mg ha -1 (season 2) (Figure 2a and b), and in the Vertisols fluctuated between 6.1 and 11.5 Mg ha -1 (season 1) and between 6.4 and 11.4 Mg ha -1 (Figure 2a and b).In general the highest yield in the three soils was achieved with 80 kg N ha -1 (Figure 2a and b), but too were observed differences between seasons for the same order soil which could be associate to its different climatic conditions (data not shown).Whole-plant dry matter production varied between 12.2 and 21.6 Mg ha -1 (season 1) and between 17.0 and 25.1 Mg ha -1 (season 2) in the Inceptisols; 16.8 and 24.6 Mg ha -1 (season 1) and between 13.3 and 21.7 Mg ha -1 (season 2) in the Alfisols; and 12.4 and 23.8 Mg ha -1 (season 1) and between 10.3 and 18.5 Mg ha -1 (season 2) in the Vertisols, and the highest DM production in the three soils was achieved with the 160 kg N ha -1 rate (data not shown).Whole-plant N concentration ranged from 5.8 to 6.6 g kg -1 (season 1) and from 8.5 to 8.7 g kg -1 (season 2) in the Inceptisols; 6.2 to 6.9 g kg -1 (season 1) and from 7.6 to 7.7 g kg -1 (season 2) in the Alfisols; and 7.1 to 7.6 g kg -1 (season 1) and from 7.2 to 7.9 g kg -1 (season 2) in the Vertisols (data not shown), and as in DM production the highest whole-plant N concentration was achieved with the 160 kg N ha -1 rate (data not shown).Differences between the DM production between seasons for the same soil order could response to its different climatic conditions (data not shown).The N uptake fluctuated between 71 and 142 kg ha -1 (season 1) and between 148 and 210 kg ha -1 (season 2) in the Inceptisols; 103 and 169 kg ha -1 (season 1) and between 102 and 168 kg ha -1 (season 2) in the Alfisols; and 88 and 181 Mg ha -1 (season 1) and between 81 and 134 kg ha -1 (season 2) in the Vertisols (Figure 3a and b).The highest N uptake in the six soils was achieved with 160 kg N ha -1 .Grain yields (Figure 2a and b) were similar to those observed by several authors (Artacho et al., 2009;Hirzel et al., 2011a;Ortega, 2007) for the same cultivation area.Considering the mean of both seasons, the Vertisols had higher yield than the Inceptisol, which may be associated with its physical properties (structure and clay type) and its relationship with protecting organic N in the fine fraction of the soil (Elliott, 1986;Greenland, 1965;Videla et al., 2004).The N uptake increased in association with the increase in N rate (Figure 3a and b), however the highest grain production in the six soils occurred with the 80 kg ha -1 rate (Figure 2a and b).This indicates that the highest N rate used (160 kg ha -1 ) produced excessive consumption and no yield response or a negative response (Vanotti and Bundy, 1994), which was pointed out by Hirzel et al. (2011a) and Ortega (2007) in N fertilization studies for the same production zone.Mean differences obtained of the grain yield for Inceptisols and Alfisols between seasons indicate the effect of the interaction between the climate within the same season and the response to the N application, as was indicated by Ortega (2007) for the same production zone.
The simple linear regressions relating the mineralized N in incubations without shaking at 20 and 40ºC and the extracted N in the field crop are presented in the Table 3.For incubations at 20°C in general for both seasons the highest coefficient of determination (R 2 ) was in the 21days, which was highly significant in Inceptisols, Vertisols and in one of the Alfisols soils (Table 3).The highest R 2 in the Alfisols were obtained in the 14-days incubation, which was slightly higher than the 21-days incubation value, but both values were significant (Table 3).For the incubations at 40°C in general the highest R 2 in all the soils was obtained at 7-days (Table 3), which was highly significant.However, the R 2 for the Inceptisol at 28-days in the first season was slightly higher than at 7-days, but both were highly significant (Table 3).A similar situation was presented for the R 2 in the Vertisol at 14-day in the second season (Table 3).The differences in mineralized N for temperatures and incubation times allow for determining an optimal incubation time for each *, ** Significant at the 0.05 and 0.01 probability levels; NS, not significant; Y, N uptake (kg ha -1 ); X, N mineralized (mg kg soil -1 ).
temperature (Table 3 and Figure 1a to f) since N mineralization responds to these two factors (Angus et al., 1994;Bushong et al., 2007;Scott et al., 2005;Wilson et al., 1994a).Although soil type interacted with incubation times, using the regression coefficient criterion and the significance level between mineralized ammonium-N and N absorbed by the crop, it is possible to determine the appropriate incubation time for each temperature (Table 3).For both seasons, the incubation times and temperatures suggest were 21-days by 20ºC and 7-days by 40°C, but in general the maximum R 2 values were obtained with incubations to 40ºC (Table 3).
On the other hand the gradients of the equations were positive for all the soils and temperatures evaluated, showing the positive relationship between the total N uptake and the N-NH 4 + mineralized (Table 3), as had been indicated by some authors (Hirzel et al., 2011b;Sahrawat, 2006;Wilson et al., 1994b).In addition, the relationship obtained by the N uptake and N mineralizated in this study for anaerobic incubations in the first season by 21-days to 20ºC were of 1.39, 1.01 and 1.90 kg mg -1 in inceptisol, alfisol and vertisol respectively; while that for incubations by 7-days to 40ºC this relationship were of 16.73, 1.53 and 2.59 kg mg -1 in inceptisol, alfisol and vertisol respectively (Figures 1a, b,  c, and Figure 3a).For the second season the relationship between N uptake and N mineralizated for incubations by 21-days to 20°C this relationship were of 1.17, 1.03 and 2.05 kg mg -1 in inceptisol, alfisol and vertisol respectively; while that for incubations by 7-days to 40°C this relationship were of 11.68, 2.54 and 1.45 kg mg -1 in inceptisol, alfisol and vertisol respectively (Figure 2a, b, c and Figure 3b).For this index of relationship between the N uptake and N mineralizated, all the values fluctuated between 1.01 and 2.69 kg mg -1 , except in the inceptisol used in the second season, which could be associate to the high Mn content (Table 1) that reduce the N mineralization (Chang and Broadbent, 1982).For each soil order different capital letters for the medium values of the treatments with a same N rate (0, 80 and 160 kg ha -1 ) indicate significant differences between seasons according to Tukey's test (p<0.05).For each soil order different lower case letters for the medium values of the treatments in the same season indicate significant differences between the N rates used (0, 80 and 160 kg ha -1 ) according to Tukey's test (p<0.05).
Table 5.Index of relationship between nitrogen applied and nitrogen uptake by the rice crop (kg N applied by kg N uptake -1 ) (IRNN).Different letters indicate significant differences according to Tukey's test (p<0.05).The IRNN was calculated in base of the N rate that allowed the maximixed grain yield (80 kg ha -1 ).

Soils
Optimizing N applied as fertilizer was determined by equation 2 where GY (Mg grain ha -1 ) is obtained from yield results from both seasons under study (Figure 2a and b); NUI-Rice (kg Mg grain -1 ) (Table 4) is the relationship between N uptake (Figure 3a and b) and GY for the N rate that maximizes GY (Figure 2a and b).The N soil mineralized (kg ha -1 ) is soil N supply through mineralization under incubation conditions without shaking at 20°C for 21 days or 40°C for 7 days (Table 3), and IRNN (kg N applied for kg N uptake -1 ) (Table 5) was calculated on the basis of the N rate that maximizes GY (80 kg ha -1 ) (Figure 2a and b).The NUI-Rice values for each soil order were similar between seasons (p<0.05) and exhibited differences between N rate in the same soil order in only the first season evaluations in Alfisols and Vertisols (p<0.05)(Table 4).In general, NUI-Rice values were directly proportional to the N rate being used, with the exception of the Inceptisol and Vertisol in the first season (Table 4), which was associated with the marked response of the crop faced with low N rates that produce a dilution effect of this nutrient in the plant (Hirzel et al., 2011a) and a decrease in the N need index per Mg grain to be produced.When comparing soils for the N rate that maximized yield (80 kg ha -1 ) (Figure 2a and b), Inceptisols and Alfisols presented a higher NUI-Rice value than Vertisols (mean values of 15.3 vs.11.7), which is associated with the highest GY (Figure 2a and b) and the lowest N uptake (Figure 3a and b) found in the Vertisols for the first and second season, respectively; this causes a dilution effect of N and a lower need index of this nutrient per yield unit.In this regard, some studies relating N uptake to GY allow obtain NUI-Rice values fluctuating between 8.3 and 43 kg N Mg grain -1 (Hossain et al., 2005;Peng et al., 2006;Witt et al., 1999;Ying et al., 1998) and with mean values that were higher than those found in the present study.
Although there was no significant difference associated with the high coefficient of variation (51.94%) in IRNN values (Table 5), quantitative differences were found between orders as well as for the same soil order, which were associated with the differences in N uptake in each season and soil being evaluated (Figure 3a and b).In general, the highest mean values were found in Vertisols followed by Inceptisols and with a lower value and higher stability in Alfisols (Table 5).These variations for the same soil order corroborate the fact that the N optimization model that was applied cannot be generalized for soil order and must be soil-specific; mineralizable N (soil N supply) also shows a greater GY, Grain yield (Mg grain ha -1 ); NUI-Rice, N uptake index in the rice crop (kg N Mg grain -1 ); IRNN, Index of relationship between N applied and N uptake by the rice crop (kg N applied by kg N uptake -1 ) as effect of the N fertilization (the supply of N soil without N is discounted).
association with chemical soil properties, such as reducible Fe and OM content (Sahrawat andNarteh, 2001, 2003).Finally, simulations that were performed with the optimization model generated in the present study (Table 6) for the real maximum GY conditions (Figure 2a and b), and mineralized N without adding N at different temperatures (Figure 1a to f) showed differences in magnitude of the N rate to be used that fluctuated between 8 and 33 kg N ha -1 for the six evaluated soils; this is agronomically acceptable for the productive conditions of rice soils in Chile where total N rates do not surpass 112 kg N ha -1 (Table 6).These values are similar to those pointed out in previous studies by Hirzel et al. (2011a, b) and Ortega (2007) and lower than those found by Artacho et al. (2009) to maximize GY in the same study area.

Conclusions
Nitrogen mineralization in anaerobic incubation conditions at different times and temperatures showed a quadratic response that was directly proportional to incubation time, N rate used, and increase in incubation temperature.At the same time, mineralized N exhibited patterns of different magnitude, including in soils of the same order; therefore, this N supply capacity indicator is soil-dependent.Nitrogen uptake for the rice crop in field conditions was highly correlated in a linear way with mineralized N for both 21-days at 20ºC and 7-day at 40ºC.For almost all the soils studied the index of relationship between the N uptake and N mineralizated fluctuated between 1.01 and 2.69 kg mg -1 . Finally, the determination of the need for N to be applied in the rice crop for the evaluated soils can be represented by a linear optimization model that associates grain yield potential, N need per yield unit, natural soil supply through mineralization, and the N rate to increase uptake to meet the crop need that is not covered by the natural soil supply.

Figure 2a .Figure 2b .
Figure 2a.Grain yield of rice in three paddy rice soils fertilized with three N rates (0, 80 and 160 kg ha -1 ) for the first season of evaluation.Different letters over the bars of the same soil indicate significant differences according to Tukey's test (p<0.05).

Figure 3b .
Figure 3a.N uptake in whole plant of rice in three paddy rice soils fertilized with three N rates (0, 80 and 160 kg ha -1 ) for the first season of evaluation.Different letters over the bars of the same soil indicate significant differences according to Tukey's test (p<0.05).

Table 1 .
Physical and chemical properties of the Inceptisols, Alfisols and Vertisols soils (0 to 20 cm depth) before crop establishment for both seasons.

Table 2 .
Contrast and statistical analysis of sources of variation for incubations without shaking at different temperatures, for different soils, incubations times, and N rates.

Table 3 .
Regression coefficients and lineal equations between total N uptake in rice crop for Inceptisols, Alfisols and Vertisols rice paddy soil in Chile during the season 2011-2012 (season 1) and 2012-2013 (season 2) and mineralized N-ammonium in anaerobic conditions without shaking for different incubation times.

Table 4 .
Nitrogen Uptake Index in the rice crop (NUI-Rice) (kg N Mg−grain -1 ) for Inceptisols, Alfisols and Vertisols rice paddy soil for both season of evaluation.

Table 6 .
Simulated N application rates according to the proposed optimization model.