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a Universidad Autónoma de Chapingo, Km 38.5 Carretera México-Texcoco, Chapingo, Mexico and Biometrics and Statistics Unit, CIMMYT, Apdo. Postal 6-641, 06600 Mexico D.F., Mexico
b Biometrics and Statistics Unit, CIMMYT, Apdo. Postal 6-641, 06600 Mexico D.F., Mexico
c Wheat Progr., CIMMYT, Apdo. Postal 6-641, 06600 Mexico D.F., Mexico
d Dep. of Plant Sci., Lab. of Plant Breeding, Wageningen Univ., P.O. Box 386, 6700 AJ Wageningen, the Netherlands
* Corresponding author (j.crossa{at}cgiar.org)
Received for publication August 7, 2000.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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Abbreviations: A, April • AMMI, additive main effect and multiplicative interaction • D, December • EV, total monthly evaporation • F, February • FR, factorial regression • G x E, genotype x environment interaction • J, January • M, March • MFR, multiple factorial regression • mT, mean minimum temperature sheltered • MT, mean maximum temperature sheltered • mTU, mean minimum temperature unsheltered • NL, linear N effects • NQ, quadratic N effects • PLS, partial least squares • PR, total monthly precipitation • SH, mean sun hours per day • T x E, treatment x environment interaction
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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The presence of T x E complicates the interpretation of the results and confounds the observed average performance of the agronomic treatments with their true values. Thus, significant resources in agronomy research are devoted to studying and interpreting T x E through replicated (or unreplicated) multienvironment trials. The standard analysis of variance for multienvironment trial data does not explore any underlying structure within the observed T x E and fails to determine patterns of response for agronomic treatments and environments. The simple regression of agronomic treatment means on the environment means (Yates and Cochran, 1938; Finlay and Wilkinson, 1963; Eberhart and Russell, 1966) models the T x E in one dimension by estimating a set of straight lines (one for each treatment over the environments). The heterogeneity of slopes accounts for the T x E; however, it usually explains only a small proportion of it and leaves a great deal of the T x E variability unexplained. The additive main effect and multiplicative interaction (AMMI) model (Kempton, 1984; Gauch, 1988) partitions the T x E in multiplicative components by means of the principal component analysis. The AMMI model describes the T x E in more than one dimension, and it offers better opportunities for studying and interpreting T x E than analysis of variance and regression on the mean.
Recently, statistical models that incorporate large number of external variables (environmental and genotypic variables) into the analysis of multienvironment trials have been used for studying and explaining G x E (Vargas et al., 1998; Vargas, et al., 1999; Crossa et al., 1999). Two of these models are the factorial regression (FR) model (Denis, 1988; van Eeuwijk et al., 1996) and the partial least squares (PLS) regression method (Aastveit and Martens, 1986). Multiplicative models for describing interaction, such as FR or AMMI, are useful because they usually use fewer degrees of freedom than the analysis of variance and they express the T x E as a string of product and (bilinear) terms. The results of the multiplicative decomposition obtained from PLS can be presented graphically in the form of a biplot with treatments, environments, and covariables represented as vectors in a two-dimensional space. Results from the AMMI analysis can also be represented in a biplot that can be enriched with some covariables so that a similar biplot as that obtained with the PLS can be obtained (Vargas et al., 1999).
Factorial regression models have two main advantages. One is that hypotheses related to the significance of the effects for the available external covariables can be tested. A second advantage is that standard selection procedures for variable subsets, like stepwise regression, can be used for model construction. Vargas et al. (1999) found, for two data sets, that FR combined with a stepwise forward selection procedure identified the same covariables as a PLS-based search procedure. One data set used by the authors consisted of several combinations of agronomic cultural practices: two levels of tillage, summer crop, and manure and three rates of N fertilization. The resulting 24 treatments were evaluated during 10 consecutive years, and the effect of several climatic covariables on the T x E were studied. However, this study did not investigate the interaction of the agronomic factors with years.
The aim of this study was to find a parsimonious description of the T x E existing in the 24 agronomic treatments evaluated during 10 consecutive years by (i) investigating the factorial structure of the treatments to reduce the number of treatment terms in the interaction and (ii) using quantitative year covariables to replace the qualitative variable year. We first retained only the most relevant factorial T x E terms by conventional F tests and by looking at the size of the interaction sum of squares that was explained by individual T x E terms. Next, we performed multiple factorial regression (MFR) for specific T x E terms using standard forward selection procedures for finding year covariables that could replace the factor year in those T x E terms. Subsequently, we compared the results of the final MFR with those of a PLS-based analysis to achieve extra insight in both the T x E and final MFR model. We also discuss the parallels with extended AMMI analyses.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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A basic model for the analysis of the two-way table of treatment yield by environment data is the analysis of variance model that, in matrix notation, is given by
 | (1) |
= (i) is a I x 1 vector of main effects of treatments, ß = (ßj) is a J x 1 vector of main effects of environments, and ß = (ß)ij is the I x J interaction matrix (not a vector product) where each element of the matrix specifies the interaction effect for the ith treatment in the jth environment. 1I and 1J are unit vectors of size I x 1 and J x 1, respectively. The common constraints are 1'I = 1'Jß = 0 and 1'Iß1'J = 0.
Factorial Regression Models
The T x E is modeled directly in relation to environmental covariables (with the regression coefficient depending on the treatment) or in relation to treatment covariables (with the regression coefficient depending on the environment). A FR model for the mean of the ith treatment in the jth environment, for which the interaction includes G (centered) treatment covariables xi1 to xiG, can be written in matrix notation as
 | (2) |
I - 1), represented by the I x G matrix X = (xig) and multiplied by the unknown environmental effects (or environmental potentialities), 
j1 to jG, denoted by the J x G matrix 
= (jg). Convenient constraints on the parameters are sum to zero over i for the parameters i and over j for ßj and jg. The treatment covariables are known, but the environmental potentialities should be estimated.
A FR model in which the T x E term contains H (centered) environmental covariables, zj1 to zjH, can be written as
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i1 to iH (H J - 1), collected in the I x H matrix = (ih) and multiplied by the values of the environmental covariables that are collected in the J x H matrix Z = (zjh). The values of the environmental variables are known, but the treatment sensitivities need to be estimated.
Partial Least Squares Regression
The main objective of the PLS method is to identify a linear combination of the explanatory variables that gives latent vectors that optimally predict the response variable using an iterative procedure. The number of PLS factors to be retained is determined by a cross-validation procedure (Stone, 1974) and an F test proposed by Osten (1988). For the multivariate PLS, the response variable is represented by the matrix Y of treatment performance on environments, and the matrix Z = (z1,..., zS) represents S environmental explanatory variables, such as temperature and precipitation. These matrices can be expressed in a bilinear form as
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 | (5) |
Therefore, when T x E is explained using S environmental covariables (Z), Vargas et al. (1999) described the above equations using the transpose of Y such that, for T = ZW and = QW', E(Y') = (TQ')' = QW'Z' = Z' (the same as the last term of Eq. [3]). The rows of Matrix T contain the Z scores indexed by environments; the rows of Matrix W have the Z weights indexed by the environmental covariables; the rows of the Matrix Q include the Y loadings indexed by treatments; and Matrix has the PLS approximation to the regression coefficients of Y to the explanatory covariables Z.
Results of the bilinear decomposition obtained from PLS can be summarized in a graphical form that includes representation of treatments, environments, and covariables, i.e., Matrices T, W, and Q are shown in the same biplot. The PLS biplot approximates interactions of treatments on environments (projections of rows of T on the rows of Q or vice versa), and it also approximates regression coefficients of treatment (environments) on environmental (treatments) covariables (projection of rows of W on the rows of Q or vice versa). A perpendicular projection of the treatments on one environment vector, extended in either direction, gives the relative values of the treatments for the G x E.
Additive Main Effect and Multiplicative Interaction
The AMMI model (Gollob, 1968; Mandel, 1971; Kempton, 1984; Gauch, 1988), or biadditive model (Denis and Gower, 1994), written in matrix notation is
 | (6) |
= (
ik) is an I x K matrix, = (jk) is a J x K matrix, and K is the number of multiplicative (bilinear) terms in the model. ik is a treatment interaction parameter (or score) that measures treatment sensitivity to a hypothetical environmental factor denoted by environmental interaction parameter (or score) jk. 
= (
kk) is a K x K diagonal matrix where kk is a scaling constant obtained from the singular value decomposition of the residual matrix consisting of the two-way table of means corrected for treatment and environment main effects (residual from additivity)—(T x E)ij = 
ij - i. - .j + .. (where ij is the mean of the ith treatment on the jth environment and i., .j, and .. are the mean of the ith treatment, the mean of the jth environment, and the overall mean, respectively) (Gabriel, 1978)—and are ordered such that k 
k+1. The kth bilinear term of '—k = 1,..., K—is formed by a score ik specific to Treatment i, a scale constant factor kk, and a score jk specific to Environment j. The normalization and orthogonality constraints are 1'I = 1'Jß = 0 and 1'I = 1'J = 0 where 0 is a vector of zeros of size 1 x K and ' = ' = IK. Biplots derived by plotting the cultivar and site markers (scores) of the first two multiplicative terms of the AMMI model are also useful for summarizing T x E patterns.
Experimental Data
The CIMMYT experimental station located in the Yaqui Valley near Ciudad Obregon, Sonora, Mexico is the main location in Mexico used by the CIMMYT wheat (Triticum aestivum L.) breeders to both screen and select segregating material and yield test advanced lines under conditions of high yield potential and irrigation. Therefore, it is imperative that the management of the station, in terms of cultural and production practices, is appropriate to allow for expression of full yield potential for those breeding nurseries and yield trials that are used by the breeders to assess yielding ability.
In the mid-1980s, there was concern that soil-related issues—including low organic matter levels, soil compaction, and inadequate N inputs—may have been constraining yields. The experiment reported in this study was initiated to investigate several feasible cultural and/or management practices—including deep subsoiling, use of summer legumes (including a legume green manure crop) in rotation with wheat, and comparing the use of chemical N fertilizers alone or in combination with chicken (Gallus gallus domesticus) manure—that could likely lead to expression of high yield potential in the wheat crop. Deep knifing was practiced to break up compacted soil layers, which often form just below the depth of the normal cultivation horizon (usually 30 cm), permitting better penetration of roots to nutrients and water available at deeper soil levels. Organic animal manure was applied because of its unique nutritional properties, which a number of studies show are not as easily supplied in inorganic form. The leguminous green-manure crop sesbania (Sesbania sp.) was grown in the summer and incorporated before land preparation to provide an extra source of N as well as crop residues, which can contribute positively to soil organic matter. The trial was developed with a long-term perspective to evaluate the effect of year on performance for various treatments.
The data set consisted of one experiment, including 24 treatments for cultural practices, conducted over 10 yr (1988–1997) in Ciudad Obregón, México (Vargas et al., 1999). Each year the experiment was arranged in a randomized complete block design with three replicates. Treatments resulted from the combination of four factors: tillage at two levels (T = with deep knife, t = without deep knife), summer crop at two levels (S = sesbania, s = soybean), manure at two levels (M = with chicken manure, m = without chicken manure), and N fertilization rate at three levels (0 = 0 kg N ha-1, n = 100 kg N ha-1, and N = 200 kg N ha-1), resulting in 2 x 2 x 2 x 3 = 24 treatments. Treatment 1 is TSM0, Treatment 2 is tSM0, Treatment 3 is TsM0, and so on, so that Treatment 23 is TsmN and Treatment 24 is tsmN. Three levels of applied inorganic N were used representing a zero baseline, a moderate level of application (100 kg ha-1), and a relatively high level of application (200 kg ha-1).
The elements of the data matrix Y of size 10 x 24 were the grain yield interaction residuals ij - i. - .j + .. where ij is the response of the ith treatment in the jth environment, i. is the mean of the ith treatment, .j is the mean of the jth environment, and .. is the grand mean. There were 27 explanatory covariables in the Z matrix of size 10 x 27 (years x environmental variables): mean minimum temperature sheltered [°C] (mT), mean minimum temperature unsheltered [°C] (mTU), mean maximum temperature sheltered [°C] (MT), total monthly precipitation [mm] (PR), mean sun hours per day (SH), and total monthly evaporation [mm] (EV). All were measured during the growth cycle in December (D), January (J), February (F), March (M), and April (A).
All covariables were centered before analysis. Moreover, for PLS and for reasons of consistency with earlier analyses (Vargas et al., 1999), the columns of the Y matrix were standardized.
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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Only six treatment x year interaction (T x E) terms were highly significant (P < 0.001): year x tillage, year x summer crop, year x manure, year x N, year x summer crop x N, and year x manure x N. The four-factor interaction of year x summer crop x manure x N was marginally significant (P 
0.05), whereas the rest of the interaction terms were nonsignificant.
The analysis of variance including only the six highly significant interaction terms and partitioning the N effects into linear (NL) and quadratic (NQ) is shown in Table 2. Note that only 81 of the 207 df for interaction are used and that 87% of the sum of squares is explained, leaving a nonsignificant deviation. In terms of degrees of freedom and proportion of the year x treatment explained, these results were similar to those obtained by the AMMI model (Table 1). The AMMI with three bilinear interaction terms (87 df) explained 81% of the T x E, whereas in Table 2, 81 df described 87% of the interaction. However, the AMMI model still left a significant variation on the residuals, whereas this analysis did not. The year x N term contributes the most (45%) to the T x E sum of squares with only 18 df. The terms year x NL, year x summer crop x NL, and year x manure x NL explained at least 75% of the interaction. On the contrary, the corresponding NQ (year x NQ, year x summer crop x NQ, and year x manure x NQ) described, at the most, only 25% of the T x E.
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The first strategy for selecting the best covariables is to perform a MFR with the stepwise selection procedure for each of the 27 environmental covariables x factorial effect interactions; for example, compute a MFR for the environmental covariables x tillage interaction and select the environmental covariable that accounts for most of the variability. Similarly, this is done for the other five interaction terms (summer crop, manure, N, summer crop x N, and manure x N) that were significant. Then, with the environmental covariables selected in this manner, a MFR model is fitted.
Results for the MFR of the 27 environmental covariables x tillage interactions showed five significant covariables in the following order of importance: EVD, EVM, PRM, MTA, and mTM. However, only the EVD x tillage sum of squares was relevant, accounting for 68% of the whole year x tillage sum of squares (Table 3). (The contribution of the other four covariables to the year x tillage sum of squares was negligible.) The interaction between tillage and the environmental variable EVD may be explained by the fact that, in years when EV was higher in December, mild soil water deficit before scheduled irrigations might have been avoided in treatments where tillage had permitted roots to penetrate deeper into the soil profile. Alternatively, because yield was, on average, 0.5 Mg higher in years showing a response to tillage, high EVD (which is a function of higher radiation) may have been associated with better early stand establishment and more tillering. This in turn would provide a basis for higher yield potential in favorable years, especially where tillage permitted greater access to nutrients and water with depth.
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For manure, covariables PRD, SHF, MTD, MTM, and MTA were found to be significant, but only the first two were important, contributing to 56% of the year x manure sum of squares. This interaction may be explained by the ability of manure to buffer the detrimental effects of (i) mild water deficit (low PRD), which could otherwise reduce tillering and by (ii) low radiation during the critical spike growth stage (SHF). Both factors are important in determining yield potential. Both factors could also be related to improved nutritional status associated with manure application due to better nutrient availability in dryer soil for the first factor and higher leaf N levels permitting better canopy development and light interception for the second.
Nitrogen was the best contributor to the year x treatment interaction sum of squares where seven covariables were found to be significant: mTF, mTJ, MTA, mTM, PRM, EVM, and mTA. Only the first four were considered for further analyses, accounting for the 94% of the year x N sum of squares. No systematic trend in yield was apparent to explain the interaction between N levels and minimum temperatures. However, there was an interaction between lower maximum temperatures in April and N level. Cooler temperatures during the final stages of grain filling may delay senescence, and thus permit those lines with higher leaf N to prolong grain filling.
For year x summer crop x N interaction, the order of significant covariables was: MTF, mTJ, mTA, EVA, and EVM; however, the proportion of sum of squares accounted for by each covariable was relatively low, so only MTF was selected because it explained 46% of the year x summer crop x N sum of squares. Response to N was lower when maximum temperatures in February were higher where the summer crop was soybean. (Soybean treatment would be associated with reduced N availability compared with the green-manure summer crop.) This could be explained by the fact that a higher capacity for photosynthesis (associated with higher leaf N) is best realized under cooler conditions. Therefore, higher temperatures during the critical spike growth stage (i.e., in February) would reduce the potential benefit of higher leaf N.
Finally, for year x manure x N interaction, the significant covariables were: mTUM,nSHJ, MTM, PRJ, and MTF. Only the first two (mTUM and SHJ) were selected because they contributed to 78% of the year x manure x N sum of squares. In years with a high minimum temperature in March, higher N levels had less effect on yield when manure was present while in years with cooler minimum temperatures in March, the response to N was similar with or without manure. Warmer night temperatures during grain filling (i.e., March) would accelerate the cycle, and it is possible that the higher leaf N made available by higher levels of organic and inorganic N was not subsequently taken advantage of. No systematic trend was observed between the interaction of N level with manure and the environmental variable SHJ. It is interesting to note that, in almost all of the six significant year x treatment interaction terms, the environmental covariables selected left relatively low deviation sum of squares; however, they were still significant.
With the objective of finding a more parsimonious model, that is, a model that includes a small number of environmental covariables explaining as much of the T x E as possible, a MFR was fitted with the environmental covariables previously selected. This model (Table 3) accounted for 68% of the whole year x treatment interaction using only 18 df (out of 207 df). Notice that the most important variables contributing to the sum of squares are those related to the main effect of N, and four of them (mTF, mTJ, MTA, and mTM) accounted for 43% of the entire year x treatment interaction with only 8 df.
When the N effect is partitioned into linear and quadratic components, it is always found that the linear components are the most important (Table 4). The terms mTJ x NQ, MTA x NQ, and SHJ x manure x NQ were not significant, and thus were deleted from the model. The new model explained 67.63% of the year x treatment sum of squares with only 15 df. If the NQ are eliminated from the model, 62.39% of the year x treatment interaction is accounted for with 11 df.
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The last strategy tried selecting the most relevant environmental covariables for computing individual FR analyses by including in the model only the main effects of year and treatments and the interaction of each factor (tillage, manure, summer crop, and N) with each of the 27 environmental covariables. The covariables with the largest R2 were selected. The best individual models (data not shown) were: EVD x tillage, EVA x summer crop, PRD x manure, mTF x N, MTA x N, MTF x summer crop x N, and mTUM x manure x N. Again, these covariables are the same as the final MFR model given in Table 3 (and Table 4).
Biplots
The first bilinear interaction term of the AMMI analysis of the T x E accounted for 54% of the T x E sum of squares, the second accounted for 14%, and the third 13%, using 31, 29, and 27 df, respectively (Table 1). The first two bilinear terms accounted for 68% of the T x E sum of squares and used 60 of the total 207 df available in the interaction, whereas the first three bilinear terms explained 81% of the T x E with 87 df. These results are similar to those found in the factorial analyses of variance in Tables 1 and 2. However, the AMMI model does not allow decomposing of the whole T x E into its agronomic factorial components. It also does not allow partitioning of the year x treatment interaction into environmental variables x treatment interaction using the FR model and the MFR with the stepwise variable selection procedure.
The AMMI biplot with the first two bilinear terms and enriched with the seven environmental covariables with R2 > 0.50 values is shown in Fig. 1. The main results from the AMMI biplot were: (i) the four highest-yielding years (1994, 1988, 1997, and 1993) were separated from the four lowest-yielding years (1995, 1992, 1989, and 1996); (ii) the nine highest-yielding treatments (9, 19, 21, 17, 11, 12, 10, 23, and 18; five treatments had 200 kg N ha-1 and four had 100 kg N ha-1) are separated from the nine treatments with the lowest grain yield (1, 2, 3, 4, 5, 6, 7, 8, and 16; all had 0 kg N ha-1, except Treatment 16, which had 100 kg N ha-1); (iii) years 1988, 1990, 1991, and 1997 were positively associated with the covariables EVD, EVJ, EVA, SHJ, and MTF and had below-average values for mTM and mTUM; and (iv) years 1989, 1992, 1993, 1994, and 1995 had above-average values for covariables mTM and mTUM and below-average values for the other environmental covariables.
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The PLS biplot (Fig. 2) contains roughly five clusters of environmental covariables. The first cluster is in the lower left quadrant and includes correlated variables mTF, mTUF, MTA, and MTF. The second cluster is in the lower right quadrant and comprises correlated variables EVJ, EVF, EVM, EVA, MTJ, MTM, SHD, SHJ, and SHF. The third cluster involves mTA, mTUA, MTD, and EVD. The fourth group had mTJ, mTUJ, PRM, and PRJ. The fifth cluster includes mTM, mTUM, mTD, mTUD, PRD, and PRF.
In general, SH, EV, and MT are grouped in the right quadrants of the biplot, whereas PR, mT, and mTU are grouped in the left quadrant of the biplot. It is expected that with more sun hours, there will be higher maximum temperatures and more evaporation; also, with more precipitation, there will be fewer sun hours, and thus, lower temperature. This is clear for the lower right cluster of variables comprising MT, EV, and SH. The group of environmental variables located in the right upper quadrant indicates that minimum temperature in April with maximum temperature and evaporation in December had a similar effect on the T x E for the treatments located in that quadrant. The two groups of variables in the left upper quadrant indicate that minimum temperatures in December, January, and March are related to precipitation in December, January, and March.
From an agronomic perspective, if the crop was irrigated, variable precipitation should not be a limiting production factor. However, it was associated with treatments that had low average production (left quadrants of the biplot). Furthermore, the most highly productive treatments are associated with high N levels (100 and 200 kg ha-1) and no precipitation. The explanation may be that precipitation is associated with leaching of N (especially if the texture of the soil is coarse). In addition, higher precipitation is also associated with clouds, which reduce radiation. While radiation is the major yield-limiting factor when N and water are nonlimiting, high radiation may also be associated with higher temperatures and excessive evaporative demand. These factors may be confounding because a crop is most productive with a combination of high radiation for photosynthesis and cooler temperatures, which permit slower developmental rates. As already outlined, accelerated development rate may be especially prejudicial to yield during spike growth (February) and to a lesser extent during grain filling (March–April). Excessive evaporative demand may reduce the ability of the plant to cool itself directly by not permitting sufficient evapotranspiration or indirectly by reducing soil moisture.
It is interesting to note that the order of inclusion of the environmental covariables in the stepwise selection procedure for each factor effect (tillage, summer crop, manure, N, summer crop x N, and manure x N) corresponds to selecting covariables for different cluster groups depicted in the PLS biplot of Fig. 2. For example, in the case of tillage, the stepwise procedure first selected EVD from the cluster in the upper right quadrant. Next, it selected EVM from cluster located in the lower right quadrant. Then, it selected covariable PRM in the upper left quadrant cluster followed by covariable MTA in the lower left quadrant. Finally, covariable mTM was selected in the center left quadrant. This makes sense for the environmental variable EV because deep tillage allows roots to access water at a depth in the soil profile permitting sustained growth in years with high evaporative demand when the upper soil profile may become relatively dry before scheduled irrigation. The other variables would also be expected to influence water availability to the crop, directly in the case of precipitation and indirectly in the case of temperatures, which influence evaporative demand.
For summer crop, the order of inclusion of environmental covariables was EVA and SHF from second cluster, EVD from third cluster, and PRD and mTUM from fifth cluster. In the case of manure, the sequence was PRD from the fifth cluster, SHF from second cluster, MTD from third cluster, MTM from second cluster, and MTA from the first cluster. The factors summer crop, manure, and N have a direct effect on the nutrition of the crop, may interact with environmental variables as discussed previously.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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The analyses of this study show a basis for the interaction of agronomic practices with weather variables. For example, the interaction of deep tillage with evaporative demand confirms the benefit of this treatment under conditions that can lead to rapid drying of the soil surface layers. Similarly, the use of manure, which has been associated with more vigorous crop establishment (Badaruddin et al., 1999), was shown to be more beneficial in years where precipitation was low during crop establishment (i.e., December). Such analyses could be used to permit a more strategic and economically sound deployment of management factors by enabling the prediction of yield responses in light of long-term weather patterns.
Table A1. Mean grain yield (kg ha-1) of 24 treatments (Treat) evaluated over 10 yr.
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T, with deep knife; t, without deep knife; S, sesbania; s, soybean; M, with chicken manure; m, without chicken manure; 0, 0 kg N ha-1; n, 100 kg N ha-1; N, 200 kg N ha-1.
Table A2. Grain yield (kg ha-1) of the treatment by environment interaction [T x E] (residuals) of 24 treatment (Treat) evaluated over 10 yr.
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T, with deep knife; t, without deep knife; S, sesbania; s, soybean; M, with chicken manure; m, without chicken manure; 0, 0 kg N ha-1; n, 100 kg N ha-1; N, 200 kg N ha-1.
Table A3. Environmental variables (Var) collected during the 10 yr that 24 treatments were evaluated.
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