Stability analysis of farmer participatory trials for conservation agriculture using mixed models

Field Crops Research 121 (2011) 450–459

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Stability analysis of farmer participatory trials for conservation agriculture using mixed models Anitha Raman a , Jagdish K. Ladha a,∗ , Virender Kumar a , Sheetal Sharma a , H.P. Piepho b a b

International Rice Research Institute (IRRI), 1st Floor, CG Block, NASC Complex, DPS Marg, Pusa, New Delhi 110 012, India Universitaet Hohenheim, Bioinformatics Unit, 70593 Stuttgart, Germany

a r t i c l e

i n f o

Article history: Received 26 October 2010 Received in revised form 31 January 2011 Accepted 1 February 2011 Keywords: Resource conserving technologies Stability analysis SAS mixed model Rice–wheat cropping system Farmers’ participatory trials

a b s t r a c t Normally, the data generated from farmer participatory trials (FPT) are highly unbalanced due to variation in the number of replicates of different treatments, the use of different varieties, farmers’ management of the trials, and their preferences for testing different treatments. The incomplete nature of the data makes mixed models the preferred class of models for the analysis. When assessing the relative performances of technologies, stability over a range of environments is an important attribute to consider. Most of the common models for stability may be fitted in a mixed-model framework where environments are a random factor and treatments are fixed. Data from on-farm trials conducted in the Indo-Gangetic Plain (IGP) of South Asia under the umbrella of Rice–Wheat Consortium (RWC) were analyzed for grain yield stability using different stability models. The objective was to compare improved resource management technologies with farmers’ practice. The variance components of an appropriate mixed model serve as measures of stability. Stability models were compared allowing for (i) heterogeneity of error variances and (ii) heterogeneity of variances between environments for farmers-within-environment effects. Mean comparisons of the treatments were made on the basis of the best fitting stability model. Reducedtill (non-puddled) transplanted rice (RT-TPR) and reduced-till drill-seeded wheat using a power tiller – operated seeder with integrated crop and resource management RTDSW(PTOS)ICRM ranked first in terms of both adjusted mean yield and stability. © 2011 Elsevier B.V. All rights reserved.

1. Introduction On-farm farmer participatory trials (FPT) involve active participation by the farmers in evaluating a technology under a wide range of farm conditions. The purpose and strength of farmer participatory testing lies in effectively assessing the effect of farmer resources and management on the technology (Petersen, 1994). FPTs are conducted across different locations and years to test different technologies within the target area. The data generated from these multi-environment trials are highly unbalanced due to variations in the number of replications of different treatments, the choice of different varieties, farmers’ management of the trials and their preferences for testing any subset of treatments. The variability inherent in on-farm and participatory work can produce irregularity in design and the need for more flexible statistical methods than are normally available to researchers (Stroup et al., 1993). The statistical methods used for the analysis of multi-environment varietal testing across years and sites can serve as useful tools in analyzing data from on-farm participatory

∗ Corresponding author. Tel.: +91 11 25843802/1292; fax: +91 11 25841801. E-mail address: [email protected] (J.K. Ladha). 0378-4290/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.fcr.2011.02.001

trials (Riley and Alexander, 1997). These include the simple analysis of variance, regression approach, multivariate methodologies, the additive main effects and multiplicative interaction (AMMI) model as well as the powerful and flexible mixed-model which uses restricted maximum likelihood methodology (REML) algorithm. Kidula et al. (2000) suggested that the traditional methods of analysis of variance (ANOVA) which emphasize hypothesis testing and significance levels cannot accommodate the complexity of FPTs data. This is largely because the main focus in FPTs is on prediction and taking action. Therefore, they recommended a combination of mixed-model procedures and stability analysis in order to arrive at meaningful conclusions. Likewise, Coe (2007) pointed out that the standard tools based on ANOVA are not appropriate. He demonstrated with examples the usefulness of mixed-model methodology for analysing FPT data with irregular design. Virk et al. (2009) successfully used restricted maximum likelihood (REML) to analyze quantitative traits of very highly unbalanced on-farm participatory varietal selection (PVS) trials. Parsad et al. (2009) emphasized the usefulness of mixed models to analyze the data generated from FPTs, considering the farmer or field effects as random and treatment effects as fixed. When assessing the relative performance of various technologies/practices, stability of their performances is an important

A. Raman et al. / Field Crops Research 121 (2011) 450–459

attribute to consider. Stability can be ascertained using various stability statistics (for review see Lin et al., 1986; Westcott, 1987; Becker and Leon, 1988; Piepho, 1998a). Traditional measures of stability include environmental variance (Lin et al., 1986), coefficient of variation (Francis and Kannenberg, 1978) and Shukla’s stability variance (Shukla, 1972). Modified stability analysis as suggested by Hildebrand (1984) used the regression approach of Finlay and Wilkinson (1963) and Eberhart and Russell (1966) to assess the stability of treatments under different farmer management systems over a wide range of environmental conditions. There are three indicators of stability in regression analysis (i) coefficient of regression (b), (ii) variance of deviations from regression (sb2 ), and (iii) treatment mean. The regression coefficients which have a mean of unity indicate the rate at which the performance of a treatment varies relative to the changes in the environment. The variance of deviations indicates the reliability of the regression relationship. Denis et al. (1997) and Piepho (1999) suggested that most of the common stability measures may be embedded in a mixed-model framework where environments are a random and treatments are a fixed factor. Piepho (1999) showed how mixed model analyses of unbalanced data for the most common stability measures are readily available through the variance structures fitted using SAS procedure MIXED. Piepho and van Eeuwijk (2002) demonstrated with a realistic example the choice of an appropriate model and the interpretation of variance components as measures of stability. In their analysis the environments (locations, years) were considered as random factor and genotypes as fixed. An alternative approach to the regression analysis is the additive main effects and multiplicative interaction (AMMI) model (Kempton, 1984; Zobel et al., 1988; Gauch, 1992). The AMMI model was originally proposed as a fixed effects model. Assuming environments (or treatments) as random, the treatment × environment interaction can be analyzed in a mixed-model framework with a factor-analytic covariance structure to model the multiplicative terms (Piepho, 1997b). The rice–wheat (RW) system is the lifeline of millions of food producers and consumers in the Indo-Gangetic Plains (IGP) of South Asia. The system has contributed to reducing poverty and hunger during the Green Revolution. Recently, however, widespread stagnation or decline of crop productivity and rising cost of cultivation have been reported. Since the demand of these two cereals has been projected to increase by more than 50% in 2020 and resources such as water and labor are going to be scarce, enhancing productivity and input-use efficiency are urgently needed. A number of improved land and crop management practices suitable for farmers in the region often termed as resource-conserving technologies (RCTs) have been developed and disseminated in the IGP under the umbrella of the Rice–Wheat Consortium (RWC) (for review see Gupta et al., 2002; Ladha et al., 2009b). The new RCTs have been integrated into the existing portfolio of technologies already being practiced by farmers in the framework of integrated crop and resource management (ICRM) (Ladha et al., 2009a). ICRM includes optimal land preparation, water management, crop establishment as well as nutrient, pest and weed management. Researchers and extensionists evaluate rice–wheat production component technologies within the framework of ICRM in farmers’ fields in order to promote the successful ones at large to enhance sustainability and profitability of the farmers. On-farm farmer participatory trials are being conducted to compare various improved component technologies (RCTs) such as reduced, zero-tillage, drillseeding either on flat or on raised beds, and nutrient management with that of typical farmer practice. The trials wherein the RCTs form the treatments are fully managed by the participating farmers in their fields under a range of conditions with a view to assess their overall performance and consistency. Often, the FPTs are conducted without a proper design at different locations/farmer fields and

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years. The data generated have large variability which complicates analysis. The objectives of the paper were to (a) illustrate the yield stability analysis of a highly unbalanced data that originated from FPTs, incorporating heterogeneity of error variances and heterogeneity of variances between environments at farmer level, and (b) perform mean comparisons for the treatments using the best fitting stability model. The data used in this analysis came from 1985 on-farm FPTs conducted during 2005–2008 at various sites in Bangladesh, India and Nepal. Appendix A provides the list and brief description of technologies used. 2. Materials and methods 2.1. Trial management The study was conducted at 6 locations in the IGP of Bangladesh (Kushtia and Dinajpur), India (Modipuram, Karnal and Ballia) and Nepal (Bhairahawa) from 2005 to 2008. Table 1 provides the list of number of participating farmers and technologies at different sites. The trials were researcher designed and farmer managed. Farmers used a wide range of rice and wheat varieties. The most common rice varieties were Swarna (MTU = 7029) and Sarjoo – 52. Other rice cultivars included Sambha Mahsuri (BPT – 5204), Sonum, HUBR – 3022, Sarbati, HKR – 47, HKR – 26, Pusa – 1121, Pioneer – 71, Garima, Moti, Kalinga, IDR – 763, Jaisuria and Sengra; and in wheat, UP – 2338, PBW – 343, PBW – 502 and Malviya – 234. Farmers chose technologies and sometimes made minor modifications to suit their local needs. Therefore the number of technologies (referred to as treatments) used by the farmers varied from farmer to farmer, meaning that farms constitute incomplete blocks. 2.2. Statistical analysis The data were analyzed using the site × year cross classification (henceforth referred to as environments – Table 2) thereby leading to a simpler statistical model. The data were first subjected to regular analysis of variance with fixed effects for treatment, environment, farmers nested within environments and treatment by environment interaction. Yield yijk of the ith treatment for the kth farmer in the jth environment is modelled as: yijk =  + ti + ej + fkj + (te)ij + εijk

(1)

where all effects except the residual error term are fixed.  is the overall mean, ti is the treatment main effect, ej is the environment main effect, fkj is the effect of the kth farmer within jth environment, (te)ij is the interaction between treatment i and environment j and εijk is the error. Heterogeneity of error variances among environments was investigated by examining a plot of the standardized residuals against the fitted response. A mixed model was then fitted by considering treatment as fixed effect, and environment, farmer within environment and treatment × environment effects as the random effects. The treatments are considered fixed as the treatments included in the study were carefully selected and are the only treatments of interest (Searle et al., 1992). When assessing stability, the prime objective is to assess variability of yields across environments from a target population of environments. Thus, most stability measures are, in fact, variance components or related quantities. These measures make sense only if a random set of environments is studied, and this dictates that the environment factor be random. Farmers within environment represented a random sample of farmers within the environment. Four variance structures which represented six stability measures were fitted to the treatment × environment interaction using the MIXED procedure of SAS (Littell et al., 2006). This used the REML procedure for estimating variance compo-

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Table 1 Technologies and total number of participating farmers (2005–2008) in rice and wheat. Treatment

Rice

Treatment

India Ballia

Wheat Bangladesh

Modipuram

India Ballia

Nepal Karnal

52 8 11 – – – 71

156 14 92 49 11 23 345

CT-BCW RT-DSW RT-DSW(PTOS)-(ICRM) Bed-DSW ZT-DSW ZT-DSW-(ICRM) Total

9 9 9 – – 9 36

50 – – 63 – 113

46 – – 24 26 – 96

7 19 – – 35 – 61

24

23 93

34 1 42 2 2 – 81

2006–2007 CT-TPR CT-DrumR RT-DSR RT-TPR Bed-TPR ZT-DSR Total

19 1 12 – – 16 48

28 – 22 44 8 – 102

20 – 36 – – 3 59

82 10 6 – – – 98

149 11 76 44 8 19 307

CT-BCW RT-DSW RT-DSW(PTOS)-(ICRM) Bed-DSW ZT-DSW ZT-DSW-(ICRM) Total

9 9 9 – – 9 36

54 5 – 6 70 – 135

38 – – 9 39 – 86

21 – – – 42 – 63

77 4 – – 70 151

2007–2008 CT-TPR CT-DrumR RT-DSR RT-TPR Bed-TPR ZT-DSR Total

59 – 18 6 2 21 106

14 – 14 2 – – 30

17 – 17 – – – 34

– 0 – – – –

90 49 8 2 21 170

CT-BCW RT-DSW RT-DSW(PTOS)-(ICRM) Bed-DSW ZT-DSW ZT-DSW-(ICRM)Total

44 18 44 – – – 88

48 – – 7 90 – 163

10 – – 10 10 – 30

18 – – – 22 – 40

– 18 – – – – –

247

232

174

169

822

Grand total

160

411

212

164

216

– Indicates none.

Total

Modipuram

24 – 20 47 9 – 100

Grand total Grand total (rice + wheat)

46 5 19 –

Karnal

Total

21 – – 20 65

136 28 30 24 124 29 371

199 14 13 15 151 79 471

120 44 17 122 321 1163 1985

A. Raman et al. / Field Crops Research 121 (2011) 450–459

2005–2006 CT-TPR CT-DrumR RT-DSR RT-TPR Bed-TPR ZT-DSR Total

Nepal

A. Raman et al. / Field Crops Research 121 (2011) 450–459

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Table 2 Rice and wheat environments (site × year classification). Rice

Wheat

Year

Site

Environment

Year

Site

Environment

2005 2005 2005 2006 2006 2006 2007 2007 2005 2006 2007

Ballia Karnal NepalTarai Ballia Karnal NepalTarai Ballia Karnal Modipuram Modipuram Modipuram

1 2 3 4 5 6 7 8 9 10 11

2005 2005 2005 2005 2005 2006 2006 2006 2006 2006 2007 2007 2007 2007

Ballia Bangladesh Karnal Modipuram NepalTarai Ballia Bangladesh Karnal Modipuram NepalTarai Ballia Bangladesh Karnal Modipuram

1 2 2 4 5 6 7 8 9 10 11 12 13 14

nents. Our stability analyses were based on variance–covariance structures for treatment-within-environment effects hij , which in model (1) take the form hij = ej + (te)ij . Specifically, we consider the variance–covariance matrix for the random vector hj = (h1j , h2j , ..., hpj ), where p is the number of treatments. The variance structures were

distributed with zero mean and unit variance. The interaction is thus described as the product of the sensitivity or the tendency of a treatment to respond to an environmental change (factor loadings) and a measure of the characteristic of the environment (factor scores). ıij is a residual which may either have constant 2 associated with treatment variance ı2 or a specific variance ı(i)

(i) Compound symmetry (CS): CS is often an overly simplistic structure for var(hj ) which requires just two parameters, 2 ) which is the the homoscedastic diagonal elements (e2 + te variance corresponding to each treatment and a constant 2 = var[(te) ]. Accordcovariance e2 , where e2 = var(ej ) and te ij ing to this model the treatments do not differ in stability. (ii) Heterogeneous compound symmetry: Being an extension of the compound symmetry model, this structure has p + 1 parameters. This includes the p treatment-specific variances 12 , 22 , ..., p2 on the diagonal and each pair of treatments i and j have their own covariance on the off-diagonals given by  i  j where  is the common correlation between treatments whose value is less than unity. (iii) Stability variance components: Shukla’s stability variance model (Shukla, 1972) is another extension of the CS model, in which 2 a treatment-specific interaction variance component te(i) = var[(te)ij ] is fitted. The treatment with a small stability variance is considered as most stable. (iv) Factor-analytic covariance structure: Mixed models with multiplicative terms are closely related to the factor-analytic variance–covariance structure (Piepho, 1997b). The variances of the treatments often differ and the responses of some pairs of treatments are more similar than those of others. This is handled efficiently by the factor-analytic model (Piepho and van Eeuwijk, 2002). Analysing multi-environment trial data with a factor-analytic variance–covariance structure was recommended by Piepho (1997a,b), Piepho (1998b), Smith et al. (2001), Resende and Thompson (2004), Kelly et al. (2007) and Burgueno et al. (2008). But some of these take treatments random and environments fixed, e.g. Piepho (1998b) and Smith et al. (2001), which is a slightly different use of the model. The factor-analytic structure for the interaction of treatment i in environment j is given by:

i (Piepho, 1998a). A factor-analytic (FA) structure involving one factor together with equal or unequal specific variances for the treatments corresponds to the Finlay–Wilkinson model – FA1(1) and Eberhart–Russell model – FA(1), respectively (Piepho, 1997a). When it involves q multiplicative terms together with an environment main effect, it corresponds to the mixed model version of AMMI(q) – FA1(q) or FA(q) structure. Two sets of stability models were fitted allowing either for (i) heterogeneity of variances between environments for errors or (ii) heterogeneity of variances between environments for both error and farmers-within-environment effects. In the latter case, a CS structure was fitted to gjk , where gjk is a vector of effects gijk = fjk + εijk for the kth farmer in the jth environment, and the parameters of this structure were allowed to vary between environments. The CS model accounts for correlations among observations on different treatments tested by the same farmer. There are two parameters for each environment, (1) the diagonal variance corresponding to each farmer and (2) the off-diagonal covariance between farmers. Note that this model allows for heterogeneity of variance simultaneously for both farmer effects fjk and errors εijk . In both cases multiple mean comparisons among the treatments across environments for the best fitting model were performed using the algorithm for a compact letter display of comparisons for unbalanced data (Piepho, 2004). The Akaike Information Criterion (AIC) was used to select the best-fitting variance–covariance structure (stability model). The smaller the AIC the better is the performance of the model. Since REML was used, only models with the same fixed-effects structure can be compared. AIC is preferred over the Bayesian Information Criterion (BIC), because the latter has a penalty that involves sample size in terms of independent observational units, and the concept of “effective” sample size is not well defined for mixed models, where random effects give rise to possibly complex dependencies among observations. In fact, there is no established definition of BIC for mixed models (Pauler, 1998).

(te)ij =

q 

im wjm + ıij

m=1

where im is the factor loading for the factor m associated with treatment i, which can be interpreted as the sensitivity of the ith treatment to environmental changes, wjm is the mth factor (environmental) score for environment j which are random normally

3. Results 3.1. ANOVA The conventional analysis of variance for grain yield for both rice and wheat showed highly significant (p < 0.0001) environ-

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Table 3 Akaike’s Information Criterion (AIC) values for stability models with heterogeneous error variances and homogeneous variance across environments for farmer within environment effect. Model

Rice

Wheat

Compound symmetry Heterogeneous compound symmetry Finlay–Wilkinson Eberhart–Russell AMMI Shukla

1799.7 1804.1 1803.6 1801.8 1805.4 1797.6

1717.4 1715.2 1718.1 1709.6 1700.7 1705.5

ment (ej ), treatment × environment interaction [(te)ij ] and farmer within environment effects (fkj ). Treatment effects were highly significant (p < 0.0001) in case of wheat, whereas treatments were non-significant (p = 0.0615) at 5% level in case of rice. A plot of residual vs. predicted values for the model that accommodates heterogeneity of error variances across environments for rice and wheat had a completely random scatter of points indicating a well fitting model (data not shown).

than at the level of treatment × environment interaction effects. CT2 = 0.08, SE = 0.16) DrumR had the lowest stability variance (te(2)

2 2 = 0.11, SE = 0.06) and RT-TPR (te(5) followed by CT-TPR (te(3) = 0.12, SE = 0.11) which were at par. ZT-DSR had the highest stability 2 = 0.52, SE = 0.5) (Table 5). variance (te(6) In wheat, assuming heterogeneity of errors, AMMI model with one multiplicative term [AMMI(1)] was the best model to assess stability (AIC = 1700.7) (Table 6). ZT-DSW-(ICRM) had a relatively large factor loading (6 = 2.14, SE = 0.87) which indicates higher sensitivity to changing environmental conditions. RT-DSW-(PTOS)(ICRM) was the best performer in terms of stability (4 = 0.61, SE = 0.22) followed by ZT-DSW (5 = 0.65, SE = 0.17). Fitting heterogeneous variance across environments for the farmer within environment effect (Table 5) showed considerable improvement in the fit for AMMI (1) model (AIC = 1579.7). Again, RT-DSW (PTOS)-(ICRM) (4 = 0.60, SE = 0.22) had an above-average stability to environmental changes while ZT-DSW-(ICRM) had an above average sensitivity (6 = 2.19, SE = 0.89) to environmental changes (Table 5).

3.2. Stability analysis

3.3. Mean comparison

In rice, assuming heterogeneity of errors and homogeneous variances across environments for the farmer within environment effect, the best fitting model based on the lowest AIC value (Table 3) was the Shukla model (AIC = 1797.6). The parameters of all six stability models are presented in Table 4. Based on Shukla’s model, RT-TPR had the lowest stability variance, in other words maxi2 mum stability (te(5) = 0.11, standard error (SE) = 0.09) followed by

In rice, based on the Shukla’s model with heterogeneous error, ZT-DSR was the highest yielder (4.82 tonnes SE = 0.41) but with a comparatively bigger standard error (Table 7). The mean yield of RT-TPR (4.74 t ha−1 , SE = 0.34) was similar to that of farmers’ practice CT-TPR (4.50 t ha−1 , SE = 0.30). The Shukla model incorporating heterogeneous variances for farmer-within-environment effect produced very similar results. The AMMI-1 model with heterogeneous error in wheat did not show significant differences between the treatment means (Table 7). Based on the AMMI-1 model with heterogeneous variances for farmer-within-environment effect, ZT-DSW-(ICRM) (4.14 t ha−1 SE = 0.68) was the best yielder but with larger standard error as compared to all other treatments. Bed-DSW (4.16 t ha−1 , SE = 0.26) and RT-DSW-(PTOS)-(ICRM) (3.93 t ha−1 , SE = 0.27) were closer in terms of mean yield.

the conventional farmer’s practice CT-TPR ( 2 te(3) = 0.14, SE = 0.07). ZT-DSR had the highest stability variance or minimum stability 2 (te(6) = 0.31, SE = 0.32). The stability variances of Bed-TPR, CTDrumR and RT-DSR converged to 0, indicating maximum stability (Shukla, 1972). Incorporating heterogeneity of variances between environments for farmers-within-environment effect improved the fit for Shukla’s model with an AIC value of 1701.1 indicating that heterogeneity may be dominant at the farmer level rather

Table 4 REML parameters for stability models with heterogeneous error variance for the 6 treatments tested in 11 on-farm rice environments. Parameters corresponding to treatment × environment interaction Treatment

AMMI – 1 i

Bed-TPR 0.43 CT-DrumR 0.24 CT-TPR 0.71 RT-DSR 0.48 RT-TPR 0.77 ZT-DSR −0.17 Other variance components Farmer (environment) 0.63 Environment 0.53 Environment-specific residual variances Env 1 Env 2 Env 3 Env 4 Env 5 Env 6 Env 7 Env 8 Env 9

Shukla

Eberhart–Russell

Finlay–Wilkinson

Heterogeneous compound symmetry

Compound symmetry

2 ı(i)

2 te(i)

i

2 ı(i)

i

ı2

i2



e2

0.03 0.03 0.03 0.03 0.03 0.03

0 0 0.14 0 0.11 0.31

0.70 1.10 1.014 0.85 1.16 −1.61

0 0.15 0 0.09 0.06 0

0.70 1.09 1.0 0.90 1.13 −1.38

0.05 0.05 0.05 0.05 0.05 0.05

0.477 0.966 1.034 0.846 1.267 0

0.95 0.95 0.95 0.95 0.95 0.95

0.08 0.08 0.08 0.08 0.08 0.08

0.17 0.31 0.38 0.44 0.10 0.19 0.34 0.24 0.04

0.63 0.84

0.63

0.63

0.62

0.62 0.90

0.17 0.31 0.38 0.44 0.10 0.19 0.34 0.24 0.04

0.17 0.31 0.38 0.43 0.10 0.20 0.33 0.24 0.04

0.17 0.31 0.38 0.43 0.10 0.19 0.33 0.24 0.04

0.17 0.31 0.38 0.43 0.10 0.19 0.34 0.24 0.04

0.17 0.31 0.38 0.43 0.10 0.19 0.34 0.24 0.04

i is the coefficient of regression in the case of Eberhart–Russell and Finlay–Wilkinson models and is the sensitivity of the tth treatment to environmental changes in the case 2 2 is the specific variance associated with treatment i. te(i) in the Shukla model is the stability variance associated with each treatment. ı2 is the deviation of AMMI model. ı(i) from regression. i2 in the compound symmetry model is the variance component corresponding to the ith treatment. e2 in the compound symmetry model is the variance component corresponding to the treatments.

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Table 5 Best fitting stability models for rice and wheat incorporating heterogeneity of variances between environments for farmers-within-environment effect. Rice Treatment

Wheat Shukla 2 te(i)

Treatment

AMMI – 1 i

Parameters corresponding to treatment × environment interaction Bed-TPR 0 Bed-DSW 0 CT-DrumR 0.08 CT-BCW 0.91 CT-TPR 0.11 RT-DSW 0.71 RT-DSR 0 RT-DSW(PTOS)-(ICRM) 0.6 RT-TPR 0.12 ZT-DSW 0.66 ZT-DSR 0.52 ZT-DSW-(ICRM) 2.2 Other variance components Environment 0.93 0.67 Heterogeneity of variances between environments for both farmers-within-environment and error effects. (compound symmetry structure) 0.17 0.06 Env 1 Variance (fjk ) 0.38 0.5 Covariance (εijk ) Env 2 Variance 0.32 0.02 Covariance 0.05 0.02 Env 3 Variance 0.51 0.1 Covariance 0.07 0.23 Env 4 Variance 0.31 0.02 Covariance 2.92 0.18 Env 5 Variance 0.11 0.14 Covariance 0.04 0.09 Env 6 Variance 0.27 0.13 Covariance 0.25 0.33 Env 7 Variance 0.3 0.03 Covariance 1.07 0 Env 8 Variance 0.24 0.09 Covariance 0.5 0.1 Env 9 Variance 0.04 0.21 Covariance 0.58 0.07 Env 10 Variance 0.13 0.07 Covariance 2 0.28 Env 11 Variance 0.11 1.04 Covariance 0.58 0.31 Env 12 Variance – 0.04 Covariance – 0 Env 13 Variance – 0.06 Covariance – 0.06 Env 14 Variance – 0 Covariance – 0.05

4. Discussion With on-farm/farmer participatory trials new technologies are tested for wide adoption. The difficulty in analyzing data from these trials is the great variation among the chosen farmers due to the quality and quantity of their resources and their methods of evaluation (Nair, 1993). Farmers are as heterogeneous as their environments (Crossa et al., 2002). Within these trials, information can be at various levels, i.e. sites, farms within sites or plot within farms, and variation in the responses may arise due to variability at site-to-site, farm-to-farm or plot-to-plot level. The usual analysis of variance is inappropriate for data with such multi-layered structure and differing amount of information at each level. The different layers of variability are effectively incorporated and accounted for by a mixed model. Mixed-model analysis also allows multi-layered data information to be combined from multiple experiments conducted over time and space (Virk et al., 2009). Farmers are most interested in technologies that are low risk and perform well across a wide range of environments with respect to grain yield. Such technologies are likely to be widely accepted. The farmer’s decision on adopting a technology depends on a variety of factors but the yield component of the decision is most often attributed to stability - for sustenance and economic benefits. Farmers perceive yield stability as the most important socio-economic aim to minimize crop failure, especially in marginal environments (Fikere et al., 2008). On the other hand, stability analysis of treatments that effectively accounts for the treatment × environment

2 ı(i)

0.0003 0.0003 0.0003 0.0003 0.0003 0.0003

interaction is paramount for researchers conducting on-farm trials. Treatments may differ in stability across environments. Considering treatments as fixed and environments as random, this heterogeneity of stability can be modeled using a suitable variance–covariance structure within the mixed model framework. Different concepts of stability require different covariance structures. This leads to a variance–covariance matrix of the treatment × environment effects where the diagonal elements represent the treatment-specific variances and the off-diagonals are the pairwise covariances. A simple structure is the compound symmetry with only two parameters in case the heterogeneity model is complex for the data. One way to model heterogeneity of stability is in the form of genotype specific variances as in the case of Shukla’s model. Alternatively multiplicative models that give rise to a factor-analytic covariance structure account for correlation among interactions. The choice of the most appropriate model is of fundamental importance to identify the best treatment. Where treatments are evaluated in different environments, different experiments often have different levels of error variation as the trials are conducted with different levels of precision. In addition to the heterogeneous error variances, there often are heterogeneous interaction variances. Our data set has served to demonstrate both types of heterogeneity in the context of on-farm trials. Heterogeneity of treatment × environment interactions has been used as a measure of treatment stability, while including the

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Table 6 REML parameters for stability models with heterogeneous error variance for the 6 treatments tested in 14 on-farm wheat environments. Parameters corresponding to treatment × environment interaction Treatment

AMMI – 1 i

Bed-DSW 0 CT-BCW 0.91 RT-DSW 0.71 RT-DSW(PTOS)-(ICRM) 0.61 ZT-DSW 0.65 ZT-DSW-(ICRM) 2.14 Other variance components Farm 0.20 Environment 0.62 Environment-specific residual variances Env 1 Env 2 Env 3 Env 4 Env 5 Env 6 Env 7 Env 8 Env 9 Env 10 Env 11 Env 12 Env 13 Env 14

Shukla

Eberhart–Russell

Finlay–Wilkinson

Heterogeneous compound symmetry

Compound symmetry

2 ı(i)

2 te(i)

i

2 ı(i)

i

ı2

i2



e2

0.0004 0.0004 0.0004 0.0004 0.0004 0.0004

0.63 0.06 0 0.003 0 0.27

0.49 0 0.08 0.01 0.04 0.18

0 0.97 0.79 1.12 0.71 1.60

0 0.94 0.82 0.91 0.68 1.56

0.08 0.08 0.08 0.08 0.08 0.08

12.31 0.93 0.67 0.9 0.56 2.39

0.95 0.95 0.95 0.95 0.95 0.95

0.14 0.14 0.14 0.14 0.14 0.14

0.20 0.78

0.19

0.07 0.02 0.10 0.02 0.11 0.14 0.03 0.08 0.20 0.07 1.13 0.04 0.06 0.004

0.07 0.02 0.10 0.02 0.11 0.14 0.03 0.08 0.20 0.07 1.12 0.04 0.06 0.004

0.19

0.07 0.02 0.10 0.02 0.11 0.14 0.03 0.08 0.20 0.07 1.11 0.04 0.06 0.004

0.19

0.07 0.02 0.10 0.02 0.11 0.14 0.03 0.08 0.20 0.07 1.11 0.04 0.06 0.004

0.19 0.70 0.07 0.02 0.10 0.02 0.11 0.14 0.03 0.08 0.20 0.07 1.11 0.04 0.06 0.004

0.07 0.02 0.10 0.02 0.11 0.14 0.03 0.08 0.20 0.07 1.10 0.04 0.06 0.004

i is the coefficient of regression in the case of Eberhart–Russell and Finlay–Wilkinson models and is the sensitivity of the tth treatment to environmental changes in the case 2 2 is the specific variance associated with treatment i. te(i) in the Shukla model is the stability variance associated with each treatment. ı2 is the deviation of AMMI model. ı(i) from regression. i2 in the compound symmetry model is the variance component corresponding to the ith treatment. e2 in the compound symmetry model is the variance component corresponding to the treatments.

heterogeneity of farmer × environment effects further improved the fit for the best fitting stability model. A simple compound symmetry structure was fitted to the farmer × environment effect but other structures may also be considered. Investigation of variance stratification is paramount. Failure to account for heterogeneity can lead to inefficient and possibly misleading inferences for fixed effects (Littell et al., 2006). Modeling of variance–covariance structure also serves as a prerequisite for valid inferences on mean responses (Denis et al., 1997; van Eeuwijk, 2006). Treatment means are adjusted for site and farm effects. Compared to simple arithmetic treatment means, computation of adjusted means based on a mixed model for unbalanced data means makes sure that treatments not tested at good farms are adjusted upwards and treatments not tested at bad farms are adjusted downwards (Coe, 2007). The Wald-type F-statistics reported by REML packages are used to make inferences about the fixed effects, accounting for the variance–covariance model that is selected.

Therefore a combination of mixed-model and stability analysis may serve as an aid to successfully interpret data from on-farm trials and draw meaningful conclusions from them. Both yield and stability of performance should be considered simultaneously to make recommendations precise. Rice is commonly grown by transplanting rice seedlings into puddled soil (CT-TPR). This practice requires large resources (labor, water, and energy) which are becoming increasingly scarce and costing more to the farmers (Ladha et al., 2009a). Soil puddling also deteriorates soil physical properties (Sharma et al., 2003; Gathala et al, personal communication) and adversely affects the performance of the succeeding wheat crop (Kumar et al., 2008; Kumar and Ladha, 2011). All these factors force to identify alternative practices (RCTs) of growing rice which are equally or more productive and sustainable or stable across time and space. Based on the best fitting Shukla model, reduced tillage (RT-TPR) and farmers’ conventional tillage (CT-TPR) were similar in terms of both stability and predicted yield. Therefore reduced tillage (RT-TPR) could be

Table 7 Mean comparisons based on best fitting stability models for rice and wheat incorporating error variances and heterogeneity of variances between environments for farmerswithin-environment effects. Rice yield (t ha−1 )

Wheat yield (t ha−1 )

Treatment

Heterogeneous error variance

Heterogeneity of variances between environments for farmers-within-environment effects

Treatment

Heterogeneous error variance

Heterogeneity of variances between environments for farmers-within-environment effects

Bed-TPR CT-DrumR CT-TPR RT-DSR RT-TPR ZT-DSR

4.29 b a 4.01 a 4.50 c b 4.62 c 4.74 c b 4.82 c a

4.25 a 4.15 b a 4.43 b a 4.59 b 4.96 b 4.97 b a

Bed-DSW CT-BCW RT-DSW RT-DSW(PTOS)-(ICRM) ZT-DSW ZT-DSW-(ICRM)

4.16 3.21 3.47 3.92 3.43 4.16

4.16 c 3.22 a 3.47 b 3.93 c 3.42 b 4.14 c b

Means followed by a common letter are not significantly different at 5% level of significance.

A. Raman et al. / Field Crops Research 121 (2011) 450–459

recommended in place of farmers’ conventional tillage (CT-TPR). RT-TPR provides an opportunity to grow rice without soil puddling and saves irrigation water without compromising on yield. RT-TPR increased the income of the farmers by US$ 63 ha−1 with 90 mm less irrigation water application without compromising yield (Ladha et al., 2009a). Bed-TPR, CT-DrumR and RT-DSR could also be rated as most stable. However, it should be noted that the variances of these treatments converged to zero as a result of the boundary constraint imposed by default on all variance components. ZT-DSR was poor in terms of stability with a large standard error but yielded well. Many researchers have reported inconsistent performance of ZTDSR (Kumar and Ladha, 2011). ZT-DSR offers greater potential in reducing production costs and savings in labor, water, and energy, and is therefore, more attractive to the farmers. Results suggest the need for further refinement of ZT-DSR before introducing to large scale dissemination in different environments/regions/ecosystems. In farmers’s conventional practice in rice–wheat rotation, wheat is conventionally established by repeated ploughing (6–8 ploughing), cultivating, planking, and pulverizing of topsoil. The long turn around period (3–5 weeks) coupled with intensive tillage

457

operations delays wheat planting resulting in significant yield loss (Pathak et al., 2003). Therefore, timely planting of wheat after rice is crucial for maximizing wheat yields in the rice–wheat cropping system. The RCT options evaluated in the current analysis yielded more with high stability than conventional farmer’s practice (CTBCW) except ZT-DSW-(ICRM). The ZT-DSW-(ICRM) treatment was tried in those areas where crop management was sub-optimal. The pronounced instability may therefore be attributed to a substantial variation in farmers’ management practices in these areas due to non-availability of appropriate technology in some farms. RT-DSW(PTOS)-(ICRM) and ZT-DSW were good in terms of stability which supports their widespread adoption in South Asia (Harrington and Hobbs, 2009). In conclusion, this study successfully demonstrates the use of model procedures and stability analysis for assessing the performance of various resource conserving technologies from farmers participatory trials which were conduced under a range of farmers management and environment constituting highly unbalance data. Appendix A

Descriptions of rice and wheat technologies evaluated at on-farm farmer’s participatory trials. Abbreviation

Treatment

Description

Rice CT-TPR (395)a

Conventional-till (puddled) transplanted rice

CT-DrumR (24)

Conventional-till (puddled) drum-seeded rice

RT-TPR (101)

Reduced-till (non-puddled) transplanted rice

RT-DSR (217)

Reduced-till (non-puddled) dry drill-seeded rice

Bed-TPR (19)

Raised-bed transplanted rice

ZT-DSR (63)

Zero-till drill-seeded rice

This is the most common farmer’s practice in the region. In this method, land is plowed, puddled, and leveled; 21–40-d-old seedlings are transplanted at random or in rows Land preparation was similar as in CT-TPR i.e. ploughing, puddling, and leveling; and sprouted seeds are sown in rows on puddled soil surface by using a drum seeder Land preparation consisted 2–3 dry tillage followed by planking/leveling and ponding water but no puddling; 21–30-d-old seedlings are transplanted at random or in rows Land preparation was similar as in RT-TPR. Rice was drill seeded in rows by a zero-till ferti-seed-drill at 2–3 cm depth in a well-prepared moist soil and leveled, followed by one light irrigation applied for good germination Land preparation and bed making was similar to that under Bed-DSW (see under wheat treatments). Rice seedlings (21–30 d-old) were trasplanted on both sides of moist beds. Furrows are kept flooded for up to 21 DAT Fields are flush-irrigated to moisten the soil and allow weeds to germinate. After about 2 weeks, glyphosate/paraquat is applied to kill all weeds. Then, a zero-till drill seeder is used to drill rice seeds at shallow depth (2–3 cm), followed by a light irrigation to have a quick and uniform germination

Wheat CT-BCW (455)

Conventionally tilled broadcasted wheat

RT-DSW (60)

Reduced till drill seeded wheat

RT-DSW(PTOS)-(ICRM) Reduced-till drill-seeded wheat using a power tiller – (87) operated seeder (PTOS) with integrated crop and resource management (ICRM). Bed-DSW (56)

Raised-bed drill-seeded wheat

ZT-DSW (397)

Zero-till drill-seeded wheat

ZT-DSW-(ICRM) (108)

Zero-till drill seeded wheat with integrated crop and resource management

a

This is the most common farmers’ practice for establishing wheat crop. Seeds are broadcast manually in thoroughly prepared fields with 4–5 plowings/harrowings by a tractor or a power tiller. After sowing, laddering is practiced to cover seeds Tillage involved 2–3 tractor passes instead of 4–5 by tine cultivator or a disc harrow and subsequently seeding was done by using seed-cum-fertilizer drill The PTOS is a tiller with an attached seeder and a soil-compacting roller. The PTOS is used to till shallow (4–5 cm depth), sow seeds in rows at adjustable distance, and cover seed and compact the soil at the same time in a single pass. All improved crop management practices were followed Land preparation was similar to that under CT-BCW. A bed former-cum-zero-till drill is used to form 37 cm-wide raised beds and 30 cm-wide furrows in well-prepared, pulverized soil and wheat is sown in rows on both sides of moist beds Glyphosate/paraquat were applied to kill the existing weeds prior to seeding. Wheat seed is drilled at 4–5 cm depth in moist soil by a zero-till ferti-cum-seed drill, without any tillage and in the presence of anchored crop residues Land preparation and sowing of wheat was done as explained in ZT-DSW. In addition, all improved crop management practices were followed

The number in parenthesis in the “abbreviation” column indicates the number of records available for that treatment in the data set.

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Appendix B SAS code for stability models incorporating heterogeneous error variances /*COMPOUND SYMMETRY MODEL*/ proc mixed data = temp covtest; class trt env farm; model gyld = trt/ddfm = kr; random farm/sub = env; random int trt/sub = env; lsmeans trt/pdiff; repeated/group = env; run; /*HETEROGENEOUS COMPOUND SYMMETRY MODEL*/ proc mixed data = temp covtest; class trt env farm; model gyld = trt/ddfm = kr; random farm/sub = env; random trt/sub = env type = csh; lsmeans trt/pdiff; repeated/group = env; run; /*SHUKLA MODEL*/ proc mixed data = temp covtest; class trt env farm; model gyld = trt/ddfm = kr; random farm/sub = env; random int/sub = env; random int/sub = env group = trt; lsmeans trt/pdiff; repeated/group = env; run; /*FINLAY–WILKINSON MODEL*/ proc mixed data = temp covtest; class trt env farm; model gyld = trt/ddfm = kr; random farm/sub = env; random trt/sub = env type = FA1(1); lsmeans trt/pdiff; repeated/group = env; run; /*EBERHARD–RUSSELL MODEL*/ proc mixed data = temp covtest; class trt env farm; model gyld = trt/ddfm = kr; random farm/sub = env; random trt/sub = env type = FA(1); lsmeans trt/pdiff; repeated/group = env; run; /*AMMI MODEL*/ proc mixed data = temp covtest lognote; class trt env farm; model gyld = trt/ddfm = kr; random farm/sub = env; random int/sub = env; random trt/sub = env type = fa1(1); lsmeans trt/pdiff; repeated/group = env; run; SAS codes for stability models incorporating heterogeneity of variances between environments for farmers-within-environment effects /*SHUKLA MODEL*/ data temp; set temp; field = N ; proc mixed data = temp covtest; class trt env farm field; model gyld = trt/ddfm = res notest; random int/sub = env; random trt/sub = env group = trt; lsmeans trt/pdiff; parms (1)(1). . .. . . (1); repeated field/subject = farm*env group = env type = CS; run;

Appendix B (Continued) /*AMMI MODEL*/ proc mixed data = temp covtest; class trt env farm field; model gyld = trt/ddfm = res notest; random int/sub = env; random trt/sub = env type = FA1(1); lsmeans trt/pdiff; parms (1)(1). . ..(1); repeated field/subject = farm*env group = env type = CS; run;

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