Yield of spring barley mixtures as a function of varietal and environmental characteristics

Transcription

1 Yield of spring barley mitures as a funtion of varietal and environmental harateristis Lars Kiær 1, Ib Skovgaard 2 and Hanne Østergård 1 1 Biosystems Department, Risø National Laboratory DTU, 4000 Roskilde, Denmark 2 Dep. of Natural Sienes, Faulty of Life Sienes, Univ. of Copenhagen, 1870 Frederiksberg C, Denmark Keywords: field trials, meta-regression, spring barley, variety miture, yield Introdution To design good variety mitures it is important to understand the influene of varietal and environmental harateristis on miing effet, e.g. what harateristis are more benefiial when all mied varieties epress it highly and what harateristis are more benefiial when the mied varieties epress it to varying etent. However, as it is generally impossible to manage more than a few eperimental ombinations in eah field trial, information on general relationships and fators of importane for the suessful design of variety mitures may be overlooked. Using meta-regression (e.g. Houwelingen et al. 2002), numerous results of suh trials an be ombined, and the influene of varietal and environmental fators on miing effet an be eluidated. Here, two speifi hypotheses were investigated: 1. Variation in straw length among omponent varieties will inrease miing effet due to enhaned potential for resoure utilization 2. Miing effet will inrease with more stressful environments due to inreased importane of mehanisms like omplementarity and ompensation Methodology Data We used results from 15 designed field trials of spring barley, inluding si three-omponent variety mitures and their mainly high-yielding omponent varieties (part of the Danish BAR-OF trials; Østergård et al. 2005). Eah field trial onstituted an environment ombined from 4 loalities, 4 years and 3 management systems: onventional (inl. industrial fertilizer), organi (inl. animal manure), and low-input organi (lover grass undersown, no manure). Fungiides were not used in any of the management types. Grain yield (hkg/ha) was assessed for all mitures and omponent varieties and used as the response variable in the estimation of the effets of miing. Statistial analyses Relative and absolute estimates of miing effet on grain yield were alulated for eah miture in eah environment (Table 1). As grain yields are higher in more produtive environments, so are the absolute differenes between varieties. The normalization of the relative measure, on the other hand, is epeted to remove suh sale-dependene. To illustrate this, eah of the two measures was plotted against the average yield of the mitures omponent varieties in eah environment.

2 Table 1. Formulas for estimating absolute and relative measures of miing effet size, as well as their variane. Here, y is the effet size estimate, and m are LSMeans of yield measurements for a speifi miture and the average of its omponent varieties in a given environment, respetively, and σ 2 is the variane of LSMeans. Estimate Absolute measure y = m of miing effet Relative measure of miing effet y = m Estimate variane σ y = σ σ 1 m σ y = Estimates of miing effet were weighted aording to their preision (inverse variane) and used in a number of random-effet meta-analysis models. A meta-analysis of the overall miing effet was onduted using the model: Yi = β 0 + U i + e i, i = 1,, 90, (model 1) where Y i denotes the weighted miing effet estimate from the speifi miture-environment ombination i, β 0 the model interept, and e i internal eperimental error with known variane. U i aptures the (normal distributed) random effets between miture-environment ombinations. To estimate the average miing effet of the si mitures, the following meta-analysis model was used: Yi = β 0 + β 1 Z 1i + + β 5 Z 5i + U i + e i, i = 1,, 90, (model 2) where Z 1i,, Z 5i are binary (0/1) dummy variables for eah of the mitures 2 to 6, β 1,, β 5 are the regression estimates orresponding to fator levels, and the remaining items are defined as in model (1). Two harateristis were then introdued as ovariates in meta-analysis model (1): a varietal harateristi (variation in average straw length among omponent varieties) as well as an environmental harateristi (environmental yield potential, measured as 95%-quantiles of all yield measurements in the environment). Two simple and a joint regression model were used: Yi = β 0 + β 1 X 1i + U i + e i, i = 1,, 90, (model 3) Yi = β 0 + β 2 X 2i + U i + e i, i = 1,, 90, (model 4) Yi = β 0 + β 1 X 1i + β 2 X 2i + U i + e i, i = 1,, 90, (model 5) where X 1i denotes the value of the straw length variation for result i, X 2i denotes the value of the yield potential for result i, β 1 and β 2 are the aording regression parameters, and the remaining items are defined as in model (1). Goodness-of-fit of eah model was eamined using a hi-square test statisti, Q (Hedges and Olkin 1985), whih is a measure of the variation not eplained by the model (residual heterogeneity).

3 a 8 b 0.25 Absolute miing effet Conventional Organi Low-input Relative miing effet Av erage yield of omponents (hkg/ha) Av erage yield of omponents (hkg/ha) Figure 1. Absolute (a) and relative (b) estimates of miing effet as a funtion of yield potential of the growing environments. Eah management system is marked with distint symbols. Results The relative measure of miing effet is relatively stable aross yield potentials, as indiated in Figure 1. The meta-analyses below were based on relative miing effets. One partiular environment had etraordinarily little eperimental variation, and the aordingly massive weighting of that environment in the meta-analyses had signifiant impat on the results. For eample, the order of the lass estimates for single mitures (model 2) hanged markedly due to its presene. Hene, that environment was eluded from the data set. The meta-analysis without any ovariates (model 1) showed a signifiant overall miing effet of 1.1% on grain yield (Fig. 2; p = ). This meta-analysis model was able to eplain all variation among miture-environment ombinations, i.e. there was no residual heterogeneity (p = ). The meta-regression based on individual mitures (model 2) revealed, nonetheless, that the effet (regression estimates) varied among mitures, providing results in aordane with previous findings (Østergård et al. 2005; Kiær et al. 2006). For eample, the miture with grey squares in Figure 2 shows primarily positive effets, whereas the miture with the empty irles shows equally many positive and negative effets. The regression on miing effet of neither variation in straw length (model 3; Fig. 3a; β = ; p = 0.95) nor environmental yield potential (model 4; Fig. 3b; β = ; p = 0.53) ould be distinguished. The meta-regression using both of these (model 5) also did not demonstrate any signifiant slopes (p = 0.83). Similar to the model without ovariates (model 1) these models (2-5) left no uneplained variation (not shown). Disussion Meta-analyses with and without ovariates were applied to test hypotheses and eluidate fators of importane for miing suess. The simple meta-analysis showed signifiant overall inrease in yield due to miing of varieties in spite of slightly opposing results between individual trials. However, the metaregressions were unable to support the two hypotheses: the miing effet was not affeted by omponent variation in straw length, and the miing effet was slightly inreasing with environmental yield potential, whih was atually arguing against the hypothesis. Further

4 Meta-estimate Figure 2. Plot of all estimates of miing effet and their 95% CLs. The estimates are ordered by inreasing effet size. Eah of the si mitures are plotted with a distint symbol. The overall meta-estimate is shown at the bottom of the plot. analyses must be done to investigate whether these trends an be found in other data sets and whether further ovariates may assist interpretation. The results also show that eperimental trials with etraordinarily small eperimental variation may influene the onlusions of the analysis. The eluded trial was performed at an eperimental farm whih is known to provide rather homogenous growing onditions. This information is not readily inluded in the urrent use of weighting. In the work to ome, we will assess the appropriateness of the urrent appliation of inverse variane as weights in metaanalysis of field trial data. Other ritial issues that need further investigation inlude the possible lak of independene between estimates due to shared environments and ommon omponent varieties of mitures.

5 a b Relative miing effet on yield (%) YieldEffRel Variation in straw length of omponents (m 4 ) Environmental yield potential (hkg/ha) Figure 3. Meta-regression of miing effets against variation in straw length of the miture s omponents (eah averaged aross environments) (a) and environmental yield potential (b).cirle diameters are proportional to the weights of the data points in the meta-regression model. Referenes Hedges LV and Olkin I (1985). Statistial methods for meta-analysis. Aademi Press, Orlando. Houwelingen HC, Arends LR and Stijnen T (2002). Advaned methods in meta-analysis: multivariate approah and meta-regression. Statist. Med. 21: Kiær LP, Skovgaard IM and Østergård H (2006). Meta-analysis is a powerful tool to summarize variety miture effets - eemplified by grain yield and weed suppression of spring barley. In: Østergård H and Fontaine L (Eds.). Proeedings of the COST SUSVAR workshop on Cereal rop diversity: Impliations for prodution and produts, Jun La Besse, Frane (ITAB, Paris, 2006), pp Østergård H, Kristensen, K and Jensen JW (2005) Stability of variety mitures of spring barley. In: Lammerts van Bueren ET, Goldringer I and Østergård H, (Eds.) Proeedings of the COST SUSVAR/ECO-PB Workshop on Organi Plant Breeding Strategies and the Use of Moleular markers, January Driebergen, The Netherlands, page pp