Control of Interplot Interference in Grain Maize: A Multi-Site Comparison

located on neighboring plots, and it may artificially favor some cultivars and penalize others. Interplot interferInterplot interference is known to be potentially a major source ence has been extensively studied for cereals, in particuof bias in cultivar trials of several plant species, but there are few lar for wheat (Triticum aestivum L.), where a relationpublished results concerning grain maize (Zea mays L.) in France. ship with height has been recognized (Kempton et al., Two series of field experiments were conducted in the North and in the South of France from 1994 to 1996 to quantify interference in 1986; Goldringer et al., 1994; Clarke et al., 1998). In grain maize trials and compare methods of control. Each experiment grain maize cultivar trials, interference is potentially a typically consisted of a reference trial with two or three unharvested major concern, since plots usually consist of only two rows on each side of each plot, a four-row-plot trial with one unharto four seeded rows and cultivars may exhibit large vested row on each side of each plot, and a two-row-plot trial. Trials phenotypic differences. Consequently, there may be had seven cultivars in 1994 and 1996, and four additional cultivars in large interference effects exerted on a large proportion 1995. Interference was found to occur in two-row-plot trials and to of each plot. Interference has been found to occur for be related to plant height. When a cultivar was 10 cm shorter than grain maize in a few studies in the USA (Kiesselbach, each of its neighbors, its yield was reduced by 0.16 Mg ha21 in the 1923; Genter, 1958; Pendleton and Seif, 1962; Ziegler, North series and by 0.30 Mg ha21 in the South series on average. 1980; Esgar and Bullock, 1999). Interference effects may Interference appeared much lower in the four-row-plot trials. Methods be due to differences in plant height, maturity, vigor, for controlling interference were assessed by comparing their cultivar estimates with those from the reference trials. Bias due to interference leaf area, density, or planting date. On the contrary, in the two-row-plot trials was reduced by using models for interferOlson (1928) and Bowman (1989) found little evidence ence, but the four-row-plot trials appeared as a more reliable method of interference. Fewer published references exist for to avoid such bias. grain maize in Europe, but interference effects have been reported in France (Lorgeou, 1986) and in Belgium (Van Waes, 1997). I between plots is known to occur in Interplot interference is a source of bias for cultivar cultivar trials for many cultivated species (see Talbot comparisons and so needs to be controlled as well as et al., 1995; Kempton, 1997 and references therein). It possible. There exist several alternative or complemenis mainly caused by competition between the cultivars tary methods to do this, either when defining plot size, choosing the design, or analyzing the data (Kempton, 1997; Monod et al., 1997). O. David and H. Monod, Unité de biométrie, INRA, Domaine de Vilvert, 78352 Jouy-en-Josas Cedex, France; J. Lorgeou, AGPM, StaFirst, interference may be limited by enlarging plot tion expérimentale, 91720 Boigneville, France; G. Philippeau, ITCF, size and leaving border rows of each plot unharvested; Station expérimentale, 91720 Boigneville, France. Received 8 March 2000. *Corresponding author ([email protected]). Abbreviations: msd, mean square difference; REML, restricted maximum likelihood. Published in Crop Sci. 41:406–414 (2001). DAVID ET AL.: INTERPLOT INTERFERENCE IN GRAIN MAIZE 407 signs. There were seven cultivars and six replicates per trial however, this will increase the management cost, land in 1994 and 1996. There were four additional cultivars and area, and amount of seed required. Interference may five replicates per trial in 1995. Two experiments of the South also be limited at the design stage, by carefully choosing series had to be discarded because of damage by wild animals. the allocation of cultivars to plots. Thus, in the designs proposed by David and Kempton (1996) and David et Plot Sizes al. (1996), cultivars of similar heights are grouped on In one trial per experiment, plots consisted of eight or six neighboring plots. This method can be applied provided seeded rows and only the two central rows were harvested. reliable prior information is available on cultivars and We called this trial the reference trial because the interplot on interference, so that cultivars can be classified into interference on the harvested rows was expected to be negligigroups with similar interference effects. When prior inble compared with the other trials. In the other trials, plots formation is not available, bias may be reduced by using consisted of either four seeded rows with the two central rows harvested, or of three seeded rows with the central row neighbor-balanced designs (Azaı̈s and Druilhet, 1995). harvested, or of two seeded and harvested rows. For conveSometimes, the methods above cannot be applied, or nience, we shall denote by m/n a trial with m seeded rows per they are insufficient to eliminate interference. In this plot and with the n central rows harvested. Thus the reference case, interference bias may still be reduced at the analytrials are either 8/2 or 6/2 trials, and the other ones are 4/2, sis stage by including interference effects in the statisti3/1 or 2/2 trials. Interplot interference is expected to be maxical model and calculating adjusted cultivar means. Sevmum for the 2/2 trials, whereas the 4/2 and 3/1 trials represent eral models for interference are available (Kempton, a compromise between a small size of plots and the ability to 1997), and the problem now is to choose the most adecontrol interference. The plots were 5 m long in the 8/2, 6/2, quate one. In addition, some models for interference 4/2, and 2/2 trials, and 10 m long in the 3/1 trials. increase the variance for cultivar comparisons by a large Experimental Designs amount. If such models are to be used, then an efficient Four types of complete block designs were considered: (i) design should also be used. Efficient designs for interferclassical randomized complete block designs, (ii) neighborence models include neighbor-balanced designs (Azaı̈s balanced designs, (iii) grouped designs, where only cultivars et al., 1993) and optimal designs for height-related interof similar heights and maturity appear on neighboring plots, ference (David et al., 2000). (iv) control designs, where plots for the test cultivars are sepaThis paper is based on a 3-yr experimental study of rated by plots with the same control cultivar. Neighbor-balinterference in grain maize cultivar trials, conducted in anced designs were constructed and randomized according to France from 1994 to 1996 (see Lorgeou et al., 1997). the methods described in Azaı̈s et al. (1993). In these designs, The main motivation for the study was to determine all pairs of distinct cultivars occur on neighboring plots an practical recommendations on how best to control inequal number of times. Grouped designs were constructed terplot interference over a series of grain maize cultivar and randomized according to the methods described in David trials. When the research started, a large number of and Kempton (1996). In control designs, the design for the test cultivars was a classical randomized complete block design. official trials were still conducted with two rows per For all trials, each complete block was a line of plots with plot, while other official and recommendation trials had a border plot on either side. Neighbor-balanced and grouped one unharvested row on each side of each plot. To give designs were circular, which means that the cultivar on a boruseful recommendations, it was necessary (i) to evaluate der plot was the same as the cultivar on the inner plot at the quantitatively the bias due to interplot interference in other end of the same block. Thus, the cultivars on the inner such trials and (ii) to compare experimentally several plots of blocks had the same neighbors as if blocks were possible methods to reduce this bias, through plot size, circular. For control designs, the border plots received the experimental design, and statistical analysis. Attention control cultivar. For randomized complete block designs, the was paid to the consequences of interference on individcultivar on each border plot was one of the test cultivars or, ual trials but, more importantly, over series of trials. occasionally, an additional standard cultivar. The plot sizes and experimental designs tested in each experiment are summarized in Table 1. They varied from one MATERIALS AND METHODS year to the next because the objectives evolved. In 1994 and Experimental Sites 1995, comparing different designs was one of the main objectives. In 1996, the main objectives were to compare plot sizes The experiments were conducted on experimental sites of and methods of analysis; neighbor-balanced designs were used GEVES (Groupement d’Etude des Variétés et Semences, the in all trials because they are more efficient to compare interferFrench official registration group), AGPM (Association Génence models (Druilhet, 1999). érale des Producteurs de Maı̈s), and three breeding companies The trials in all experiments were conducted with standard (Pau Semences, SDME-KWS, and Verneuil Semences). There methods for cultivar trials in France. Interplot and interrow were two series of experiments, corresponding to two different spacings were 80 cm, and the seeding density was approximaturity groups of cultivars. The North series was associated mately 100 000 plants/ha in the North series and 85 000 plants/ with early cultivars, which are grown mainly North of the ha in the South series. Loire river in France, while the South series was associated with late cultivars, grown mainly in the South of France. Cultivars Main Features of the Experiments The cultivars were chosen from among those recently tested in French official trials and resistant to lodging. The selected Within each experiment, several complete block trials were cultivars had large differences for height and for other characconducted concomitantly, all with the same set of cultivars but with different plot sizes and different experimental deters which might be related to interplot interference. This was 408 CROP SCIENCE, VOL. 41, MARCH–APRIL 2001 Table 1. Plot sizes and design methods tested within each ex(2) yij 5 bj 1 uv 1 l.(Dh)ij 1 ε9ij, periment. where (Dh)ij denotes the difference in height (in cm) between Design methods Plot i and its neighbors, and l is a regression coefficient. More precisely, if i 2 1 and i 1 1 denote the left and right neighbors Reference trial 4/2 3/1 2/2 Experiment Year Location (8/2 or 6/2) trial trial trials of Plot i, then (Dh)ij 5 (h(i21), j 1 h(i11), j)/2 2 hi, j. In the case of interference related to height, it is expected that l will be North series (early varieties) negative and its value will correspond to the average yield N94B 1994 Beaulay R† R R R and N decrease per cm height difference between a plot and the N94V Verneuil N N – R and N N95B 1995 Beaulay N – N – average of its neighbors. N95C Compiègne N N – G and C The third model takes into account interference through N95R Rennes N – – N varietal neighbor effects: N96B 1996 Beaulay N N – N N96V Verneuil N N – N (3) yij 5 bj 1 uv 1 fu 1 fw 1 ε′′ij , N96C Compiègne N N – N N96R Rennes N N – N where fu and fw denote the interference effects of Cultivars South series (late varieties) u and w. The parameter f is negative for the more aggressive (discarded) 1994 Montpellier (R) (R) – (R and N) cultivars and positive for cultivars sensitive to interference S94Mn Montardon R R R R and N from neighbors. S95Mr 1995 Montpellier N N – N The three models are linear models and Model (1) is a S95Mn Montardon N – N – submodel of the other two. Thus interference can be assessed S95P Pont-Long N – – G and C S96Mr 1996 Montpellier N N – N by testing the hypothesis [l 5 0] in Model (2) and the hypothe(discarded) Montardon (N) (N) – (N) sis [fv 5 0 for all v] in Model (3). Model (2) is much more S96P Pont-Long N N – N parsimonious than Model (3), since it includes only one param† C, control design; G, grouped design; N, neighbor-balanced design; R, eter for interference whereas Model (3) includes n 2 1 inderandomized complete block design. pendent parameters, where n is the number of cultivars. Note that Model (3) cannot be applied to control designs, since only the control cultivar is neighbor to measured plots. necessary to ensure sufficient power to compare design and The objective of a cultivar trial is to estimate and compare analysis methods with respect to interplot interference. The pure stand cultivar effects pv, that is, the effect of Cultivar v FAO indexes of the cultivars varied between 250 and 300 for when it is surrounded by itself. For Models (1) and (2), pv 5 the North series, and between 400 and 560 for the South series. uv, whereas for Model (3), pv 5 uv 1 2fv (see Kempton, 1997, The names of the seven early and late cultivars used in all the p. 112). trials of the North and South series respectively appear in Fig. 1. The four additional cultivars used in 1995 were DK248, Comparison between Trial Methods EPERON, DK300, and RAISSA for the North series, and MADERA, DUNIA, DK512, and CARAMAN for the to Control Interference South series. As used in this article, a trial method will refer to the combination of plot size, design and analysis of a cultivar trial. Measurements To compare the ability of various trial methods to control interference, we need to compare their estimates of pure stand In this paper, we restrict our attention to grain yield as cultivar effects with those given by a method of reference the main response, and to final plant height as a character where interference is supposed to be negligible. For each expotentially associated with interference. Many characters were periment, the reference method will be the reference trial measured on plots (including the border plots) during the analyzed with Model (1). The trial methods to be assessed growing season, especially in 1994, but preliminary analyses will be combinations of 4/2, 3/1, or 2/2 plots, with randomized of the 1994 results (not presented) showed that only height complete block, neighbor-balanced, grouped, or control dedifferences between neighboring plots were consistently assosigns, and analysis with Models (1), (2) or (3). ciated with interference for yield (see Lorgeou et al., 1997). Our main criterion to compare trial methods will be the The one or two harvested rows of each plot were harvested mean square difference (msd), which we now define. Let p*v in bulk with a plot combine, one replicate of each trial at a denote the estimates of (centered) cultivar effects given by time. Plant height was defined as the distance between the the reference method, and let p v denote the estimates given ground and the ligule of the highest leaf before harvest. It by another trial method represented in the same experiment. was measured on 10 successive plants in the middle of each The mean square difference (msd) for the tested method (with harvested row, and the average was used as the plot value. respect to the reference method) is defined by Statistical Methods for the Analysis msd 5 1/n ov51...n (p v 2 p*v )2, of Individual Trials where the summation is over the n cultivars tested in the Three different models were considered for the analysis of experiment. A small value of msd indicates that the tested a single trial. Consider the Plot i of Block j, and suppose it trial method gives cultivar estimates close to those of the received Cultivar v, while its left and right neighbors received reference method, and so it indicates that interference has Cultivars u and w respectively. The first model is the classical been small or that it has been corrected efficiently. In contrast, one for a complete block design: uncorrected interference will cause bias in the estimates and so it will increase the value of msd. (1) yij 5 bj 1 uv 1 εij, The expectation of msd is in fact the sum of three terms: (i) the average variance of p*v , (ii) the average variance of where yij denotes the yield on Plot ij, bj the mean of Block j, uv the direct effect of Cultivar v, and εij is an error term. p v , and (iii) the average squared bias of p v with respect to p* v . The first term depends only on the reference trial, and so The second model takes into account interference through a covariate: it is equal for all methods tested in the same experiment. The DAVID ET AL.: INTERPLOT INTERFERENCE IN GRAIN MAIZE 409 Fig. 1. Relationship between cultivar heights and cultivar interference effects estimated in 2/2 trials with Model (3)9 applied to (A) the North and (B) the South series of experiments. The extended models are sum of the second and third terms is the mean square error on cultivar estimates when the tested method is used. So the (1)9 yeij 5 m 1 Me 1 Bej 1 uv 1 Tev 1 εeij, msd criterion includes not only the bias, but also the extra(2)9 yeij 5 m 1 Me 1 Bej 1 uv 1 Tev 1 l.(Dh)eij variability caused by interference or by the adjustments for interference. Consequently, it will also be large if a method 1 Le.(Dh)eij 1 ε9eij, estimates cultivar effects with poor precision. (3)9 yeij 5 m 1 Me 1 Bej 1 uv 1 Tev 1 fu Joint Analysis of Each Series of Experiments 1 fw 1 Feu 1 Few 1 ε′′eij, As mentioned in the introduction, evaluating interference where yeij is the response on Plot i of Block j of Experiment and methods of control over a series of trials was a major e; m is the general mean; Me is the main effect of experiment objective of the study. To do this, Models (1), (2), and (3) e; Bej is a block effect nested within the experiments; uv is were extended to cope with a set of trials, by including experithe main effect of Cultivar v; Tev is an experiment-cultivar ment main effects, interactions between experiments and cultiinteraction term; (Dh)eij is the height-difference measured for vars, and interactions between experiments and interference Plot (eij); l is the average regression coefficient for the heighteffects. The experiments corresponded to different locations difference covariate and (l 1 Le) is the coefficient for experiand/or years, but because of the relatively small number of ment e; fu is the interference main effect of Cultivar u and experiments and because of a lack of balance, we did not try Feu is an experiment-cultivar interaction term for varietal interference effects; εeij, ε9 eij, and ε′′eij are error terms. to distinguish between year and site effects. 410 CROP SCIENCE, VOL. 41, MARCH–APRIL 2001 The three models were applied separately to the reference were quite large in some trials, due to soil or density trials, the 4/2 trials, and the 2/2 trials. We refer to the Results heterogeneity, drying conditions, or lodging. In the section for more details on which trials were chosen in each South series, they were larger in the trials with no border case. For each type of trial and for each model, first an analysis rows, which suggests that interference increased the of variance was performed. Then, all factorial effects involving block-cultivar interaction. experiments, that is, the effects denoted by M, B, T, L, and F In the North series, average heights in the reference above, were assumed to be random and to follow independent trials ranged from 180 cm (N95C and N96C) to 215 cm centered Gaussian distributions with a common variance for (N95B). On average, DK250 was the shortest cultivar each model term. The corresponding mixed models were analyzed by restricted maximum likelihood (REML) (see Pat(183 cm) and BEMOL was the tallest (217 cm). In the terson, 1997); the msd criterion was then applied to the estiSouth series, average heights in the reference trials varmated main effects of the seven cultivars assessed in all ied more widely, ranging from 167 cm (S95Mr) to 313 cm experiments. (S95Mn). On average, DURANDAL was the shortest cultivar (231 cm) and NATALIA and RAFAELA were Software the tallest (268 cm), with SAMSARA and CECILIA not Most calculations, including all the analyses of individual far behind. There was a significant cultivar-experiment trials, were performed with the S-PLUS (MathSoft, Inc., Caminteraction for height in both series, resulting in different bridge, MA) statistical package. The joint analyses of variance cultivar rankings between experiments. were performed with the GLM procedure of SAS (Cary, NC). For the REML joint analyses, we used the VCOMP and Interference in Individual Trials REML directives of Genstat (NAG Ltd., Oxford, UK). When using statistical softwares, the f interference effects of Models In the North series, the height-difference covariate (3) and (3)9 were declared through covariates associated with was significant at the 5% level in none of the reference each cultivar. In order to ensure that the estimated cultivar trials, in two out of nine 4/2 or 3/1 trials, and in seven effects or means corresponded to pure-stand effects or means, out of eleven 2/2 trials (Table 3). For the nine 2/2 trials the covariate associated with Cultivar v was given the value with a randomized complete block or a neighbor-bal22 on the plots receiving Cultivar v, 1 on the plots which anced design, the average estimated value of the l coefwere neighbor to Cultivar v, and 0 for all the other plots. In ficient was equal to –0.023 Mg ha21 cm21. In almost all the mixed Model (3)9, the Fev effects were assumed to follow trials, the estimated coefficient was either negative or the same distribution, independently. So when using the REML directive of Genstat, the variances of the parameters close to zero. However, it was significant and positive associated with the neighbor covariates were constrained to in the 4/2 trial performed at Beaulay in 1996. A possible be equal by the RELATION option of the VCOMP directive. reason, to be taken with much caution, is that the central rows could grow better when the border rows were RESULTS depressed by interference. Cultivar interference effects from Model (3) were significant at the 5% level in one Preliminary Analyses reference trial, in none of the 4/2 or 3/1 trials, and in As expected, there were large site and year effects Table 3. Estimated values of the lambda coefficient in Model (2) on yield, with yields ranging between 6 Mg ha21 and 15 for each trial. Mg ha21 (Table 2). The standard errors of observations Estimated value of the coefficient for the height-difference covariate (Mg ha21 cm21) Table 2. Yield means and standard errors of observations of all trials when analysed with Model (1). Reference 2/2 trials Experiment trial 4/2 and 3/1 trials Mean and standard error of observations for yield (Mg ha21) N94B 20.005 20.011† (4/2) 20.028‡ (R)§ 20.006 (3/1) 20.028‡ (N) Reference N94V 20.007 20.002 20.034‡ (R) Experiment trial 4/2 and 3/1 trials 2/2 trials 20.007 (N) N95B 20.005 20.006 – N94B 12.7 0.29 12.7 0.35 (4/2) 12.7 0.47 (R)† 12.4 0.45 (3/1) 12.4 0.62 (N) N95C 20.009 20.002 0.002 (G) 20.034 (C) N94V 11.7 0.45 11.6 0.48 11.3 0.47 (R) 11.5 0.41 (N) N95R 20.002 – 20.028‡ N96B 20.009‡ 0.033 20.042‡ N95B 11.7 0.43 11.1 0.48 – – N95C 6.7 0.53 6.4 0.36 6.2 0.46 (G) N96V 0.004 20.001 20.014 N96C 20.004 20.007 0.001‡ 6.7 0.66 (C) N95R 10.1 0.65 – – 10.6 0.73 N96R 0.003 20.012 20.023‡ N96B 10.6 0.49 11.3 0.51 11.3 0.52 S94Mn 20.039‡ 0.006 (4/2) 20.018 (R) N96V 12.0 0.32 12.1 0.39 11.9 0.48 20.018‡ (3/1) 20.046‡ (N) N96C 7.7 0.96 9.3 0.64 7.8 0.86 S95Mr 0.007 0.047 20.027 N96R 9.5 0.35 9.2 0.51 9.7 0.39 S95Mn 20.001 20.010 – S95P 20.012 – 20.024‡ (G) S94Mn 11.5 0.50 12.2 0.38 (4/2) 12.3 0.79 (R) 11.2 0.48 (3/1) 12.3 0.56 (N) 20.051 (C) S96Mr 0.005 0.007 0.022 S95Mr 12.6 0.68 13.7 0.87 13.5 1.03 S95Mn 12.2 0.41 11.3 0.41 – – S96P 20.009 20.015 20.057 S95P 9.1 0.38 – – 9.2 0.62 (G) † Numbers are in italic type when the height-difference covariate was 9.2 0.74 (C) significant at the 0.05 probability level. S96Mr 10.6 0.49 13.7 0.73 13.8 0.97 ‡ indicates trials where the varietal interference effects of Model (3) were S96P 11.0 0.62 10.9 0.47 11.0 1.02 significant at the 0.05 probability level. § C, control design; G, grouped design; N, neighbor-balanced design; R, † C, control design; G, grouped design; N, neighbor-balanced design; R, randomized complete block design. randomized complete block design. DAVID ET AL.: INTERPLOT INTERFERENCE IN GRAIN MAIZE 411 seven 2/2 trials with either a classically randomized or neighbor effects were significant (see, e.g., the randomized complete block 2/2 trial of N94V). Thus, even when a neighbor-balanced design. In the South series, the estimated coefficients l in a model with interference effects seems adequate, using this model may not improve the estimation of cultivar the 2/2 trials were all negative except for Montpellier in 1996. As the precision was lower than in the North effects. Two main reasons are suggested to explain this phenomenon. First, the modeling of interference effects series, they were significantly different from zero in only two cases, although they tended to be larger (in absolute may be too grossly approximated in Model (3). Second, adjustment for interference effects increases the varivalue) than in the North series. The estimated coefficients were smaller and non-significant in the reference ance of cultivar estimates, especially when Model (3) is used, and for designs which are not adapted to an trials, except at Montardon in 1994. The results in the 4/2 and 3/1 trials were intermediate, except for the highly interference model (see, e.g., the msd values for grouped designs and Model (3) in Table 4). positive value at Montpellier in 1995. Cultivar interference effects were significant at the 5% level in one reference trial, in one 4/2 or 3/1 trial, and in two 2/2 Joint Analyses of the Experiments trials with a neighbor-balanced or a grouped design. The joint analyses were performed on the experiments containing a reference trial, a 4/2 trial and a 2/2 Mean Square Differences trial, i.e., N94B, N94V, N95C, N96B, N96V, N96C, and N96R (seven experiments) for the North series, and For each experiment, the mean square difference with the reference method was calculated for the 4/2, 3/1 and S94Mn, S95Mr, S96Mr, S96P (four experiments) for the South series. They were performed separately on the 2/2 trials analyzed by Models (1), (2) and (3) (Table 4). With Model (1), the msd values were smaller for 4/2 or reference trials, on the 4/2 trials, and on the 2/2 trials. In the experiments with several 2/2 trials, only the neigh3/1 trials than for 2/2 trials, except for N96C and S95Mr. Model (2) tended to decrease msd compared with Model bor-balanced trial was used; there was no neighborbalanced trial in N95C, so the grouped design was (1) for 2/2 trials, particularly in the trials where the height-difference covariate was significant, such as the used instead. The main features of the analyses of variance with 2/2 trials of N95R and N96B. In contrast, applying Model (2) increased msd in several 4/2 trials, especially Model (2)9 and Model (3)9 are listed in Table 5 and Table 6 respectively. The interference main effects are in experiments N96B and S95Mr where the covariate was significant, but with an unexpected positive coefthe most important to consider here, since they represent the effects which appeared repeatedly over the ficient. Model (3) was ineffective at reducing msd in 4/2 trials. series of trials. In the North series and for both models, they were non-significant in the reference and 4/2 trials It increased msd in several 2/2 trials also, sometimes by a very large amount, irrespective of whether or not the but highly significant in the 2/2 trials. There were some small interaction between experiments and interference, Table 4. Mean square differences between variety effects estieven in the reference and 4/2 trials. This suggests that mated from the reference trial and each of the other trial interplot interference may have occurred in these trials, methods. but it was small and not very consistent from one siteMean square difference with the reference method year to another. The results for the South series confirm (Mg2 ha22) Table 5. Analyses of variance of the series of experiments with 4/2 and 3/1 trials 2/2 trials Model (2)9. Model Model F-ratio values Experiment (1) (2) (3) (1) (2) (3) Source DF† Reference trials 4/2 trials 2/2 trials N94B 0.04† 0.05 0.06 (4/2) 0.20 0.08 0.13 (R)‡ 0.06 0.04 0.11 (3/1) 0.16 0.13 0.14 (N) North series N94V 0.03 0.03 0.18 0.12 0.11 0.37 (R) Experiment 6 722.18*** 848.06*** 559.48*** 0.05 0.03 0.10 (N) Variety 10 53.26*** 59.48*** 50.38*** N95B 0.08 0.08 0.20 – – – Height difference 1 1.74 0.35 12.40*** N95C 0.11 0.11 0.20 0.17 0.18 0.46 (G) Blocks 34 1.66* 5.18*** 1.70* 0.32 0.36 – (C) Exp.-Variety 36 5.75*** 8.22*** 5.78*** N95R – – – 0.35 0.18 0.29 Exp.-Height diff. 6 0.33 2.20* 1.97 N96B 0.10 0.49 0.51 0.32 0.15 0.20 N96V 0.05 0.05 0.13 0.23 0.17 0.07 Error (mean square)‡ 212 0.282 0.214 0.321 N96C 0.23 0.19 0.25 0.15 0.15 0.74 South series N96R 0.05 0.12 0.38 0.17 0.11 0.07 Experiment 3 186.11*** 184.07*** 95.89*** S94Mn 0.08 0.08 0.10 (4/2) 0.39 0.32 0.66 (R) Variety 10 23.15*** 21.81*** 13.14*** 0.06 0.05 0.14 (3/1) 0.33 0.32 0.48 (N) Height difference 1 0.77 2.45 13.68*** S95Mr 0.53 1.09 1.62 0.21 0.26 0.69 Blocks 19 3.22*** 4.16*** 0.73 S95Mn 0.17 0.22 0.42 – – – Exp.-Variety 18 8.92*** 11.15*** 7.24*** S95P – – – 0.13 0.17 1.32 (G) Exp.-Height diff. 3 2.25 6.23*** 4.26** 0.19 0.19 – (C) S96Mr 0.13 0.17 0.69 0.16 0.19 0.31 Error (mean square) 125 0.332 0.389 0.677 S96P 0.10 0.06 0.05 0.52 0.43 0.38 * indicates significance at P 5 0.05. ** indicates significance at P 5 0.01. † For each plot size within each experiment, the smallest value of the mean square difference is in italic. *** indicates significance at P 5 0.001. † DF, degrees of freedom. ‡ C, control design; G, grouped design; N, neighbor-balanced design; R, randomized complete block design. ‡ Expressed in Mg2 ha22. 412 CROP SCIENCE, VOL. 41, MARCH–APRIL 2001 Table 6. Analyses of variance of the series of experiments with cultivar effects obtained from 4/2 trials were more conModel (3)9. sistent with the reference than those obtained from 2/2 F-ratio values trials. The data from 4/2 trials were also analyzed with Model (1)9 using the first three blocks of the trials only, Source† DF‡ Reference trials 4/2 trials 2/2 trials in which case 4/2 and 2/2 trials have the same land area North series or similar areas. The resulting msd values were equal Interference 10 1.30 0.97 4.59*** to 0.025 (Mg ha21)2 for the North series and to 0.057 Exp.-Interference 36 1.53* 1.10 1.58* Error (mean square)§ 172 0.252 0.218 0.275 (Mg ha21 )2 for the South series, and were lower than South series or equaled those obtained using 2/2 trials. For 4/2 trials, Interference 10 1.17 2.33* 2.45* Model (1)9 was well adapted and the models for interferExp.-Interference 18 1.53 1.39 1.22 ence resulted in no improvement. On the contrary, the Error (mean square) 100 0.314 0.381 0.711 estimates of cultivar effects from 2/2 trials were closer * indicates significance at P 5 0.05. to those of the reference when models for interference *** indicates significance at P 5 0.001. were used. Model (2)9 performed better in the North † For brevity, only the lines relative to interference effects are presented in the table. series, and Model (3)9 performed better in the South ‡ DF, degrees of freedom. region. Figure 2 shows how the adjustment by Model § Expressed in Mg2 ha22. (3)9 on the 2/2 trials affected the consistency with the reference trials. In most cases, adjustment correctly led that there were interference main effects mainly in the to an increase or decrease of cultivar effects. However, 2/2 trials. The interaction between experiments and inseveral cultivars were overcorrected, especially DK250 terference in Model (2)9 was larger than in the North and MAGISTER in the North series. series for the 4/2 and 2/2 trials. We now consider the REML analyses of Models (1)9, (2)9, and (3)9 as mixed models, with random effects for DISCUSSION all terms depending on the experiment. For the 2/2 trials, the estimated average height-difference coefficient l Interference occurred in our study. This was verified was equal to 20.016 Mg ha21 cm21 (standard error: at two levels: first, when interference models were ap0.006) in the North series, and to 20.030 Mg ha21 cm21 plied to the 2/2 trials, interference effects were repeat(standard error: 0.013) in the South series. Because inedly significant; second, when the classical analysis with terplot interference was related to height, it is interesting Model (1) was used, the estimates of cultivar effects to look at the relation between the average cultivar were more different between 2/2 trials and reference heights (as measured in the reference trials used in the trials than would be expected in the absence of interferjoint analyses) and the cultivar main interference effects ence. Height differences between neighboring cultivars of Model (3)9 in the 2/2 trials (Fig. 1). Cultivar interferplayed a large part in interference. Other plant characence effects were closely related to cultivar heights in ters were probably involved, but they were difficult to the North series. However, they were probably detercharacterize and their influence may have varied with mined by additional characters, for example maturity, environmental conditions (Lorgeou et al., 1997). Even shape or leaf density. This may explain why BOUM the influence of height is probably quite complex and and MAGISTER were more aggressive than would be changes during the growing season. expected from their height only. In the South series, Interference depended on environmental conditions the relation with height was less clear. Two cultivars and varied to some extent between locations and years. (SAMSARA and CECILIA) were very aggressive and However, as our study demonstrated, it may be a source were very tall. However, the five other cultivars had of bias on cultivar comparisons, which is repeated over large differences in height but relatively close interfertrials for a large part. In this case, contrary to the lack ence effects. of precision due to field heterogeneity or genotypeThe msd values are in Table 7. With Model (1)9, environment interaction, interference can hardly be controlled just by increasing the numbers of replications, Table 7. Mean square differences between the reference method sites, and years. and other trial methods, for the joint analysis of the series of experiments. The bias due to interference can result in rankings of cultivars which do not reflect the behavior of cultivars Mean square differences with the reference (Mg2 ha22) in pure stand fields. In our study, some cultivars appeared to be underor over-estimated by more than 0.4 Model Reference trials† 4/2 trials 2/2 trials Mg ha21 when plots with two unguarded rows were used North series (Fig. 2). An additional problem with interference is that Model (1)9 (0) 0.014 0.060 it increases the variability within a trial, because each Model (2)9 (0.004) 0.016 0.025 Model (3)9 (0.029) 0.026 0.047 cultivar has different neighbors in different blocks and South series so is subjected to different interference effects. For exModel (1)9 (0) 0.039 0.184 ample, one validation rule for official grain maize trials Model (2)9 (0.003) 0.077 0.136 in France (the standard error of observations must be Model (3)9 (0.066) 0.105 0.079 smaller than 0.8 Mg ha21) would have led to rejection † Mean square differences for the reference trials were calculated using the same data for the reference and tested methods. of four 2/2 trials but only one reference or 4/2 trials. DAVID ET AL.: INTERPLOT INTERFERENCE IN GRAIN MAIZE 413 Fig. 2. Comparison between cultivar effects estimated in the reference trials with Model (1)9 and cultivar effects estimated in 2/2 trials with Models (1)9 and (3)9; (A) North series, (B) South series. Our study was based on specifically designed experirow on each side were sufficient to control the major part of interference. In our experiments, the use of 4/2 ments, which were carried out with a small number of aggressive and sensitive cultivars. This may explain why plots together with a standard analysis proved more efficient at reducing bias than any design and analysis the results of the present paper differ from those of Bowman (1989), who found little interference when anamethod applied to 2/2 trials. Although there were fewer 3/1 trials, similar conclusions applied to them as well. lyzing official cultivar trials on grain maize in the USA. The difference may also be explained by different culModels for interference resulted in no more improvement to the 4/2 trials. For 2/2 individual trials, Models tural practices: in the U.S. trials, plant density was lower, distance between rows was larger, and yield levels were (2) and (3) reduced bias, but Model (3) increased variance so much that it should be used with much caution. lower than in our experiments. Plots with unharvested border rows appeared as the In spite of this limit, Models (2)9 and (3)9 proved useful to reduce bias in series of 2/2 trials. Combining the most reliable method to control interference in grain maize trials. Interference effects cannot be totally disinformation from several trials probably limited the increase in variance due to the adjustment for cultivar missed in trials with such plots, and interference has actually been shown to extend to more than one row interference effects. A few other models were tested with little improvement (additional covariates, random in several other species (Kempton and Lockwood, 1984; Clarke et al., 1998). However, plots with one border interference effects, sensitivity to height difference de414 CROP SCIENCE, VOL. 41, MARCH–APRIL 2001 David, O., H. Monod, and J. Amoussou. 2000. Optimal complete pending on the cultivar), except that Model (3) usually block designs to adjust for interplot competition with a covariance performed better with random interference effects for analysis. Biometrics 56:270–274. individual trials. Druilhet, P. 1999. Optimality of neighbour-balanced designs. J. Statist. Several recommendations on design can be made Plann. Inference 81:141–152. Esgar, R.W., and D.G. Bullock. 1999. Thinning border rows differenbased on design theory and on the few experiments tially affects hybrids in corn yield trials. Crop Sci. 39:1358–1361. where different types of designs were compared. When Genter, C.F. 1958. Plot competition between corn hybrids. Agron. Model (1) is expected to be used, particularly in 4/2 J. 50:205–206. trials, neighbor-balanced designs or designs with groupGoldringer, I., P. Brabant, and R.A. Kempton. 1994. Adjustment for competition between genotypes in single-row-plot trials of winter ing of similar cultivars can still be useful to protect wheat (Triticum aestivum ). Plant Breed. 112:294–300. against small interference effects. Provided prior inforKempton, R.A. 1997. Interference between plots. p. 101–116. In R.A. mation is available, designs which group similar cultivars Kempton and P.N. Fox (ed.) Statistical methods for plant variety or the optimal designs of David et al. (2000) are well evaluation. Chapman and Hall, London. Kempton, R.A., R.S. Gregory, W.G. Hughes, and P.J. Stoehr. 1986. adapted to Model (2). However, if Model (3) is likely to The effect of interplot competition on yield assessment in triticale be used, these designs will be inefficient and neighbortrials. Euphytica 35:257–265. balanced designs should be preferred (Azaı̈s et al., Kempton, R.A., and G. Lockwood. 1984. Inter-plot competition in 1993). The control designs are not worth the extra cost variety trials of field beans (Vicia faba L.). J. Agric. Sci. (Camin land area and management cost, except possibly in bridge) 103:293–302. Kiesselbach, T.A. 1923. Competition as a source of error in comparaselection when the available seed is too low for plots tive corn yields. J. Am. Soc. Agron. 15:199–215. with border rows. Lorgeou, J. 1986. Etude des effets d’allée frontale et de concurrence sur le comportement de quelques variétés de maı̈s dans les essais ACKNOWLEDGMENTS en petites parcelles. Technical Report, AGPM, Pau, France. Lorgeou, J., O. David, G. Philippeau, B. Aizac, and H. Monod. 1997. This work was financially supported by the French MinisMéthodes de contrôle des effets de compétition interparcellaire tère de l’Agriculture et de la Pêche. We are particularly gratedans les essais variétés de maı̈s grain: analyse de plusieurs solutions. ful to Bernard Aizac (GEVES), Régis Brassart (Verneuil p. 29–47. In G. Philippeau et al. (ed.) Effets de compétition dans Semences), André Lambert (SDME-KWS) and Jean-Paul les essais variétaux de plein-champ. ITCF, Boigneville, and INRA, Sampoux (Pau Semences), and to all the people from their Versailles, France. Monod, H., O. David, and G. Philippeau. 1997. Démarche expérimen-and our companies who participated to the experimental worktale pour évaluer des méthodes de contrôle de la compétition inter-and to the discussions on the project. We thank Johan Vanparcellaire dans les essais variétaux. p. 17–28. In G. Philippeau etWaes for references on grain maize interference, and the refer-al. (ed.) Effets de compétition dans les essais variétaux de plein-ees and Rob Kempton for helpful comments.champ. ITCF, Boigneville, and INRA, Versailles, France. Olson, P.J. 1928. Competition between adjacent rows of corn. J. Am.REFERENCESSoc. Agron. 20:83–84. Patterson, H.D. 1997. Analysis of series of variety trials. p. 139–161.Azaı̈s, J.-M., R.A. Bailey, and H. Monod. 1993. A catalogue of efficientIn R.A. Kempton and P.N. Fox (ed.) Statistical methods for plantneighbor-designs with border plots. Biometrics 49:1252–1261.variety evaluation. Chapman and Hall, London.Azaı̈s, J.-M., and P. Druilhet. 1995. 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