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CROP ECOLOGY, PRODUCTION & MANAGEMENT

Control of Interplot Interference in Grain Maize

A Multi-Site Comparison

^a Unité de biométrie, INRA, Domaine de Vilvert, 78352 Jouy-en-Josas Cedex, France
^b AGPM, Station expérimentale, 91720 Boigneville, France
^c ITCF, Station expérimentale, 91720 Boigneville, France

Corresponding author (Olivier.David{at}jouy.inra.fr)

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
Interplot interference is known to be potentially a major source of bias in cultivar trials of several plant species, but there are few published results concerning grain maize (Zea mays L.) in France. Two series of field experiments were conducted in the North and in the South of France from 1994 to 1996 to quantify interference in grain maize trials and compare methods of control. Each experiment typically consisted of a reference trial with two or three unharvested rows on each side of each plot, a four-row-plot trial with one unharvested row on each side of each plot, and a two-row-plot trial. Trials had seven cultivars in 1994 and 1996, and four additional cultivars in 1995. Interference was found to occur in two-row-plot trials and to be related to plant height. When a cultivar was 10 cm shorter than each of its neighbors, its yield was reduced by 0.16 Mg ha^-1 in the North series and by 0.30 Mg ha^-1 in the South series on average. Interference appeared much lower in the four-row-plot trials. Methods for controlling interference were assessed by comparing their cultivar estimates with those from the reference trials. Bias due to interference in the two-row-plot trials was reduced by using models for interference, but the four-row-plot trials appeared as a more reliable method to avoid such bias.

Abbreviations: msd, mean square difference • REML, restricted maximum likelihood

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
INTERFERENCE BETWEEN PLOTS is known to occur in cultivar trials for many cultivated species (see Talbot et al., 1995; Kempton, 1997 and references therein). It is mainly caused by competition between the cultivars located on neighboring plots, and it may artificially favor some cultivars and penalize others. Interplot interference has been extensively studied for cereals, in particular for wheat (Triticum aestivum L.), where a relationship with height has been recognized (Kempton et al., 1986; Goldringer et al., 1994; Clarke et al., 1998). In grain maize cultivar trials, interference is potentially a major concern, since plots usually consist of only two to four seeded rows and cultivars may exhibit large phenotypic differences. Consequently, there may be large interference effects exerted on a large proportion of each plot. Interference has been found to occur for grain maize in a few studies in the USA (Kiesselbach, 1923; Genter, 1958; Pendleton and Seif, 1962; Ziegler, 1980; Esgar and Bullock, 1999). Interference effects may be due to differences in plant height, maturity, vigor, leaf area, density, or planting date. On the contrary, Olson (1928) and Bowman (1989) found little evidence of interference. Fewer published references exist for grain maize in Europe, but interference effects have been reported in France (Lorgeou, 1986) and in Belgium (Van Waes, 1997).

Interplot interference is a source of bias for cultivar comparisons and so needs to be controlled as well as possible. There exist several alternative or complementary methods to do this, either when defining plot size, choosing the design, or analyzing the data (Kempton, 1997; Monod et al., 1997).

First, interference may be limited by enlarging plot size and leaving border rows of each plot unharvested; however, this will increase the management cost, land area, and amount of seed required. Interference may also be limited at the design stage, by carefully choosing the allocation of cultivars to plots. Thus, in the designs proposed by David and Kempton (1996) and David et al. (1996), cultivars of similar heights are grouped on neighboring plots. This method can be applied provided reliable prior information is available on cultivars and on interference, so that cultivars can be classified into groups with similar interference effects. When prior information is not available, bias may be reduced by using neighbor-balanced designs (Azaïs and Druilhet, 1995).

Sometimes, the methods above cannot be applied, or they are insufficient to eliminate interference. In this case, interference bias may still be reduced at the analysis stage by including interference effects in the statistical model and calculating adjusted cultivar means. Several models for interference are available (Kempton, 1997), and the problem now is to choose the most adequate one. In addition, some models for interference increase the variance for cultivar comparisons by a large amount. If such models are to be used, then an efficient design should also be used. Efficient designs for interference models include neighbor-balanced designs (Azaïs et al., 1993) and optimal designs for height-related interference (David et al., 2000).

This paper is based on a 3-yr experimental study of interference in grain maize cultivar trials, conducted in France from 1994 to 1996 (see Lorgeou et al., 1997). The main motivation for the study was to determine practical recommendations on how best to control interplot interference over a series of grain maize cultivar trials. When the research started, a large number of official trials were still conducted with two rows per plot, while other official and recommendation trials had one unharvested row on each side of each plot. To give useful recommendations, it was necessary (i) to evaluate quantitatively the bias due to interplot interference in such trials and (ii) to compare experimentally several possible methods to reduce this bias, through plot size, experimental design, and statistical analysis. Attention was paid to the consequences of interference on individual trials but, more importantly, over series of trials.

	MATERIALS AND METHODS

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Experimental Sites
The experiments were conducted on experimental sites of GEVES (Groupement d'Etude des Variétés et Semences, the French official registration group), AGPM (Association Générale des Producteurs de Maïs), and three breeding companies (Pau Semences, SDME-KWS, and Verneuil Semences). There were two series of experiments, corresponding to two different maturity groups of cultivars. The North series was associated with early cultivars, which are grown mainly North of the Loire river in France, while the South series was associated with late cultivars, grown mainly in the South of France.

Main Features of the Experiments
Within each experiment, several complete block trials were conducted concomitantly, all with the same set of cultivars but with different plot sizes and different experimental designs. There were seven cultivars and six replicates per trial in 1994 and 1996. There were four additional cultivars and five replicates per trial in 1995. Two experiments of the South series had to be discarded because of damage by wild animals.

Plot Sizes
In one trial per experiment, plots consisted of eight or six seeded rows and only the two central rows were harvested. We called this trial the reference trial because the interplot interference on the harvested rows was expected to be negligible compared with the other trials. In the other trials, plots consisted of either four seeded rows with the two central rows harvested, or of three seeded rows with the central row harvested, or of two seeded and harvested rows. For convenience, we shall denote by m/n a trial with m seeded rows per plot and with the n central rows harvested. Thus the reference trials are either 8/2 or 6/2 trials, and the other ones are 4/2, 3/1 or 2/2 trials. Interplot interference is expected to be maximum for the 2/2 trials, whereas the 4/2 and 3/1 trials represent a compromise between a small size of plots and the ability to control interference. The plots were 5 m long in the 8/2, 6/2, 4/2, and 2/2 trials, and 10 m long in the 3/1 trials.

Experimental Designs
Four types of complete block designs were considered: (i) classical randomized complete block designs, (ii) neighbor-balanced designs, (iii) grouped designs, where only cultivars of similar heights and maturity appear on neighboring plots, (iv) control designs, where plots for the test cultivars are separated by plots with the same control cultivar. Neighbor-balanced designs were constructed and randomized according to the methods described in Azaïs et al. (1993). In these designs, all pairs of distinct cultivars occur on neighboring plots an equal number of times. Grouped designs were constructed and randomized according to the methods described in David and Kempton (1996). In control designs, the design for the test cultivars was a classical randomized complete block design.

For all trials, each complete block was a line of plots with a border plot on either side. Neighbor-balanced and grouped designs were circular, which means that the cultivar on a border plot was the same as the cultivar on the inner plot at the other end of the same block. Thus, the cultivars on the inner plots of blocks had the same neighbors as if blocks were circular. For control designs, the border plots received the control cultivar. For randomized complete block designs, the cultivar on each border plot was one of the test cultivars or, occasionally, an additional standard cultivar.

The plot sizes and experimental designs tested in each experiment are summarized in Table 1. They varied from one year to the next because the objectives evolved. In 1994 and 1995, comparing different designs was one of the main objectives. In 1996, the main objectives were to compare plot sizes and methods of analysis; neighbor-balanced designs were used in all trials because they are more efficient to compare interference models (Druilhet, 1999).

Cultivars
The cultivars were chosen from among those recently tested in French official trials and resistant to lodging. The selected cultivars had large differences for height and for other characters which might be related to interplot interference. This was necessary to ensure sufficient power to compare design and analysis methods with respect to interplot interference. The FAO indexes of the cultivars varied between 250 and 300 for the North series, and between 400 and 560 for the South series. The names of the seven early and late cultivars used in all the trials of the North and South series respectively appear in Fig. 1 . The four additional cultivars used in 1995 were DK248, EPERON, DK300, and RAISSA for the North series, and MADERA, DUNIA, DK512, and CARAMAN for the South series.

View larger version (15K): [in this window] [in a new window]   Fig. 1. Relationship between cultivar heights and cultivar interference effects estimated in 2/2 trials with Model (3)' applied to (A) the North and (B) the South series of experiments

The one or two harvested rows of each plot were harvested in bulk with a plot combine, one replicate of each trial at a time. Plant height was defined as the distance between the ground and the ligule of the highest leaf before harvest. It was measured on 10 successive plants in the middle of each harvested row, and the average was used as the plot value.

Statistical Methods for the Analysis of Individual Trials
Three different models were considered for the analysis of a single trial. Consider the Plot i of Block j, and suppose it received Cultivar v, while its left and right neighbors received Cultivars u and w respectively. The first model is the classical one for a complete block design:

where y_ij denotes the yield on Plot ij, ß_j the mean of Block j, _v the direct effect of Cultivar v, and _ij is an error term.

The second model takes into account interference through a covariate:

where (h)_ij denotes the difference in height (in cm) between Plot i and its neighbors, and is a regression coefficient. More precisely, if i - 1 and i + 1 denote the left and right neighbors of Plot i, then (h)_ij = (h_(i-1),j + h_(i+1),j)/2 - h_i,j. In the case of interference related to height, it is expected that will be negative and its value will correspond to the average yield decrease per cm height difference between a plot and the average of its neighbors.

The third model takes into account interference through varietal neighbor effects:

where _u and _w denote the interference effects of Cultivars u and w. The parameter is negative for the more aggressive cultivars and positive for cultivars sensitive to interference from neighbors.

The three models are linear models and Model (1) is a submodel of the other two. Thus interference can be assessed by testing the hypothesis [ = 0] in Model (2) and the hypothesis [_v = 0 for all v] in Model (3). Model (2) is much more parsimonious than Model (3), since it includes only one parameter for interference whereas Model (3) includes n - 1 independent 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.

The objective of a cultivar trial is to estimate and compare pure stand cultivar effects _v, that is, the effect of Cultivar v when it is surrounded by itself. For Models (1) and (2), _v = _v, whereas for Model (3), _v = _v + 2_v (see Kempton, 1997, p. 112).

Comparison between Trial Methods to Control Interference
As used in this article, a trial method will refer to the combination of plot size, design and analysis of a cultivar trial. To compare the ability of various trial methods to control interference, we need to compare their estimates of pure stand cultivar effects with those given by a method of reference where interference is supposed to be negligible. For each experiment, the reference method will be the reference trial analyzed with Model (1). The trial methods to be assessed will be combinations of 4/2, 3/1, or 2/2 plots, with randomized complete block, neighbor-balanced, grouped, or control designs, and analysis with Models (1), (2) or (3).

Our main criterion to compare trial methods will be the mean square difference (msd), which we now define. Let ^*_v denote the estimates of (centered) cultivar effects given by the reference method, and let ⁺_v denote the estimates given by another trial method represented in the same experiment. The mean square difference (msd) for the tested method (with respect to the reference method) is defined by

where the summation is over the n cultivars tested in the experiment. A small value of msd indicates that the tested trial method gives cultivar estimates close to those of the reference method, and so it indicates that interference has been small or that it has been corrected efficiently. In contrast, uncorrected interference will cause bias in the estimates and so it will increase the value of msd.

The expectation of msd is in fact the sum of three terms: (i) the average variance of ^*_v, (ii) the average variance of ⁺_v, and (iii) the average squared bias of ⁺_v with respect to ^*_v. The first term depends only on the reference trial, and so it is equal for all methods tested in the same experiment. The sum of the second and third terms is the mean square error on cultivar estimates when the tested method is used. So the msd criterion includes not only the bias, but also the extra-variability caused by interference or by the adjustments for interference. Consequently, it will also be large if a method estimates cultivar effects with poor precision.

Joint Analysis of Each Series of Experiments
As mentioned in the introduction, evaluating interference and methods of control over a series of trials was a major objective of the study. To do this, Models (1), (2), and (3) were extended to cope with a set of trials, by including experiment main effects, interactions between experiments and cultivars, and interactions between experiments and interference effects. The experiments corresponded to different locations and/or years, but because of the relatively small number of experiments and because of a lack of balance, we did not try to distinguish between year and site effects.

The extended models are

where y_eij is the response on Plot i of Block j of Experiment e; µ is the general mean; M_e is the main effect of experiment e; B_ej is a block effect nested within the experiments; _v is the main effect of Cultivar v; T_ev is an experiment-cultivar interaction term; (h)_eij is the height-difference measured for Plot (eij); is the average regression coefficient for the height-difference covariate and ( + L_e) is the coefficient for experiment e; _u is the interference main effect of Cultivar u and F_eu is an experiment-cultivar interaction term for varietal interference effects; _eij, ^'_eij, and ^''_eij are error terms.

The three models were applied separately to the reference trials, the 4/2 trials, and the 2/2 trials. We refer to the Results section for more details on which trials were chosen in each case. For each type of trial and for each model, first an analysis of variance was performed. Then, all factorial effects involving experiments, that is, the effects denoted by M, B, T, L, and F above, were assumed to be random and to follow independent centered Gaussian distributions with a common variance for each model term. The corresponding mixed models were analyzed by restricted maximum likelihood (REML) (see Patterson, 1997); the msd criterion was then applied to the estimated main effects of the seven cultivars assessed in all experiments.

Software
Most calculations, including all the analyses of individual trials, were performed with the S-PLUS (MathSoft, Inc., Cambridge, MA) statistical package. The joint analyses of variance were performed with the GLM procedure of SAS (Cary, NC). For the REML joint analyses, we used the VCOMP and REML directives of Genstat (NAG Ltd., Oxford, UK). When using statistical softwares, the interference effects of Models (3) and (3)' were declared through covariates associated with each cultivar. In order to ensure that the estimated cultivar effects or means corresponded to pure-stand effects or means, the covariate associated with Cultivar v was given the value -2 on the plots receiving Cultivar v, 1 on the plots which were neighbor to Cultivar v, and 0 for all the other plots. In the mixed Model (3)', the F_ev effects were assumed to follow the same distribution, independently. So when using the REML directive of Genstat, the variances of the parameters associated with the neighbor covariates were constrained to be equal by the RELATION option of the VCOMP directive.

	RESULTS

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Preliminary Analyses
As expected, there were large site and year effects on yield, with yields ranging between 6 Mg ha^-1 and 15 Mg ha^-1 (Table 2). The standard errors of observations were quite large in some trials, due to soil or density heterogeneity, drying conditions, or lodging. In the South series, they were larger in the trials with no border rows, which suggests that interference increased the block-cultivar interaction.

Interference in Individual Trials
In the North series, the height-difference covariate was significant at the 5% level in none of the reference trials, in two out of nine 4/2 or 3/1 trials, and in seven out of eleven 2/2 trials (Table 3). For the nine 2/2 trials with a randomized complete block or a neighbor-balanced design, the average estimated value of the coefficient was equal to –0.023 Mg ha^-1 cm^-1. In almost all trials, the estimated coefficient was either negative or close to zero. However, it was significant and positive in the 4/2 trial performed at Beaulay in 1996. A possible reason, to be taken with much caution, is that the central rows could grow better when the border rows were depressed by interference. Cultivar interference effects from Model (3) were significant at the 5% level in one reference trial, in none of the 4/2 or 3/1 trials, and in seven 2/2 trials with either a classically randomized or a neighbor-balanced design.

Mean Square Differences
For each experiment, the mean square difference with the reference method was calculated for the 4/2, 3/1 and 2/2 trials analyzed by Models (1), (2) and (3) (Table 4). With Model (1), the msd values were smaller for 4/2 or 3/1 trials than for 2/2 trials, except for N96C and S95Mr. Model (2) tended to decrease msd compared with Model (1) for 2/2 trials, particularly in the trials where the height-difference covariate was significant, such as the 2/2 trials of N95R and N96B. In contrast, applying Model (2) increased msd in several 4/2 trials, especially in experiments N96B and S95Mr where the covariate was significant, but with an unexpected positive coefficient.

Joint Analyses of the Experiments
The joint analyses were performed on the experiments containing a reference trial, a 4/2 trial and a 2/2 trial, i.e., N94B, N94V, N95C, N96B, N96V, N96C, and N96R (seven experiments) for the North series, and S94Mn, S95Mr, S96Mr, S96P (four experiments) for the South series. They were performed separately on the reference trials, on the 4/2 trials, and on the 2/2 trials. In the experiments with several 2/2 trials, only the neighbor-balanced trial was used; there was no neighbor-balanced trial in N95C, so the grouped design was used instead.

The main features of the analyses of variance with Model (2)' and Model (3)' are listed in Table 5 and Table 6 respectively. The interference main effects are the most important to consider here, since they represent the effects which appeared repeatedly over the series of trials. In the North series and for both models, they were non-significant in the reference and 4/2 trials but highly significant in the 2/2 trials. There were some small interaction between experiments and interference, even in the reference and 4/2 trials. This suggests that interplot interference may have occurred in these trials, but it was small and not very consistent from one site-year to another. The results for the South series confirm that there were interference main effects mainly in the 2/2 trials. The interaction between experiments and interference in Model (2)' was larger than in the North series for the 4/2 and 2/2 trials.

The msd values are in Table 7. With Model (1)', cultivar effects obtained from 4/2 trials were more consistent with the reference than those obtained from 2/2 trials. The data from 4/2 trials were also analyzed with Model (1)' using the first three blocks of the trials only, in which case 4/2 and 2/2 trials have the same land area or similar areas. The resulting msd values were equal to 0.025 (Mg ha^-1)² for the North series and to 0.057 (Mg ha^-1 )² for the South series, and were lower than or equaled those obtained using 2/2 trials. For 4/2 trials, Model (1)' was well adapted and the models for interference resulted in no improvement. On the contrary, the estimates of cultivar effects from 2/2 trials were closer to those of the reference when models for interference were used. Model (2)' performed better in the North series, and Model (3)' performed better in the South region. Figure 2 shows how the adjustment by Model (3)' on the 2/2 trials affected the consistency with the reference trials. In most cases, adjustment correctly led to an increase or decrease of cultivar effects. However, several cultivars were overcorrected, especially DK250 and MAGISTER in the North series.

View larger version (20K): [in this window] [in a new window]   Fig. 2. Comparison between cultivar effects estimated in the reference trials with Model (1)' and cultivar effects estimated in 2/2 trials with Models (1)' and (3)'; (A) North series, (B) South series

	DISCUSSION

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Interference depended on environmental conditions and varied to some extent between locations and years. However, as our study demonstrated, it may be a source of bias on cultivar comparisons, which is repeated over trials for a large part. In this case, contrary to the lack of precision due to field heterogeneity or genotype-environment interaction, interference can hardly be controlled just by increasing the numbers of replications, sites, and years.

The bias due to interference can result in rankings of cultivars which do not reflect the behavior of cultivars in pure stand fields. In our study, some cultivars appeared to be under- or over-estimated by more than 0.4 Mg ha^-1 when plots with two unguarded rows were used (Fig. 2). An additional problem with interference is that it increases the variability within a trial, because each cultivar has different neighbors in different blocks and so is subjected to different interference effects. For example, one validation rule for official grain maize trials in France (the standard error of observations must be smaller than 0.8 Mg ha^-1) would have led to rejection of four 2/2 trials but only one reference or 4/2 trials.

Our study was based on specifically designed experiments, which were carried out with a small number of aggressive and sensitive cultivars. This may explain why the results of the present paper differ from those of Bowman (1989), who found little interference when analyzing official cultivar trials on grain maize in the USA. The difference may also be explained by different cultural practices: in the U.S. trials, plant density was lower, distance between rows was larger, and yield levels were lower than in our experiments.

Plots with unharvested border rows appeared as the most reliable method to control interference in grain maize trials. Interference effects cannot be totally dismissed in trials with such plots, and interference has actually been shown to extend to more than one row in several other species (Kempton and Lockwood, 1984; Clarke et al., 1998). However, plots with one border row on each side were sufficient to control the major part of interference. In our experiments, the use of 4/2 plots together with a standard analysis proved more efficient at reducing bias than any design and analysis method applied to 2/2 trials. Although there were fewer 3/1 trials, similar conclusions applied to them as well.

Models for interference resulted in no more improvement to the 4/2 trials. For 2/2 individual trials, Models (2) and (3) reduced bias, but Model (3) increased variance so much that it should be used with much caution. In spite of this limit, Models (2)' and (3)' proved useful to reduce bias in series of 2/2 trials. Combining the information from several trials probably limited the increase in variance due to the adjustment for cultivar interference effects. A few other models were tested with little improvement (additional covariates, random interference effects, sensitivity to height difference depending on the cultivar), except that Model (3) usually performed better with random interference effects for individual trials.

Several recommendations on design can be made based on design theory and on the few experiments where different types of designs were compared. When Model (1) is expected to be used, particularly in 4/2 trials, neighbor-balanced designs or designs with grouping of similar cultivars can still be useful to protect against small interference effects. Provided prior information is available, designs which group similar cultivars or the optimal designs of David et al. (2000) are well adapted to Model (2). However, if Model (3) is likely to be used, these designs will be inefficient and neighbor-balanced designs should be preferred (Azaïs et al., 1993). The control designs are not worth the extra cost in land area and management cost, except possibly in selection when the available seed is too low for plots with border rows.

	ACKNOWLEDGMENTS

 
This work was financially supported by the French Ministère de l'Agriculture et de la Pêche. We are particularly grateful to Bernard Aizac (GEVES), Régis Brassart (Verneuil Semences), André Lambert (SDME-KWS) and Jean-Paul Sampoux (Pau Semences), and to all the people from their and our companies who participated to the experimental work and to the discussions on the project. We thank Johan Van Waes for references on grain maize interference, and the referees and Rob Kempton for helpful comments.

Received for publication March 8, 2000.

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