16 J. Vollmann et al. European Journal of Agronomy 12 2000 13–22
boundaries between neighbouring plots falling in different blocks Brownie et al., 1993.
Generalized lattice designs were analysed using the PLABSTAT software program Utz, 1988.
Plot residuals and covariates from neighbour plots were calculated from the raw data using a spread-
sheet program, Corel Quattro Pro Corel, Orem, UT and the appropriate field layout information.
Combined analysis of variance and covariance as well as the adjustment of entry means by neighbour
covariates were carried out using the GLM pro- cedure and the LSMEANS statement of the SAS
program SAS Institute, 1988. Phenotypic and genetic coefficients of correlation between charac-
ters were also calculated with PLABSTAT; as there is no adequate test of significance available for
Fig. 1. Schematic representation of the neighbour analysis
examining genetic
coefficients of correlation
methods applied. In EW1, EW2 and EW3, the residuals from
Thomas and Tapsell, 1985, the standard errors
1, 2 or 3 neighbour plots, respectively, are used as an environ- mental covariate to correct the plot value of a test plot for
of the coefficients were used as an indicator of
field trends.
their significance.
3. Results
method proposed by Papadakis 1937. Covariates EW2 and EW3 were calculated from plot residuals
of two EW2 or three EW3 plots Fig. 1 at As an indication of the presence of spatial field
trends detectable by lattice analysis, the efficiency each side of a test plot, respectively, because the
use of two or more neighbour plots for describing of lattice designs is presented in Table 1 for
different soybean performance experiments and for a local trend could improve the efficiency of analy-
sis in particular experiments Vollmann et al., all characters investigated. Differences in the effi-
ciency roughly demonstrate that distinct characters 1996a. For border plots missing particular neigh-
bours, covariates were calculated without the resid- were affected by spatial field variations to a clearly
different extent: time to flowering, time to matu- uals of those plots. Subsequently, a combined
analysis of variance and covariance was carried rity, the duration of the reproductive phase, and
oil content were generally less influenced by spatial out according to the model:
variations than grain yield, protein content, and x
ij =
m+t i
+ bEW
ij +e
ij ,
seed size. Moreover, differences in lattice efficiency can also be recognized between different years:
where x ij
denotes the character expression of geno- type i in replication j =plot value, m is the overall
lattice efficiencies were higher in the 1995 and 1996 trials than in 1997, which suggests that seasonal
mean value, t i
denotes the effect of genotype i, b indicates the regression coefficient of the EWij
effects influenced the magnitude of spatial varia- tions at a given experimental site.
covariate used, and e ij
represents the random error term. For each analysis of variance, one additional
Comparative results
of different ANOVA
models for controlling spatial variations in grain degree of freedom was allocated to the regression
coefficient because residuals were calculated from yield, protein and oil content, and seed size are
summarized in Table 2 using the EXP2 experiment genotype means as concomitant covariates Pearce
and Moore, 1976. Block effects were ignored as an example. The highest residual error mean
squares and CVs were obtained when the random- when applying the neighbour analysis, because the
concept of blocking would establish artificial ised complete block analysis was applied. Residual
17 J. Vollmann et al. European Journal of Agronomy 12 2000 13–22
Table 2 Comparison of various ANOVA models for the control of spatial variation in four characters of the EXP2 experiment
ANOVA model Grain yield
Protein content Oil content
Seed size MSE
a P F
b CV,
MSE a
P F b
CV, MSE
a P F
b CV,
MSE a
P F b
CV, RCB
c 175 126
0.001 17.5
421 0.179
7.0 145
0.001 5.3
74.0 0.001
5.5 6×6 lattice
d 83 023
0.001 12.0
234 0.038
5.2 124
0.001 4.9
36.7 0.001
3.9 EW1
e 71 751
0.001 11.2
334 0.181
6.2 131
0.001 5.0
46.2 0.001
4.4 EW2
e 77 168
0.001 11.6
272 0.040
5.6 137
0.001 5.2
36.3 0.001
3.9 EW3
e 86 096
0.001 12.3
263 0.061
5.5 126
0.001 4.9
33.5 0.001
3.7 a Residual error mean square.
b Probability value of entry-H0 from F-test. c Randomized complete block design.
d For the lattice design, the effective error MS is presented instead of the residual error MS, which only covers the intra-block error. e Neighbour analysis using EW1, EW2, or EW3, respectively, as neighbour covariate.
error mean squares were drastically reduced by lattice or neighbour analysis in all characters
except oil content, which seemed to be less affected by spatial heterogeneity in this experiment. In seed
protein content, significant genetic differences between entries could only be detected by lattice
or EW2-based neighbour analysis, as revealed by the respective F-tests. Correspondingly, residual
error mean square was similarly reduced after lattice or neighbour analysis of different characters
in the other experiments investigated results not shown.
The EW2 residuals of the EXP2 experiment were further utilized to visualize field trends in
four different characters Fig. 2: Rather similar patterns of trend can be recognized for grain yield,
protein content, and seed size, whereas the trend lines of oil content show a pattern that seems to
be opposite to those found in the other characters. The view of trend similarities between grain yield
and other seed characters of the same experiment is further supported by the significant and close
correlations between the respective EW2 residuals Fig. 3. Apart from EXP2, similar correlations
between EW2 residuals of different characters were detected in other experiments grown in different
seasons Table 3. Positive correlations between EW2 residuals were found between grain yield and
protein content, and between grain yield and seed
Fig. 2. Field trends of grain yield, protein content, oil content
size. This suggests that soil properties within
and seed size in each of the two replications grown in two
heterogeneous fields, which improve grain yield
consecutive blocks of 36 plots of the EXP2 experiment, as revealed by EW2 neighbour residuals.
also boost both seed protein content and seed size.
18 J. Vollmann et al. European Journal of Agronomy 12 2000 13–22
for spatial variations. Genetic coefficients of corre- lation were rather similar for each of the three
methods of statistical analysis, although the esti- mated levels of significance tended to be higher
after lattice or EW2 adjustment than after RCB analysis. Considerable differences were found
between particular phenotypic coefficients of corre- lation after an adjustment of field data. The pheno-
typic coefficient of correlation between grain yield and protein content was low r=−0.18 and statis-
tically not significant, when calculated from unad- justed genotype mean values after RCB analysis.
However, when using lattice- or EW2-adjusted means, the correlation between grain yield and
seed protein content was clearly negative Table 4. An even more drastic influence of data adjustment
on the relationship between grain yield and protein content was found in the EXP1 experiment. In
this case, the estimate of the genetic correlation between
yield and
protein content
was r
g =−
0.70, whereas the correlation between EW2 residuals of the two characters was r=+0.69
Table 3. The apparent lack of a significant phe- notypic correlation between the two characters
[Fig. 4a] might be due to a complete balancing of the negative genetic correlation by the positive
correlation between EW2 residuals, which describe the environmental variation. After adjusting geno-
typic mean values by EW2 values and lattice analysis, which were the most efficient procedures
in terms of a reduction of residual error mean
Fig. 3. Relationships between EW2 neighbour residuals of grain
square for grain yield and protein content, respec-
yield and seed characters for the EXP2 experiment.
tively, the phenotypic correlation between the two characters clearly changed to negative [Fig. 4b].
Negative correlations between EW2 residuals were always found between grain yield and oil content,
and between protein and oil content. These correla- tions between environmental covariates were sta-
4. Discussion
