Volume 12
Issue 2
Agronomy
JOURNAL OF
POLISH
AGRICULTURAL
UNIVERSITIES
Available Online: http://www.ejpau.media.pl/volume12/issue2/art01.html
THE USEFULNESS OF SOME SOIL PROPERTIES AND PLANT TRAITS FOR THE ESTIMATION OF SPATIAL VARIATION IN THE 3^{5} FIELD EXPERIMENT WITH PEA (PISUM SATIVUM L. SENSU LATO)
Janusz Gołaszewski, Dariusz Załuski, Aneta StawianaKosiorek, Paweł Sulima
Department of Plant Breeding and Seed Production,
University of Warmia and Mazury, Olsztyn, Poland
The problem of the effective control of soil variability is the main limitation on the broader use of factorial or fractional designs in agricultural experimental practice. The objective of the study was to assess the usefulness of some soil (pH, P, K, Mg, organic C) and plant traits (plant height, seed yield) for the estimation of spatial variation of the experimental field and to assess their usefulness in increasing the efficiency of 3^{5} field plot experiment with pea. Geostatistical methods were used in spatial analyses and ANOVA and ANCOVA in the analyses of the data from the experiment. The relative efficiency of the ANCOVA with information on spatial variation compared to the classic ANOVA was calculated. All of the studied soil properties and plant traits were spatially autocorrelated. The experimental semivariograms were transitive, having the range and the sill fitted with the spherical and exponential models. The range of spatial autocorrelation for soil properties was 18.573.7 m and for plant traits 1.63.7 m, while the share of structural variance (C) in the variance of sill (C_{0} + C) was 60% and 90% for soil properties and plant traits, respectively. The values of spatial descriptors predicted for each experimental plot by kriging and used as covariates in ANCOVA resulted in higher efficiency.
Key words: field experiments, factorial design at three levels, geostatistics, spatial variation.
INTRODUCTION
The changing demands of the agricultural market for the quality of raw crop products needed quick and effective testing methods of the new crop production technology. Each change in the technology is a purposeful manipulation in many agrotechnical factors that affect yield or other useful plant traits. The experimental checking of the modification may be done through factorial or fractional factorial designs. The theory of these designs is well described in literature [4,6,11,13,14,17,30,46] but the practical use is generally limited to industrial applications. It results from the specificity of the industrial studies – the scientific objectives are mainly focused on the main treatment effects estimation, while the interaction effects are of minor importance and, what is relatively easy to accomplish in industrial experimentation, it is possible to unify the experimental conditions [49]. These obvious advantages for industrial research are not in accordance with agricultural experimentation because the interaction effects, especially the twofactor interactions effects, are usually of major importance and the results of the experiments are highly related to the environmental conditions. Nevertheless, taking into account the usefulness of the designs in the testing of the multifactor influence on plant traits, there is an increasing number of works on the utilization of the designs by agricultural researchers. Such designs were applied in the experiments with different crops [23,34,38,42]. From the analysis of the works and taking into account some generalizations on the application of factorial designs made by Yates [46], Cochran and Cox [6], and Box et al. [4], it was possible to formulate some methodical observations that can be summarized as follows. Firstly, the main characteristics of the designs were that there were factorial or fractional designs with two levels and there was the assumption of linear relation between the quantitative factors and yield. This was a simplification, as it is commonly known that the relationship between many agricultural traits and the experimental factor is usually not linear. Secondly, the effect of a given factor in the presence of other factor effects is quite difficult to detect and when detected, it has a high practical value because it reflects the real effect of the factor in the production. Third, the results of the factorial design experiment may be a prerequisite for the future planning of field experiments for the precise description of the factor's level in the simple experiment.
The main limitations of the broader use of factorial designs in agricultural experimentation are difficulties in the effective control of soil variability. Because of a large number of treatments to be tested and a reduced number of replicates up to a single one, which is not common in field conditions, soil variation is controlled by grouping the treatments into incomplete blocks. It is a very effective approach but the problem is that the pivotal, from the agricultural point of view, main and interaction effects may be confounded with soil variation, which is especially distinct in fractional factorial designs when the number of studied treatments generated from the whole set of factorial design treatments is significantly reduced [2,3,17,29]. Załuski et al. [48] showed that the threshold of relative efficiency of factorial design with blocks is set at a very high level; the 3^{5} design with three large incomplete blocks of 81 plots were about 1.5 times more efficient than CRD and other analyses with spatial information included had similar or slightly higher efficiency. Nevertheless, their observations have only a theoretical meaning because such large capacity of the block in the field plot experiment will not be accepted and at the same time the arrangement of small capacity incomplete blocks for this onereplicated factorial design, i.e. with 9 experimental units per block, in a way that all the main and twofactor effects may be estimable is not possible.
In order to assure high efficiency in the field experiment, the soil variation in the experiment should be as uniform as possible. This means that it should be homogenous (continuous and isotropic) but in practice the soil is heterogeneous (zonal and anisotropic). Soil variation as a general term in field experiment methodology should not be identified only with soil fertility, as it also comprises climate and type of soil influence, effects of interplot plant competition, as well as other biotic and abiotic sources like weeds, pests, diseases, men's activities, etc. [20,21,22,26,32]. The continuity of soil variation causes spatial autocorrelation of observations from neighbouring plots and actually may violate the assumption about the independence of experimental errors. A common and easy way of the neutralization of the spatial effects is randomization. However, as van Es and van Es [44] and Grondona and Cressie [25] showed, the process does not fully reduce spatial autocorrelation and may seriously distort the treatment comparisons.
The idea of controlling soil variability in field plot experiments and the problem of autocorrelated errors from neighbouring plots is as old as the history of rational agricultural experimentation. It was Fisher who introduced the concept of experimental strategy where replications, blocking and randomization are the foundations of the proper analysis of the results of field experiments [15,16]. This concept was gradually developed and researchers investigating field experimentation methods created new approaches in which spatial variability was given more importance. One of the first such approaches was by Papadakis [37], who suggested the socalled nearest neighbour analysis in which information from adjacent plots was included into statistical analysis. Even if it was originally an intuitive approach, the statistical background was made by Bartlett [1], and then further modifications of the approach were developed [5,8,9,40,43,47]. The modifications took into consideration different components of spatial variation, like spatial plant competition effects [31], the presence of trend [28,40], twodimensional spatial variation [8], or fixed and random components of spatial variation [50]. The significant impulse for spatial approach to the methodology of field experiment was connected with the development of spatial estimation methods in the 1960s and 1970s to become distinguishable in a new science – geostatistics [33,35].
All the hitherto developed spatial approaches to field experimentation enables modelling spatial variation in field experiments using the data on traits of interest, mainly plant height and yield, and using information on spatial variation in further statistical analyses. Such approach enables modelling plot residuals or differences from neighbouring plots and even if it leads to the spatial model with spatial parameters, it is hard to assume that there are "pure" spatial variation estimates, i.e. due to not fully estimable treatments × environment interaction. In the approach presented in this work, the authors assumed that the background spatial variation should be quantified at first and then this information ought to be used to improve the efficiency. Because of many possible different spatial descriptors which may be used in the spatial analysis of the experimental field, an attempt was made to estimate the usability of some soil properties and plant traits for spatial analysis purposes and for improving experiment efficiency.
The aim of the studies were: (1) to assess the usefulness of some soil properties and plant traits in the characterization of spatial variation of the experimental field, and (2) to measure the effectiveness of an alternative approach in statistical analysis of the data from multifactorial field experiment in relation to the classic CRD analysis. There is an approach in the application of factorial designs in agricultural experimentation based on the spatial analysis of the experimental field and on using the information on the spatial variability of the field in the statistical analysis of the trait of interest (i.e. yield). The results from the field experiment established in a completely randomized factorial design 3^{5} and the additional measurements done prior to the experiment or on the check plots were utilized in the analysis of covariance.
MATERIAL AND METHODS
The study was based on the results of a oneyear (2005) singlereplicated factorial field experiment 3^{5} with pea (Pisum sativum L. sensu lato) conducted in northeastern Poland (Experimental Station – Tomaszkowo), and on spatial measurements of soil properties and plant traits on check plots. Five experimental factors were based on three levels: A – cultivars (Agra, Set, Wenus), B – PK fertilization doses (natural fertility, PK160 (60 + 100) kg·ha^{1}, PK320 (120 + 200) kg·ha^{1}, C – sowing dates (the earliest possible, 10 and 20 days after the first date, respectively), D – sowing densities (70, 100, 130 kg·ha^{1}), and E – protection (without protection, seed protection, seed protection plus plant protection). The 243 treatments applied to plots (1.8 × 4 m) were arranged randomly in three experimental strips. Pea yield per plot (in kg) was considered as a trait of interest. Around the strips, a single variety was sown to avoid edge effects. Prior to the experiment, soil samples were taken from 240 (8 × 30) sampling points at the regular grid of 5 × 5 m to estimate soil properties: soil acidity (pH in KCl), content of available phosphorus (in P_{2}O_{5}), potassium (in K_{2}O), magnesium (Mg), and organic carbon (C). They were measured with standard procedures of Tiurin (C), EgnerRiehm (P_{2}O_{5} and K_{2}O), and Schachtschabel (Mg) [36]. During harvest, in the area around the experimental strips, 486 (6 × 81) check plots of 0.5 m^{2} were marked out, and plant height (Ph) and seed yield (SYc) were measured. The seven traits were taken as the spatial descriptors of soil variation. Initial general information on the meaning of the descriptors and on the difficulty of measurements and time consuming estimates are presented in Table 1.
Table 1. Descriptors of spatial variation in the 3^{5} field experiment with pea 
Descriptors* 
Importance 
Difficulty in measurement 
Time 
Cost 
Corg 
essential for plant growth and its effects on other soil properties 
medium 
medium 
medium 
pH 
essential for plant growth and availability of nutrients to plants 
low 
low 
low 
P 
macro element – stimulates early plant growth and hastens maturity 
high 
high 
high 
K 
macro element – disease resistance and control of turgor 
high 
high 
high 
Mg 
macro element – chlorophyll 
high 
high 
high 
Ph 
varietal trait – facilitation of harvest 
low 
low 
low 
SYc 
varietal trait – main purpose of production 
low 
medium 
medium 
* Corg – organic carbon, Ph – plant height, SYc – seed yield from the check plots 
Organic carbon is the main part of organic matter in the soil (ca. 55%) and is essential for plant growth due to its effects on other soil properties. Phosphorus, potassium and magnesium are essential elements classified as the macronutrients because of the relatively large amounts of these elements required by plants. One of the main roles of phosphorus in plants is energy transfer. Phosphorus availability for plants stimulates early plant growth and hastens maturity. Potassium enhances disease resistance in plants by strengthening stems, contributes to a thicker leaf surface layer that guards against disease and water loss, controls the turgor pressure within plants to prevent wilting, and enhances seed size, flavour, texture, and development. Magnesium is an essential ingredient of chlorophyll, the green plant pigment that gives leaves their colour and enables the plant to make food from sunlight. The pH of the soil determines the availability of the macro elements for plants. Plant height and seed yield are the varietals traits. The former may determinate the easiness of harvest, and the latter is a trait of plant productivity. From the practical point of view, the descriptors differ in the complexity of measurements and the time needed to estimate the result. Relatively easy and quick are measurements of Corg (organic carbon) and pH (soil acidity), and plant traits, while measurements of macro nutrients engage higher costs and are time consuming. On the other hand, in most field experiments such measurements are obligatory in order to balance correctly the doses of fertilization.
Descriptive statistics were used to determine the measures of central tendency and the dispersion of the observed characteristics. The first step in the description of spatial variation was to assess the serial correlation coefficient [24]. The measure is generally used to test the randomness of a data set and it is useful in the characterization of the trend in soil fertility. Serial correlation coefficient r_{s} of n observations (z_{1},z_{2},z_{3}...z_{n}) calculated for rows and columns (across and along experimental strips) is:
where 
The data z_{ij} from grid points was detrended by the median polishing technique [7],
where:
trend – the largescale spatial component,
res_{ij} – the smallscale stochastic residual component,
me – the overall median,
r_{i} – the row effect,
c_{j} – the column effect.
Median polishing method is used to assess spatial trends in data sets. Sums of squares of raw and residual data were calculated to estimate the portion of variance represented by the trend [12].
Isotropic semivariances γ(h) of detrended data were computed as follows:
where:
h – a lag distance (lag is the vector that separates any two locations having both distance and direction),
N(h) – the number of pairs of residuals at each distance interval h.
The semivariogram model with the highest value of R^{2} was fitted, and the estimated parameters of the model were used in ordinary kriging of the values of soil properties and plant traits for each experimental plot.
As for statistical analysis, two models were used: ANOVA model with main and all twofactor interaction effects, and the nonsignificant higher order interactions were used as the error term, ε [10].
Where all the indexes i, j, k, l, and m take 1, 2 and 3; µ is the overall mean; α_{i}, β_{j}, ν_{k}, π_{l}, τ_{m} correspond to the main effects of factors A, B, C, D and E; the bracketed terms denote ten interactions: AB (α,β)_{ij}, ..., DE (π,τ)_{lm} and ε is the error term with zero mean and variance σ^{2}.
The second model was the ANCOVA model with soil properties and plant traits from the check plots as the concomitant variables (X):
where:
λ – the regression parameter.
The relative efficiency of ANCOVAs to ANOVA was calculated as follows [20,48]:
where MSE.Y and MSE.Y(adj.) are the mean squares errors of Y before and after adjustment, respectively, MST.X_{i} is the mean square of treatments of X, and SSE.X_{i} is the sum of squares of the error of X.
To assess the spatial autocorrelation in the residuals from ANOVA and ANCOVAs, Moran's I statistic at lag h = 1 was computed [41]:
The geostatistical analyses were supported by Surfer v. 8 (Golden Software, Inc.) and GS+ v. 7 (Gamma Design Software, LLC – Geostatistics for Environmental Sciences) and statistical analyses with Statistica v. 7.1 (StatSoft, Inc.).
RESULTS
The studied indicators of spatial variation, soil properties, and plant traits were highly differentiated (Table 2). The lowest variation expressed in coefficient of variation had pH and the highest one was stated for SYc from the check plots. The distributions of the SYc as well as of the content of P and K were positively skewed. Median polishing technique produced the data with reduced standard deviation. The reduction was more pronounced for soil properties than for plant traits.
Table 2. Descriptive statistics for the indicators of spatial variation 
Descriptors* 
N 
Mean 
SD 
CV 
Skewness 
Kurtosis 
SD (median 
Soil properties 

240 
1.13 
0.24 
21.24 
0.4188 
0.1280 
0.12 

pH 
240 
5.51 
0.36 
6.53 
0.3337 
0.0231 
0.25 
P 
240 
23.52 
4.21 
17.90 
0.7428 
0.8584 
2.94 
K 
240 
14.92 
4.00 
26.81 
1.3504 
2.4876 
2.85 
Mg 
240 
6.77 
1.25 
18.46 
0.3442 
0.2723 
0.73 
Plant traits (check plots) 

Ph 
486 
92.50 
25.00 
27.03 
0.3051 
0.3493 
20.33 
SYc 
486 
33.21 
21.66 
65.22 
0.9811 
0.2626 
15.13 
* Corg – organic carbon, Ph – plant height, SYc – seed yield from the check plots 
Serial correlation can be viewed simply as a simple correlation between two variables, one at site i and another at site i + 1. A low value of the serial correlation coefficient indicates that fertile areas occur in spots, and a high value indicates a fertility gradient [24]. For all the studied descriptors, both vertical (length, along columns) and horizontal serial correlation coefficients were relatively high and generally similar in their values (Table 3). There was a slightly stronger serial correlation vertically. Mostly, the comparison of the two mean squares for vertical and horizontal planes pointed to different perpendicular spatial variation. For pH, the content of K and Corg the horizontal mean squares (MS_{h}) exceeded the vertical ones (MS_{v}) over 2.5 times. The comparison of the two mean square values showed clearly that the spatial change of the properties was more pronounced along the length of the field. The inverse relation between vertical and horizontal mean squares was stated for Mg and P content but it was not significant.
Table 3. Vertical and horizontal serial correlation coefficients and mean squares for spatial descriptors of the experimental field with pea 
Descriptors* 
Coefficient of 
Mean squares: 
F_{emp.} 
p 

Vertically 
Horizontally 
Vertically 
Horizontally 

Soil properties 

Corg 
0.8693 
0.8362 
0.14 
0.36 
2.56 
0.035 
pH 
0.6535 
0.6515 
0.22 
0.56 
2.60 
0.033 
P 
0.6183 
0.6555 
79.50 
61.39 
1.29 
0.385 
K 
0.6535 
0.5710 
23.53 
65.57 
2.79 
0.024 
Mg 
0.7841 
0.5582 
16.12 
5.11 
3.15 
0.060 
Plant traits (check plots) 

Ph, cm 
0.7378 
0.6082 
841.95 
1655.48 
1.97 
0.093 
SYc, g 
0.4800 
0.3770 
1484.37 
1566.31 
1.06 
0.392 
* Corg – organic carbon, Ph – plant height, SYc – seed yield from the check plots 
Table 4. Parameters of isotropic models fitted with the experimental semivariograms of some soil properties and plant traits 
Corg* 
pH 
P 
K 
Mg 
Ph 
SYc 

Model** 
Sph 
Sph 
Sph 
Exp 
Sph 
Exp 
Exp 
C_{0} 
0.0064 
0.0218 
3.5500 
5.44 
0.2569 
25.2 
31.0 
C 
0.0070 
0.0467 
5.1690 
5.37 
0.2639 
206.1 
361.8 
C_{0}+C 
0.0134 
0.0685 
8.7190 
10.81 
0.5208 
231.3 
392.8 
C/(C_{0}+C) 
0.52 
0.68 
0.59 
0.50 
0.51 
0.89 
0.92 
A, m 
38.3 
18.5 
25.3 
73.7 
27.9 
3.7 
1.6 
R^{2} 
0.81 
0.98 
0.96 
0.70 
0.96 
0.89 
0.56 
* Corg – organic carbon, Ph – plant height, SYc – seed yield from the check plots 
** Sph – spherical,  
Exp – exponential, 
All the semivariograms had a range and a sill (Fig. 1, Table 4), and the spherical and exponential models were fitted to them. Generally, the two models are very similar in that they approach the sill gradually. They differ in the rate at which the sill is approached and in the fact that the exponential model actually never converges the sill. Overall, the goodness of fit of the semivariogram models expressed in R^{2} was very high. The smallest value of R^{2} = 0.56 was estimated for the semivariogram model of SYc recorded from the check plots and was the most variable descriptor in the study. The other values of R^{2} were in the range of 0.70 (K) – 0.98 (pH). The percentage of the structural variance of soil properties C in the sill (C_{0} + C) was 50–60% and accounted for about 90% in plant traits. The percentage of trend in the total variation was the lowest for Ph (7%) and Corg (17%) (Fig. 2).
Fig. 1. Empirical and theoretical semivariograms for spatial descriptors: organic carbon – Corg (a), soil acidity (b), phosphorus (c), potassium (d), magnesium (e), plant height (f) and seed yield from the check plots (g) 
Fig. 2. Percentage of trend, nugget and structural variance in the spatial variation of some spatial characteristics 
The interpretation of the results may be related to the specificity of the descriptors. Ph is a variety trait and it should be stable across the field, and the content of Corg originates from the type of soil. Other soil properties can be modified by agricultural practices, and seed yield is affected by them.
The range a at which the maximum semivariance was attained depended on the spatial descriptors (Table 4). The soil properties were autocorrelated at a longer distance, from 18.5 m for pH to 73.7 m for K. The range for plant traits was 1.6 m for yield and 3.7 m for plant height. This suggests that the autocorrelation of seed yield was limited to the two neighbouring plots, while of plant height to the three neighbouring plots, respectively. It should be noted that range 1.6–3.7 m covers the most commonly applied plot broadness in field experiments with pea (the plot breadth applied in the factorial experiment located in the field was 1.8 m).
The kriged values of pH, P, K, and Mg content, as well as Ph and SY were used as covariates in the analyses of covariance. The analyses were efficient. There was a significant linear dependence between pea seed yield from the experimental plots and all the spatial descriptors. Moran's I statistics for residuals from ANOVA and ANCOVAs at lag h = 1 set in Table 5 showed the tendency to lower autocorrelation in ANCOVAs, which was especially distinct in ANCOVAs with plant traits as the covariates.
Table 5. Moran's I statistics for residuals from ANOVA and ANCOVAs at lag h = 1 
Method* 
Experiment 
Strip I 
Strip II 
Strip III 
ANOVA 
0.667 
0.643 
0.651 
0.734 
ANCOVA 

soil properties 

Corg 
0.538 
0.316 
0.510 
0.687 
pH 
0.609 
0.636 
0.659 
0.477 
P 
0.585 
0.449 
0.570 
0.699 
K 
0.583 
0.541 
0.604 
0.503 
Mg 
0.595 
0.627 
0.644 
0.478 
plant traits (check plots) 

Ph 
0.389 
0.337 
0.425 
0.349 
SYc 
0.501 
0.370 
0.623 
0.328 
* Corg – organic carbon, Ph – plant height, SYc – seed yield from the check plots 
Table 6. The efficiency of ANCOVA of pea seed yield with soil properties and plant traits taken as concomitant variables 
Method of analysis* 
Main effects 
Interaction effects 

MSE** 
RE% 
SED 
D% 
SED 
D% 

ANOVA 
0.5083 
100.0 
0.1120 
12.3 
0.1940 
21.2 
ANCOVA 

soil properties 

Corg 
0.2572 
196.3 
0.0797 
8.7 
0.1380 
15.1 
pH 
0.2991 
169.2 
0.0859 
9.4 
0.1489 
16.3 
P 
0.3317 
152.6 
0.0905 
9.9 
0.1567 
17.2 
K 
0.2997 
168.8 
0.0860 
9.4 
0.1490 
16.3 
Mg 
0.3166 
159.9 
0.0884 
9.7 
0.1531 
16.8 
plant traits (check plots) 

Ph 
0.1363 
370.4 
0.0580 
6.3 
0.1005 
11.0 
SYc 
0.1741 
290.3 
0.0656 
7.2 
0.1136 
12.4 
* Corg – organic carbon, Ph – plant height, SYc – seed yield from
the check plots **MSE – mean square error, RE% – relative efficiency in percents, SED – standard error of difference, D% – percentage of LSD0.05 of the general mean 
There was over a twofold reduction
of MSEs in ANCOVAs in comparison with ANOVA (Table 6). The use of soil properties
in the analyses resulted in 150–200% higher efficiency and, as for plant characteristics,
the relative efficiencies were 290.3% and 370.4% for SY and Ph, respectively.
The higher the relative efficiency is, the lower differences between the means
may be detected. In the estimation of main effects, the share of LSD_{0.05} in
the general mean amounted to 12.3% in ANOVA and in ANCOVA it was in the range
of 9.9% to 6.3% when phosphorus content and plant height were used as the covariates.
The relation was maintained in the estimation of interaction effects but the
respective values were about two times higher.
DISCUSSION
The experimental field where the multifactorial experiment 3^{5} with pea was located was heterogeneous with soil fertility trend and spatial autocorrelation effects. In field experimentation, spatial variation was given special attention starting from the early methodical studies and practical suggestions for experimenters [15,39]. When modelled, the adequacy and usefulness of the obtained results from spatial analysis may depend on the spatial descriptors. In field conditions such descriptors are naturally connected with soil fertility and plant traits. The seven descriptors of spatial variation described here were differentiated in their variation across the field on the level and the range of spatial autocorrelation, however their spatial variation patterns were similar.
Soil fertility is essential for plant growth and to a great extent depends on the chemical nutrients in their available forms. Soils rich in organic matter originate from the type of soil and soil acidity that is adequate for a given crop support intake of the nutrients. The spatial variance of the studied soil properties attributed to spatial autocorrelation amounted to 60% of the total variance. Spatial variation of plant traits as genotypeenvironment interaction is the reflection of soil fertility, while plant height, as a trait that could be uniform for a cultivar is also very stable in its spatial variation. In the present studies, plant height had low variation and showed minor effects of trend and relatively high structural variance attributed to spatially autocorrelated observations but in a low range of spatial dependence. In many methodical studies, plant traits used to be the measure of spatial variation [20,21,22,32,44]. The classic methodical approach was through the socalled blind experiment without any experimental factor. In the experiment, sown with a single variety of a crop, the trait of interest was measured on small experimental units (i.e. 0.5 or 1 m^{2}) which were organized in rows and columns. The smaller the experimental unit, the better the description of spatial variation. The results from the experiments allow consideration of many methodical aspects of field experimentation, including optimum and conventional plot size estimation, capacity of the block, and the number of replications [19,27,39]. Even if the experiments are very informative, their cost limits their practical use. The presented approaches were developed on the utilization of extra information from the trait of interest (differences between neighbouring plots) or using the other trait or soil property as covariate in the analysis of covariance [1,5,37,47] and on modelling the error residuals structure and the estimation of spatial variation parameters in trend and/or autoregressive models. New opportunities for the scientific exploration of spatial variation of the experimental field gave an application of the geostatistical methods that enabled quantifying the spatial parameters: range, nugget and structural variance, as well as the prediction of the values at any point of the field. All the descriptors analyzed in the study, Corg, pH, P, K, Mg, PH and SY, showed spatial autocorrelation and their utilization in ANCOVA significantly reduced the experimental error, making the analysis of the results of a large multifactorial experiment with pea very efficient. In comparison with ANOVA, the predicted plot values of spatial descriptors used as covariates in ANCOVA lowered Moran's I statistics that were differentiated depending on the experimental strip location in the field.
To summarize the above discussion
it may be concluded that in the studies on field experimentation methods, soil
spatial effects were assessed indirectly by the effects of spatial variation
of plant traits recorded from the experimental plots or neighbouring experimental
plots. There was no cost of the additional information obtained from the modified
statistical elaboration of the results. In the course of the modification, extra
parameters were included into a model or a new variable was created from the
trait of interest or another plant trait or soil property. Up to now, for such
methodical approach, there is a lack of information on the usability of the soil
fertility factors as contrasted with the commonly used plant traits. The presented
approach needed an extra measure on spatial variation and it was an effective
approach giving up to 1.5 to 3fold higher efficiency than CRD analysis depending
on the spatial descriptor used. The efficiency was at a slightly higher or comparable
level with the efficiency of the designs with complete or incomplete blocks or
other spatial approaches as compared to CRD or RBD reported by Gill and Shukla
[18], Brownie et al. [5], and Yang et al. [45]. The presented proposal is an
alternative choice when planning a factorial or fractional experiment. It is
an open question if the gain in the efficiency will compensate for the additional
costs but it may be also assumed that in future the additional costs may be lower
because the process of soil properties measurement will be done directly in the
experimental field.
CONCLUSIONS
The directly measured soil properties and plant traits are informative descriptors of spatial variation of the experimental field. The content of organic carbon connected with the type of soil and plant height as a varietals trait is natural and relatively stable across the field descriptors and easy to measure. Even if valuable, at present, the usefulness of other soil properties, like soil acidity, available forms of potassium, phosphorus and magnesium in the soil, and seed yield reflecting the availability of the macronutrients may be treated as a secondary source of data for spatial analysis purposes. For a given experimental field with pea, the soil properties in comparison with plant traits are less variable and the range of autocorrelation of adjacent measurements is longer. The range of autocorrelation of SY and Ph, 1.6 and 3.7 m, respectively, corresponds with the common plot broadness in pea field experiments.
When spatial autocorrelation in the experimental field is present, any descriptor of spatial variation may be useful in the statistical analysis of the experimental data and helpful in the future planning of the experimental activities in the same field. In the case of spatially autocorrelated observations, the values of the spatial descriptors predicted for each plot and included into statistical analysis may significantly reduce the experimental error and enable efficient comparison of treatment contrasts. The information on spatial variation may be utilized in future experimental activities in the field. When the trait of interest from the experiment and the descriptor of spatial variation are the same, it is possible to arrange the next pea experiment in the same field without autocorrelated effects.
The application of factorial design
in a field experiment due to its specificity may require paying special attention
to the spatial variation of the experimental field. When the results from the
previously conducted experiments in the field indicate that the field is heterogeneous
and spatial effects may be present, it is advisable to consider additional measurement(s)
of a soil property or a plant trait for spatial parameters estimation and kriging
the values for experimental plots. Including the values as the covariate into
ANCOVA increases the efficiency of treatment contrasts comparison.
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Accepted for print: 12.03.2009
Janusz Gołaszewski
Department of Plant Breeding and Seed Production,
University of Warmia and Mazury, Olsztyn, Poland
Pl. Łodzki 3, 10724 Olsztyn, Poland
email: janusz.golaszewski@uwm.edu.pl
Dariusz Załuski
Department of Plant Breeding and Seed Production,
University of Warmia and Mazury, Olsztyn, Poland
pl. Łodzki 3, 10724 Olsztyn, Poland
email: dariusz.zaluski@uwm.edu.pl
Aneta StawianaKosiorek
Department of Plant Breeding and Seed Production,
University of Warmia and Mazury, Olsztyn, Poland
Pl. Łodzki 3, 10724 Olsztyn, Poland
email: anetastko@poczta.onet.pl
Paweł Sulima
Department of Plant Breeding and Seed Production,
University of Warmia and Mazury, Olsztyn, Poland
Pl. Łodzki 3, 10724 Olsztyn, Poland
email: paweł.sulima@uwm.edu.pl
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