MATHEMATICAL APPROACHES FOR IMPACT EVALUATION OF THE IRRIGATION REGIME AND FERTILIZATION ON THE GREENHOUSE TOMATO QUALITY

Abstract

The aim of the present research work was to evaluate the similarity and remoteness of the impact of different irrigation regimes for tomatoes (Vitelio variety) and their grouping by main biochemical indicators, using mathematical approaches (cluster analysis and factor analysis). Two-year data from a field experiment was used including a non-irrigation and an optimum option, as well as options for canceled irrigation and low irrigation norms (12 options in total). The experiment was carried out in Plovdiv in the period 2016-2017. Cluster analysis results were in line with the conclusions from the irrigation and fertilization regime analyses and their impact on the tomato quality indicators. The strongest positive correlation existed between the indicators common dyes and lycopene for both experimental years. There was a strong negative correlation between the indicators lycopene and beta-carotene. The basic indicators leading to the separation of the irrigation and fertilization options into clusters were the following quality indicators: titratable organic acids, ascorbic acid, common dyes, lycopene and beta-carotene combined in the first factor, responsible for 78.621% of the total dispersion of the variables.

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Agricultural University – Plovdiv
AGRICULTURAL SCIENCES Volume IX Issue 22 2017
DOI: 10.22620/agrisci.2017.22.011
MATHEMATICAL APPROACHES FOR IMPACT EVALUATION OF
THE IRRIGATION REGIME AND FERTILIZATION ON THE
GREENHOUSE TOMATO QUALITY
Velika Kuneva1, Antoniya Stoyanova2, Nikolay Valchev2, Galina Pevicharova3
1Agricultural University – Plovdiv, Bulgaria
2Faculty of Agriculture, Trakya University – Stara Zagora, Bulgaria
3Maritsa Vegetable Crops Research Institute – Plovdiv, Bulgaria
E-mail: kuneva@au-plovdiv.bg
Abstract
The aim of the present research work was to evaluate the similarity and remoteness of the impact of
different irrigation regimes for tomatoes (Vitelio variety) and their grouping by main biochemical indicators,
using mathematical approaches (cluster analysis and factor analysis). Two-year data from a field experiment
was used including a non-irrigation and an optimum option, as well as options for canceled irrigation and low
irrigation norms (12 options in total). The experiment was carried out in Plovdiv in the period 2016-2017. 
Cluster analysis results were in line with the conclusions from the irrigation and fertilization regime
analyses and their impact on the tomato quality indicators. The strongest positive correlation existed between
the indicators common dyes and lycopene for both experimental years. There was a strong negative correlation
between the indicators lycopene and beta-carotene.
The basic indicators leading to the separation of the irrigation and fertilization options into clusters were
the following quality indicators: titratable organic acids, ascorbic acid, common dyes, lycopene and beta-
carotene combined in the first factor, responsible for 78.621% of the total dispersion of the variables.
Keywords: tomato, irrigation regime, correlation, cluster analysis, factor analysis
INTRODUCTION
Vegetable crops development for a short
period during the year requires the application of
high norms of fertilization. Some research workers
have been searching for new technological
solutions for an increase in yield and quality of
greenhouse tomato production, as well as the
defining of each nutrient element quantity
necessary for better plant growth and high-grade
fruit yield. 
Bernard et al. (2009) have studied the
fertilization impact using different nitrogen levels.
They have registered that low nitrogen supply has a
weak impact on fruit yield (-7,5%), but there is a
decrease in the plant vegetative growth and an
increase in the dry substance content in fruits
leading to better fruit quality. Fruit quality is
improved because of the lower acidity (10-16%)
and the increased content of soluble sugar (5-17%).
Javaria et al. (2012) have established a
positive linear correlation between the taste
qualities, the common chemical elements /titratable
organic acids/, lycopene and the dry substance/. It
has been established that potassium concentration
increase leads to determine the quality of tomato
fruits, applied in a dose of 375 kg/ha K2O along with
the required fertilization norms N and P. After three-
year research, Oke et al. (2005) have established
that potassium impact does not contribute to
statistically proved changes in tomato quality.
Resources of nutrient substances are also
determining when analyzing the levels of true acids
and antioxidants in greenhouse tomatoes. The
average content of phenol and ascorbic acids in
tomatoes grown with chicken manure and grass
mulch /clover/ is 17,6% and 29%, respectively,
higher than tomatoes grown with mineral nutritional
solvents - Toora et al. (2006).
Parameters examination of the controlled
water deficit and it's determining the quality of
tomatoes can be helpful for the development of a
precise strategy for water recourse management,
for production optimization, and for tomato quality
improvement (Favati et al. 2009: Pevicharova et al.
2013). Using mathematical approach, the present
research work aims the following:

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1) to compare, by similarity and remoteness,
the impact of different irrigation and
fertilization regimes on tomatoes, Vitelio
variety; to divide the regimes into groups on
the base of significant qualitative indicators
using cluster analysis;
2) to examine the presence of a correlation
dependence between basic indicators for a
more objective evaluation;
3) using a factor analysis, to reduce their total
number uniting the correlated new factors.
MATERIALS AND METHODS
Two-year data of examination of different
irrigation and fertilization regimes of tomatoes,
Vitelio variety, was used – 2016 and 2017.
The experiment was set up by the block
method on a surface scheme 110+50+35, with crop
plot size of 10 m2 (V. Barov, 1982).
The following options were examined:
1)broken irrigation regime (50% of the irrigation
norm) without fertilization; 2) broken irrigation
regime (75% of the irrigation norm) without
fertilization; 3) optimum irrigation regime (100%)
without fertilization; 4) broken irrigation regime
(50% of the irrigation norm) and 50% fertilization; 5)
broken irrigation regime (75% of the irrigation norm)
and 50% fertilization; 6) optimum irrigation regime
(100%) and 50% fertilization; 7) broken irrigation
regime (50% of the irrigation norm) and 75%
fertilization; 8) broken irrigation regime (75% of the
irrigation norm) and 75% fertilization; 9) optimum
irrigation regime (100%) and 75% fertilization; 10)
broken irrigation regime (50% of the irrigation norm)
and 100% fertilization; 11) broken irrigation regime
(75% of the irrigation norm) and 100% fertilization;
12) optimum irrigation regime (100%) and 100%
fertilization.
The irrigation was conducted through a drip
irrigation system with embedded droppers at a
distance of 0,20 cm. During the first year, there
were 33 waterings with a size of the irrigation norm
-495m3/da. During the second year, the size of the
irrigation norm was 405m3/da by 27 waterings. The
crop culture was supplied with three levels of
fertilization: optimum fertilization, ½ of the
fertilization norms, ⅓ of the fertilization norms. The
impact of the main fertilization was examined,
realized with P23 (under the form of P2O5) and K25
(under the form of К2SO4) and supply with N50
during vegetation (under the form of NH4NO3) and
K66 (under the form of KNO3).
Except for a particular impact of a given
irrigation regime on the yield and the structural
elements separately (as it is usually registered in
the research articles), there was a possibility for
creating a complex evaluation of data base for all
measured indicators. For this purpose, the method
of the cluster analysis was used. According to this
analysis, the examined options were divided into
groups called clusters on the base of particular
features. The cluster analysis allows the grouping
of objects by similarity and differences. Results are
presented graphically through a dendrogram
showing the grouping of the examined options. The
method is successfully used for grouping and
evaluation of varieties and lines of various crop
cultures (Ivanova, I. et al., 2010, L. Krasteva et al.,
2010, Ilchovska М. et al., 2013 Ilchovska, M., et al,
2014, Milev M., et al, 2015.), for grouping of soil
differences (Doneva et al., 2008).
The received results can lead to an
increased precision of the evaluation of a particular
irrigation regime. It is a prerequisite for an
increased accuracy when taking particular solutions
in the practice and the real irrigation of greenhouse
tomatoes.
The evaluation of the examined irrigation
and fertilization regimes was conducted through the
comparison of the following indicators: х1- dry
substance (% of dry substance), х2- ascorbic acid,
х3 – titratable organic acids, х4 – common dyes, х5-
lycopene, x6 - beta-carotene.
The grouping of all 12 examined options of
irrigation regime was conducted through a
hierarchical cluster analysis. The method of the
intergroup combination was used (Ward, 1963,
Dyuran, B., P. Odelly, 1977). The Euclidean
intergroup distance was used as a measure:



n
iii yxyxD 1
2
)(),(
A dendrogram was created presenting
graphically the formed clusters. The dendrogram
horizontal dotted line showed the rescale distance
of the formed clusters. A correlation analysis was
conducted aiming at establishing the presence of
statistically significant correlations between the
examined indicators.
The research was continued with the
application of a factor analysis (Kline, 1994) aiming
at a reduction of the sixth initial indicators. The
factor analysis was conducted on the method of the
main components (PCA). The number of main
components was determined by the number of own
symbols of the correlation matrix, which are bigger
than 1 (Kaiser`s criterion). The own symbols show
the contribution of the own factor when explaining
the common dispersion of the variables.

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Data processing was conducted with the
statistical program SPSS.
RESULTS AND DISCUSSION
The conducted cluster analysis showed that
the impact of the irrigation regime on tomato
indicators was grouped in three main clusters.
Results are presented in a table - with the
consequent combination of clusters and intergroup
distances (Table 1), as well as graphically through
a dendrogram (Figure 1).
The first cluster was more homogenous. It
combined the options 5, 8, 6, 4 and 7 that had
similar indicators: dry substance, titratable organic
acids, common dyes and lycopene, and the options
that had broken irrigation regime and least
Euclidean distance between them.
The second main cluster included the
options 9, 11 and 12 that had small or moderate
water deficit. They had the highest similarity of
titratable organic acids and common dyes.
Options 2, 3 and 1 formed the third cluster.
They were identical in dry substance and ascorbic
acid. All of them had broken irrigation regime,
without fertilization.
Options 1 and 4 were most distant. They
had broken irrigation regime (50% of the irrigation
norm) and an intergroup distance of
17.957coefficient (Table 1).
Table 1. Combination of the clusters and the intergroup distances
Steps
Combined clusters
Coefficients
Cluster 1
Cluster 2
1
5
8
1.727
2
4
7
2.361
3
5
6
2.578
4
9
11
3.344
5
2
3
4.023
6
4
5
4.277
7
9
12
4.717
8
9
10
8.398
9
1
2
9.278
10
4
9
10.585
11
1
4
17.957
Fig. 1. A dendrogram on the base of the average intergroup distances

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The correlation components expressing the relation
between the examined indicators are presented in
the correlation matrix (Table 2).
There was a strong positive correlation
between lycopene and common dyes, and average
correlation dependence between lycopene and
titratable organic acids, with correlation coefficients
r = 0.977 and r = 0.581, respectively.
There was a strong negative correlation
between the indicators beta-carotene and titratable
organic acids, common dyes and lycopene, with
correlation coefficients: r = - 0.846; -0.742 and -0.
852. All correlation coefficients were statistically
proved at a degree of significance -
001.0

.
Table 2. A correlation matrix
i
X
1
x
2
x
3
x
4
x
5
x
6
x
1
x
1.00
-0.454
-0.037
-0.050
-0.062
0.003
2
x
1.00
-0.515
-0.127
-0.235
0.542
3
x
1.00
0.488
0.581*
-0.846**
4
x
1.00
0.977**
-0.742**
5
x
1.00
-0.852**
6
x
1.00
The conducted correlation analysis and the
statistically proved high values of r gave us a
reason to apply the methodology of the factor
analysis. The method of the main components was
applied in the factor analysis. It was concluded that
both factors had values of their own vectors bigger
than 1, which defined the choice of two main
components (Figure 2).
Fig. 2. Values of the own vectors
654321
Component Number
3
2
1
0
Eigenvalue
Scree Plot

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Table 3 shows the factor weights and the
distribution of the main component variation. The
components explain 78,621% of the total extract
dispersion. The first main component explains
53,199 % of the dispersion, and the second - 21,7
% of the dispersion.
Table 3. A factor matrix received on the method of the main components
№
Indicators
Main components
Symbols
1
2
1.
Dry substance (% of dry substance)
-0.403
-0.557
1
x
2.
Ascorbic acid
-0.211
0.881
2
x
3.
Titratable organic acids
0.831
-0.257
3
x
4.
Common dyes
0.806
0.420
4
x
5.
Lycopene
0.946
0.193
5
x
6.
Beta-carotene
-0.867
0.400
6
x
Percentage of the total variation, %
53.199
25.421
Cumulative percentage of the total variation, %
53.199
78.621
The variables
3
x
,
4
x
5
x
and
6
x
had high
factor weights in the first component. This factor
should be mainly related to titratable organic acids,
common dyes, lycopene, and beta-carotene. The
factor could be defined as general for the indicators
having the most relative weight in tomato grouping.
The second component was mainly related to the
ascorbic acid. 
The received results from the applied factor
analysis were synchronized with the results from
the cluster analysis in their grouping into clusters
according to their similarity on the base of the same
indicators.
CONCLUSIONS
The presented mathematical approach
allowed a maximum objective evaluation of the
complex impact of the control water deficit and
fertilization levels on the basic chemical
components in greenhouse tomatoes.
Cluster analysis results were synchronized
with the conclusions from the analysis of the
applied irrigation and fertilization regimes and their
indicators impact the quality of tomatoes.
As a result of the conducted correlation
analysis, correlation dependences between the
examined indicators were established. The
strongest positive correlation had the indicators
common dyes and lycopene for both experimental
years. There was a strong negative correlation
between the indicators lycopene and beta-carotene.
The basic indicators that had the strongest
impact on the grouping into clusters of the irrigation
and fertilization options were the indicators:
titratable organic acids, common dyes, lycopene,
and beta-carotene, joined in the first cluster that
explained 78,621 % of the total dispersion of the
variables.
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