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11Ceflenu,ifl ma HaciHHLiu,mBO
UDC 631.526.2:582.623:311.12
Using cluster analysis as a method of classification of the genus Salix L. representatives
M. V. Roik, Doctor of Agriculture
V. V. Balykina, postgraduate student
Institute of bioenergy crops and sugar beet NAAS of Ukraine
victoria.mamaisur@gmail.com
Purpose. To study interactions among the representatives of the genus Salix L. through the cluster analysis, form groups of closely related species and hybrid forms basing on differences of morphological parameters of leaves. Methods. Field, cluster analysis and tree graphics. Results. Willow species were grouped according to absolute parameters of leaf, and three groups of clusters were identified. The degree of affinity between species were assessed using values of an Euclidean distance. Distinctive features of leaf parameters were defined: length of a leaf blade (Ll), distance (cm) between the leaf tip and its maximum width (SDmxT) and the distance between the leaf tip (cm) and the line of its width that corresponds to the length of petiole (SLpT). Conclusions. Using the willow species collection as an example, diagnostically valuable quantitative parameters of leaves were revealed, the use of which allows to identify willow species and hybrid forms through PC applications.
Keywords: cluster analysis, hierarchical method, K-means method, species identification, leaf parameters.
Introduction. The effectiveness of the whole process of plant breeding depends on high-quality selection of parent material. Cluster analysis can be an Example of searching of advanced techniques of selection - one of the methods of mathematical processing of experimental results [1].
The formation of natural hybrids is typical for willow, so in order to improve the quality of directed hybridization it is advisable to classify samples collection, dividing them into several different groups. Some representatives of groups can be selected for further breeding work.
But not always differences between species and hybrid forms are distinct. An important diagnostic feature is the shape of different kinds of willow leaf, reflecting the complex of quantitative characteristics and varies from round to linear-lanceolate. But the parameter is characterized by considerable intraspecific variability, which complicates its use to identify the species. Mathematical methods allow for complex quantitative parameters to determine samples belonging to certain groups [2, 3].
The purpose of research - by using cluster analysis to explore the relationship between the genus Salix L., based on morphological differences in the parameters of leaves and to form groups of species and hybrid forms, closely related to each other.
Materials and methods. Analysis was performed on the basis of research conducted at the Institute of bioenergy crops and sugar beet NAAS for 2011-2014, according to the NDP 22 «Bioenergy resources» sub-programme № 5
«Solid fuels». The collection consisted of 21 species and hybrid forms of willow. For research willow leaves, picked in the spring and summer (50 leaves of five plants each sample) were used.
Differences in form and size of leaves helped to identify nine parameters to measure: the length of leaf blade (Ll), width of leaf blade (Dmx), length of petiole (Lp), distance (cm) from the top of the leaf to its maximum width (SDmxT), the distance from the base of the leaf (cm) to its maximum width (SDmxB), the width of the leaf at a distance of 0,1Dmx from the top (DmnT), the width of the leaf at a distance of 0,1Dmx from the base (DmnB), location (cm) of width of leaf corresponding to the length of the petiole from the top of the leaf (SLpT), location (cm) of width of leaf corresponding to the length of the petiole from the base of the leaf (SLpB) [4].
Samples were classified by leaf morphological characteristics using methods of cluster analysis - hierarchical cluster analysis and the method of K-means using Cluster Analysis module of STATISTISA program. Hierarchical cluster analysis method was used for making a preliminary decision about the number of clusters (groups) which should be divided amount of source material.
Results and discussion. To set the required number of clusters was used an indicator, that is entitled «metrics» - conditional distance between two clusters selected on the basis of distance measures adopted taking into account conversion values. In this case - square Euclidean distances, that was determined by using standardized values. At the point
Ceëenu,ifl ma HaciHHLiu,mBO
where a measure of the distance between two clusters is changed abruptly, the process of integration into a new cluster stops to avoid association clusters that are relatively large distance from each other.
Definition of a sufficient number of clusters can be based on analysis of incremental diagram
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of changes intercluster distance. As a sufficient number of clusters is accepted that the difference is the number of steps, after which inter-cluster distance increased abruptly [5, 6].
For the classification method of Ward was used, aimed at uniting closely located clusters. The results are shown in Figure 1.
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r-L-1 JU J-1 r^l 1 'r-1-1 rVn JL i ,-j-,
C_19 C_10 C_18 C_14 C_16 C_15 C_13 C_17 C_4 C_2 C_1 C_11 C_9 C_12 C_7 C_21 C_20 C_8 C_5 C_3 C_6
Samper number
Figure 1. Dendrohrama of clustering of willow samples by morphological parameters of leaf (method of Ward)
Figure 2 shows the graph of incremen- the graph, an abrupt increase intercluster
tal changes intercluster distance, through distance held within 19 step. Because the
his analysis was determined the required research is subject of 21 sample, it was only
number of clusters. As can be seen from three clusters.
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0 2 4 6 8 10 12 14 16 18 20
Step -Interclusterdistance
Figure 2. Graph of incremental changes of intercluster distance
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Using this method made it possible to decide about the number of clusters, required for further analysis. The results were used during clustering by the method of K-means. As a result of cluster analysis were grouped species in absolute terms of willow leaf and were defined the following groups and clusters: cluster I - S. caspica Pall., S. uralen-sis Hort. ex K. Koch., S. alba L. f. splendens, Salix rosmarinifolia L., S. purpurea L. x
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14 12 10
S. viminalis L., S. caspica Pall. x S. purpurea L., S. integra Thunb L. x S. acutifolia Mild., S. viminalis L. x S. caprea L.; cluster II -S. acutifolia Mild., S. alba L., S. alba L. local form, S. cangensis Nakai, S. viminalis L. x S. acutifolia Mild., S. caprea L. x S. purpurea L.; cluster III - S. viminalis L., S. triandra L. local form, S. triandra L., S. matsudana Vill., S. cinerea L., S. repens L., [(S. viminalis L. x S. purpurea L.) x (S. caspica Pall. x S. caprea L.)].
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2 3 4 5
Characteristics
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Cluster 1 -Q- Cluster 2 Cluster 3
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Figure 3. The average values for each cluster
In line graph (Figure 3) are shown the average value for each cluster which clearly differ from each other. This suggests about qualitative division of samples into groups. According to the graph distinctive parameters are the length of leaf blade (Ll), distance (cm) from the top of the leaf to its maximum width (SDmxT) and the location (cm) of width of leaf corresponding to the length of the petiole from the top of the leaf (SLpT).
To assess the degree of relationship between species was used value of the Euclidean distance (Table 1).
Table 1
The Euclidean distance between clusters
Cluster I Cluster II Cluster III
Cluster I Cluster II Cluster III 0,00000 2,225455 1,511736 4,95265 0,0000 3,388257 2,28535 11,48029 0,00000
The Euclidean distance is the most common measure distances between objects, which is the
geometric distance between objects in multidimensional space. In our case it is the distance between morphological parameters of leaf for each species; it is equivalent to the distance between species according to selected parameters. The more smaller the distance between objects, the more they are similar. The square Euclidean distance used when it is required to increase in order the value of the distances between each other very distant objects [7].
Since the Euclidean distances are greater than one, it can be confirmed that clusters are located at great distances from each other, so species and hybrid forms of willow, that form these clusters, have a low degree of relationship. The biggest is the distance between clusters II and III, meaning they are least similar.
As a result of analysis of variance (Table 2) were defined intergroup and intragroup variance, the difference between which the parameter shows the sample belongs to a cluster and clustering quality. Parameters with values of p > 0.05 can be removed from cluster-
Table 2
Results of analysis of variance
№ Parameters Intergroup SS df Intragroup SS df Fisher's ratio test, F Significance level, p
1 Ll 76,3648 2 64,23703 18 10,69917 0,000867
2 Dmx 8,1818 2 6,47554 18 1,64256 0,221192
3 Lp 0,4551 2 0,32265 18 7,11545 0,005284
4 SDmxT 40,5284 2 17,17839 18 21,23339 0,000018
5 SDmxB 17,1633 2 14,72036 18 10,49359 0,000953
6 DmnT 0,3531 2 0,25548 18 1,87137 0,182651
7 DmnB 0,4749 2 0,25742 18 16,6032 0,000082
8 SLpT 208,651 2 20,51737 18 91,52531 0,000000
9 SLpB 18,7042 2 7,88811 18 21,34073 0,000018
ing procedure. In our case Dmx and DmnT indicators will be removed.
The best specimens belonging to the cluster characterize parameters SLpT, SDmxT and Ll as they correspond to the biggest difference between inter- and intragroup variances, the worst (that correspond to the smallest difference of variances) - parameters Dmx, DmnT and DmnB. Characteristics F and p also characterize the contribution
Based on the assumption that the most distinctive characteristics to identify willow plants are the length of the leaf blade (Ll), location (cm) of width of leaf corresponding to the length of the petiole from the top of the leaf (SLpT) and distance (cm) from the top of the leaf to its maximum width (SDmxT), determine the following: to the cluster I belong plants with length of the leaf blade 7,86 ± 0,11 cm, with parameters SDmxT = 4,38 ± 0,10 cm and SLpT = 5,28 ± 0,16 cm; for plants that belong to the cluster II, identical parameters have the following meanings: Ll = 12,03 ± 0,08 cm, SDmxT = 7,17 ± 0,03 cm, SLpT = 9,45 ± 0,24 cm, respectively; for plants, that put together the cluster III, parameters are: Ll = 7,74 ± 1,08 cm, SDmxT = 3,85 ± 0,19 cm, SLpT = 1,42 ± 0,03 cm respectively.
Examination of cluster analysis made it possible to compare similar types and hybrid forms of willow by morphological characte-
of the parameter in the division of samples into groups. Better clustering correspond to higher values of the first and the lower - of the other parameters. According to the table above best parameter corresponds to biggest the difference (F-d) [8].
The way to determine the nature of the clusters is to check the average values for each cluster and for each measurement. Table 3 shows the parameters of the analysis of leaf.
ristics of leaf to determine significant differences between them. By applying the method of K-means was allocated groups of closely related samples to facilitate the identification of phenotypically similar species.
Conclusions. It in effectually to use cluster analysis for diagnostic species of the genus Salix L., to determine which sometimes can be quite difficult. As a result of cluster analysis collection samples divided into groups by morphological parameters of leaf based on affinity in terms of the Euclidean distance. Cluster analysis of complex of parameters of leaf allowed to detect diagnostically valuable quantitative characteristics by which it is possible to identify willow species using applications for PC. In addition, the results make it possible to assert the similarity of norm of reaction of the genetic apparatus for collection samples in regularity of detection of quantitative characteristics.
Table 3
Characteristics of groups (clusters) on morphological parameters of leaves
№ Parameters Clusters
I II III
x y x y x y
1 Ll 7,86±0,11 1,00 12,03±0,08 0,77 7,74±1,08 3,01
2 Dmx 1,15±0,03 0,49 1,52±0,03 0,52 1,70±0,07 0,76
3 Lp 0,73±0,02 0,11 0,99±0,01 0,06 0,92±0,02 0,19
4 SDmxT 4,38±0,10 0,97 7,17±0,03 0,51 3,85±0,19 1,25
5 SDmxB 3,49±0,02 0,43 4,86±0,01 0,29 2,56±0,26 1,47
6 DmnT 0,06±0,01 0,02 0,10±0,01 0,08 0,17±0,02 0,19
7 DmnB 0,08±0,01 0,02 0,10±0,02 0,05 0,41±0,01 0,20
8 SLpT 5,28±0,16 1,18 9,45±0,24 1,36 1,42±0,03 0,50
9 SLpB 2,58±0,07 0,81 2,57±0,09 0,82 0,58±0,01 0,05
Селекция та наа'нництво
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УДК 631.526.2:582.623:311.12
M. B. Poik, В. В. Балик1*на. Використання кластерного анал1зу як методу класиф1кац11 представнимв роду Salix L. Сортовивчення та охорона прав на сорти рослин. - 2015. - № 1-2 (26-27). - С. 32-36.
Мета. За допомогою кластерного анал1'зу достдити взаемозв'язки М1Ж представниками роду Salix L., сформу-вати групи вид1в 1 п'бридних форм, близькоспорщнених М1Ж собою, ^рунтуючись на в1дм1нностях морфолоп'чних параметр1в листк'в. Методи. Польовий, кластерного анал1зу й деревопод1'бно'1 графжи. Результати. Види верби згру-повано за абсолютними показниками листка й вид1лено три групи кластер1в. Оц'нено стутнь спорщненосп вид1в м1Ж собою за значенням евкл1дово1 вщстат. Визначено
в1дм1нн1 показники листка: довжина листково1 пластинки (Ll), в1дстань (см) в1д верх1вки листка до максимально!' його ширини (SDmxT) та в1дстань в1д верх1вки листка (см) до л1н1'1 ширини, що в1дпов1дае довжин1 черешка (SLpT). Висновки. На приклад1 колекц11' верби виявле-но д1агностично ц1нн1 к1льк1сн1 показники листк1в, використання яких дае можлив1сть 1дентиф1кувати види й г1бридн1 форми верби за допомогою прикладних програм для ПК.
УДК 631.526.2:582.623:311.12
Н. В. Роик, В. В. Балыкина. Использование кластерного анализа как метода классификации представителей рода Salix L. // Сортовивчення та охорона прав на сорти рослин. - 2015. - № 1-2 (26-27). - С. 32-36.
Цель. С помощью кластерного анализа исследовать взаимосвязи между представителями рода Salix L., сформировать группы видов и гибридных форм, близкородственных между собой, основываясь на различиях морфологических параметров листьев. Методы. Полевой, кластерного анализа и древовидной графики. Результаты. Виды ивы сгруппированы по абсолютным показателям листка и выделены три группы кластеров. Оценена степень родства видов между собой по значению евклидового расстояния. Определены отличительные показатели листка: длина листовой пластинки (Ll), расстояние (см) от верхушки листа
до максимальной его ширины (БОтхТ) и расстояние от верхушки листа до линии (см) ширины, соответствующей длине черешка (SLpT). Выводы. На примере коллекции ивы обнаружены диагностически ценные количественные показатели листьев, использование которых дает возможность идентифицировать виды и гибридные формы ивы с помощью прикладных программ для ПК.
Ключевые слова: кластерный анализ, иерархический метод, метод К-средних, идентификация видов, показатели листа.
Над1йшла 7.05.2015
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Сортовивчення та охорона прав на сорти рослин
