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Автор Baranov S.G., Bibik T.S.   
24.10.2012 г.

Vladimir State University, Russia; Dodoma University, Tanzania


Эта статья была опубликована в сборнике научных трудов "Актуальные проблемы современной науки" (том 1, №3, 2012г.) c материалами IX Международной Телеконференции (29 октября - 3 ноября 2012 года) 


The influence of fluctuating asymmetry on the plants described in many guides and scientific publications. Most of the work represented a deviation from the strict bilateral asymmetry (FA) as a result of the stress of the environment. The increase in the FA interpreted as a result reducing developmental stability of the organisms.

Most of the works on the evaluation of the FA performed are using the bilateral asymmetry leaf blades. Only a few works performed in the field of the FA flowers. For example, in South Africa leaves and flowers of plants of about 20 representatives of different families have been analysed on FA [2].

The insect-pollinated flowering plants have shown that bees tend to collect nectar from symmetric flowers [4]. Some other study showed correlation between flower and leaves FA [3].

The modern approach to defining fluctuating asymmetry is based on the quantification of the properties of the form of the body or its parts. In this case, the deviation of pre-selected points from the corresponding points of some average models is taking into account. Comparing the deviations from the left and right sides conclude about asymmetry result including the fluctuating asymmetry [1].

Most plants possess bilateral symmetry of flowers, as well as leafy plate. The flowers with radial asymmetry lie outside the field of view of the study of the stability and require a special approach.

It is logically to assume that the deviation of the asymmetry in the high or low way at the same time leads to a change in form, different from the perfectly symmetrical form (shape).

However, the evaluation of index FA is not easy task. The one of the reason is the difficulty of selecting suitable symmetry points (landmarks) and their amount reliable for FA index detection. There are various approaches to the defining FA, for example, including the comparing the area halves leaf plate.

The objective of the present work was to study the form and compare it with the asymmetry (FA) of inflorescences of four plant species.

In the base of the programs TPS family there is an aligning principle of all the points of interest to the user.

The (XY) coordinates (in two dimensional Cartesian coordinate system) are arranged around the zero point. The averaged model of a polygon is constructed first with known (XY) for each point.

The shape analysis is based on the so-called Procrustes method.

The basic idea of the shape analysis is applying the possible configurations and determining the most appropriate one for all samples (e.g. flowers) configuration.

It uses the method of least squares. Numerically the form is analyzed as a deviation in the variance between the points of the average shape (aligned centroid) and the corresponding points of real samples.

How is the FA detected numerically? On the definition of fluctuating asymmetry FA is numerically equal to the difference between the values ​​of the right and left sides on absolute value ​​(no signs).

FA index can be found as the difference of coordinates (XY) values ​​between the left and right homological points.

Statistical evaluation is determined by the method of analysis of variance as a paired difference between left and right values ​​of (XY) (F- test).

In the software package TPS (J. Rohlf, 2010) factor "size" is supposed to be rejected after alignment as well as the landmarks outside the confidence interval of the sample.

The task of present study is to determine the fluctuating asymmetry of homologous points of inflorescences four plants and identification of the most suitable plant species for testing unfavourable ecological situation. The analysis of the form in comparison to the FA index is also conducted.

The common species in Central Tanzania Ipomea alba (f.Convolvulaceae Vent.), Coreopsis verticulata (f. Asteraceae, Compositae), Digitalis purpurea L. (f.Scrophulariaceae) and Hibiscus engleri K.Schum ( f. Malvaceae) have been used.


Materials and Methods

Site and collecting

The photography have done at the wet season (April-March-May 2012) using the camera Panasonic DMC-FZ100. This site is about 2 km to the north-west of Dodoma town (6°10′23″S 35°44′31″E) in the central part of Tanzania. The site locality was a part of woodland area of the forest-steppe subtropical zone with elevation about 1500 m. The vegetation consisted of tall grasses and forbs steppe community. Anthropogenic factors included annual burning of dry vegetation, trashing soil and degradation due to grazing and walking. The area at least 10 km2 was used. All flowers were chosen for photography randomly. Under this the next conditions were undertaken: the flowers of each species were chosen on equal distance from each other, about 2—3 m (coreopsis and ipomoea) and 4-5m (hibiscus and digitalis). The flowers of one size were pictured.



JPG file format used in the TPS program to determine the coordinates of points (landmarks) for the next comparison between the shape of the sample and the overall average shape.

For the aligned centroid obtaining the method of least squares was applied.

The criterion F (F Goodle), for description of the corresponding form of samples to the average centroid was used.

One of the real points was pre-defined as lying on the Y-axis. The assumption is that the centre of the centroid (00) coincides with the centre of the inflorescence. Thus the two points defined the axis of bilateral symmetry (Fig. 1). All chosen points were classified as the landmarks or first type (true landmarks).





Fig.1. Bilaterally-symmetrical landmarks and axis of symmetry

 1 - Ipomea alba (two pairs of bilaterally-symmetrical landmarks: a-d; b-c), 2 - Сoreopsis verticulata (three pairs: f-d; g-c; h-b), 3 - Hibiscus engleri K.Schum (two pairs; e-d; a-c), Digitalis purpurea L. (two pairs: b-c; c-d)


FA testing

FA index has been defined as [5]: 

, where:       (1)




where: Х and Y – are the coordinates of landmarks conditionally left (L) and right (R) side;

k – the amount of pairs homological landmarks;

i – natural series (1,2,3… k) .

The projection of homologous landmarks on the tangential space were used that taking into account the angle to the zero point.

Thus, each point received new coordinates (XY) in the tangential space; the constellation of points was concentrated around the point (00).

PAST soft was used to find the distance between the points, for example between the left and right homologous points that can also be used to determine the FA and its statistical significance using the Fisher criterion (F).

Previously, each pair of landmarks (two to three pairs) was tested on the directional asymmetry (NA) and antisymmetry.

The two variables of the sample were tested for the mean difference from zero. (XY) of left and right landmarks were tested. If the hypothesis that the difference between zero was rejected (P < 0), it indicates the presence of NA.

Antisymmetry was tested on tabulated data of kurtosis [5].

If the value of kurtosis of the difference (XYr - XYl) is higher of the tabulated values, it signals about presence of antisymmetry, i.e. the presence of significant deviation from the normal distribution.

To detect the components of variances and deviations the 2 way ANOVA has been fulfilled.

This analysis allows:

a) to detect individual variation in the sample;

b) to detect statistical significance of factor “side” (left and right) and make a conclusion about directional asymmetry presence;

c) after repeatable measurements to find a measurer error, affected FA value.

In frame of this analysis FA was found on formula

σ2 = (MSis - MSm)/M,       (2)



σ2FA index as non-directional asymmetry variance after removing measurement error;

MSis mean square interaction “side” and “individuals”;

MSm mean square measurement error;

М – amount of measurements (in this case is equal three)

Shape analysis. Deviation of the shape from average geometric shape was detected by the comparing the sum of variance of the centroid (average of the polygon) and the sum of variance of polygons in the sample. By the sample the 60-80 digital flower images for each species of plant were assumed.



FA testing

Index of FA in the coordinates of the tangential space was determined by comparing the (XY) of the left and right homologous points on the known formula (1).

The results are presented in Table 1. Fisher's exact test was used to determine statistical significance of null hypothesis about difference between variance (XY) left and right side.

Under homologous distances the segments joining homologous points on the left and the right sides have undertaken. These distances as the metric traits were used for FA analysis, here the F criterion was applied also.

Table 1. FA correspond formula (1) and FA through the analysis of distances




formula (1)







Hibiscus engleri K.Schum






Сoreopsis verticulata






Ipomea alba






Digitalis purpurea L.






Note: ns – statistically insignificant (P > 0.05)

The two way ANOVA has been carried out for one species Digitalis purpurea L. separately for two pairs of landmarks. The null hypothesis about the same (XY) value of left and right homological landmarks was tested.

The component of variance (deviation) “side” and “individuals” showed insignificant level (Р > 0.05).

The interaction of both factors showed the high value of mean square (0.01) and the low value mean square measurement error towards significant F value of FA 10 (F = 4.7;Р = 0.0000).

The FA10 value was equal 0.0002, which is less than on formula (1) (Tab.1). It is explainable because of rejection of measurement error.

Testing of directional and antisymmetry

The directional asymmetry were absent (P >0.05; two-sample t-test with different variances). The result corresponded to the data of 2-way ANOVA (insignificant factor “side”).

The presence of antisymmetry and deviation from normality have been obtained for all species

The value (ХУrХУl) showed high kurtosis (k > 7.54) that is said about leptokurtic form of distribution. So kurtosis value was higher tabulated (n = 80-90; α = 0.05).

The significant FA result has been detected only for one pair of landmarks.

Shape tasting

The smallest deviation of shape from average aligned model has been detected for hibiscus (F = 8.68; d f =192; P = 0.0000). For other flowers F criteria was higher (14.6 - 26.7; d f =192; P=0.0000).


Discussion and conclusion

Oure experience in the using of TPS programs showed that:

a) The program is quick and powerful alternative to the linear measurement and allows to use a variety of homologous points on the contour of the object;

b) Fluctuating asymmetry, as a slight deviation from symmetry is a small fraction of the variability of the shape, the comparison with the shape does not play a significant meaning in the environmental study on the sustainability of development or a more detailed investigation is warranted;

c) Hibiscus can be a suitable species for evaluation of sustainable development in sub-tropical areas, as this plant (Hibiscus engleri K.Schum) had the highest value for the FA impurity antisymmetry.

An appropriate detailed study of fluctuating asymmetry to be carried out at three-fold measurements for measurement error. The two-factor analysis (individual x side) is a convenient way to get components of variation of FA testing. Also in field of interest is an obtaining correlation between the FA flowers and leaf plates.

Two-factor analysis conducted on the basis of the coordinates (XY) in the tangential space has at least the two advantages. It analyzes the geometric position in two dimensions, whereas the traditional two-factor analysis shows the differences in the distances (in our case) or in the number of matching traits on the right and left sides.

Second, conventional ANOVA leads to less accurate results die to bigger measurement error.

Two points on every measured distance make doubled error of measurement

which biases the value of the index FA.

The next softs have been used in this study. TPSDig is for digitizing of landmarks. TPSRelw is for detection deviation of shape. TPSUtil is for transforming TPS fails to NTS fails. PAST was used for obtaining the coordinates in tangential space. STATISTICA 8 was used for 2-way univariate ANOVA.




1.      Klingenberg С.Р., Barluenga M., Meyer A. Shape analysis of symmetric structures: quantifying variation among individuals and asymmetry // Evolution. 2002. Vol. 56. P. 1909-1920.

2.      Michael D. Jennions. The allometry of fluctuating asymmetry in southern African plants: flowers and leaves// Biological Journal of the Linnean Society (1996), 59: 127–142.

3.      Møller, A.P., Eriksson, M. Patterns of fluctuating asymmetry in flowers: implications for sexual selection in plants. J. Evol. Biol. 1994, 7, 97-113.

4.      Møller A.P. Bumblebee preference for symmetrical flowers. Proceedings of the National Academy of Science USA. 1995, 92: 2288–2292.

5.      Palmer A.R., Strobeck С. Fluctuating asymmetry analysis revisited / Ed. M. Polak, Developmental instability (DI): causes and consequences. Oxford Univ. Press, 2003. P. 279-319. 

Последнее обновление ( 13.11.2012 г. )

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