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Автор Bibik T.S., Sergey G. Baranov *   
11.10.2011 г.

Vladimir State University, Russia, Department of Botany and Ecology

* University of Dodoma, Dodoma, Tanzania, Department of biology, postal


Эта статья была опубликована в  сборнике научных трудов "Естествознание и гуманизм" с материалами Шестой Международной Телеконференции (24-29 октября 2011 года). Информационная страница сборника. 


 Fluctuating asymmetry of the plants: not all traits are used for developmental stability testing

The statistical type of distribution in random population FA (fluctuating asymmetry) values of the traits from leaf trees was studied. The populations of trees with varying degrees of anthropogenic stress were used. The normal distribution of FA values was noted only for 30-50% samples. The largest FA value was observed for a little amount of populations. It was found that even a small part of samples showed their capacity to estimate the developmental instability (less than 10% of all used bilateral traits).

Keywords: stability of the development, fluctuating asymmetry, statistical distribution, environmental stress


1. Introduction

Fluctuating asymmetry (FA), or random non-directional deviations from perfect symmetry in bilaterally symmetrical traits, has recently been proposed to be a useful indicator of genetic and environmental stress [9]. Papers on fluctuating asymmetry varied in systematic affiliation of the studied species, both animals and plants. Also the numerous traits are used for calculating of the fluctuating asymmetry index. Some studied bilaterally symmetrical traits vary in a wide range, others in a narrow range, depending on their biological characteristics. The indexes of fluctuating asymmetry are used in determination of the population developmental stability. The studies of stability of development in populations of trees and herbaceous plants, which are major environmental group producing the biomass of ecosystems are particularly useful. However, the FA index can, though not always, reflect the stress caused by the environment. The increasing of the FA index value means reducing of the developmental stability of populations. In some studies, the absence of such reaction is mentioned and even the back dependence between the FA index and developmental stability [4, 7]. In practice of fluctuating asymmetry, authors are using a variety of methodological approaches that are continuously improving. It is known that only for the normal distribution of values it is possible to detect the standard deviation and standard error in the data group. However, as evidenced by numerous studies in the field of biological statistics, normal distribution of random samples of FA is quite rare. Consequently, approaches to determining FA value should take into account the distribution of values. When studying FA plants, lognormal distribution of values of the right and left traits was typical, therefore this was the reason to use the logarithms of these values to determine the index of the FA using the formula

FA = |LogR - LogL|,

and such transformation leads to the normalization (obtaining a sample with a normal distribution). Also other transformations are used, for example Box-Cox power transformations. Advantages and disadvantages of such methodical approaches are still debatable [1, 3 , 8]. The homogenization of variation spread in a number of values can lead to equalization of the confidence interval with a tedious midpoint to the mean, for example, the arithmetic mean. In recent works as a reasonable measure for the normalization of the sample, some authors use the coefficient of variation, as well as the correlation coefficient between right and left values of a bilaterally symmetrical trait [8, 2, 6]. Is it ever reasonable normalization? Logically it is acceptable if the majority of the studied samples have a distribution described by nonparametric statistics. The question becomes difficult and specific, taking into account the researchs conducted on different types of populations of plants, with different traits as some of trait could have Gaussian (normal), some could have not normal, some trait could have both types of distributions. Assuming the luck of scrutiny of this issue the task of present study included: a) analysis of the type of distribution of fluctuating asymmetry values of some woody species and herbaceous plant species, b) based on sampling with normal distribution of data determination of the level of stability of populations depending on environmental stress.


2. Materials and methods

The plant species common in region of middle Russia were selected, 30-40 m close to industrial plants, roads, traffic and other stress sources associated with other environmental factors. The leaf plates were gathered in the Vladimir region (200 km to the east from Moscow) in 2007-2009.

There were used such tree species as oak (Quercus robur), black poplar (Populus nigra), European maple (Acer platanoides), silver birch (Betula pendula Roth.), small-leaved lime (Tilia cordata). From three up to six characteristics of each species were used. From each population about 100-150 leaf plates were collected; most of the same size, 10-15 leaves from individual tree. The homologous, bilaterally symmetrical metric traits, such as the width of the leaf plates, the length of the paired veins and others were used as the studied traits. Under population it was meant a group of plants as a relatively isolated group, habitat in certain environmental conditions like the follows: the proximity of industrial pollution (highway toxic facilities), the relief, the features of the environment, such as the area cover of urban asphalt, the degree of soil density, different types of waste. The stress meant as a sum of all negative factors, stress level was recorded on five-point assessment. Five points was assigned as a high level of environmental stress. Three points was signed as an average level, one point was signed as low stress level.


3. Statistical methods

It is known that the increase of traits size value increases the value of fluctuating asymmetry [5]. Therefore the absence of difference value traits among samples of leaves of each species from different populations was conducted. Under the sample, the variety of the FA values of each bilaterally symmetrical trait for each species was assumed. The null hypotheses (р = 0) about absence of distinguishes between traits value (R + L)/2 was tested where R and L are the values of right and left side homological traits of the leaf. Also error measurement was detected. Standard error was evaluated after triple measuring R and L within one hundred leaves in every species and was detected as 0-15% of value FA in a sample. Fluctuating asymmetry population was asssumed as the absolute mean difference (R – L) divided by the sum of (R + L). Nonparametric test of Kolmogorov-Smirnov (K-S test) for normality of distribution was provided. It means the null hypothesis about absence of difference between the cumulative distribution of the sample and the estimated cumulative distribution of the same sample |R - L| / (R + L) was tested. If statistics was significant (p < 0.05) the hypothesis of the normal distribution was rejected. The selected traits were tested on a statistically significance in the one-way ANOVA (p = 0.05), because one factor of presence/absence of stress was taken into consideration.


4. Results

The results are presented in Table 1. Only a small number of populations had a normal distribution of the values |R − L| / (R + L) lacking directional asymmetry and/or antisymmetry. For example from seventy five populations Betula pendula (first line), only eight had a normal distribution values |R − L| / (R + L) (K-S test, p > 0.05). Only five populations from eight with a normal distribution showed a statistically significant difference in the ANOVA (F2.65 = 5.36, р = 0,001; F3.93 = 12.97, p = 0.0005). These data were referred to two homological bilaterally symmetrical traits.


Table1.The populations used for FA detection. The species of plants, the total number of populations, number of samples with normal distribution FA values of traits and number of samples statistically distinguished.



species, amount of populations


total number of the samples (number of populations x number of traits)

with normal distribution of trait value FA = |R – L| / (R + L); (% from total)

significant statistically, p < 0.05; (% from total)

Betula pendula, 15


8 (10.7)

5 (6.7)

Tilia cordata, 21


10 (9.5)

8 (7.6)

Quercus robur, 13


 10 (12.9)

7 (9.0)

Maple European, 15


10 (11)

7 (7.8)

Populus nigra, 11


8 (24,2)



The level of stress ranged from plus two to plus four. It is not always that the largest index FA corresponded to high level of stress.

Thus less than 50% of populations of trees and less than 50% of traits significantly differed with the value of fluctuating asymmetry. Only three species Betula pendula Roth., Tilia cordata and Quercus robur showed high level of FA referred to high level of stress.

Different traits reflected stress range in differ manner. For example, leaf’s width of Betula pendula showed stress adequately thereby length of the second vein showed a high value of FA with low level of stress.


5. Conclusions

As it follows from work of Richard Palmer, reliable traits for developmental stability study are those which are available, free of phototaxis, vary in wide range of FA value and reflect directly the stress level [5]. The obtained results do not mean that for testing of the stress it is needed to use the traits obtained in this study as statistically significant. In every geographical area with a number of unique environmental factors statistically significant values traits of fluctuating asymmetry could reflect environmental stress directly or inversely. If the traits refer to narrow range of FA value, it means traits do not reflect (or weak reflect) the level of environmental stress. So in every case researcher should choose the reasonable traits which are adequate i.e. possibly could show direct relation FA level. The bilaterally symmetrical traits with indirect relation FA-stress require a special study in the field of sustainable development. Normal distribution of samples with values FA occurred in 30-50% of cases. For woody plants of the middle part of Russia, this result can serve as a statistical measure and should be taken into attention. The species such as Betula pendula Roth., Tilia cordata and Quercus robur showed the level of fluctuating asymmetry of individual traits directly corresponding to the level of middle and high degree of technogenic pressure, indicating that these tree plants are acceptable for bioindication of developmental stability (or instability). Among samples with normal distribution about only 50% were statistically significant and could be used to assess the developmental stability. The above said makes it possible to conclude that not every trait should be used for detection of developmental stability (instability) of the populations. With the integrated assessment of the stability by using multiple bilaterally symmetrical traits it would be more correct to average or to use other integrative treatment for statistically significant traits within the normal distribution of values of fluctuating asymmetry.


1. Baranov, S.G., Gavrikov D.E. [Baranov S.G., Gavrikov D.E.], 2006. The developmental stability estimation technique by the example of birch (Betula pendula). - Bull. Russian Medical Academy, Siberian dep., N2 (48): 13 - 17. [In Russian with English summary].

2. Dongen, S. V., 1998., How Repeatable is the Estimation of Developmental Stability by Fluctuating Asymmetry? - Proceedings: Biological Sciences, Vol. 265, No. 1404 (Aug. 7): 1423-1427.

3. Graham, J. H. et al., 2003. Growth models and the expected distribution of fluctuating asymmetry. -Biological Journal of the Linnean Society, 80: 57-65.

4. Hodar, J. A., 2002. Leaf fluctuating asymmetry of Holm oak in response to drought under contrasting climatic conditions. - Journal of Arid Environments, 52: 233-243.

5. Palmer, A. R., Strobeck C., 1986. Fluctuating asymmetry: measurement, analysis, patterns. - Annual Review of Ecology and Systematics 17: 391-421.

6. Trubyanov, A. B., Glotov, N. V., 2010. Fluctuating asymmetry: Trait variation and the left-right correlation. - Doklady Biological Sciences, Vol. 431, No.1: 103-105.

7. Velickovic, M., Perisic S., 2006. Leaf fluctuating asymmetry of common plantain as an indicator of habitat quality / Plant Biosystems . V. 140, Issue 2 July: 138-145.

8. Whitlock, M., 1998.The Repeatability of Fluctuating Asymmetry: A Revision and Extension. - In Proceedings of the Royal Society of London. Series B: Biological Science, Vol. 265, No. 1404 (Aug. 7), pp. 1429-1431.

9. Zakharov, V.M., 2003. Linking developmental stability and environmental stress: A whole organism approach - in Developmental Instability: Causes and Consequences" (Polak M., ed), Oxford University Press, New York, pp. 402-414.

Последнее обновление ( 16.01.2012 г. )

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