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 (2429 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 3050% 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 nondirectional
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 BoxCox 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, 3040 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 20072009.
There were used such tree species as oak (Quercus robur), black poplar (Populus nigra), European maple (Acer platanoides), silver birch (Betula pendula Roth.), smallleaved
lime (Tilia cordata). From three up
to six characteristics of each species were used. From each population about
100150 leaf plates were collected; most of the same size, 1015 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 fivepoint
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 015% 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 KolmogorovSmirnov (KS 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 oneway 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) (KS test, p > 0.05). Only five
populations from eight with a normal distribution showed a statistically
significant difference in the ANOVA (F_{2.65} = 5.36, р = 0,001; F_{3.93} = 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

samples

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

75

8
(10.7)

5 (6.7)

Tilia
cordata, 21

105

10 (9.5)

8 (7.6)

Quercus robur, 13

78

10 (12.9)

7 (9.0)

Maple
European, 15

90

10 (11)

7 (7.8)

Populus
nigra, 11

33

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 FAstress
require a special study in the field of sustainable development. Normal
distribution of samples with values FA occurred in 3050% 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.
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