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 insectpollinated
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
preselected 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 socalled 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 (AprilMarchMay 2012) using the camera Panasonic DMCFZ100. This
site is about 2 km to the northwest 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 foreststeppe 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 km^{2 }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 45m (hibiscus and digitalis).
The flowers of one size were pictured.
Measuring
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
predefined as lying on the Yaxis.
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. Bilaterallysymmetrical
landmarks and axis of symmetry
1  Ipomea alba (two pairs of
bilaterallysymmetrical landmarks: ad; bc),
2  Сoreopsis
verticulata (three pairs: fd; gc; hb), 3  Hibiscus
engleri K.Schum (two pairs; ed; ac), Digitalis
purpurea L. (two pairs: bc; cd)
FA testing
FA index has been defined as [5]:
, where: (1)
(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 (XY_{r}  XY_{l})
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
σ^{2
}= (MS_{is } MS_{m})/M, (2)
where:
σ^{2}– FA index as nondirectional asymmetry variance after
removing measurement error;
MS_{is }– mean square
interaction “side” and “individuals”;
MS_{m }– 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 6080 digital flower
images for each species of plant were assumed.
Results
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
Species

FA

formula (1)

distances

index

F

p

F

p

Hibiscus engleri K.Schum

0.0006

2.260

0.000

ns

ns

Сoreopsis verticulata

0.0004

0.444

0.001

2.01

0.004

Ipomea alba

0.0001

ns

ns

ns

ns

Digitalis
purpurea L.

0.001

0.64

0.019

0.69

0.042

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; twosample ttest with different variances). The
result corresponded to the data of 2way ANOVA (insignificant factor “side”).
The presence of antisymmetry
and deviation from normality have been obtained for all species
The value (ХУ_{r} – ХУ_{l}) showed high kurtosis (k > 7.54) that is said about leptokurtic form of distribution.
So kurtosis value was higher tabulated (n
= 8090; 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 subtropical
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 threefold measurements for
measurement error. The twofactor 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.
Twofactor 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 twofactor 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 2way univariate ANOVA.
References
1. Klingenberg С.Р., Barluenga M., Meyer A. Shape analysis of symmetric structures: quantifying variation among individuals and asymmetry // Evolution. 2002. Vol. 56. P. 19091920.
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, 97113.
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. 279319.
