**Annotation**

**The deviation from perfect bilateral Synnnetry is a phenomenon, which mean the turns in metabolic paths responsible for developmental homeostasis. **To assess the asymmetry, the measurement accuracy is important. This study demonstrates that the measurement accuracy is significant in determining the statistically significant directional asymmetry (DA) in the *Betula pendula* Roth leaf blade. The results showed that DA is highly variable at an individual level (tree) depending on the population, and is a common kind of asymmetry in birch leaves. The results obtained should be taken into account when testing the stability of development of birch and other woody plants.

Introduction

**Directional asymmetry (DA) is one of the types of asymmetry with a clear predominance of either right or left structures. **Fluctuating asymmetry (FA) is characterized by a slight and statistically insignificant deviation from zero of the difference between the values of the right and the left parts of the homologous bilaterally symmetric trait, with the normal distribution of this difference [1, 2]. According to modern concepts, FA refers to a certain type of variability - random, or fluctuating [3].

**Various bilaterally symmetrical traits have not the same variability in the magnitude of the FA. **Since the FA is a considered indicator of instability, traits with DA are not used in the integral environmental monitoring. Other mean - DA can serve as indicator of destabilizing of development. However, the presence of asymmetry in the mix of DA and FA and the ability of directional asymmetry to inherit raise the interest in this kind of asymmetry. In many studies was shown the importance of phenotypic plasticity and its contribution to the total amount of measured FA. The sides or repeated body parts of many sessiled organisms can be consistently exposed to differential environmental conditions, and therefore inflate the amount of FA [1, 4-8].

**The most widely used method is the method of normalizing difference, when differences in the magnitude of the metric traits are related to the sum of the values of these traits. **An alternative method is considered to be the geometric morphometric methods (GMMs) [9-11]. This takes into account the labels that are placed on the bilaterally symmetric structures. Research rejects these labels from the centroid points of consensus figure, which is drawn by the averaging of landmarks in Cartesian coordinates and the value of the FA shape of an organ (or the whole organism evaluated). The value of FA is determined in a mixed two-factor analysis Ofvariance on the magnitude of the mean square variance residuals of two factors interaction: "sample" (random) and "side" (fixed). The first factor is denoted by the code values corresponding to the level of population variability, to the individual or to the organ (leaf blade). Factor "side" is denoted only by two code values ("right" and "left"). The magnitude of variance of residues in the model, i.e., the deviation from the consensus symmetrical shape, is calculated. The value of the mean square of the factor "side" indicates the presence of directional asymmetry including its genotypic effect. According to Leamy et al and other many sources, the fluctuating asymmetry is encoded by several genes on the principle of epistatic effect [12-14]. In plants DA appears approximately in 10% of some dimensional traits, for example in the leaf blades of woody plants, as silver birch [15]. In English oak with heterogeneous structure of leaf blade the amount of such traits was higher and DA tested in GMMs revealed in all populations observed.

**Phenogenetics can be characterised as a study of homologous phenes and their individual combinations in evolutionary-ecological aspects. **Currently, population ecology (in the field of phenogenetic monitoring) is actively developing by employing phenotypic traits, like phenogenetically markers. It is known that in ANOVA directional asymmetry mixed with FA gives an undesirable bias in the value of the FA. This fact does not prevent testing the value of DA, but the phenotypic effect of fluctuating asymmetry is not available or awkward for testing [1, 2], although the some approaches are used [6, 7].

**In previous studies the correlation obtained between the magnitude of the FA index, found by linear measurements and the value of the FA index, produced by the method of geometric morphometries. **Such a correlation cannot be regarded as mandatory, and depends on the magnitude of linear traits, making a greater contribution to the shape Ofbilaterally symmetrical halves. The magnitude of the FA and the stability / instability of development depended on a combination of factors, among which the following were significant: the value of vehicle’s and industrial emissions and the height of the relief. The climatic factor was significant in the follow-up observational time.

**The study of the relation between genotypic and phenotypic effect in populations of the plants was carried out only indirectly, depending on the habitat and climatic peculiarities, with the use of traditional linear methods for FA and DA testing. **The apparent simplicity of the methodology very often led to a distortion of the results. Most of the work on phenogenetics employed the geometric morphometric method in the study on populations of rodents and insects. Recent studies of the fluctuating asymmetry of birch leaves indicated the presence of a paradoxical non-monotonous effect and hormesis if the relatively small toxic dose increases the value of asymmetry and contrary, high dose decreases asymmetry.

**Some studies appeal the size of leaf not the FA indicates stress level and the shape of leaves margin can play a serious role in variation of reproducibility of fluctuating asymmetry. **The unbiased estimation of asymmetry, both at the population and individual level also is in focus. Nevertheless the index of FA as an index of developmental stability remains the tool of environmental stress.

**The aim of this study was to test the level of phenotypic and genotypic variability of silver birch, or warty/weeping birch (Betulci pendula Roth) leaf blade’s shape at relatively normal, baseline environmental conditions. **To test the phenotypic variability, its environmental variance component was used, as a value of leaf blade fluctuating asymmetry. To test the genotypic variability several components were used, like the value of shape leaf directional asymmetry. The working hypothesis was the following: asymmetry as an element of the form (shape) leaf blade includes genotypic and environmental components of variation, detected by geometric morphometric methods.

Materials and methods

**The silver birch has a very wide area; in Russia it is bounded in the north of the Arctic Circle, and in the south it is bounded of the 50th parallel of north latitude. **Vladimirskay oblast (29 084 km^{2}; 56°5'0" N; 40°37'0" E) was chosen for study. The sites included as very close (2-5 km in limit of cities) as well remote ones 70-90 (km). So “populations” considered as relatively conditional ones and pronounced better as Cenopopulations, as they included other species and forms of plants. The collection of sheet plates was carried out in 2016, September. 50 leaf blades from each population of 10 trees were selected using trees of the same age and the same generative stage of development. In a whole the leaves were sampled from trees of age 15-25 years according to the method developed by Kryazheva, *et al* and adopted by Gelashvili *et al *for populations under different environmental stress level. The trees were located on distance 2-3m of each other. From each tree 5 plates were taken from the shortened shoots (brachioblasts) randomly on the height 1.5-2 m under conditions Ofrelatively the same sun lightening. To reduce the allometric measurement error, leaves with a maximum leaf half-width equal to 3-3.5 cm were selected. The leaf collection sites varied in altitude elevation that assumed the physicochemical properties of soil.

**The leaves are harvested in regular intervals, from the lower part of the tree crown and storage dry under the paper press for two weeks. **The images of leaves were taken using a Panasonic DMC-FZ100 camera, and JPG file format was used. Files for data manipulation and digitization were created using the TPS software package. Every plate was photographed twice to calculate measurement error. The 12 landmarks were labelled in the same order on each picture, after setting a scale factor. The landmarks were digitised twice and were classified as homological landmarks type I, as represented by pair labels on the endpoints of the lateral vessels.

**For testing of both kinds of asymmetry the method of Procrustean analyses (Procrustes ANOVA), as analogue of 2 way mixed model ANOVA (individual x side) which is used for FA value test in metric and in meristic traits. **Procrustes fit is a space in limit of centroid size. Accordingly this method, the right and left point were aligned along with the mirror-reflected landmarks. The Procrustes alignment included the original and the mirrored configurations of a sample combined, and superimposes all of them simultaneously. For averaging consensus formation the method of least squares was used. In detail this method is observed in many basic studies, for example in [9].

**In present study the MorphoJ1.06d package was used, available on web site www.morphometrics.org. **The total TPS file for population sample consisted of 200 TPS files (50 leaf blades ^{x} 2 photo x 2 measurements).

**The sampling procedure resulted in a nested dataset, with leaves nested within trees and trees nested within populations. **Thus the plan consisted of table 200 x *4,* f_{lrs}t column included coordinates and served as identificator, others columns included coded values for factors: population, tree, leaf and measurement. After creating a Procrustean space (Procrustes fit) the Procrustean analysis was conducted on each individual biosystem level.

**The magnitude of the fluctuating asymmetry was determined by the mean square MS and the value of the F-Goodall criterion evaluating the interaction of one of the random factors: "population", "tree", "leaf with a fixed factor "side". **The magnitude of DA was tested on the value of MS of factor "side" and on the value of F-Goodall criterion.

**To test antisymmetry, the third type of bilateral asymmetry, which has a bimodal distribution of the histogram of the frequencies of the difference between the values of the right and the left attributes and the negative value of the kurtosis, the program MorphoJ provides permutational multiplication of samples normalizing their distribution. **In previous studies conducted by the traditional linear method, such properties were not met in metric traits. The directional asymmetry of the linear characteristics was verified by the t-test with the verification of the null hypothesis HO, on the equality of the right and left attributes. Auxiliary programs were the packages PAST 3.03 and STATISTICA 10.

Results discussion

**The leaf blade represented a true replication, because each plate was measured twice. **The author takes into account the point of view Klingenberg about two types of errors: digitization and measurement (labelling). Therefore, a repeated survey of each plate was carried out, with a double marking on each image. The additional random factor "measure" took into account the measurement error, as the sum of the errors in photographing and labelling. The imaging and digitizing were performed as separate effects in the model with one nested into the other (Table 1):

TablelMeasurement Error

Source |
SS |
MS |
df |
F |
P |

Population |
|||||

Error imaging |
17.40 |
0.001 |
15820 |
9.43 |
<.0001 |

Error digitizing |
19.33 |
0.001 |
31780 |
||

Tree |
|||||

Error imaging |
12.09 |
0.001 |
14380 |
7.21 |
<0001 |

Error digitizing |
14.02 |
0.000 |
30340 |
||

Leaf |
|||||

Error imaging |
2.69 |
0.000 |
7980 |
2.89 |
<.0001 |

Error digitizing |
4.62 |
0.000 |
23940 |

**Procrustes analysis of variance of the amounts of shape variation attributable to population, tree and leaf blade that was photographed and digitized twice. **Sums of squares and mean squares are in units of squared Procrustes distance. The measurement error was up to 16.8% of the value of the sum square of total SS variation in Procrustes ANOVA for shape leaf variation. Error of imaging and digitizing were less on leaf level in comparison to level of population and tree.

**The increase in the accuracy of the measurement indicates a large fraction of the magnitude of the F-Goodall criterion (quotient effects MS ‘side’ on MS ‘individual xside’). **The DA value variance was coming higher at the order from "tree" to "leaf. The most statistically significant difference was in the population at high DA values; F = 7.52 for “tree”; F = 15.09 for “leaf’. Thus, with a change in the level of the biosystem in the direction from the population to a lower level, there was an increase in the magnitude of the directional asymmetry (df = 10).

**Only one population, showed a ‘clear’ fluctuating asymmetry of the leaf blades. **This population was not special (in town Gus with 150 thousand dwellers, 131 m above sea level). Only weak negative correlation (Pearson’s r = -0.32; p> 0.05) was detected between values of FA (F-Goodall criterion) and altitude elevation.

No difference found between remote and closest population sites in discriminate analysis or in principal component analysis.

**The traditional method of normalizing difference showed a statistically significant presence of directional asymmetry in two populations. **Population from town Gus had not indicated DA in linear traits as well.

**Traits with directional asymmetry, including the angle between the middle and second veins, demonstrated a relationship between the linear method and the geometric morphometry method, which assesses the asymmetry of the shape. **No high kurtosis values (more than 4) were found in the samples (R - L) that indicated the absence of antisymmetry, as the third possible kind Ofbilateral asymmetry.

**Conclusion: As a species Betulapendula shows a high phenotypic plasticity from complete absence of DA (pure FA) to highly significant level DA. **The results showed that the presence of directional asymmetry in the context of the plate shape is a common type of asymmetry in the birch leaf blades. So studies showed that in the Vladimir region, similar study conducted in 2015, showed the presence of DA in populations with a level of statistical significance p = 0.007; F- Goodall = 3.19 [15]. Accordingly, the "tree" factor showed a higher statistical significance (p < 0.001; F-Goodall = 4.97.

**The leaf blade also showed higher significance (F-Goodall = 12.17; p <0.001), that confirmed the hypothesis of the presence of directional asymmetry in leaf blades a year earlier, under relatively similar environmental conditions. **Only one population from seven showed “pure” fluctuating asymmetry.

**The study shows that the variability of linear characteristics affects the asymmetry of the shape leaf blade. **Variation of unemployed linear traits can significantly change the shape of the leaf blades.

**Thus, total asymmetry of shape Containedjoined components of the genotypic and phenotypic variability. **The ratio of the F (MS) of the interaction of the studied factor level with the factor "side" to the magnitude of the directed asymmetry, as the genotypic component of variability, can be represented as an inverse relationship.

The dependence value mixed FA from elevation altitude is corresponding to the study ofBetula pubescence as well as to previous study conducted in 2015.

The method of geometric morphometry could be seemed as more preferable for evaluating fluctuating asymmetry and stability of development.

**This method takes into account the shape of the organ, i.e. **lamina. The method of the normalizing difference takes into account only the sum of the values of the FA of the individual bilateral traits anyone of which cannot be free of directional asymmetry or antisymmetry.

**There is a controversial means on technogenic stress factors influencing developmental stability of birch species. **In spite of a big body studies two opposite ideas arise: from direct dependence on value of FA and developmental instability to reducing FA value in response to stress.

**The presented study confirmed the heterogeneity DA contributes the biasing in FA value in inter individual and intra individual levels. **Mixed FA as a rule corresponds to high error of measurement and heterogeneity in variance of left and right homological traits. Study showed high heterogeneity in DA value and possible confounding effect on FA value.

It means a high individual and among individual variability in asymmetry including genotype effect of DA.

Thus, a working hypothesis is confirmed about the joint presence of both components of variability: genotypic and phenotypic in the asymmetry of the shape of the leaf blade.

Fluctuating asymmetry in its pure form was met only in 1 out of 10 cases population studied, that should be taken into account in assessing the stability of development of the birch and possibly of other woody plants.

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