RU2556985C2 - Method for comparative indication by birch leaves fluctuating asymmetry - Google Patents

Abstract

FIELD: food industry.

SUBSTANCE: invention refers to engineering biology and comparative environmental bioindication. The method involves collecting leaves from registered birch trees and measurements of each leaf collected. During measurement, each leaf is placed with the side turned towards the spring top. For measurement, a calliper compass and a ruler are used. Leaves are sampled from each birch from at least two birch groves growing under conditions different in terms of air pollution with hanging shortened springs orientation by cardinal point with the help of a compass. The width of sample leaves collected is measured on the left and on the right with leaf halves. One additionally measures (to the left and to the right from the leaf halves) the length of the second order vein which is the second from the base. Then statistic modelling is performed based on the measurement data. Comparative indication of the ecological condition of the environment round the birch groves is performed based on the obtained statistical indicators.

EFFECT: technology allows to increase measurement accuracy for quality evaluation of ambient air pollution.

5 cl, 13 tbl, 10 dwg

Description

The invention relates to engineering biology and comparative bioindication of the environment by measuring the most important parameters of the growth organs in the form of birch leaves with a simple and small leaf blade. The invention can be applied to seasonal indication of air pollution, mainly after reaching a generative age state by a birch tree.

There is a method of measuring leaves in woody plants (see the same book: Fedorova A.I., Nikolskaya A.N. Workshop on Ecology and Environmental Protection: Textbook Village M .: Humanit Publishing Center VLADOS, 2001. 288 S. S.123-126), when 20-25 leaves of birches and other tree species growing under different environmental conditions are cut, put into packets, and then dried between sheets of newsprint in the laboratory and measure the parameters of each sheet, and then the measured data are processed by average values.

The disadvantage is the low sensitivity (accuracy) of the indication and the high complexity of the practical application of the method due to the mixing of leaves from different trees in one sample.

There is also a method of measurement by the method of V.M. Zakharov fluctuating asymmetry of birch leaves (V. Zakharov. On the assessment of asymmetry of bilateral features as a population characteristic / V. M. Zakharov, V. V. Zyuganov // Ecology. - 1980. - No. 1, pp. 10-16), including taking leaves from reference trees growing under the same environmental conditions of location, and leaves from one tree are stored separately so that the results can be analyzed individually for each birch, and for this it is necessary to bind the leaves collected from one tree for petioles, and all leaves with the wounds for one sample should be folded into a plastic bag, and a label should be put on it that indicates the number of the sample, place of collection, making the most detailed location, date of collection, and for short-term storage the collected material is stored in a plastic bag on the bottom shelf of the refrigerator, and for long-term storage, you can fix the material in a 60% solution of ethyl alcohol or herbarize, while for measurement, each sheet is placed in front of itself with the side facing the top of the shoot, from each sheet with they measure the five parameters of the sheet on the left and right sides of the sheet, and a measuring compass, a ruler and a protractor are used for measurements, and length measurements are taken with a compass gauge, and the angle between the veins is measured by a protractor.

The main disadvantage of this method is that the principle of individuality of fluctuating asymmetry is violated when 100 leaves are taken in each sample (10 leaves from 10 plants). This is done for the sake of the existing theory of arithmetic mean. But the leaves do not have such a parameter, so each leaflet has its own parameter values that need to be determined. Then, from these parameters, it is necessary to select the most significant ones and conduct thorough statistical research on them. But the existing classical statistics cannot say anything about the individual properties of each of the 100 leaves; it considers these 100 leaves only as homogeneous random events. As our studies have shown, each leaf is not a coincidence, but a pattern.

The technical result is a simplification of the method and an increase in the accuracy of indicating the quality of the local birch leaves surrounding the local environment, as well as an increase in the measurement performance of only the most important parameters of the test leaves and an increase in the productivity and accuracy of processing the obtained measurement results.

This technical result is achieved in that a method for comparative indication of the fluctuating asymmetry of birch leaves, including taking leaves from reference birch trees growing under the same environmental conditions of growth, and leaves from one tree are stored separately so that the results can be analyzed individually for each birch, and for this, leaves collected from one tree should be tied for petioles, and all leaves collected for one sample should be folded into a polyethylene ket, put a label in it, which indicates the sample number, place of collection, making the most detailed location, the date of collection, and for short-term storage, the collected material is stored in a plastic bag on the bottom shelf of the refrigerator, and for long-term storage you can fix the material at 60 % solution of ethyl alcohol or herbarize, while for measurement each sheet is placed in front of itself with the side facing the top of the shoot, for measurement use a measuring compass, ruler and protractor, and length gauges are taken with a measuring instrument, and the angle between the veins is measured by a protractor, characterized in that at least two birch trees differing in air pollution are taken for comparative indication, the collection and taking of test leaves from each birch tree of both birch trees is carried out according to the orientation of the shortened shoots on four sides of the world by compass, while taking the leaves taken, measurements are made along the lengths of the left and right at the halves of the sheet, the second from the base of the leaf of the vein of the second order, and if necessary additionally measure the width of the sheet halves, the measured data is carried out statistical modeling and statistical indicators are judged on the environmental condition compared birch and behavior over the last period of the year in terms of the asymmetry of the two halves of the test leaves.

On two birches differing in air pollution, no less than five birches are taken, hanging short shoots on four cardinal directions are selected from each birch when taking at least four test leaves of different sizes and shapes from one shortened shoot, about the same height of taking a leaf sample, while taken from at least 80 sheets, the measurements are performed along the length to the left and right of the second from the base of the second-order vein sheet and, if necessary, additionally measure the width of the left and right halves of the sheet, Eren carried middle leaf and the length of the left and right from the base of the second sheet allows the second order veins look factorial communication only between four parameters of test leaves.

According to the measured data, statistical modeling is carried out, for this purpose, rank distributions of four parameters of test leaves are introduced to assess the quality factor of the experiment and refinement of the rating of four parameters, and according to rank distributions, the occurrence of leaves along the length of the vein on the left and right sides of the sheets is established, according to the statistical indicators of occurrence, judge about ecological condition of compared birch forests,

About the behavior of birch forests for the last period of the year in terms of asymmetry of the parameters of two halves of test leaves, and comparative indication is performed according to the limiting values of the length of the vein of test leaves.

The essence of the invention lies in the fact that fluctuating asymmetry is a manifestation within individual variability, i.e. characterizes the differences between homologous structures within the same individual. If the level of fluctuating asymmetry is a characteristic of an individual, which means that it is possible to assess the difference between different groups of individuals under different conditions of pollution, according to the average regression line of the revealed pattern. Moreover, it is noted that in pure environmental conditions wave components appear, and the coefficient adequacy of even deterministic models decreases with increasing pollution.

The invention also consists in the fact that the method of V.M. Zakharov performed in excess of five parameters. It is enough to have only two parameters with strong bonds between them. But at the same time, leaves gather at least four pieces from each side of the world in at least five trees. The result is only 80 test leaves instead of 100 for the prototype.

The essence of the invention also lies in the fact that when comparing two different pollution conditions (it is predetermined that the clean and dirty sides of the square) there is the possibility of scientific and technical understanding of changes in the patterns obtained. And then these distinguishing features of the measurement results according to the revealed patterns allow us to apply by analogy to new experiments. The result is a truly comprehensive scientific and technical solution.

The novelty of the technical solution lies in the fact that for the first time the comparative indication is divided into two parts:

1) collecting and taking test leaves using separate distinctive features of the prototype, but according to the new orientation pattern of hanging shortened shoots on four cardinal points when taking at least four test leaves of different sizes and shapes from one shortened shoot, then at least 5 registration birches in each pollution zone;

2) the measurement of only two parameters of the leaf (the width of the left and right halves of the leaf, and the measurements are carried out in the middle of the leaf blade; the length on the left and right of the second from the base of the leaf of the second-order vein) allows you to search for factor relationships only between the four parameters of the test leaves.

The positive effect is that the experiment is greatly simplified in comparison with the prototype. The complexity of the measurement is reduced by taking test leaves (instead of 100 faceless leaves for calculating the arithmetic mean values of the parameters of only 80, but already like really test leaves) by 100/80 = 1.25 times. At the stage of measuring the leaves themselves, only two factors are taken instead of five (4 parameters instead of 10), that is, labor saving is 5/2 = 2.5 times. But at the same time, the mathematical interpretation of the obtained measurement data increases slightly:

1) the rank distributions of four parameters of test leaves are introduced to assess the quality factor of the experiment and refine the rating of four parameters;

2) a detailed statistical analysis of 4 samples for the clean zone and 4 more samples for the contaminated zone is introduced, which allows to reveal the behavior of two populations of 80 test leaves;

3) an additional comparison of two zones is introduced - relatively clean and contaminated (to reduce the complexity, a comparative experiment was performed on the bottom of the same birch, but on two sides of the street, which gave equal conditions for comparison).

Thus, the proposed scientific and technical solution has significant features, novelty and a positive effect. In the scientific, technical and patent literature, information materials discrediting the novelty of the invention have not been found.

Figure 1 shows a map of the city square with accounting trees located on both sides of the street (clean western zone with trees No. 1-5 and eastern polluted zone with birches No. 6-10); figure 2 shows the measurement scheme of each sheet according to our proposed method; figure 3 shows a diagram of the measurement of the length of the vein on two halves of a birch leaf; figure 4 is a graph of the change in the number of formulas (ordinate) depending on the requirements for the acceptable level of the correlation coefficient; figure 5 shows the dynamics of the number of rows of the correlation matrix depending on the acceptable level of the correlation coefficient (abscissa); in Fig.6 is the same in Fig.5 for the columns of the correlation matrix; Fig.7 shows graphs of comparative indications along the left width of the sheet; on Fig - graphs of comparative indications on the right width of the sheet; figure 9 shows graphs of comparative indications along the left length of the vein; figure 10 is the same in figure 9 along the right length of the vein.

The method of comparative indication of the fluctuating asymmetry of birch leaves includes such actions.

The collection of material should be carried out after stopping the growth of leaves (in the middle lane since July). Therefore, the period of the comparative indication from the beginning of the growing season to the moment of experiments is taken into account.

For comparative indications, at least two birch trees differing in air pollution are taken; from each birch tree of both birch forests, the collection and sampling of leaves is carried out according to the orientation of the hanging short shoots on the four cardinal directions along the compass, while the measurements taken along the leaves taken along the left and to the right of the sheet halves, second from the base of the second-order vein sheet, and if necessary, additionally measure the width of the sheet halves, according to the measured data, carry out statistical modeling and according to Atistic indicators judge the ecological state of the compared birch forests and their behavior over the past period of the year by the asymmetry indicators of both halves of the test leaves.

On two birches differing in air pollution, no less than five birches are taken, hanging short shoots on four cardinal directions are selected from each birch when taking at least four test leaves of different sizes and shapes from one shortened shoot, about the same height of taking a leaf sample, while taken from at least 80 sheets, the measurements are performed along the length to the left and right of the second from the base of the second-order vein sheet and, if necessary, additionally measure the width of the left and right halves of the sheet, Eren carried middle leaf and the length of the left and right from the base of the second sheet allows the second order veins look factorial communication only between four parameters of test leaves.

According to the measured data, statistical modeling is carried out, for this purpose, rank distributions of four parameters of test leaves are introduced to assess the quality factor of the experiment and refinement of the rating of four parameters, and according to rank distributions, the occurrence of leaves along the length of the vein on the left and right sides of the sheets is established, according to the statistical indicators of occurrence, judge about the ecological state of the compared birch forests, on the behavior of birch forests for the last period of the year in terms of the asymmetry of the parameters of two lovinok test leaf, wherein the relative indicator is performed by the limiting values of length of test leaf veins, in particular at intervals of values of the absolute and relative asymmetry along the length of the veins.

Example. In the city of Zvenigovo of the Mari El Republic, a small landscaped land of elongated rectangular shape is located in the middle of Chekhov Street. The total area of the square is about 0.56 ha. The square is surrounded on the north and east by a dirt road, on the south side is a forest. On both sides of the square (east and west sides) are houses.

For the experiment, 10 birches were selected (Fig. 1). Moreover, trees No. 1-5 are located on the western (less illuminated due to shadow from neighboring trees of the square), and trees No. 6-10 are located on the eastern (more illuminated due to the lack of trees on the street) side of the square in question. At the same time, on the eastern side of the street there is a large intensity of traffic. Therefore, pollution is higher in comparison with the western one on the eastern side.

On the western side of the square, near the border of the birch forest, an unauthorized dirt road has been laid for cars to get to their houses. Therefore, the distance from the road to the test branches and trunks of birch trees No. 1-3 does not coincide with the map in figure 1.

The experimental technique. For each accounting birch of at least five pieces, leaf collection was planned from the lower part of the tree crown from four cardinal points in azimuth φ, deg. The direction of light was determined using a compass. Leaves of at least four 4 pieces of different sizes and shapes were collected only from shortened shoots.

Thus, you need to find out how the five trees on each side of the street behave in two differently polluted places.

In this case, the parameters for each sheet are taken, according to our scientific and technical solution, the following factors (figure 2):

1 - the width of the left b 'and right b ”halves of the sheet (the measurement is carried out in the middle of the leaf blade), mm;

и справа

второй от основания листа жилки второго порядка, мм.2 - length on the left

and right

second from the base of the leaf of the vein of the second order, mm

и

. На западной стороне находятся учетные березы №1-5, а на восточной стороне №6-10. На каждом учетом дереве березы выбирались укороченные побеги с четырех сторон света. А на каждом укороченном побеге брались по четыре пробных листа для анализа показателей флуктуирующей асимметрии.The results of the experiment. A comparison of the two sides of the city square is shown in table 1. It shows the four parameters of the sheet b ', b ”,

and

. On the western side are registered birches No. 1-5, and on the eastern side No. 6-10. At each count, shortened shoots from four corners of the world were selected for the birch tree. And on each shortened shoot, four test sheets were taken to analyze fluctuation asymmetry indicators.

Table 1 The results of measurements of birch leaves growing in the square Side of the world Sheet number Azimuth φ, deg West side East side Tree number Width b, mm Length l _W , mm Tree number Width b, mm Length l _W , mm left b ' right b ”

left

right

left b ' right b ” left

right

YU one 180 one 19 21 31 32 6 13 fifteen 24 24 2 180 fourteen fifteen 24 25 16 16 27 29th 3 180 twenty 19 35 34 fourteen 16 19 25 four 180 twenty twenty 35 37 17 eighteen 25 26 FROM one 0 16 16 26 28 fifteen 16 24 25 2 0 17 17 31 29th fourteen 13 23 23 3 0 21 22 33 thirty fifteen fourteen 22 23 four 0 19 twenty 33 34 16 fifteen 24 25 3 one 270 17 twenty 31 32 19 eighteen 31 33 2 270 19 21 thirty thirty eighteen twenty 27 thirty 3 270 17 19 31 thirty eighteen 22 29th 33 four 270 17 17 31 thirty fourteen 13 24 23 AT one 90 twenty eighteen 34 32 19 eighteen thirty thirty 2 90 eighteen 19 29th thirty eighteen 17 26 26 3 90 21 21 34 34 eighteen 21 29th thirty four 90 fifteen fifteen 25 23 twenty 23 32 34 YU one 180 2 fifteen 17 28 31 7 17 eighteen 28 thirty 2 180 19 22 31 32 twenty twenty 25 36 3 180 17 eighteen thirty thirty twenty twenty thirty thirty four 180 13 13 thirty 25 23 22 35 34 FROM one 0 16 fourteen 25 23 23 22 36 36 2 0 fifteen fifteen 25 23 23 22 36 36 3 0 16 16 25 24 22 21 32 33 four 0 fourteen fourteen 22 23 19 eighteen thirty 28 3 one 270 16 17 25 24 23 25 31 39 2 270 fifteen fifteen 21 24 21 21 35 35 3 270 eighteen eighteen thirty 31 23 24 36 39 four 270 fourteen fifteen 25 25 13 13 twenty 21 AT one 90 fifteen 17 26 26 17 19 28 31 2 90 16 17 27 28 eighteen 17 thirty 29th 3 90 eighteen 17 thirty 31 eighteen eighteen 28 thirty four 90 16 17 31 28 17 17 28 29th YU one 180 3 16 16 25 25 8 17 16 27 27 2 180 17 twenty thirty thirty 19 twenty 28 thirty 3 180 fifteen fourteen 24 22 eighteen 17 27 27 four 180 16 twenty 26 27 16 13 24 29th

Side of the world Sheet number Azimuth φ, deg West side East side Tree number Width b, mm Length l _W , mm Tree number Width b, mm Length l _W , mm left b ^' right b ”

left

right

left b ' right b ” left

right

FROM one 0 eighteen 16 29th 28 16 fourteen 26 24 2 0 eighteen 19 thirty 28 16 17 26 27 3 0 17 19 26 26 16 eighteen 28 28 four 0 twenty 22 35 32 eighteen 17 23 22 3 one 270 eighteen 22 35 35 16 fifteen 29th 28 2 270 23 22 37 38 19 16 29th 29th 3 270 19 22 35 35 21 24 35 38 four 270 17 eighteen 29th thirty twenty eighteen 35 33 AT one 90 fifteen 16 29th 32 22 23 33 32 2 90 22 21 34 33 24 25 36 39 3 90 fourteen fifteen 25 22 eighteen eighteen 29th thirty four 90 twenty 19 31 31 21 23 34 37 YU one 180 four twenty 17 34 35 9 16 fifteen 26 27 2 180 fifteen fourteen 27 28 19 19 32 31 3 180 17 16 29th 29th 19 eighteen 31 thirty four 180 fifteen 13 25 24 21 19 32 32 FROM one 0 12 fourteen 16 25 16 16 25 26 2 0 19 eighteen 34 34 eighteen fifteen 27 25 3 0 19 19 27 27 17 16 26 26 four 0 10 10 24 26 fifteen 17 27 28 3 one 270 13 12 26 28 21 22 32 33 2 270 eighteen eighteen 22 28 21 16 thirty 29th 3 270 fourteen 16 25 27 19 17 thirty 29th four 270 fifteen fourteen 25 25 21 twenty 31 29th AT one 90 16 16 27 29th eighteen 19 thirty thirty 2 90 eleven 10 22 22 17 16 thirty 29th 3 90 16 eighteen 29th 31 twenty eighteen 32 32 four 90 19 19 thirty 32 eighteen 19 28 thirty YU one 180 5 fourteen fourteen 23 21 10 21 19 33 32 2 180 12 fifteen twenty 23 22 eighteen 33 35 3 180 13 fifteen twenty 24 eighteen 16 25 23 four 180 12 10 19 twenty 19 twenty thirty 33 FROM one 0 fourteen fifteen 28 28 17 22 thirty 34 2 0 eighteen fourteen thirty 28 twenty 21 32 34 3 0 10 eleven twenty 22 17 eighteen 31 34 four 0 12 eleven 22 21 24 23 40 38 3 one 270 13 12 27 26 19 17 21 25 2 270 eleven 10 17 eighteen 21 24 33 26 3 270 13 fourteen 22 23 16 17 28 28 four 270 12 13 22 24 22 twenty 34 21 AT one 90 16 fifteen 24 24 22 21 33 31 2 90 17 16 28 28 17 eighteen 28 28 3 90 16 fifteen 23 26 17 16 29th thirty four 90 fourteen eighteen 25 27 16 13 27 thirty

Based on these data, an analysis is made and a comparison of the two sides of the city square. This allowed us to identify the mathematical patterns of behavior of two populations of test birch leaves.

Statistical analysis of samples. Table 2 shows the results of calculations by the following formulas (figure 2).

The width of the sheet in the middle of its length is

where b 'is the width of the left and b ”right halves of the sheet, mm, the total length of two veins will be equal

и справа

второй от основания листа жилки второго порядка, мм.with length on the left

and right

second from the base of the leaf of the vein of the second order, mm

Asymmetry (absolute) will be calculated by the difference in the values of the sheet parameters on the left and on the right, that is, by the expression

where y ', y ”- respectively, left and right halves of the sheet width b or l _{W the} length of the vein.

The relative asymmetry will be equal to

It is applicable for comparing clean and contaminated areas.

table 2 Analysis of asymmetry indicators of birch leaves in the square Side of the world Azimuth φ, deg West side of the square East side of the square Tree number Width b, mm AS _b , mm Δ _b ,% Length l _W , mm As _l , mm Δ _l ,% Tree number Width b, mm As _b, mm Δ _b ,% Length l _W , mm As _l , mm Δ _l ,% YU 180 one 40 -2 10.00 63 -one -3.17 6 28 -2 -14.29 48 0 0.00 180 29th -one -6.90 49 -one -4.08 32 0 0.00 56 -2 -7.14 180 39 one 5.13 69 one 2.90 thirty -2 -13.33 44 -6 27.27 180 40 0 0.00 72 -2 -5.56 35 -one -5.71 51 -one -3.92 FROM 0 32 0 0.00 54 -2 -7.41 31 -one -6.45 49 -one -4.08 0 34 0 0.00 60 2 6.67 27 one 7.41 46 0 0.00 0 43 -one -4.65 63 3 9.52 29th one 6.90 45 -one -4.44 0 39 -one -5.13 67 -one -2.99 31 one 6.45 49 -one -4.08 3 270 37 -3 16.22 63 -one -3.17 37 one 5.41 64 -2 -6.25 270 40 -2 10.00 60 0 0.00 38 -2 -10.53 57 -3 10.53 270 36 -2 11.11 61 one 3.28 40 -four -20.00 62 -four 12.90 270 34 0 0.00 61 one 3.28 27 one 7.41 47 one 4.26 AT 90 38 2 10.53 66 2 6.06 37 one 5.41 60 0 0.00

Side of the world Azimuth φ, deg West side of the square East side of the square Tree number Width b, mm AS _b , mm Δ _b ,% Length l _W , mm As _l , mm Δ _l ,% Tree number Width b, mm As _b, mm Δ _b ,% Length l _W , mm As _l , mm Δ _l ,% 90 37 -one -5.41 59 -one -3.39 35 one 5.71 52 0 0.00 90 42 0 0.00 68 0 0.00 39 -3 -15.38 59 -one -3.39 90 thirty 0 0.00 48 2 8.33 43 -3 -13.95 66 -2 -6.06 YU 180 2 32 -2 12.50 59 -3 10.17 7 35 -one -5.71 58 -2 -6.90 180 41 -3 14.63 63 -one -3.17 40 0 0.00 61 -eleven 36.07 180 35 -one -5.71 60 0 0.00 40 0 0.00 60 0 0.00 180 26 0 0.00 55 5 18.18 45 one 4.44 69 one 2.90 FROM 0 thirty 2 13.33 48 2 8.33 45 one 4.44 72 0 0.00 0 thirty 0 0.00 48 2 8.33 45 one 4.44 72 0 0.00 0 32 0 0.00 49 one 4.08 43 one 4.65 65 -one -3.08 0 28 0 0.00 45 -one -4.44 37 one 5.41 58 2 6.90 3 270 33 -one -6.06 49 one 4.08 48 -2 -8.33 70 -8 22.86 270 thirty 0 0.00 45 -3 13.33 42 0 0.00 70 0 0.00 270 36 0 0.00 61 -one -3.28 47 -one -4.26 75 -3 -8.00 270 29th -one -6.90 fifty 0 0.00 26 0 0.00 41 -one -4.88 AT 90 32 -2 12.50 52 0 0.00 36 -2 -11.11 59 -3 10.17 90 33 -one -6.06 55 -one -3.64 35 one 5.71 59 one 3.39 90 35 one 5.71 61 -one -3.28 36 0 0.00 58 -2 -6.90 90 33 -one -6.06 59 3 10.17 34 0 0.00 57 -one -3.51 YU 180 3 32 0 0.00 fifty 0 0.00 8 33 one 6.06 54 0 0.00 180 37 -3 16.22 60 0 0.00 39 -one -5.13 58 -2 -6.90 180 29th one 6.90 46 2 8.70 35 one 5.71 54 0 0.00 180 36 -four 22.22 53 -one -3.77 29th 3 20.69 53 -5 18.87 FROM 0 34 2 11.76 57 one 3.51 thirty 2 13.33 fifty 2 8.00 0 37 -one -5.41 58 2 6.90 33 -one -6.06 53 -one -3.77 0 36 -2 11.11 52 0 0.00 34 -2 -11.76 56 0 0.00 0 42 -2 -9.52 67 3 8.96 35 one 5.71 45 one 4.44 3 270 40 -four 20.00 70 0 0.00 31 one 6.45 57 one 3.51 270 45 one 4.44 75 -one -2.67 35 3 17.14 58 0 0.00 270 41 -3 14.63 70 0 0.00 45 -3 -13.33 73 -3 -8.22 270 35 -one -5.71 59 -one -3.39 38 2 10.53 68 2 5.88 AT 90 31 -one -6.45 61 -3 -9.84 45 -one -4.44 65 one 3.08 90 43 one 4.65 67 one 2.99 49 -one -4.08 75 -3 -8.00 90 29th -one -6.90 47 3 12.77 36 0 0.00 59 -one -3.39

Side of the world Azimuth φ, deg West side of the square East side of the square Tree number Width b, mm AS _b , mm Δ _b ,% Length l _W , mm As _l , mm Δ _l ,% Tree number Width b, mm As _b, mm Δ _b ,% Length l _W , mm As _l , mm Δ _l ,% 90 39 one 5.13 62 0 0.00 44 -2 -9.09 71 -3 -8.45 YU 180 four 37 3 16.22 69 -one -2.90 9 31 one 6.45 53 -one -3.77 180 29th one 6.90 55 -one -3.64 38 0 0.00 63 one 3.17 180 33 one 6.06 58 0 0.00 37 one 5.41 61 one 3.28 180 28 2 14.29 49 one 4.08 40 2 10.00 64 0 0.00 FROM 0 26 -2 15.38 41 -9 43.90 32 0 0.00 51 -one -3.92 0 37 one 5.41 68 0 0.00 33 3 18.18 52 2 7.69 0 38 0 0.00 54 0 0.00 33 one 6.06 52 0 0.00 0 twenty 0 0.00 fifty -2 -8.00 32 -2 -12.50 55 -one -3.64 3 270 25 one 8.00 54 -2 -7.41 43 -one -4.65 65 -one -3.08 270 36 0 0.00 fifty -6 24.00 37 5 03/27 59 one 3.39 270 thirty -2 13.33 52 -2 -7.69 36 2 11.11 59 one 3.39 270 29th one 6.90 fifty 0 0.00 41 one 4.88 60 2 6.67 AT 90 32 0 0.00 56 -2 -7.14 37 -one -5.41 60 0 0.00 90 21 one 9.52 44 0 0.00 33 one 6.06 59 one 3.39 90 34 -2 11.76 60 -2 -6.67 38 2 10.53 64 0 0.00 90 38 0 0.00 62 -2 -6.45 37 -one -5.41 58 -2 -6.90 YU 180 5 28 0 0.00 44 2 9.09 10 40 2 10.00 65 one 3.08 180 27 -3 22.22 43 -3 13.95 40 four 20.00 68 -2 -5.88 180 28 -2 14.29 44 -four 18.18 34 2 11.76 48 2 8.33 180 22 2 18.18 39 -one -5.13 39 -one -5.13 63 -3 -9.52 FROM 0 29th -one -6.90 56 0 0.00 39 -5 -25.64 64 -four 12.50 0 32 four 25.00 58 2 6.90 41 -one -4.88 66 -2 -6.06 0 21 -one -9.52 42 -2 -9.52 35 -one -5.71 65 -3 -9.23 0 23 one 8.70 43 one 4.65 47 one 4.26 78 2 5.13 3 270 25 one 8.00 53 one 3.77 36 2 11.11 46 -four 17.39 270 21 one 9.52 35 -one -5.71 45 -3 -13.33 59 7 23.73 270 27 -one -7.41 45 -one -4.44 33 -one -6.06 56 0 0.00 270 25 -one -8.00 46 -2 -8.70 42 2 9.52 55 13 47.27 AT 90 31 one 6.45 48 0 0.00 43 one 4.65 64 2 6.25 90 33 one 6.06 56 0 0.00 35 -one -5.71 56 0 0.00 90 31 one 6.45 49 -3 12.24 33 one 6.06 59 -one -3.39 90 32 -four 25.00 52 -2 -7.69 29th 3 20.69 57 -3 10.53 Amount 2619 -31 - 4421 -29 - 2953 eleven 85.79 4712 -54 -

Side of the world Azimuth φ, deg West side of the square East side of the square Tree number Width b, mm AS _b , mm Δ _b ,% Length l _W , mm As _l , mm Δ _l ,% Tree number Width b, mm As _b, mm Δ _b ,% Length l _W , mm As _l , mm Δ _l ,% 162.59 128.60 178.71 Average 32.74 -0.39 2.03 55.26 0.36 1.61 36.91 0.14 1.07 58.90 -0.68 2.23

Table 3 shows the indicators that are used for the comparative indication (in bold).

Table 3 Comparison of the sides of the urban square in terms of asymmetry of birch leaves Statistical indicators West side clean East side, dirty The ratio is dirty / clean. By arithmetic mean values of indicators The number of measured leaves, pcs. 80 80 1.00 Average sheet width, mm 32,74 36.91 1.13 The average asymmetry in width, mm -0.34 0.14 - * The average relative asymmetry of the width,% -2.03 1,07 - * The average length of the vein of a birch leaf, mm 55.26 58.90 1,07 The average asymmetry of the length of the vein, mm -0.36 -0.68 1.89 The average relates, asymmetry of the length of the vein,% -1.61 -2.23 1.39 Sheet Width Limits Minimum absolute asymmetry -four -5 1.25 Maximum absolute asymmetry four 5 1.25 Absolute Asymmetry Interval (max-min) 8 10 1.25 Minimum relative asymmetry -25.00 -25.64 1,03 Maximum relative asymmetry 25.00 27.03 1,08 Relative asymmetry interval (max-min) 50.00 52.67 1.05 Limit values of leaf vein length Minimum absolute asymmetry -9 -eleven 1.22 Maximum absolute asymmetry 5 13 2.60 Absolute Asymmetry Interval (max-min) fourteen 24 1.71 Minimum relative asymmetry -43.70 -36.07 0.83 Maximum relative asymmetry 12.77 47.27 3.70 Relative asymmetry interval (max-min) 56.47 83.34 1.48 Note. * In the halves of birch leaves on the western side, right-side asymmetry is observed along the width of the leaf, and in birch leaves on the contaminated eastern side of the square, left-side asymmetry is observed.

The analysis shows that comparing the two zones across the width of the sheet halves does not give a noticeable difference. This can be seen in the diagram of the structure of the sheet in figure 2 and figure 3, when due to the ribbing of the shape of the sheet, the width is not precisely determined. So far, it is measured according to the prototype in the middle of a sheet folded in half, and at the same time, measurements are performed only along the inner contour of the sheet. External counteraction and ribbing of the sheet are not yet taken into account.

In addition, in the contaminated zone, the direction of asymmetry changes along the width of the birch leaves, which requires further research. Therefore, it can be recommended to use only the measurement of the length of the vein (Fig. 3), but more accurate measurements of asymmetry with an error in the division price of 0.1 mm are needed. This provides the scale available on the geodetic protractor.

According to the value of the average relative asymmetry, the length of the vein is 2.23 / 1.61 = 1.39 times longer on the polluted side of the street. According to table 3 in two zones, the interval of relative asymmetry is 1.48 and therefore the length of the vein varies statistically significantly from the influence of air pollution.

The length of the leaf vein becomes a systemically determining factor.

Rating of leaf parameters. The general equation of a trend (trend), that is, a determinate regularity without taking into account wave disturbances for all 10 ² = 100 factor relations, has the form

where y is an indicator or a dependent quantitative factor (in our example, a leaf parameter);

x is an explanatory variable or an influencing factor;

a ₁ ... a ₈ - model parameters obtained by identification on a PC.

We can write the wave equation in the form of a formula

,

,

where A is the amplitude (half) of the wave (y axis), p _i is the half-period (x axis).

Equation (2) appears after trend (1) and in biological objects shows their vibrational adaptation to the environment. With an increase in pollution, that is, with an increase in anthropogenic impact, the number i≤m of wave components decreases. It is assumed that the measurements were carried out with high accuracy.

Tables 4 and 5 show the results of a complete factor analysis and two factor ratings: first, as influencing variables, and second, as dependent indicators.

Table 4 The rating of factors and the correlation matrix of factor analysis of the plastic signs of birch leaves according to the proposed method for environmental assessment of the environment on the western side of the square Influencing factors x Dependent y Amount ∑r _x Place I _x b ' b ”

Width b ', mm 1,0000 0.8640 0.8391 0.8107 3,5138 2 Width b ”, mm 0.8610 1,0000 0.7672 0.7979 3,4261 four Length

mm 0.8439 0.7647 0,9992 0.9056 3,5134 one 0.9264 3,5342

, ммLength

mm 0.8062 0.7953 0.8965 0,9993 3.4973 3 0.8996 3,5004 Amount ∑r _y 3,5111 3.4240 3,5020 3,5135 13.9506 - 3,5051 3,5344 13.9746 Place i _y 2 four 3 one - 0.8718 0.8734 Note. The numerator shows the values of the trend correlation coefficient (1), and the denominator shows the correlation coefficient of the trend with the wave function (2)

The coefficient of correlative variation of the birch leaf population under clean environmental conditions will be 13.9506 / 4 ² = 0.8718 for trends and 0.8734 for additional wave components when applied to trends.

Table 5 The rating of factors and the correlation matrix of factor analysis of the plastic attributes of birch leaves by the proposed method for environmental assessment of the environment on the eastern side of the square Influencing factors x Dependent y Amount ∑r _x Place I _x b ' b ”

Width b ', mm 1,0000 0.8023 0.8474 0.7223 3.3720 one Width b ”, mm 0.8034 1,0000 0.7532 0.7003 3.2569 four Length

mm 0.8590 0.7655 0.9968 0.7694 3,3907 one Length

mm 0.7409 0.7584 0.7912 1,0000 3,2905 3 Amount ∑r _y 3.4033 3.3262 3,3886 3.1920 13.3101 - Place i _y 2 four 3 one - 0.8319

The coefficient of correlative variation of the birch leaf population under environmental conditions will be 13.3101 / 4 ² = 0.8319 with trends. Additional wave components with the appearance of air pollution are not obtained. This is the most important hallmark of the level of air pollution.

The pollution coefficient will be equal to 0.8734 / 0.8319 = 1.05. In other words, the east side is dirtier than the west side by 4.99%.

. А как показатель первое место получает длина жилки

. Этим снова доказывается тот факт, что длина жилки становится единственным параметром для характеристики системы (популяции) из 80 пробных листьев.Among the influencing variables in both tables, the leaf parameter, the length of the vein,

. And as an indicator, the first place is the length of the vein

. This again proves the fact that the length of the vein becomes the only parameter for characterizing a system (population) of 80 test leaves.

Rank distribution of leaf parameters. Such distributions make it possible to evaluate the quality of the initial data, i.e., the quality factor of the obtained measurements.

Select the diagonal cells from tables 4 and 5 and give in table 6.

Table 6 Rank distribution of leaf parameters Influencing factors x Dependent factors (indicators) in West clean side Eastern polluted side b ' b ”

b ' b ”

Width b ', mm 1,0000 1,0000 Width b ”, mm 1,0000 1,0000 Length

mm 0,9992 0.9968 Length

mm 0,9993 1,0000

As can be seen from table 6, both statistical samples are representative and have a correlation coefficient very close to unity. This fact means that with at least 80 test leaves, units can be placed on diagonal cells.

Binary relations of leaf parameters. Table 7 shows all binary relationships between factors by trends in the form of formula (1). Moreover, on the clean side, the length of the vein received a wave of indignation.

Table 7 Binary relations between leaf parameters Influencing factors x Dependent factors (indicators) y West clean side Eastern polluted side b ' b "

b ' b ”

Width b ', mm 0.8640 0.8391 0.8107 0.8023 0.8474 0.7223 Width b ”, mm 0.8610 0.7672 0.7979 0.8034 0.7532 0.7003 Length

mm 0.8439 0.7647 0.9264 0.8590 0.7655 0.7694 Length

mm 0.8062 0.7953 0.8996 0.7409 0.7584 0.7912

All dependencies have strong factor relationships and have a correlation coefficient of more than 0.7. This indicates the fact that the selection of five factors of two (leaf width and vein length) was performed reliably. We will increase the requirement for adequacy to 0.8 and place the selected cells in table 8.

Table 8 Binary relations with a correlation coefficient of at least 0.8 Influencing factors x Dependent factors (indicators) y West clean side Eastern polluted side b ' b ”

b ” b ”

Width b ', mm 0.8640 0.8391 0.8107 0.8023 0.8474 Width b ”, mm 0.8610 0.8034 Length

mm 0.8439 0.9264 0.8590 Length

mm 0.8062 0.8996

With this level of adequacy, there were eight patterns on the clean side of the square, and only four patterns remained on the dirty side. Then the advantage of the net side will be 8/4 = 2.

The number of significant equations becomes one of the criteria for the environmental assessment of the quality of the territory.

We will tighten the adequacy requirement to 0.84 (Table 9).

Table 9 Binary relations with a correlation coefficient of at least 0.84 Influencing factors x Dependent factors (indicators) y West clean side Eastern polluted side b ' b ”

b ” b ”

Width b ', mm 0.8640 0.8474 Width b ”, mm 0.8610 Length

mm 0.8439 0.9264 0.8590 Length

mm 0.8996

, то есть правая сторона листа просто отпала. Доводим требование до 0,85 (табл.10).The benefits of the net side will increase to 5/2 = 2.5. On the dirty side of the square, there were connections between b 'and

, that is, the right side of the sheet simply fell away. We bring the requirement to 0.85 (Table 10).

Table 9 Binary relations with a correlation coefficient of at least 0.85 Influencing factors x Dependent factors (indicators) y West clean side Eastern polluted side b ' b ”

b ” b ”

Width b ', mm 0.8640 Width b ”, mm 0.8610 Length

mm 0.9264 0.8590 Length

mm 0.8996

The number of significant equations has become 4/1 = 4.0.

And, finally, upon reaching an acceptable correlation coefficient up to [r] = 0.86, we obtain that on the eastern side of the square there will not be any adequate regularity.

But between two pairs of leaf width and vein length, four significant patterns remain.

The impact of the requirements for the level of adequacy. As an example, we consider the entire table of 160 test leaves and 10 parameters to increase the requirements for the adequacy of the desired patterns from zero to one.

Then the number of binars, as well as the number of rows and columns of the matrix, can be determined according to table 10.

Table 10 Binary relations with 10 leaf parameters Influencing factors x Dependent factors (y indicators) b ' b ”

α ' α ” b ', mm 0.8465 0.8340 0.7694 0.3125 0.3292 0.6943 0.6361 0.1124 0.1182 b "mm 0.8476 0.7671 0.7902 0.2555 0.2851 0.6485 0.7045 0.1059 0.0937

,мм

mm 0.8368 0.7694 0.8473 0.2854 0.2817 0.7236 0.6475 0.2141 0.2222

mm 0.7693 0.7889 0.8410 0.3595 0.2593 0.6839 0.6857 0.1625 0.1777

mm 0.2826 0.2336 0.2501 0.2767 0.5198 0.2510 0.2753 0.4171 0.3355

mm 0.3132 0.3437 0.3193 0.2639 0.5122 0.3251 0.3127 0.3332 0.3853

mm 0.6938 0.6529 0.7285 0.6816 0.2538 0.3147 0.6686 0.1292 0.0846

mm 0.6124 0.6921 0.6323 0.6920 0.2713 0.2955 0.6744 0.1782 0.1101 α ', deg 0,0658 0,0368 0,0698 0.1037 0.4087 0.2466 0,0775 0,0516 0.6378 α ”, degree 0.1082 0.0949 0,0568 0,0755 0.3257 0.3525 0,0717 0,0736 0.6612

Thus, the ecological situation can be estimated by changing the required adequacy by the allowable value of the correlation coefficient [r].

Such regularities can be obtained if the values of the correlation coefficient of all binary relations (according to the data of Table 10) are distributed on the interval scale of the correlation coefficient, for example, in increments of 0.1 (Table 11).

For clarity of transitions, when one by one the parameters of the test sheet are lost with increasing demands on the correlation coefficient, they are marked with numbers 1, 2 and 3.

The allowable correlation coefficient shows the right border of the interval scale. Given an acceptable value of [r], one can evaluate the level of reliability of the study needed in factor analysis.

Table 11 Characteristic of a statistical sample of 160 leaf samples Allowed correlation coefficient Number of binary relationship formulas The number of remaining rows in the matrix The number of remaining columns of the matrix 0 90 10 10 0.1 78 10 10 0.2 68 10 10 0.3 fifty 10 10 0.4 36 10 10 0.5 34 10 10 0.61 ¹ 32 8 8 0.6612 ² thirty 6 6 0.7 fifteen 5 6 0.73 ³ 12 four four 0.77 8 four four 0.8 6 four four 0.84 four four four 0.8410 3 3 3 0.8465 2 2 2 0.8473 one one one 0.8476 0 0 0

и

2 - порог существования α' и α”; 3 - предел для значений коэффициента корреляции

и

.Notes: 1 - significance is lost

and

2 - the threshold of existence of α 'and α ”; 3 - limit for the values of the correlation coefficient

and

.

A zero correlation coefficient is formed when calculating the arithmetic mean value.

In this case, biologists conduct a surface analysis, since the arithmetic mean of the studied factor does not reflect (through the behavior of multiple samples) the essence of the behavior of the population of leaf samples.

The number of binary relations will be 10 ² -10 = 90 pcs.

Table 11 also displays the patterns of dynamics of the requirements for the adequacy of the measurements. After identifying the general model (1), the following formulas were obtained:

- the number of formulas (figure 4) of the correlation matrix for the allowable correlation

- the number of rows in the correlation matrix (figure 5)

- the number of columns in the correlation matrix (Fig.6)

From the residuals in figures 4, 5 and 6 it is seen that with increasing requirements for the allowable correlation coefficient, additional vibrational perturbations of all three statistical indicators appear.

The highest values of these statistics remain after 0.73 leaf width and vein length.

Patterns of numbers at the same ranks. Let us return to the rank distributions (Table 12) and find out the number (number) of one rank values (Table 13) for the four leaf parameters.

The number of rank distributions is an indicator of the occurrence of leaves with a given parameter value.

Table 12 Rank distribution of four parameters of 80 test leaves West clean side Eastern polluted side r ₁ b ' r ₂ b ” r ₃

r ₄

r ₁ b ' r ₂ b ” r ₃

r ₄

0 23 0 22 0 37 0 38 0 24 0 25 0 40 0 39 one 22 0 22 one 35 one 37 0 24 0 25 one 36 0 39 2 21 0 22 one 35 2 35 one 23 one 24 one 36 0 39 2 21 0 22 one 35 2 35 one 23 one 24 one 36 one 38 3 twenty 0 22 one 35 2 35 one 23 one 24 one 36 one 38 3 twenty 0 22 one 35 3 34 one 23 2 23 2 35 2 37 3 twenty one 21 2 34 3 34 one 23 2 23 2 35 3 36 3 twenty one 21 2 34 3 34 2 22 2 23 2 35 3 36 3 twenty one 21 2 34 3 34 2 22 2 23 2 35 3 36 3 twenty one 21 2 34 four 33 2 22 3 22 3 34 four 35 four 19 2 twenty 2 34 5 32 2 22 3 22 3 34 four 35 four 19 2 twenty 3 33 5 32 2 22 3 22 four 33 5 34 four 19 2 twenty 3 33 5 32 3 21 3 22 four 33 5 34 four 19 2 twenty four 31 5 32 3 21 3 22 four 33 5 34 four 19 2 twenty four 31 5 32 3 21 3 22 four 33 5 34 four 19 3 19 four 31 5 32 3 21 four 21 four 33 5 34 four 19 3 19 four 31 5 32 3 21 four 21 5 32 6 33 four 19 3 19 four 31 6 31 3 21 four 21 5 32 6 33 5 eighteen 3 19 four 31 6 31 3 21 four 21 5 32 6 33 5 eighteen 3 19 four 31 6 31 3 21 four 21 5 32 6 33 5 eighteen 3 19 four 31 6 31 3 21 5 twenty 5 32 6 33 5 eighteen 3 19 5 thirty 6 31 four twenty 5 twenty 5 32 6 33 5 eighteen 3 19 5 thirty 7 thirty four twenty 5 twenty 5 32 7 32 5 eighteen four eighteen 5 thirty 7 thirty four twenty 5 twenty 6 31 7 32 5 eighteen four eighteen 5 thirty 7 thirty four twenty 5 twenty 6 31 7 32 5 eighteen four eighteen 5 thirty 7 thirty four twenty 5 twenty 6 31 7 32 6 17 four eighteen 5 thirty 7 thirty four twenty 5 twenty 6 31 8 31 6 17 four eighteen 5 thirty 7 thirty 5 19 6 19 6 31 8 31 6 17 four eighteen 5 thirty 7 thirty 5 19 6 19 7 thirty 8 31 6 17 four eighteen 5 thirty 7 thirty 5 19 6 19 7 thirty 9 thirty 6 17 four eighteen 6 29th 8 29th 5 19 6 19 7 thirty 9 thirty 6 17 5 17 6 29th 8 29th 5 19 6 19 7 thirty 9 thirty 6 17 5 17 6 29th 8 29th 5 19 6 19 7 thirty 9 thirty 6 17 5 17 6 29th 9 28 5 19 7 eighteen 7 thirty 9 thirty 6 17 5 17 6 29th 9 28 5 19 7 eighteen 7 thirty 9 thirty 6 17 5 17 6 29th 9 28 5 19 7 eighteen 7 thirty 9 thirty 7 16 5 17 7 28 9 28 5 19 7 eighteen 7 thirty 9 thirty 7 16 5 17 7 28 9 28 6 eighteen 7 eighteen 7 thirty 9 thirty 7 16 5 17 7 28 9 28 6 eighteen 7 eighteen 8 29th 9 thirty 7 16 5 17 8 27 9 28 6 eighteen 7 eighteen 8 29th 9 thirty 7 16 6 16 8 27 9 28 6 eighteen 7 eighteen 8 29th 9 thirty 7 16 6 16 8 27 9 28 6 eighteen 7 eighteen 8 29th 9 thirty 7 16 6 16 8 27 9 28 6 eighteen 7 eighteen 8 29th 10 29th 7 16 6 16 8 27 9 28 6 eighteen 7 eighteen 8 29th 10 29th

West clean side Eastern polluted side r ₁ b ' r ₂ b ” r ₃

r ₄

r ₁ b ' r ₂ b ” r ₃

r ₄

7 16 6 16 9 26 10 27 6 eighteen 7 eighteen 9 28 10 29th 7 16 6 16 9 26 10 27 6 eighteen 7 eighteen 9 28 10 29th 7 16 6 16 9 26 10 27 6 eighteen 7 eighteen 9 28 10 29th 7 16 6 16 9 26 10 27 6 eighteen 8 17 9 28 10 29th 8 fifteen 6 16 9 26 eleven 26 6 eighteen 8 17 9 28 10 29th 8 fifteen 7 fifteen 10 25 eleven 26 6 eighteen 8 17 9 28 10 29th 8 fifteen 7 fifteen 10 25 eleven 26 7 17 8 17 9 28 10 29th 8 fifteen 7 fifteen 10 25 eleven 26 7 17 8 17 9 28 eleven 28 8 fifteen 7 fifteen 10 25 eleven 26 7 17 8 17 9 28 eleven 28 8 fifteen 7 fifteen 10 25 12 25 7 17 8 17 10 27 eleven 28 8 fifteen 7 fifteen 10 25 12 25 7 17 8 17 10 27 eleven 28 8 fifteen 7 fifteen 10 25 12 25 7 17 8 17 10 27 eleven 28 8 fifteen 7 fifteen 10 25 12 25 7 17 8 17 10 27 eleven 28 8 fifteen 7 fifteen 10 25 12 25 7 17 9 16 10 27 12 27 9 fourteen 7 fifteen 10 25 12 25 7 17 9 16 10 27 12 27 9 fourteen 7 fifteen 10 25 13 24 7 17 9 16 10 27 12 27 9 fourteen 8 fourteen 10 25 13 24 7 17 9 16 eleven 26 12 27 9 fourteen 8 fourteen eleven 24 13 24 8 16 9 16 eleven 26 13 26 9 fourteen 8 fourteen eleven 24 13 24 8 16 9 16 eleven 26 13 26 9 fourteen 8 fourteen eleven 24 13 24 8 16 9 16 eleven 26 13 26 9 fourteen 8 fourteen eleven 24 13 24 8 16 9 16 eleven 26 13 26 9 fourteen 8 fourteen 12 23 13 24 8 16 9 16 12 25 13 26 10 13 8 fourteen 12 23 fourteen 23 8 16 9 16 12 25 fourteen 25 10 13 8 fourteen 13 22 fourteen 23 8 16 9 16 12 25 fourteen 25 10 13 8 fourteen 13 22 fourteen 23 8 16 10 fifteen 12 25 fourteen 25 10 13 9 13 13 22 fourteen 23 8 16 10 fifteen 13 24 fourteen 25 10 13 9 13 13 22 fourteen 23 8 16 10 fifteen 13 24 fourteen 25 eleven 12 9 13 13 22 fourteen 23 8 16 10 fifteen 13 24 fifteen 24 eleven 12 10 12 13 22 fifteen 22 9 fifteen 10 fifteen 13 24 fifteen 24 eleven 12 10 12 fourteen 21 fifteen 22 9 fifteen eleven fourteen 13 24 16 23 eleven 12 eleven eleven fifteen twenty fifteen 22 9 fifteen eleven fourteen fourteen 23 16 23 eleven 12 eleven eleven fifteen twenty fifteen 22 10 fourteen 12 13 fourteen 23 16 23 12 eleven 12 10 fifteen twenty 16 21 10 fourteen 12 13 fifteen 22 16 23 12 eleven 12 10 16 19 16 21 10 fourteen 12 13 16 21 17 22 13 10 12 10 17 17 17 twenty eleven 13 12 13 17 twenty eighteen 21 13 10 12 10 eighteen 16 eighteen eighteen eleven 13 12 13 eighteen 19 eighteen 21

In table 13 we accept the following conventions:

Nb 'is the occurrence of leaves with the same width of the left side;

Nb ”- the same on the right side of the sheet;

- встречаемость листьев с одинаковой длиной левой жилки;

- the occurrence of leaves with the same length of the left vein;

- то же с правой стороны листа.

- the same on the right side of the sheet.

In this case, the occurrence will be very different on both sides of the square. In other words, the occurrence of leaves by their size in the rank distribution becomes a very good indicator criterion.

Table 13 The number of single-rank distributions of 80 test leaves West clean side Eastern polluted side r ₁ Nb ' r ₂ Nb ” r ₃

r ₄

r ₁ Nb ' r ₂ Nb ” r ₃

r ₄

0 one 0 6 0 one 0 one 0 2 0 2 0 one 0 3 one one one four one 5 one one one 5 one 3 one four one 2 2 2 2 5 2 5 2 3 2 5 2 four 2 four 2 one 3 6 3 8 3 2 3 four 3 9 3 6 3 2 3 3 four 8 four 8 four 8 four one four 6 four 5 four 5 four 2 5 8 5 9 5 9 5 7 5 10 5 7 5 7 5 5 6 10 6 9 6 6 6 5 6 13 6 6 6 5 6 6 7 eleven 7 eleven 7 3 7 8 7 eleven 7 fourteen 7 10 7 four 8 10 8 9 8 5 8 3 8 eleven 8 10 8 6 8 3 9 8 9 3 9 5 9 eleven 9 3 9 eleven 9 9 9 13 10 5 10 2 10 12 10 four 10 3 10 5 10 7 10 9 eleven 5 eleven 2 eleven four eleven 5 eleven 2 eleven 2 eleven 5 eleven 6 12 2 12 four 12 2 12 6 12 5 12 four 12 four 13 2 13 6 13 7 13 5 13 5 fourteen one fourteen 6 fourteen 2 fourteen 5 fifteen 3 fifteen four fifteen one fifteen 2 16 one 16 2 16 one 16 four 17 one 17 one 17 one 17 one eighteen one eighteen one eighteen one eighteen 2

Separately, we consider the western and eastern sides of the square, and graphically show the formulas in pairs in figures 7-10.

The western side of the square receives the following formulas:

- ranking distribution of leaf occurrence (Fig. 7) in width on the left side of 80 test sheets

- the occurrence in the right half of the leaves (Fig. 8) has the formula

- the occurrence of leaves with left-sided vein length (Fig.9)

N ₁ = 4.18074exp (-0.033580r ₃ ), N ₂ = A ₁ cos (πr ₃ / p ₁ + 4.60797),

A ₁ = 1.8208510 ^-49 r ₃ ^84.74737 exp (-7.40918r ₃ ^1.03742 ),

p ₁ = 16.65062-1.15567r ₃ ^0.94294 , N ₃ = A ₂ cos (πr ₃ / p ₂ +0.77338)

A ₂ = 0.016314r ₃ ^13.27823 exp (-3.10298r ₃ ), p ₂ = 0.030571 + 0.10113r ₃ ^0.93743 ;

- the ranking distribution of occurrence of leaves with right-sided vein length (Fig. 10) receives a formula

N ₁ = 1.06262r ₄ ^0.98015 exp (-0.000392r ₄ ^3.06794 ),

N ₂ = A ₁ cos (πr ₄ / p ₁ -0.49710), A ₁ = -0.52446r ₄ ^1.81314 exp (-0.34470r ₄ ),

p ₁ = 1.86117, N ₃ = A ₂ cos (πr ₄ / p ₂ -0.31351),

A ₂ = 0.029790r ₄ ^4.38236 exp (-0.54476r ₄ ), p ₂ = 1.31690-0.00292094r ^1.90213 .

Thus, a characteristic property for the clean side is the presence of complex wave patterns of vibrational adaptation of the leaves to the surrounding air.

The eastern side of the square is determined by the following formulas:

- the occurrence of leaves (Fig.7) the width of the left half

- the occurrence of leaves (Fig) on the right half

- the occurrence of leaves (Fig.9) along the length of the left vein

- the occurrence of birch leaves (figure 10) along the right length of the vein

Thus, contamination causes a loss of vibrational adaptation in contaminated leaves.

The advantage of the proposed method is the technical simplicity of execution, since the equipment requires only a measuring compass and a geodetic protractor with a scale of 0.1 mm.

Therefore, the invention can be widely implemented in school environmental circles, school forestry, and even in kindergartens, as well as in geographical and other expeditions with an additional study of the quality of the territory by the properties of birch foliage.

To create a wave theory, it is necessary to increase the accuracy of measurements by an order of magnitude, that is, instead of a measurement error of ± 0.5 mm for measurements with an ordinary millimeter ruler with a division price of 1 mm, it is necessary to switch to measurements on a geodetic protractor with a division price of 0.1 mm and an error of ± 0 , 05 mm.

Claims (5)

1. A method of comparative indication of the air environment surrounding birch trees growing under different conditions according to the fluctuating asymmetry of birch leaves, including taking leaves from reference birch trees, taking measurements of each leaf taken, with each sheet being measured with the side facing the top of the shoot, and the measurements are carried out with a measuring compass and a ruler, characterized in that the test leaves are taken from each birch from at least two growing under different conditions of air pollution along the orientation of the hanging short shoots on four cardinal directions by compass, while the width of the test leaves taken is measured on the left and right of the sheet halves and additionally measured on the left and right of the sheet halves is the length of the second from the base of the second-vein leaf, then statistical modeling is carried out according to the measured data , and a comparative indication of the ecological state of the environment surrounding the birch forests is carried out according to the obtained statistical indicators. 2. The method according to claim 1, characterized in that the leaves from one tree are stored separately for analysis of the results individually for each birch, while the leaves collected from one birch are tied for petioles, and all leaves collected for one sample are folded into a polyethylene bag, put the label on the same one with the sample number, place of collection, making the most detailed location and the date of collection, while for short storage the collected material is stored in a plastic bag on the bottom shelf x lodilnika, and for long-storage material is fixed in 60% ethyl alcohol solution or gerbariziruyut. 3. The method according to claim 1, characterized in that at least five birches are taken in each birch, on each of which hanging hanging shoots are selected on four cardinal directions and at least four test leaves of different sizes and shapes are taken from one shortened shoot at the same height of sampling the leaves, and measuring the length on the left and right of the second from the base of the second-vein leaf and the width of the left and right halves of the leaf is performed on at least 80 leaves taken, and the width is measured in the middle of the leaf blade. 4. The method according to claim 1, characterized in that according to the measured data of the test leaves, rank distributions of four parameters are introduced, according to which statistical modeling is carried out to assess the quality factor of the method and refine the rating of four parameters, and the occurrence of leaves along the length of the vein is determined by rank distributions the left and right sides of the leaves, and the ecological state of the compared birch forests is judged by the statistical indicators of occurrence. 5. The method according to claim 1, characterized in that according to the parameters of the asymmetry of the two halves of the test leaves, a comparative indication of the behavior of birch forests for the last period of the year is performed, performed according to the limit values of the length of the vein of the test leaves, in particular, according to the intervals of absolute and relative asymmetry values length of vein.

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