The Influence of the Forest Factors on the Variability of the Tree-ring Chronologies of the common Pine in the conditions of the Muromtsevo District Forestry of the Vladimir Region

Rumyantsev Denis Evgenievich ORCID: 0000-0001-9871-9504 Doctor of Biology Professor, Department of Forestry, Ecology and Forest Protection, Mytishchi Branch of the Bauman Moscow State Technical University 141005, Mytischi, Moscow region, Russia,1st Institutskaya street, 1, LT2 dendro15@list.ru Other publications by this author

Epishkov Anton Alekseevich individual entrepreneur 141005, Russia, Moscow region, Mytishchi, Iaya Institutskaya str., 1, of. LT2 kam_ant1983@mail.ru

Introduction The method of cross-dating of tree-ring chronologies was first formulated by Andrew Douglass, it was based on a visual qualitative analysis of the conjugacy of short-term (one-year) fluctuations in the width of annual rings in different tree organisms ^[10].

  At the same time, only the years of local growth extremes were taken into account. The method was further developed in the works of the German forester and botanist Bruno Huber. He came to the conclusion that in the temperate climate of Europe, it is more efficient to use the variability of all annual rings of the time series for cross-dating and proposed to conduct a statistical assessment of the similarity between dendrochronological series by calculating the "coefficient of parallel variability" ^[12],[13]. The Huber similarity coefficient between two dendrochronological series was calculated as the ratio of the number of time intervals dissimilar in response to the increment to the total number of time intervals. The domestic dendrochronological school, as a rule, used another indicator similar to it, proposed in the dissertation of T.T. Bitvinskas ^[1],[2] – the synchronicity coefficient. It was calculated already as the ratio of time intervals similar in reaction to the total number of time intervals. Currently, this approach has become more widespread in the world dendrochronological practice compared to Huber's approach.Relatively unimportant due to the rare frequency of occurrence of such cases and, accordingly, their small influence on the magnitude of the calculated value of the similarity coefficients remained the question of situations with equality in the reaction of radial increment.

To resolve it on an objective basis, most dendrochronologists currently use the GLK coefficient (gleichl?ufigkeit coefficient) for dating, which characterizes the similarity between two dendrochronological series, taking into account such cases, not by a score of "1" or a score of "0", but by a score of 0.5. In particular, it can be calculated using the TSAP-Win program (RINNTECH) ^[7].

 Currently, the method of cross-dating is used to solve the following practical tasks: monitoring the accuracy of measurements of annual rings on individual wood samples;  establishment of the date of termination of cambial activity in the trunk of a tree; establishment of the date of construction of wooden buildings; dating of archaeological wood; dating of the time of creation of art objects; diagnosis of the condition of the tree at the time of felling; establishment of the time of felling of the tree; establishment of the time of drying of the tree.

The last two tasks are primarily relevant for forestry. They make it possible to monitor the legality of the turnover of round timber and to identify violations of forest legislation by methods of forensic botanical examination ^{[3],[5],[6],[8],[11],[15]}. There is no effective alternative to these methods for solving the set range of issues.

T.T. Bitvinskas (1972) was the first to study the variability of the synchronicity coefficient in natural cenopopulations. At the II All-Union Meeting on Dendrochronology and Dendroclimatology held in Kaunas in 1972, he expressed the following: "It is of great interest to study the question of how much the variability of the width of the annual layers of individual trees for certain calendar years coincides with the variability of the average width of the annual layer of planting." One of the concepts introduced by Bitvinskas into the practice of estimating the group variability of radial increment was the general convergence of a number of curves. Initially, an average chronology was calculated for each sample area based on individual time series of radial increment. Then the synchronicity coefficient between the average chronology and each of the individual chronologies was calculated. Then, from the totality of the obtained values of the synchronicity coefficient, the average value was calculated.

The study of the group variability of time series of radial increment in terms of synchronicity is of practical interest for the development of methods of forensic botanical examination, improving them to such an extent that they become available to a wide range of forestry specialists. At the same time, such studies are of fundamental interest from the point of view of the genetics of the population of forest-forming breeds and the development of breeding methods for productivity and sustainability. The purpose of this work is to study the variation of the synchronicity coefficient in the cenopopulations of Scots pine depending on the types of forest on the material of tree-ring chronologies from the Muromtsevo forestry of the Vladimir region.Materials and methods The object of the study was the pine forests of the Muromtsevo forestry of the Vladimir region.

Materials for the study were collected as part of the R&D of the Federal Forestry Agency (2008-2011).

The selection of wood samples on the territory of the Muromtsevo district forestry was carried out in August 2009. Temporary trial areas were laid within the limits of separate taxing allotments, in which stands of the I-III bonitet were located. In nature, the test areas were not beaten off, but for each accounting tree, geographical coordinates were determined using the GPS navigator GPSMAP 60Cx. A geobotanical description and a description of the parameters of the accounting trees were performed on each test area.

Wood samples were taken using a Pressler drill from trees of the I-III growth class according to Kraft at a height of 1.3 m. Wood samples were taken from 20 accounting trees, one drill core from each accounting tree.

The measurement of the width of the annual rings on the wood samples was carried out using the LINTAB device. During the work, the accuracy of measurements was constantly monitored based on the use of the visual cross-dating procedure in the TSAP-Win program. The TSAP-Win software package provides a calculation of the synchronicity coefficient called the GLK coefficient (gleichl?ufigkeit coefficient), which characterizes the similarity between two dendrochronological series and is calculated as follows:

?i= (Xi+1 - Xi )if ?i >0; Gix = +1/2 if ?i =0; Gix = 0 (very rare)

if ?i <0; Gix = -1/2 for two curves G(x,y) = (1/n-1)

  n-1?i=1 |Gix + Giy|

where G = GLK, X and Y are dendrochronological series; n is the length of dendrochronological series, years; i is the moment of time ^[14].

The resulting measurement results using the TSAPWin program were saved as a file in Excel CSV format and subsequently data was processed in a Microsoft Excel spreadsheet processor.

It is appropriate to explain separately that in the work they operate with ideas about two types of average values of the synchronicity coefficient. First, the average chronology for the trial area is calculated by the width of the annual ring. Next, the synchronicity coefficient of each individual chronology with the average chronology is calculated. The average value is calculated from the resulting set of values (the number of which corresponds to the number of scientific trees on the test area). As a result, we get the indicator that T.T. Bitvinskas ^[2] called "the general convergence of a number of curves". Based on the average breakdown area (the total convergence of a number of curves), group averages can be calculated, for example, averages for the type of forest.

The work was carried out on the basis of a database (a bank of dendrochronological data) created on the instructions of the Federal Forestry Agency by MGULES scientists in 2009.

Results and discussion To study the variation of the synchronicity coefficient, 33 test areas located in the Vladimir region of the Muromtsevo forestry were analyzed.

The trial areas were located in different forest growing conditions. Geographical coordinates of the first test area (MPP2): latitude 55°55.349’00’; longitude 040°58.348’00’.

 In order to exclude trees growing in unfavorable conditions from the analysis, green–mossy pine forests were mainly selected for analysis, since the annual layers of oppressed trees growing on soils with excessive waterlogging (sphagnum pine forests, long-mossy pine forests) contain false or fallen annual rings, which complicates the procedure of experimental data processing. Based on the materials of the taxation description, an array of data was collected for each test area, presented in Table 1. Typical undergrowth species in the test areas were common mountain ash and brittle buckthorn, goat willow, long-eared willow, gray alder, common juniper, common bird cherry were also found. Spruce and birch were the most common in the forest, linden, pine, oak, maple, aspen were also found.

Table 1 Characteristics of trial plazastable 1characteristics of trial plots Code PPKvartal, excl.

The types of forest are dominated by pine forests of the green-mossy group of forest types. This is important from the point of view of conducting calculations, since to a certain extent they unify the sample according to the criterion of the type of forest, which eliminates errors in measurements if this process depends on the type of forest. The influence of the forest type on the variation of the synchronicity coefficient was considered separately by us.The following species were mainly found in the living ground cover.

Blueberry pine: blueberries, lingonberries, hairy ozhika, European hoof, meadow marjanica, double-leaved mayberry, common sour, hard-leaved starling, raspberry, Schreber's pleurocium, European weekling, ivy budra, flattened planus, May lily of the valley and others. Lingonberry pine: cowberry, blueberry, male cowberry, Schreber's pleurocium, cladonia, common heather and others. Sour pine: common sour, forest boneberry, blueberry, raspberry, male cowberry, hairy sedge, ground strawberry, wild strawberry, yellow green, hard-leaved star and others. Mixed pine: meadowsweet, dioecious nettle, female stalk, common vine, pungent buttercup, mother and stepmother, forest horsetail. Based on the data obtained, as a result of processing wood samples in the TSAP-Win program, for each sample area characterizing a separate cenopopulation of pine, the coefficients of synchronicity between the average group chronology and individual chronologies were calculated.

  These data made up an array of values of the synchronicity coefficient. It included 595 values.  Then the average value of the synchronicity coefficient, the maximum value of the synchronicity coefficient and the minimum value of the synchronicity coefficient were calculated. Further, the data for each test area were recorded in a general table, and the number of occurrence of each coefficient for all test areas was calculated. For the obtained arrays of values of the synchronicity coefficient, the values of the frequency of occurrence in the sample were calculated.

The obtained data is reflected in the graph in Figure 1. Figure 1. The values of the frequency of occurrence of the synchronicity coefficients between the individual chronology and the average chronology of the STANDFIG.

1. Values of the frequency of occurrence of synchronicity coefficients between the individual chronology and the average chronology of the standard, after analyzing the graph presented in Figure 1, we can conclude that the values of the synchronicity coefficient in the test areas have high indicators.

The distribution graph of the frequency of occurrence of values visually corresponds to the normal distribution graph.  With the correct dating of tree-ring chronologies, the values of the synchronicity coefficient are most in the range of 47% - 89%.  Lower and higher values are rare. The data obtained can be used for cross-dating of tree-ring chronologies to monitor the accuracy of measurements.

For dendrochronology, the question of whether the average, maximum and minimum values of the synchronicity coefficient in the cenopopulation are related in their variation is of theoretical interest. Based on the material we received, we performed this kind of analysis. Its result is reflected in Figure 2 and in Table 2. Fig. 2 Graphs of variation of average, maximum and minimum values of synchronicity coefficients Fig.

2 Graphs of variation of average, maximum and minimum values of synchronicity Coefficients Figure 2 shows the average, minimum and maximum values of the synchronicity coefficient for each of the sample areas analyzed by us.

As a result, we observe the coefficient dynamics series on the test areas. As can be seen from the data in Figure 2, there are coincidences in the fluctuations of the coefficient dynamics series: smaller average values of the synchronicity coefficient on the test area often correspond to smaller minimum and maximum values of the synchronicity coefficient, and vice versa: large – large.

In order to give a quantitative assessment of the pattern we found, we used the correlation analysis procedure in the MS Excel program. The results of the performed calculations reflect the data in Table 3.Table 2. Values of correlation coefficients between the series of synchronicity coefficients between chronologiesTable 2. Values of correlation coefficients between series of synchronicity coefficients between chronologies

The correlation relationship between the maximum and minimum values of the synchronicity coefficient is very weak, practically absent – the correlation coefficient is 0.3. The estimates for assessing the strength of the connection are given by us on the basis of the textbook by G.F. Lakin ^[4].

The main result of the work was the analysis of the variation of the values of the synchronicity coefficient depending on the types of forest. These data can be useful for the formation of methods of forensic botanical examination using methods of dendrochronology. As we have already noted in the introduction, this is important for answering the questions:

1. establishing the date of construction of wooden buildings?

2. dating the time of creation of art objects?

3. diagnostics of the dry condition of the tree at the time of cutting?

4 setting the time of tree felling?

The answers to these questions make it possible to monitor the legality of the turnover of round timber and to identify violations of forest legislation by methods of forensic botanical examination.

Data on the variation of the synchronicity coefficient depending on the type of forest are given in Table 3.Table 3. Variation of the values of the synchronicity coefficient in the test areas Table 3. Variation of the values of the synchronicity coefficient in the test areas

As a result, our sample of trial areas was divided into 5 groups: blueberry pine, sour pine, lingonberry pine, mixed grass pine, orlyak pine. The results of calculating averages for average coefficients, averages for maximum coefficients, averages for minimum values of the synchronicity coefficients for each of the groups by forest type reflect the diagrams in Figures 3, 4, 5.Fig. 3. Average values of the synchronicity coefficient for test areas embedded in different types of forests Fig.

3. Average values of the synchronicity coefficient for test areas laid in different types of Forests. .

4. Average maximum values of the synchronicity coefficient for test areas embedded in different types of forests Fig.

4. Average maximum values of the synchronicity coefficient for test areas laid in different types of forests.

5. Average minimum values of the synchronicity coefficient for test areas embedded in different types of forests Fig.

5. Average minimum values of the synchronicity coefficient for test areas laid in different types of FORESTS According to the diagram shown in Figure 1, it can be seen that the range of variation between different groups is not very large and is several percent.

For example, the maximum value is observed for blueberry pine (85%), the minimum value is observed for eagle pine (77%), the range of variation between them is 8%, the variation between other groups is somewhat less. Consequently, within the framework of solving the research tasks set by us, the maximum values of the synchronicity coefficients for areas from different types of forests are less correctly combined into a general sample during analysis than the average averages.

According to the diagrams presented in Figure 4, it can be seen that the range of variation is somewhat larger than for the average for the average, but also only a few percent. For example, the maximum value is observed for sour pine (63%), the minimum value is observed for lingonberry pine (57%), the range of variation between them is 6%, and the variation between other groups is even smaller. Therefore, within the framework of solving the research tasks set by us, it is incorrect to combine the minimum values of the synchronicity coefficients for areas from different types of forests into a common sample during analysis.

According to the diagram shown in Figure 5, it can be seen that the range of variation is greater than for the averages based on the average values of the synchronicity coefficients, but also amounts to several percent. For example, the maximum value is observed for sour pine (63%), the minimum value is observed for lingonberry pine (57%), the range of variation between them is 6%, the variation between other groups is even smaller. Therefore, within the framework of solving the research tasks set by us, it is incorrect to combine the minimum values of the synchronicity coefficients for areas from different types of forests into a common sample during analysis.

Conclusion Thus, studies were carried out characterizing the variation of the synchronicity coefficient in the cenopopulations of Scots pine in the conditions of the Muromtsevo district forestry of the Vladimir region.

These are unique, unparalleled data of theoretical and practical significance. It is confirmed that the synchronicity coefficient is a reliable indicator of similarity between dendrochronological series. In the course of the study, the graying main conclusions were obtained:

1) The distribution graph of the frequency of occurrence of values visually corresponds to the normal distribution graph.  With the correct dating of tree-ring chronologies, the values of the synchronicity coefficient are most often in the range of 62% - 78%. Lower and higher values are rare. The data obtained can be used for cross-dating of tree-ring chronologies to monitor the accuracy of measurements.

2) There is a fairly close relationship between the average value of the synchronicity coefficient in the cenopopulation and the minimum value of the synchronicity coefficient in the cenopopulation, as well as between the average value and the maximum (correlation coefficient 0.64-0.67), but it cannot be considered functional and these indicators in research papers are recommended to be analyzed independently in the future.

3) There is a very weak correlation between the maximum and minimum values of the synchronicity coefficient, it is practically absent – the correlation coefficient is 0.3.4) The range of variation among the averages for the average values of the synchronicity coefficients between groups from different types of forest is small and amounts to several percent.

For example, the maximum value of the coefficient is observed for sour pine (71%), the minimum value is observed for eagle pine (67%). The range of variation between them is 4%, the variation between other groups is even smaller. Therefore, in the framework of solving research problems, it is correct to combine the average values of the synchronicity coefficients for areas from different types of forests into a common sample during analysis.