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2944__TECHNICAL SCIENCE / «€©LL©(MUM"J©UrMaL>>ff]]3P73,2(0]9
Boyko Taras1, Ruda Mania1, Paslavskyi Mykhailo 2, Sokolov Serhiy 3 1Lviv Polytechnic National University 2Ukrainian National Forestry University 3Luhansk Taras Shevchenko National University DOI: 10.24411/2520-6990-2019-10370 CALCULATION OF PROTECTIVE EFFICIENCY AND RELIABILITY OF THE FOREST COMPARTMENT OF COMPLEX LANDSCAPE SYSTEM
Abstract.
The article deals with description and calculation of the labile reliability and protective efficiency of complex landscape system (CLS). For the forest compartments of the CLS of the Dniester Precarpathian region, the phy-tocoenotic cycle (including forest floor) is identified as an autonomous and completely independent link in the general soil-biotic cycle. Thus, the reliability of the annual renewal of living above-ground phytomass, that is, labile phytocoenotic reliability can be taken (with certain adjustments) as an indicator of the overall reliability of the forest compartment, including the inertial one, associated with a much longer soil-biotic cycle of metabolism, which corresponds to the first level of partial functional stability of forest compartments which we called labile phytocoenotic reliability. The second inertial soil-biotic level of the reliability offorest compartments, which covers the wider and slower metabolic cycle and includes the reliability component, is associated with the processes offormation and dynamics of soil organic matter and describes the calculation models with the inclusion of the parameter of the humus mass.
Keywords- landscape complex, protective efficiency, reliability, compartment, homeostasis
I. INTRODUCTION
First of all, it is necessary to determine, in relation to what the reliability of a complex landscape system (CLS) should be considered - to its structure or functioning. Most often, the reliability is understood as its structural invariance (or feebly marked change that does not extend beyond a certain critical point) despite variations of functional parameters [1-4]. This approach involves concepts such as homeostasis and the margin of CLS homeostasis, as well as the norms of anthropogenic loads on the CLS. However, the quantitative assessment of structural reliability by itself is very problematic [5]. Much more realistic and practically important for CLS is the definition of its protective effectiveness, which "... increases the efficiency of the flow of energy and the circulation of nutrients... improving the ability of the community to withstand all sorts of disturbances" [6], p.379. This approach is based on a different concept of protective effectiveness, such as the ability of the system to change its structural characteristics in order to maintain the initial level (mode) of functioning [7]. Thus, you can calculate the protective efficiency and reliability directly by the discrete parameters of the biological cycle. Therefore, we will consider the functional stability of CLS rather than the structural one.
II. LABILE PHYTOCOENOTIC RELIABILITY
Biological cycle is a complex polycyclic process, consisting of a multitude of elementary soil processes, as well as of multi-ordinal nature, in terms of time, of cycles of production of living organic matter, its decomposition, mineralization and humification [8-10]. In the forest compartments of the SLC of the Dniester Precarpathian region, with their dominant sod-podzolic process under conditions of prevailing soil flushing regime, small biological cycles are largely "detached"
from the processes of humification of mortmass [11]. It looks like "... an autonomous cycle of elements between living organisms and their dying residues entering the forests on the surface of the soil [11, p. 115]. Here is an obvious manifestation of the partial phyto-coenotic cycle as a shortened (and, accordingly, accelerated) component of the overall biological cycle.
This statement was confirmed by the empirical data regarding coniferous forests. Significant partial relation of humus mass with the annual production of the forest compartment, as well as with masses of the forest floor or roots was not detected. Also, there is no reliable multiple correlation [12]. It is only on the zone ecotones of the forest and the steppe, where the vaporization regime of the soil dominates and the turf-meadow process develops, that rather a close connection between the mass of humus with masses of roots and forest floor has been revealed. However, it turned out here as well that the partial reduction of organic material stock in the soil under conditions of global warming, which is caused by the decrease in masses of forest floor and roots, does not exceed 20-25% of the total change in the humus mass, and in most forest compartments this share remains below 10% [12]. The connection of humus mass with annual production of green mass is also very feebly marked. In the CLS of the Dniester Precarpathian region, the participation of humus in the shortened biological cycle is quite insignificant.
Thus, in general for the forest compartments of the CLS of the Dniester Precarpathian region, the phyto-coenotic cycle (including forest floor) can be distinguished as an autonomous and completely independent link in the general soil-biotic cycle. In this link, the annual cycle of renewal and decomposition of living above-ground phytomass is the most dynamic. This is a rapid cycle, according to F. Duschofur [13]. It will
correspond to the first level of partial functional stability of forest compartments, which we call labile phyto-coenotic reliability.
The labile reliability can be expressed by two complex discrete parameters of the metabolism, according to [14-16], - by the coefficient of the annual turnover of the above-ground phytomass (KR = PV / BL) and the forest floor-litter index (KY = PV / ML), that is, by the coefficient of annual destruction, according to our terminology [12, 17]. Here, PV is an annual product of green mass, BL is a total live above-ground phytomass, ML is the mass of forest floor. Both of these parameters serve as means for the initial provision of the movement of organic matter (and energy) to all trophic chains, and therefore, characterize the "work" of plant matter at the reliable functioning of the ecosystem.
The measure of labile reliability was determined by calculating the territorial variations of some function of the CLS status within a certain statistical sample [17, 18]. We indicate the indexes of resistant and elastic-plastic (or simpler - elastic) reliabilities of the phyto-coenotic level, respectively, as lpe3 (1) and Inp (1). The index of elastic reliability of the forest compartment, as a measure of the Euclidean distance from its optimal functional state, was calculated by the formula:
Inp = 1 -
^(akr )2 +(aky )2
(i)
where (AKRuiKRmxZKRl■ (AKR) - (KY-x -KY,) .
(KK„ - KR™,) (ky^ - k^„ )'
Thus, the reliability index was evaluated in dimen-sionless units. If KRt — KRmax and KYt — 0, then I (y) — 1. As can be seen, both predictors are treated as being equivalent, that is, they are taken with unity "weights". Similarly was calculated the index of potential resistant reliability lpe3 (1) of the CLS. In this case, the minimum value KR and the maximum value KY were considered as optimums. The index of resistant reliability will tend to be unity at KR i —► KRmin and KY, —* KYmax.
Reliability indexes of the CLS characterize its ability to withstand the totality of disturbing impacts and indicate its distance from critical states. Since the minimum and maximum values of KR and KY are derived from a specific statistical sample, it is obvious that each of the indexes does not characterize the absolute, but the relative reliability of the CLS within the territory to which this sample corresponds. The indexes indicate the corresponding portion of the maximum possible reliability which is peculiar to this natural system.
The parameter of Inp reflects the known law of the required variety of systems [19] which states: for the system to be self-preserving, the diversity of its states or responses (adaptations) must be at least as diverse as external impacts. The reliability (invariance) of the CLS is provided by two factors: its multicoupling nature and multi-channel compensation of external disturbances [19].
Consider the contribution of each of the two predictors to the reliability of forest compartments, using data from the established sample plots (polygons) of the Dniester Precarpathian region. The elastic reliability Inp has a fairly tight, parabolic relationship with the annual turnover of above-ground phytomass:
Inp = - 0.173 + 20.95 ■ KR - 98.08■ (KR)2 (2)
(R2 = 0.996)
Within the range of small values of KR (0.01 — 0.05), the elastic reliability increases most strongly (0.05 — 0.63), and then this growth weakens. The maximum Inp = 0.90-0.98 is reached at KR = 0.09-0.10. The partial link of Inp with the mass of the forest floor ML is insignificant.
Resistant reliability Ipe3 most clearly, although not so strongly, correlates with the mass of the forest floor:
Ipe3 = 0.374 + 0.002161 ■ ML (3)
(R2 = 0.996)
With an increase in the mass of the forest floor, the sensitivity of the forest compartment to external effects clearly weakens: at the change of ML from 50 to 200 t / ha, the magnitude of lpe3 increases from 0.45-0.50 to 0.80. In this case, within the range of small masses of the forest floor (up to 70 t / ha), there is a "blur" field of lpe3 values - from 0.25-0.30 to 0.40-0.50.
Thus, while the initial response of the forest compartment to external signals depends mainly on the reserve fund in the form of the forest floor mass, the further adaptive-renewal potential is determined almost exclusively by the annual turnover of the above-ground phytomass. The KR parameter in the first case plays a negative role, while in the second case it turns out to be a positive factor for functional recovery.
The development time of the elastic reliability of the forest compartment, necessary to restore the initial level of closure of the shortened biological cycle, can be estimated as follows. At the empirical association of the coefficient of utilization of dead phytomass (KU) with ML and the total dead above-ground mass (BD), it was found that in a coniferous forest with the accumulation of mortmass up to 40-60 t / ha, no more than 40% of it is used by the next trophic levels, and in order to ensure continuous flow of organic matter in this chain, with its utilization up to 98%, a constant presence in the forest of 10-15 t / ha of dead mass is enough [18]. Based on the figures in this work, a simple calculation shows that with high annual production of green mass (8-10 t / ha and more), characteristic of the most productive forests, the "work" of mechanisms of elastic reliability for 1.5-2 years will be enough to restore the previous level of functioning. For forest compartments with a relatively low productivity of green matter (up to 3-5 t / ha), this period extends to 4-5 years.
Obviously, the functional restoration potential of the forest compartment should be manifested, in other equal conditions, more effectively and with less time than its original ability to withstand external effects.
III. INERTIAL SOIL-BIOTIC RELIABILITY
In calculations of the labile reliability of forest compartments, the predictors do not include humus mass HU, whose essential role in stabilizing a CLS is well-known. The calculation models incorporating the HU parameter describe the second level of forest compartment reliability which covers the broader and slower metabolic cycle and includes the reliability component associated with the processes of formation and dynamics of the organic matter of the soil. Let us call this level inertial soil-biotic reliability and denote
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the resistant and elastic reliabilities of this level by Ipe3 (2) and Inp (2), respectively. Ultimately, this level describes the stability of soil organogenesis as a gradual cycle, according to the terminology of [20].
We will replace KY with the mass of forest floor ML and introduce the humus mass HU as a characteristic of the structural link of metabolism, that is, we will expand the participation of the detrital link in the reliability of the ecosystem. Considering the coefficient at KR as unitary, we write the formulas for calculating the inertial indexes of Inp (2) and Ipe3 (2) with new parameters in the normalized form and with the "weight" coefficients a and b in the following form:
2 i Iö(2) =
1 1(1-KR)2 + a • ML2 + b • (1-HU)2
1 + a + b
(4)
2; pe3(2) = 1-
KR2 + a • (1 - ML)2 + b • HU2
1 + a + b
.(5)
We will take "weight" coefficients a = b = 1, which means, same as before, equal participation of all considered factors in the formation of the reliability of forest compartments. The results of calculations of Inp (2) and Iipe3 (2): the CLS of the Dniester Precarpathian Region: resistant Ipes(2: KR - -0.289; ML - +0.565; HU - -0.146; Innp (2): KR - +0346; ML - -0.461; HU -+0.193, and they are already significantly different from the data calculated by the formula (5.10) and its analogue for Ipe3, see. [12, 17].Territorial contrasts in the indexes of both types of inertial reliability of forests between compartments are quite clearly zonal in nature. At the border of forest-steppe and steppe zones, the leading role in the resistant reliability is played by the mass of forest floor, and in the elastic one - by the mass of humus, with equally slight effects of the parameter KR.
Resistant reliability is characterized by a more "blurred" parabolic link (this "blurring" is due to a large number of significant predictors):
Ipes(X) = 2,27 ■ Ipes -1,309 ■ \lpes\l - 063 84; (6)
R = 0,711; R2 = 0,505
At values of Ipe3 being ~ 0.5, its almost linear relationship with Ipe3 (2) is observed, and the phytocoe-notic resistant reliability is somewhat higher than the soil-biotic one (moreover, at this boundary the latter
has an enormous spread of points). With subsequent growth of Ipe3 to 0.7-0.8, the Ipes(2) parameter stabilizes at the level of 0.40-0.65.
Thus, the reliability of the annual renewal of living above-ground phytomass, that is, labile phytocoenotic reliability, can be accepted (with certain adjustments) as an indicator of the overall reliability of the forest compartment, including the inertial reliability associated with a much longer soil-biotic cycle of metabolism. The obtained conclusion seems to be important in the methodological sense. The measures of labile reliability are based on simpler and more rigorous ratios of the parameters of biological cycle compared to measures of inertial reliability, where one has to deal with very different characteristic time periods of metabolic predictors and, in particular, the need for the division of humus into labile and conservative fractions, according to [21], which turns out to be difficult to solve when working with field empirical material.
Further approximations in the calculations of indexes of inertial reliability are related to the introduction of "weight" coefficients a and b for predictors. These coefficients are sought empirically - by minimizing a certain "potential" that would become a constant for perfectly space-homogeneous ecosystem which in this case is associated with a forest compartment. As such "potential", the coefficient of variability Kvar was proposed in [22], introduced in 1895 by K. Pearson, and it represents the ratio of the standard deviation of this value to its mean value, multiplied by 100%. Thus, we obtain the third modification of the reliability indexes. This modification might give us the most adequate values for reliability indexes, since the weight coefficients obtained characterize the contribution of each metabolic index which is considered in one or another reliability.
IV. RESULTS AND DISCUSSION
Although the expressions for reliability indexes are nonlinear, it is possible to estimate the contribution of metabolic parameters by means of linear multiple regression. Let us give an example equation of linear regression of the indexes of the resistant Ipe3 (3) and the elastic Inp (3) of the inertial reliability of the forest compartments of the CLS of the Dniester Precarpathian region. Normalized parameters KRn, MLn and HUn are used with regression coefficients instead of weight ones. In the equations, the predictors are listed in order of decreasing their significance which is defined by the module of t-statistics (lower index for each predictor).
Ipe3(3) = -0,616432- KR_24 59 - 0,292029- HU_l340 + 0,0876923- ML+^36 + 0,868979, R2 = 0,962; Degr = 1,6%; P<10-6. Inp(3) = -0,446277- ML_2126 + 0,305833- KR+1170 R2 = 0,954; Degr = 1,9%; P<10-6.
(7)
+ 0,124198- HU+546 + 0,460671;
Here, R2 and P are, respectively, the determination coefficient and the Pearson significance criterion. Verification of the models was carried out by the criterion of its degradation Degr which was calculated using the method of the D.M. Allen crossvalidation [23]. The model is considered to be successfully verified, if during the forecasts at new points of observation Degr <50%.
Hence the following shares of the participation of all predictors in the reliability indexes are obtained:
KR ML HU
Ipes(3) -61,9 +8,8 -29,3
Inp(3) +34,9 -50,9 +14,2
As can be seen, the introduction of regression coefficients does not change the sign of "weight", but provides a much clearer understanding of the mechanisms
of forest compartment functioning which provide it with both resistant and elastic reliabilities. First of all, the inclusion of the humus mass in the calculations of reliability indexes by formulas (4) and (5) substantially modifies these indexes calculated by the original formula (1) and its analogue for lpe.3. In this case, this is especially true for the CLSs of the Dniester Precarpa-thian region with their relatively small values of HU. The mechanisms of elastic and resistant reliabilities cannot function without the participation of a humus mass, whose role in stabilizing the forest compartment increases with decreasing its content (see formula 7), which corresponds to the known Liebig's Law of the Minimum (laws of limiting factors) [11].
It is also obvious that the high resistant reliability of the forest compartment is maintained mainly by weakening the autotrophic biogenesis (-KR) and, secondly, by decelerating the destruction processes (ML, see also formulas 6 and 7), while the implementation of the restorative potential is determined mainly by the increase in the activity of the detrital link of metabolism, which is evidenced by the high negative correlation of Inp with the mass of the forest floor (see formula 7). The growth of autotrophic biogenesis (+ KR) also contributes to this. The role of this process in ecogenetic successions can be both commensurate with the active detritogenesis, which reduces ML, and secondary.
Conclusions
Thus, in the process of perceiving adverse climatic signals, the forest compartment switches from one of the major mechanisms of its functioning to others -from the rate of autotrophic biogenesis to the rate of decomposition of forest litter. In this case, two mutually opposite mechanisms of manifestation of the known [9, 16, 24] buffer properties of the litter are revealed. In the initial period of the manifestation of resistant reliability, the growth of ML marks the transition of the forest compartment into a more stagnant category, according to the classification of [24]. At the second, functional restoration stage, when the processes of elastic-plastic reliability are included, the mass of forest floor decreases and this means the transition of the forest compartment into a more active category.
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