Abstract. With the help of determination analysis (DA) the study of connections between biotic and abiotic components of pond and river ecosystem is conducted. DA allows to get rid of many shortages which are intrinsic to traditional methods mathematical statistics. It is capable effectively to work with variables which distribution is not normal, and also with qualitative variables, it is not sensitive to availability of zero values in arrays of data. DA does not impose any restrictions on primary ecological data, operating only with conditional frequencies of comparing events. With the help of DA the solving of problem of ecological standardization is possible, i.e. determination of ranges of environmental factors values at which condition of different parts of biota is ecologically satisfactory.

1. INTRODUCTION

Fundamental knowledge on the functioning of natural superorganism systems can be acquired not only in specially organized and planned experiments but also through analysis of ecological monitoring data obtained by standard techniques. These data are accumulated during decades, can spread all over large territories, but do not always conform to the requirements of metrology, statistical reproducibility, etc., essential for valid use of the traditional statistical methodsfor their analysis.

The analysis of last ecological literature (Budilova et al., 1995) shows, that analysing multidimensional databases obtained during a research of natural ecosystems, one can more often apply either classical statistical methods, such as dispersion and regression analysis, or methods only formally concerning statistical ones: component analysis, cluster analysis, multidimensional scaling. Owing to fact that for all these methods now there are packages of the applied computing programs (for example, SYSTAT, SPSS, STATISTICA, etc.), these methods became available for a wide range of ecologists which have not, as a rule, adequate mathematical and statistical education. Meanwhile, the applicability of indicated methods to the analysis of ecological data observations (ecological monitoring), related to category so-called "passive experiments", is rather problematic.

It is known, specifically, that regression and dispersion analysis of variance are founded on a series of rather rigid premises, 3 of which are most important: 1) observations results should be independent accidental variables disrtibuted normally; 2) sample evaluations of observations should be homogeneous, i.e. should not depend on quantity of observations results; 3) errors in definition of independent variables in an ideal case should be equal to zero or, at least, slightingly small on comparison with error in the definition of quantity of observations results.

The long-term experience of work with data of ecological monitoring convinces that for these data any of the premises is defaulted. However, if it is possible to overcome difficulties connected to first two premises by "normalizing" transformations of quantity of observations results, then the realization of the 3rd requirement practically is impracticable because the errors in the definition of such variables as number of species, nutrient concentration are, etc. connected not so much to imperfection of techniques as to heterogeneity of distribution of these indices in real biotopes space.

It is also necessary to add that even at realization of all above mentioned premises statistical models as a whole and regression models as its part can’t be used for establishment or proof of availability of “cause-consequence” connections in investigated system. As far back as 1928 G.Azzi (Azzi, 1928) warned of the thoughtless interpretation of significance of correlation coefficients by way of evidence of causal connection between correlating variables. Many years after D.Hayes has formulated the same idea more sharply: "it is impossible to look standardly at regression equations, as we do with structural equations immediately representing causal processes" (Hayes, 1980). “Killing” (for application of regression for analysis of passive experiments results) example is given in the book of V.Nalimov and N.Chernova (Nalimov & Chernova, 1965). They solved the task of description of chemical process which is more simple system than ecosystem. The authors discovered that yield of some product depended only on 3 variables. 11 regression equations (from linear to incomplete equation of 3rd degree) were obtained, for each of them coefficient of multiple correlation was close to 0.9, so that it is impossible to make a choice of "the best" or "the most adequate" models. It is necessary to agree with the judgement of the authors: "there is no sense to attach any value to individual regression coefficients". However, it is also necessary to state that this judgement remained unknown for majority of ecologists both in Russia and abroad.

Irrespective of ultimate goals of ecological monitoring and organization of appropriate observations system the outcome of these observations always represents a rectangular table. If values of measuring variables are arranged in columns, the number of such columns can reach several tens that correspond to number of variables. Each line in such matrix contains measured values of the mentioned variable in one sample selected in a defined time and in a defined place. It is clear that number of such lines can be measured in hundreds. In other words, initial data obtained by the monitoring program, represent a matrix with dimensionality m*n, where m — number of lines, n — Number of columns, and this dimensionality is rather great.

To work with such matrixes experts in statistical analysis of experimental data recommend to use diverse methods of multidimensional statistics. The advantages of these methods are apparently indisputable: 1) instead of study of each variable separately and its connections with remaining ones it is possible at once to investigate whole array of data and receive an information about influence of all variables and their interactions on investigated ecosystem; 2) taking into consideration present universal computerization, all difficulties connected with large volume of evaluations are removed. Earlier multidimensional statistical methods were used by only few contributors, who possessed big computers and staff of assistants-programmers as well. Now not less (and sometimes more) powerful personal computer stand on a desk of each experimenter, and modern (and rather popular!) statistical softwares, such as a Stadiya, Statgraphics, Systat, SPSS, etc., allow to realize analysis of data even in that case, when researcher has only approximate idea about algorithm of appropriate evaluations and principles of its construction. It is enough to create the file of initial data and "to load" proper existing program module from software, being guided in higher degree by "friendly interface", which each such software is supplied with.

However, in this apparent simplicity the considerable danger is also made, because initial data not always answer those, rather rigid, demands which standard statistical methods make on. Naturally, in statistical textbooks these requirements are always specified. The most important of them are: normality of variables distributions, homogeneity of dispersions, stability of frequencies. However, no one of such textbooks doesn’t contain indications what is a result of violation of these requirements.

It is also necessary to notice that the traditional statistical approaches often are not adapted to data processing combining numerical and non-numerical (qualitative) variables, to combined analysis of data of different nature and different levels of description, to analysis of nonlinear and nonquasilinear variables correlations, though just the nonlinear relationships predominate in real ecosystems.

Many shortages of traditional statistics are not peculiar to the method of determination analysis (DA), which operates only with conditional frequencies of multidimensional events, not addressing to coefficients of correlation or covariance, to measures of proximity and relationship, i.e. to usual toolkit of mathematical statistics which imposes too rigid requirements for initial data.

Nowadays the sufficient experience of determination analysis application in humanitarian sciences, particularly in sociological research (Chesnokov, 1982), is accumulated. Besides the authors undertake first steps for adaptation of the method in biological research (Zamolodchikov et al., 1992; Bulgakov et al., 1992; Levich et al., 1996).

2. THEORETICAL PRINCIPLES OF DETERMINATION ANALYSIS OF ECOLOGICAL DATA

“Cause-consequence” regularities are usually described by the following "if X, then Y". For example, in ecosystems X can be aggregate of values of some complex of factors, and Y can characterize ecosystem condition. One of singularities of complicated systems operation is fact that similar judgments have a conditional character: in some cases the judgment appears true, in another cases — false. The degree of judgment reliability is obviously defined by 1) frequency A which attend the occurance of condition Y in empirical data among all cases when the researched complex of factors has the value X, and 2) frequency C which attend the occurance of factors values X in empirical data among all cases when ecosystem has the condition Y. A is called “accuracy”, and C — “completeness” of the judgment "if X, then Y". These values are conditional frequencies of the event (X, Y) (Chesnokov, 1982). The conditional judgments represent a way of description, special case of which contains strict and univalent functional assotiations Y(X) taking place when studying "well organized" (usually laboratory) experiments (accuracy and completeness of such assotiations equals 100 per cent).

Accuracy and completeness of rule "if X, then Y" can characterize significance of mutual contingency of events X and Y. The research of increments of conditional frequencies, when set of factors changes, is also of interest. Such increments can characterize importance of factors and their complexes in researched regularities. The technique of the analysis of conditional frequencies easily allows to carry out interarray data processing, namely — to calculate reliability of the rule "if X, then Z", when the reliabilities of rules "if X, then Y" and "if Y, then Z" are known, and the array of experimental data including a variable X and Z simultaneously is absent.

The offered analysis of conditional frequencies and their increments allows to decide effectively the tasks of pattern recognition in multidimensional spaces of data: to build clusters, typologies, taxa; to construct aggregated variables, integrated indices, etc. (thereby supplementing method of principal components, component analysis, multidimensional scaling and other similar methods of multidimensional statistics).

In the field of ecological research the analysis of accuracy, completeness, importance of interconnections between ecosystem characteristics, besides standard task of testing of hypothesis about mutual influence of variables, allows (with the help of optimization procedure) to discover the boundaries of normal functioning area in space of ecological factors and to calculate ecologically tolerable levels (ETL) of abiotic factors influencing an ecological condition of biotic ecosystem components (Levich, 1994; Levich & Teriokhin, 1997; Maximov et al., 1999a). Found ETL can be used as regional norms of factors disturbing ecological well-being in the tasks of ecological standardization, ecological mapping and prediction.

3. DETERMINATION ANALYSIS OF INFLUENCE OF ENVIRONMENTAL FACTORS ON ECOLOGICAL CONDITION OF BIOTA

3.1. Responses of fish-breeding pond biocoenosis to change of nutrient load

The initial data for determination analysis were taken from fish-breeding ponds (Astrakhan region) functioning as fish polycultures (herbivorous fish and carp). For four years (1987-1990) 12 ponds (Bulgakov et al., 1992) were investigated. In 4 of them fertilization experiment have carried out. During the experiment possibility of regulating the structure of phytoplankton community for improvement of food basis of herbivorous fish (mainly, obligatory phytoplanktofag silver carp Hypophthalmichthys molitrix) is checked. It is known (Savina, 1968; Omarov & Lazareva, 1974), that the most preferable algae in the terms of assimilation and absence of toxical effect for fish are representatives of green, Euglenophyta and Bacillariophyta. At the same time blue-greens, as a rule, are avoided by silver carp because of their low food value or even toxicity. In one’s turn, it is established that high dozes of mineral nitrogen introduced into a reservoir, and the high ratios of nitrogen-to-phosphorus results in a raise of fish productivity (Vinberg & Lyakhnovich, 1965). The increased nitrogen load in fertilizers stimulates development of Chlorococcales as favourite food for silver carps (Sokolskaya, 1981; Ivashechkina, 1988; Uliyanov, 1988). Thus, with the help of DA it was necessary to check up enumerated hypothesises about existing of trophic relationships in the chain "nutrients — microalgae — silver carp” in fish-breeding pond.

The set of variables, for which there were data on all ponds, included the following blocks:

1) Fish characteristics — productivity of each fish species and total fish productivity;

2) Amount of introduced nitrogenic and phosphoric fertilizers (sum for a season and separately for April - May, June - July, August - September);

3) Hydrochemical parameters of ponds — dissolved oxygen content, pH, concentration of mineral forms of nitrogen and phosphorus, ratio of nitrogen-to-phosphorud concentrations;

4) Biomass of phytoplankton phyla (Chlorococcales, Volvocales, green, Bacillariophyta, blue-greens, Euglenophyta) and total phytoplankton biomass;

5) Biomass of zooplankton taxa (Copepoda, Cladocera, Rotatoria) and total zooplankton biomass.

For variables of blocks 3-5 yearly averaged values of appropriate parameter, and also averages for April - May, June - July, August - September were used as separate variables.

For preparation of data insertion into DA-system the whole series of 12 values for each variable was marked by qualitative indication "little" or "much". The partition on two indicated classes in each case happened nonlinearly so that each class contained not less than 4 and no more than 8 samples. In addition, for hydrochemical variables the boundary between classes started proceeding from the appropriate spefications of threshold limit concentrations (TLC). With the help of DA investigated of contingencies (rules) between on the one hand high fish productivity (i.e. in the class "much") and on the other — whole complex of remaining mentioned above variables. Besides, the rule is conditional judgment connecting a cause and a consequence in investigated phenomenon. For example, "if amount of nitrogen fertilizers introduced in June-July (the explaining variable) corresponded to the class "much", then the value of silver carp productivity (explained variable) also corresponded to the class "much". The significance of a rule, as it was indicated above, is set by criteria of "aacuracy" and "completeness". Let's explain their sense in the considered example. For silver carp productivity number of observations in the class "much” equals 5, for amount of nitrogen fertilizers — 7. The amount of concurrent observations has made 3. Therefore, of 7 cases, when much nitrogen fertilizers were introduced, in 3 cases the value of productivity concerned to the class "much". So, A = 3/7 = 43%. In addition, in investigated array of data productivity had these values 5 times, that is C = 3/5 = 60%. For the analysis not all rules were selected, but only those which correspond to defined thresholds of accuracy and completeness (accordingly not less than 50 and 60 %).

Contingencies defining high productivity of silver carp practically completely confirmed all suggestions about ways of raise of ecological effectiveness at passage from zero (nutrients) to second (herbivorous fish) trophic level (Fig. 1). High yield of silver carps biomass is attended by: 1) increased amount of nitrogen and reduced amount of phosphorus; 2) high concentration of all mineral forms of nitrogen and low concentration of mineral phosphorus and, accordingly, increased ratio N:P concentration in water; 3) enlarged content of dissolved oxygen; 4) increased biomass (absolute and relative) of green algae and reduced biomass of blue-green algae. As to Bacillariophyta, significant contingencies are not found, and Eugleno

phyta are present in the class "little" by relative biomass. It is also remarkable that when the ponds had high silver carp producrivity, biomass of zooplankton in them was a little, that could be stipulated by competition between two groups of herbivorous organisms for similar phytoplankton resource.

It is obvious that the data of determination analysis of the whole complex of trophic connections in fish-breeding pond as a whole have coincided with authors’ ideas about regularities of ecosystem functioning. Basic premises of improving of "ichthyological" reservoir quality (at the expense of magnification of fertility of herbivorous component) are: redistribution of specific structure of phytoplankton in direction of Chlorococcales and green as a whole dominance and reduction of blue-greens role; sufficient air saturation of water; high background of mineral nitrogen and high ratio of nitrogen-to-phosphorus in water, that is achieved by appropriate selection of fertilizers amount.

In addition, the value of obtained results could be higher if we had much more than 12 observations. After all, the more number of coincidences of two independent events, the more foundations to consider these results as not accidental. It is clear that, for example the rule "of 50 observations with high ratio of nitrogen-to-phosphorus 40 ones have coincided with high fish productivity" is more significant than the rule "of 5 observations with high ratio of nitrogen-to-phosphorus 4 ones have coincided with high fish productivity", though the accuracies of both rules are identical and are equal 80%.

3.2. Hydrochemical indicators of river water quality and their influence on zooplankton community.

The data on hydrochemistry, hydrology (1st array) and hydrobiology (number of zooplankton species, 2-nd array) in the three sites of Sura river (Perm region) — actually river bed, Surskoye reservoir and site of the reservoir adjacent to dam— were used in describing work (Maximov et al., 1999b). The samples was taking during five years (1993-1997) in the river and reservoir only in summer months (a few samples per month), and in the site adjacent to dam — one time per month during all the year. 199 observations were conducted in all.

The 1st array included numerical values of following abiotic variables: BOD, concentration of Fe, Mn, NH₄, NO₂, NO₃, PO₄, carbohydrates, phenols, dissolved oxygen, suspended substances, and also water temperature and pH.

11 species and 3 larva stages of zooplankton which was met not less than in 20% of observations were selected from the array of hydrobiological data: Bosmina coregoni, Bosmina longirostris, Chydorus sphaericus, Daphnia cucullata, Daphnia longispina, Epistylis sp., Euchlanis dilatata, Eudiaptomus sp., Eudiaptomus gracilis, Keratella quadrata, Mesocyclops leuckarti, larvae of Copepoda, other larvae, nauplii. Each of 14 groups was divided into two classes: "little” (low number) and "much" (high number). Zero values of number were not eliminated from the analysis, and also are included into the class "little", as, actually, value of number equal to zero is not necessary indicate species absence in the sample. At existing techniques of number measurement very high probability exists that no one example of the species with low abundance doesn’t occur in the field of vision of researcher. Thus, the introduction of qualitative variable in DA allows not to reflect how to relate to zero values — either to equate them really to zero or to consider them missed. In our case, as the part of observations with zero number for all species practically exceeded 50%, so classes "little” and "much" hardly differed by their fullness. Since the class “little”, besides zero, included values of number < 0.15*10³ cells/L, it was appeared to be approximately in 3 times more (by number of observations) than class "much".

With the help of optimization procedure we tried to become clear, whether changes of hydrochemical and hydrological indices influence on number of separate species. For evaluation of this influence it was establishing what interval on a scale of values of abiotic variables the most authentically explains high number of species. In addition, it was supposed that BOD, concentrations of Fe, Mn, carbohydrates, phenols and suspended substances can reduce a number only in the range of high values, therefore at optimization only top level of unknown interval was set. For content of oxygen situation was inverse — only decrease of this index can lead to unfavorable consequences for zooplankton, therefore low border of interval was fixed. As to concentration of NH₄, NO₂, NO₃, PO₄, temperature and pH, any conditions were not superimposed beforehand on possible boundaries, because both too high and too low values of these variables can evoke deviations from satisfactory condition of organisms. Since the researched classes of explained variables (high number of species) were appeared to be fullnessless (for majority of species — 25-30% of total number in sample), and the amount of observations in the limits of optimized range of abiotic factors, on the contrary, was large (as a rule, more than 50%), so it was impossible to calculate researched rules with high accuracy: as a rule, it did not exceed 30-40%. Therefore, at the optimization low border of completeness (51%) was set, after that accuracy was maximized. With the help of plots representing completeness dependence on accuracy (Fig. 2) it’s easy to see what possible maximum of accuracy could be calculate in the limits of the established threshold of completeness.

The conducted accounts (Tab. 1) show that of 14 species and larval groups of zooplankton 11 ones (Bosmina coregoni, B. longirostris, Chydorus sphaericus, Daphnia cucullata, D. longispina, Eudiaptomus sp., Keratella quadrata, Mesocyclops leuckarti, Copepoda larvae, other larvae, nauplii) demonstrate, as a rule, homogeneity in terms of values of safe ranges of abiotic factors. The safety in this case is understood as a condition of an organism which means that it’s number remains in limits of high values selected by us. Here number of separate species and larval stages of zooplankton is the indicator of ecological condition of biocoenosis; by virtue of this circumstance it is possible to name obtained ranges as ecologically tolerable levels (ETL) (Levich, 1994; Maximov et al., 1999a) of the factors influencing biocoenosis. Looking at the responses of 3 other species not relating to indicated group, one could notice that regarding many factors they are more tolerance, i.e. ETL of these factors have the wider boundaries. For Epistylis sp. this assertion concern concentrations of Fe, Mn, O₂, NH₄ (top level), NO₂ (low level), phenols, PO₄ (top level); for Euchlanis

dilatata — BOD, concentrations of Fe, O₂, Mn, NH₄ (top level), NO₂ (top level), carbohydrates, PO₄ (top level) suspended substances, pH (low level), temperature (top level); for Eudiaptomus gracilis — concentrations NO₂ (low level), NO₃ (top level), pH (low level), PO₄ (top level), temperature (low level). At the same time for majority of indices ETL found for these 3 species essentially differ, that, probably, once again speaks about the special position of each of them in zooplankton community. It is curious to compare obtained ETL with state drinking TLC also represented in Tab. 2. For majority of indices (except concentrations of Mn, NO₂, NO₃, O₂) boundaries obtained by us appear wider than standard norms. So that it is possible to state that zooplankton community of Sura river is sufficiently stable to influence of environmental factors, and TLC defined under laboratory conditions not adequately reflect its adaptive potential.

The causes of exclusive position of three marked species are probably in their special ecological status. So, it is known that E.dilatata and E.gracilis are eurybionts which easily adapt to inhabitance in the widest limits of environmental factors. Hence their limits of tolerance follow which are the widest among all species for majority of indices.

4. CONCLUSION

The obtained results have shown that determination analysis can be rather effective tool for detect of connections between various ecosystem components, particularly for searching for and calculation of values of factors influencing biotic indicators of natural ecosystem quality. The further perspectives of the method application are connected to research of integrated ecosystem characteristics such as generalized class of water quality by abiotic indices, saprobe index of water organism communities. The wider use of the multifactor approach is possible (when a few factors participate simultaneously in the analysis as explaining variables), for example at analysis of connections between biotic and abiotic parts of ecosystem. With the help of DA procedures called context insertion it is possible to study any connections in ranges of any chosen fragment from common array of data (for example, at the research of one specific hydrographic area to carry out the analysis separately for large rivers forming this area).

It’s necessary to notice that the scientific tasks, which we could assert the offered approach to, are extremely actual. Particularly, the task of analysis of relationships between different factors in complicated multifactor systems requires new methodical approaches. The task of searching for causes of ecological trouble becomes especially important in connection with unsatisfactory substantiation of existing systems of ecological control (Maximov et al., 1999a). With the help of DA the task of searching for regional ETL of environmental factors presenting potential danger for various biotic components of ecosystems is facilitated.

Keywords Ecosystem ecological state, abiotic factors, determination analysis, ecolgically tolerable levels

REFERENCES