### Wstęp do badań ilościowych nad zmiennością ichtiofauny paleogenu Karpat

#### Abstract

Introduction to quantitive studie on variation of Paleogene ichtiofauna of the Carpathians

This paper is a continuation of palaeoichtiological and geological studies carried out by A. Jerzmańska and J. Kotlarczyk in the eastern part of the Polish Carpathians. The finding of two fossil fish assemblages, a siublittoral-neritic one and a bathypelagic one, within the Menilite beds (Palaeogene), permitted a qualitative correlations of the localities containing the same assemblages. Already a preliminary analysis of the collected material (Fig. 1) indicated quantitative differences in the composition of the two fish assemblages from these localities. (In the opinion of the authors generic determinations are more adequate for statistical analysis than specific determinations). The authors had to resort to simple statistical methods for proving the significance of these differences and the possible similarities. The descriptions of the determined genera and of the outcrops which yielded the fish faunas were published by Jerzmańska, 1960 (the specimens determined as Cottidae in this paper are now regarded by the author as belonging to the family Gempylidae), 1968, Jerzmańska and Jucha 1963, Jerzmańska and Kotlarczyk 1968. Descriptions of fish from the localities Równe and Krępak II were not published previously. The Równe locality (Silesian unit) represents the lower part of the Menilite beds, and is situated near the Rogi locality, while the locality Krępak II (Skole unit) represents the uppermost part of the Menilite beds in the profile at Krępak. The deep-water assemblage is present in the localities Lubno, Sobniów, Jamna A—C, Skopów, Malawa I, Kotów, Krępak II, Łodzinka and Babice II (the latter three represent the upper bathypelagic zone, according to Jerzmańska, 1968). The shallow-water assemblage is present at Rudawka Birczańska I, II, and III, Malawa II, Leszczawa, Krosno, Klarowieć, Bobrka, Wisłok Wielki, Winnica, Rogi, Równe and first of all at Jamna D—G. Only 16 localities were selected for statistical studies (Table 1), as the number of individuals collected in other localities was small. Localities from which less than 60 specimens were collected could be only partly utilized. The fish occur in siliceous shales marking episodes of quiet sedimentation, ranging in thickness from a few mm to several mm. Layers of these shales are separated by sandstones, marls or cherts of variable thickness, forming individualized lithological units (designated A, B, C,...). The variation of the ichtiofauna of the Menilite beds in time cannot be discussed in details, as only one locality was sampled systematically — layer after layer, and it represents only a part of the whole profile of the Menilite beds. The major part of the material studied represents bulk samples collected from many layers of siliceous shales in the individual outcrops.

STATISTICAL MODELS

The statistical model of the investigated ichtiofauna is a fish population of a definite ecologic character, constant in the space of the sedimentary basin and during the period of occurrence of the assemblage. Samples taken from such a population (fish assemblages from the individual localities) should provide the same estimate of the population, and therefore the distribution of genera in the localities, or the percentages of individual genera in the assemblages should be the same. The rank correlation was used for testing the similarity of distribution of the individual genera in pairs of localities. The Spearman’s coefficients (rs) calculated according to the formulas (1), (2) and (3), and their critical values calculated according to the formula (4) are listed in Table 3. The obtained results are not highly significant. A positive rank correlation was obtained only for three assemblages from nearby localities Rogi, Winnica and Równe) within the Silesian unit, and only in one case between localities situated in two different tectonic units (Równe, Leszczawa). Comparisons of localities with bathypelagic and with neritic assemblages yielded significantly negative correlations coefficients. A comparison of assemblages from individual localities with a model assemblage consisting of pooled several richest localities showed significant positive rank correlation only for some of the compared pairs. The chi-square test for goodness of fit was utilized both in the form of the formula for comparison of two empirical distributions (6) and the general formula (5). The results of these tests are listed in Table 5. The null hypothesis stating that the compared assemblages do not differ significantly has been not rejected only for the sample Jamna D—G (neritic assemblage) and the same sample reduced by the frequency of one — rather unusual layer El, which contains three genera not found elsewhere. On a significance level reduced to 0,01 a similarity appears between the localities Równe and Winnica. The comparison of fish assemblages from the individual localities with model assemblages (with the use of formula (5)) permit to accept the null hypothesis only for pairs Rogi — Model 3, and Leszczawa — Model 2. Therefore it is concluded that significant differences occur between localities in the same ecologic type Of assemblage. The stability of contribution of the individual genera in fish samples from various localities was analysed with the use of the percentage index. The tests were carried out according to formula (7), (8), (9) and (10). The results, shown in Table 8, concern only selected pairs of localities. Among the localities with the. neritic assemblage a great similarity was stated only for the pair Rogi—Winnica (differences only in the genera Capros and Glossanodon) and for the pair Równe—Leszczawa. In the remaining pairs only a few genera show similar percentages. Among the localities with the bathypelagic assemblage (Jamna A—G —Skopów, Lubno—Sobniów) similarities were stated only for some genera. Therefore the null hypothesis had to be rejected. Some problems concerning the variation of the fish assemblages with time can be discussed on the basis of evidence provided by the systematically sampled outcrop at Jamna. The three tested statistical models were: 1. the contribution of fish from the consecutive different lithologic complexes corresponds to the frequency of fish-bearing layers in these complexes; 2. the proportion of ubiquitous genera (Clupea, Lepidopus) in the individual lithologic complexes is proportional to the total number of fish in these complexes; 3. a linear relationship exists between the frequency of the individual genera and the sequence of stratigraphically arranged fish-bearing layers. The first two models were tested by the chi-square method of Gregory (1970). The results of the analysis of the first model are shown in Table 9. The null hypothesis is rejected and it is concluded therefore that a relation exists between the number of fish and some privileged horizons. The model 2 was accepted. The results were checked by the formula (6) and similar results were obtained (Table 10). The proportios of ubiquitous genera to the total number of fish suggest the autochtonous character of the ecologic assemblages. Assuming that the neritic-sublittoral assemblages were moving into the deep-water basin temporarily devoid of autochtonous batypelagic fauna (e.g. because of the presence of H2S) and supporting only a pelagic fauna, it should be expected that in fossil thanatocenoses the proportion of ubiquitous pelagic genera should be increased by the specimens introduced with the neritic fauna. However the percentage of ubiquitous genera in the total number of fish in the consecutive lithologic complexes is constant, slightly diminishing in the lower part of the shallow-water assemblage (Table 11). The model 3 was tested for the ubiquitous genera Clupea and Lepidopus in 24 layers of the Jamna profile, for the above two genera and the genera Vinciguerria and Centriscus in 13 layers of the bathypelagic assemblage, and for the Glossanodon genus in 11 layers of the neritic assemblage. The rank correlation coefficient values range from — 0,456 to + 0,318. In all cases these coefficients are not significant, and often they have values near to 0, indicating the lack of linear correlation of these genera with the time axis, and their random distribution. Such analysis was not possible for other genera because of the small numbers of specimens. The problem of minimal size of the samples is of great importance as it bears on the validity of results and on the practical problems of field exploration of the fossil fish. Some indications are provided by the analysis of the generic composition of fish collected in one outcrop by one operator and with the use of the same method during three consecutive years. The sum of frequencies of fish genera in the three samples was used as a model compared with the use of the chi-square test with the individual samples. Comparisons of pairs of samples were also made (Table 12). In two cases the compared pairs fitted at the significance level of 0,05, and in two others at the level of 0,01. In two further cases the null hypothesis was rejected. It is concluded tentatively that samples consisting of c. 100 specimens give a good representation of the population of the sampled outcrop. On the other hand, the analysis of percentage indicators (Table 13), shows a similarity of proportion of only one half to two third of the total number of genera, suggesting an inadequate sample size. The minimum sample size can be estimated from formula (11) used for random sampling with replacement. Assuming that the fish population in all layers and the whole area is infinite, the sampling without replacement does not change the population, and practically is equivalent to sampling with replacement. Setting the confidence level (1 — alfa) at 0,95 and assuming a permissible maximum error (d) at 5% or 10%, the required sample sizes are 384 and 96, respectively. In the case of samples consisting of c. 100 specimens (Winnica, Skopow, Jamna A—C, Lubno, Babice II) the structure index was determined with a 10 % error. On the other hand, the differences of frequency of fish genera between the very numerous samples from the localities Jamna D—G and Rogi are significant and can not be caused by an error of estimation.

CONCLUSIONS

In spite of the shortcomings of the analysed material (e.g. in the analysis of goodness of fit by the chi-square test the class frequencies were in some cases smaller than 5 and for subject-matter reasons the neighbouring classes could not be pooled), the statistical analysis lead to conclusions which could not be reached without the use of statistical methods. 1. There is a lack of similarity between fish assemblages from various localities, qualitatively belonging to one biocenose (neritic or bathypelagic). Even in the very numerous samples (Jamna and Rogi) the differences are significant both for genera and for whole assemblages. It is worth noting that differences between bathypelagic assemblages are also significant, although, because of life conditions, these assemblages are represented by cosmopolitan genera, and this should result in a homogenous character of the thanatocenoses. As the samples represent rather large time intervals, the authors conclude that the observed changes are the consequence of succession within the bathypelagic and the neritic assemblage. 2. No linear variation with time has been found in the fish assemblage. It is possible that the rank correlation method is not sensitive to quantitative differences, or the genera studied in the Jamna profile are not the genera responsible for the variations of the population (because of small frequencies some genera were not taken into account), or the variation was studied in a too small time interval. It is also possible that some other statistical model of the variation would be more adequate. 3. The proportion of ubiquitous fish genera in the individual lithologic complexes is proportional to the total number of fish in these complexes both in the bathypelagic and in the neritic assemblage. This indicates the autochtonous character of the ecological fish assemblages. 4. If the determination of the size of representative sample is methodologically correct, the minimum sample size amounts to c. 400 specimens. However it is very difficult to obtain such large samples from one locality. 5. Further quantitative-statistical studies of fossil fish in the Carpathians should be based upon material collected systematically from individual layers. Such studies may contribute to a detailed correlation of the Menilite beds.

This paper is a continuation of palaeoichtiological and geological studies carried out by A. Jerzmańska and J. Kotlarczyk in the eastern part of the Polish Carpathians. The finding of two fossil fish assemblages, a siublittoral-neritic one and a bathypelagic one, within the Menilite beds (Palaeogene), permitted a qualitative correlations of the localities containing the same assemblages. Already a preliminary analysis of the collected material (Fig. 1) indicated quantitative differences in the composition of the two fish assemblages from these localities. (In the opinion of the authors generic determinations are more adequate for statistical analysis than specific determinations). The authors had to resort to simple statistical methods for proving the significance of these differences and the possible similarities. The descriptions of the determined genera and of the outcrops which yielded the fish faunas were published by Jerzmańska, 1960 (the specimens determined as Cottidae in this paper are now regarded by the author as belonging to the family Gempylidae), 1968, Jerzmańska and Jucha 1963, Jerzmańska and Kotlarczyk 1968. Descriptions of fish from the localities Równe and Krępak II were not published previously. The Równe locality (Silesian unit) represents the lower part of the Menilite beds, and is situated near the Rogi locality, while the locality Krępak II (Skole unit) represents the uppermost part of the Menilite beds in the profile at Krępak. The deep-water assemblage is present in the localities Lubno, Sobniów, Jamna A—C, Skopów, Malawa I, Kotów, Krępak II, Łodzinka and Babice II (the latter three represent the upper bathypelagic zone, according to Jerzmańska, 1968). The shallow-water assemblage is present at Rudawka Birczańska I, II, and III, Malawa II, Leszczawa, Krosno, Klarowieć, Bobrka, Wisłok Wielki, Winnica, Rogi, Równe and first of all at Jamna D—G. Only 16 localities were selected for statistical studies (Table 1), as the number of individuals collected in other localities was small. Localities from which less than 60 specimens were collected could be only partly utilized. The fish occur in siliceous shales marking episodes of quiet sedimentation, ranging in thickness from a few mm to several mm. Layers of these shales are separated by sandstones, marls or cherts of variable thickness, forming individualized lithological units (designated A, B, C,...). The variation of the ichtiofauna of the Menilite beds in time cannot be discussed in details, as only one locality was sampled systematically — layer after layer, and it represents only a part of the whole profile of the Menilite beds. The major part of the material studied represents bulk samples collected from many layers of siliceous shales in the individual outcrops.

STATISTICAL MODELS

The statistical model of the investigated ichtiofauna is a fish population of a definite ecologic character, constant in the space of the sedimentary basin and during the period of occurrence of the assemblage. Samples taken from such a population (fish assemblages from the individual localities) should provide the same estimate of the population, and therefore the distribution of genera in the localities, or the percentages of individual genera in the assemblages should be the same. The rank correlation was used for testing the similarity of distribution of the individual genera in pairs of localities. The Spearman’s coefficients (rs) calculated according to the formulas (1), (2) and (3), and their critical values calculated according to the formula (4) are listed in Table 3. The obtained results are not highly significant. A positive rank correlation was obtained only for three assemblages from nearby localities Rogi, Winnica and Równe) within the Silesian unit, and only in one case between localities situated in two different tectonic units (Równe, Leszczawa). Comparisons of localities with bathypelagic and with neritic assemblages yielded significantly negative correlations coefficients. A comparison of assemblages from individual localities with a model assemblage consisting of pooled several richest localities showed significant positive rank correlation only for some of the compared pairs. The chi-square test for goodness of fit was utilized both in the form of the formula for comparison of two empirical distributions (6) and the general formula (5). The results of these tests are listed in Table 5. The null hypothesis stating that the compared assemblages do not differ significantly has been not rejected only for the sample Jamna D—G (neritic assemblage) and the same sample reduced by the frequency of one — rather unusual layer El, which contains three genera not found elsewhere. On a significance level reduced to 0,01 a similarity appears between the localities Równe and Winnica. The comparison of fish assemblages from the individual localities with model assemblages (with the use of formula (5)) permit to accept the null hypothesis only for pairs Rogi — Model 3, and Leszczawa — Model 2. Therefore it is concluded that significant differences occur between localities in the same ecologic type Of assemblage. The stability of contribution of the individual genera in fish samples from various localities was analysed with the use of the percentage index. The tests were carried out according to formula (7), (8), (9) and (10). The results, shown in Table 8, concern only selected pairs of localities. Among the localities with the. neritic assemblage a great similarity was stated only for the pair Rogi—Winnica (differences only in the genera Capros and Glossanodon) and for the pair Równe—Leszczawa. In the remaining pairs only a few genera show similar percentages. Among the localities with the bathypelagic assemblage (Jamna A—G —Skopów, Lubno—Sobniów) similarities were stated only for some genera. Therefore the null hypothesis had to be rejected. Some problems concerning the variation of the fish assemblages with time can be discussed on the basis of evidence provided by the systematically sampled outcrop at Jamna. The three tested statistical models were: 1. the contribution of fish from the consecutive different lithologic complexes corresponds to the frequency of fish-bearing layers in these complexes; 2. the proportion of ubiquitous genera (Clupea, Lepidopus) in the individual lithologic complexes is proportional to the total number of fish in these complexes; 3. a linear relationship exists between the frequency of the individual genera and the sequence of stratigraphically arranged fish-bearing layers. The first two models were tested by the chi-square method of Gregory (1970). The results of the analysis of the first model are shown in Table 9. The null hypothesis is rejected and it is concluded therefore that a relation exists between the number of fish and some privileged horizons. The model 2 was accepted. The results were checked by the formula (6) and similar results were obtained (Table 10). The proportios of ubiquitous genera to the total number of fish suggest the autochtonous character of the ecologic assemblages. Assuming that the neritic-sublittoral assemblages were moving into the deep-water basin temporarily devoid of autochtonous batypelagic fauna (e.g. because of the presence of H2S) and supporting only a pelagic fauna, it should be expected that in fossil thanatocenoses the proportion of ubiquitous pelagic genera should be increased by the specimens introduced with the neritic fauna. However the percentage of ubiquitous genera in the total number of fish in the consecutive lithologic complexes is constant, slightly diminishing in the lower part of the shallow-water assemblage (Table 11). The model 3 was tested for the ubiquitous genera Clupea and Lepidopus in 24 layers of the Jamna profile, for the above two genera and the genera Vinciguerria and Centriscus in 13 layers of the bathypelagic assemblage, and for the Glossanodon genus in 11 layers of the neritic assemblage. The rank correlation coefficient values range from — 0,456 to + 0,318. In all cases these coefficients are not significant, and often they have values near to 0, indicating the lack of linear correlation of these genera with the time axis, and their random distribution. Such analysis was not possible for other genera because of the small numbers of specimens. The problem of minimal size of the samples is of great importance as it bears on the validity of results and on the practical problems of field exploration of the fossil fish. Some indications are provided by the analysis of the generic composition of fish collected in one outcrop by one operator and with the use of the same method during three consecutive years. The sum of frequencies of fish genera in the three samples was used as a model compared with the use of the chi-square test with the individual samples. Comparisons of pairs of samples were also made (Table 12). In two cases the compared pairs fitted at the significance level of 0,05, and in two others at the level of 0,01. In two further cases the null hypothesis was rejected. It is concluded tentatively that samples consisting of c. 100 specimens give a good representation of the population of the sampled outcrop. On the other hand, the analysis of percentage indicators (Table 13), shows a similarity of proportion of only one half to two third of the total number of genera, suggesting an inadequate sample size. The minimum sample size can be estimated from formula (11) used for random sampling with replacement. Assuming that the fish population in all layers and the whole area is infinite, the sampling without replacement does not change the population, and practically is equivalent to sampling with replacement. Setting the confidence level (1 — alfa) at 0,95 and assuming a permissible maximum error (d) at 5% or 10%, the required sample sizes are 384 and 96, respectively. In the case of samples consisting of c. 100 specimens (Winnica, Skopow, Jamna A—C, Lubno, Babice II) the structure index was determined with a 10 % error. On the other hand, the differences of frequency of fish genera between the very numerous samples from the localities Jamna D—G and Rogi are significant and can not be caused by an error of estimation.

CONCLUSIONS

In spite of the shortcomings of the analysed material (e.g. in the analysis of goodness of fit by the chi-square test the class frequencies were in some cases smaller than 5 and for subject-matter reasons the neighbouring classes could not be pooled), the statistical analysis lead to conclusions which could not be reached without the use of statistical methods. 1. There is a lack of similarity between fish assemblages from various localities, qualitatively belonging to one biocenose (neritic or bathypelagic). Even in the very numerous samples (Jamna and Rogi) the differences are significant both for genera and for whole assemblages. It is worth noting that differences between bathypelagic assemblages are also significant, although, because of life conditions, these assemblages are represented by cosmopolitan genera, and this should result in a homogenous character of the thanatocenoses. As the samples represent rather large time intervals, the authors conclude that the observed changes are the consequence of succession within the bathypelagic and the neritic assemblage. 2. No linear variation with time has been found in the fish assemblage. It is possible that the rank correlation method is not sensitive to quantitative differences, or the genera studied in the Jamna profile are not the genera responsible for the variations of the population (because of small frequencies some genera were not taken into account), or the variation was studied in a too small time interval. It is also possible that some other statistical model of the variation would be more adequate. 3. The proportion of ubiquitous fish genera in the individual lithologic complexes is proportional to the total number of fish in these complexes both in the bathypelagic and in the neritic assemblage. This indicates the autochtonous character of the ecological fish assemblages. 4. If the determination of the size of representative sample is methodologically correct, the minimum sample size amounts to c. 400 specimens. However it is very difficult to obtain such large samples from one locality. 5. Further quantitative-statistical studies of fossil fish in the Carpathians should be based upon material collected systematically from individual layers. Such studies may contribute to a detailed correlation of the Menilite beds.