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Measuring Recurrence of Marine Biotic Gradients: A Case Study from the Pennsylvanian-Permian Midcontinent THOMAS D. OLSZEWSKI Department of Geological Sciences, Indiana University, Bloomington, IN 47405 MARK E. PATZKOWSKY Department of Geosciences, The Pennsylvania State University, University Park, PA 16802

PALAIOS, 2001, V. 16, p. 444–460 The aim of this study was to determine whether biotic associations of Pennsylvanian-Permian brachiopods and bivalves from the northern Midcontinent differ in their degree of recurrence through time. The study interval includes 2.5 Myr that can be divided into 5 full and 2 partial composite depositional sequences separated by subaerial unconformities. These stratigraphic packages represent replicate natural experiments in establishing the benthic marine ecosystem of the basin. Based on cluster and ordination analyses, two discrete biofacies can be recognized—one dominated by brachiopods and the other by bivalves. Within each of these, environmental gradients can be recognized. The brachiopod gradient is interpreted to reflect the degree of water-column oxygenation, whereas the bivalve gradient is interpreted to reflect the transition from restricted to open-marine conditions. Comparison of measured recurrence with randomized data indicates that the ecological segregation of the two biofacies is maintained to a significant degree through the succession of depositional sequences in the study interval. In contrast, the gradients within each biofacies, although recognizable, are not maintained rigidly from sequence to sequence. There is also no significant difference in gradient recurrence between the two biofacies. These results imply that there is no need to call upon strong interspecific interactions to maintain the structure of these paleocommunities through time.

represented by the modern world. In contrast, although there are limitations imposed by taphonomy and stratigraphic resolution (Kidwell and Flessa, 1995; Martin, 1999 and references therein), paleoecologists can examine the fossil record of biological communities through time. The aim of this paper is to identify and characterize the consistency of species associations through time using Pennsylvanian-Permian bivalves and brachiopods of the North American Midcontinent as a case study. Recent paleoecological studies of marine invertebrates (e.g., Brett and Baird, 1995; Westrop, 1996; Tang and Bottjer, 1996; Patzkowsky and Holland, 1997; Olszewski and Patzkowsky, in press) have focused on compositional change at the scale of entire basins, combining taxonomic lists from a variety of environments. In this study, the focus is on changes within biofacies rather than the entire basin. Cluster analysis has been used to define paleocommunity types, gradient analysis to examine inter-specific associations within paleocommunity types, and recurrence analysis to test for changes in associations through time. In order to put the results in a broader context, they are compared with those of other recent studies covering different groups, environments, and ages (Bennington and Bambach, 1996; Holterhoff, 1996; Pandolfi, 1996). STRATIGRAPHIC FRAMEWORK

A question of long-standing interest to ecologists and paleoecologists concerns the degree of integration in biological communities (Jackson, 1994). This issue frequently is cast as a debate between advocates of strong interdependence of species (Clements, 1916) and strong independence of species (Gleason, 1926). Ecologists have tested these alternative hypotheses by examining how species compositions change along environmental gradients (Whittaker, 1967). In a Clementsian world, species composition and abundance are expected to be very consistent over a range of environmental conditions because the species that make up a community form an integrated entity (Ricklefs, 1990). In a Gleasonian world, species composition and abundance should vary from site to site as conditions change because every species reacts to environmental change independently (Ricklefs, 1990). Ecologists generally study species associations in the single time slice

This study focuses on a 2.5-Myr interval of late Pennsylvanian to early Permian rocks (Fig. 1) of the northern Midcontinent (Fig. 2). At this time of global ‘‘icehouse’’ climatic conditions (Fischer, 1984), an ice sheet was present at the south pole (Ziegler et al., 1997), leading to cyclical eustatic and climatic changes analogous in frequency, amplitude, and effect to those of the Quaternary (Veevers and Powell, 1987). These are reflected in the cyclothemic stratigraphy of Pennsylvanian-Permian rocks in the Midcontinent (Heckel, 1984, 1986, 1995). Cyclicity occurs at two scales in the study interval. At the finest resolution, meter-scale cycles occur in both open-marine, platform settings and nearshore, coastal settings (Miller and West, 1993; Miller et al., 1996; Olszewski, 2000). These cycles are very thin (1 to 5 m), unconformity-bounded depositional sequences and, therefore, represent temporally significant packets of rock (Posamentier et al., 1988; Van Wagoner et al., 1988) averaging 50,000 years or less in duration. At a larger scale (that of the classical cyclothems), composite depositional sequences, composed of 8 to 13 meterscale cycles, can be recognized (Miller and West, 1993,

Copyright Q 2001, SEPM (Society for Sedimentary Geology)

0883-1351/01/0016-0444/$3.00

INTRODUCTION

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FIGURE 2—Study area. Shaded area indicates exposure of upper Pennsylvanian through lower Permian rocks used in this study. Northsouth geographic zones are also indicated (see Table 2).

ments on the platform. Each composite sequence, therefore, can be treated as a replicate natural experiment in setting up a benthic marine ecosystem that provides a means of measuring the recurrence of ecological associations. DATA

FIGURE 1—Stratigraphic study interval. Stratigraphic column modified from Zeller (1968) and Baars et al. (1994). Roman numerals denote composite depositional sequences. I through V are complete sequences. 0 and VI are partial sequences.

1998; Olszewski, 2000). Open-marine carbonates, marine mudrocks, and condensed sections dominate their transgressive and early highstand phases. Late highstand deposits include peritidal carbonates, deltaic sandstones, and pedogenic mudrocks. Correlation of meter-scale cycles reveals angular unconformities at the boundaries of composite sequences (Olszewski, 2000), indicating that these too are temporally significant packages of rock. The 51 meter-scale cycles identified in the study interval (Olszewski, 2000) provide a means of examining trends in paleoecological communities at relatively high temporal resolution (;5·104 year). The five complete and two partial composite sequences (Fig. 1) are separated by extensive subaerial unconformities. This means that their deposition required re-establishment of marine environ-

Data consist of fossil bivalve and articulate brachiopod collections (plus the calcareous inarticulate genus Petrocrania) from two sources: 341 collections from Mudge and Yochelson’s (1962) monograph on the stratigraphy and paleontology of the Pennsylvanian-Permian Midcontinent and 132 additional collections made in 1997 through 1999 (‘‘new collections’’). Each collection represents the assemblage of fossils found in a bed at a site; they were not combined to create composite lists by geologic unit or location. The entire data set is included in Olszewski (2000) and can be accessed at the Pennsylvania State University’s Electronic Theses and Dissertations website (http:// etda.libraries.psu.edu/). All fossils were identified to as fine a taxonomic level as possible. Although many specimens were identifiable to species, a large proportion could only be determined to genus. Therefore, to make use of as much data as possible, all statistical analyses were conducted at the genus level. This choice did not have a strong influence on patterns of ecological association for two reasons. First, most genera in the study interval are monospecific. Second, most polyspecific genera in the data set are dominated by one species. For example, in Mudge and Yochelson’s (1962) data, Neospirifer is reported 116 times: 38 as N. sp. indet., 7 as N. cf. N. kansasensis, and 71 as N. dunbari. If the proportion of 7 to 71 is representative of the relative frequency of these two species, then only 11 of the 116 Neospirifer occurrences are expected to be N. cf. N. kansasensis. These figures, which are typical of other genera as well, indicate that the number of associations gained by using genera rather than species provides more information (in a statistical sense) than including many rare species and rejecting specimens not identified to the species level. Because the interest of this study was in associations of

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TABLE 1—Descriptive statistics of data subsets. S is the richness of collections included in each data subset. ‘‘New collections’’ are those made for this study and added to those of Mudge and Yochelson (1962). ‘‘All collections’’ denotes Mudge and Yochelson (1962) collections plus ‘‘new collections.’’ ‘‘All genera’’ indicates inclusion of both brachiopod and bivalve genera (as opposed to just one group or the other). An occurrence denotes the presence of a taxon in a collection regardless of its abundance. In a presence–absence data matrix, where 1 indicates presence and 0 indicates absence, the total number of occurrences is simply the sum of the matrix (i.e., the number of 1’s).

All collections

New collections All genera, by sequence, S$2

Brachiopods, by sequence, S$2

Bivalves, by sequence, S$2

Data subset

Taxa

Collections

Occurrences

Specimens

All genera, S $ 2 All genera, S $ 4 Brachiopods, S $ 2 Bivalves, S $ 2 Bivalves, S $ 3 All genera, S $ 2 I II III IV V I II III IV V I II III IV V

40 35 23 16 12 34 31 27 31 23 26 20 16 20 17 16 11 11 9 4 10

474 317 382 128 60 132 157 61 147 29 82 119 41 140 25 49 49 27 18 5 39

2,593 2,191 2,080 367 225 865 844 314 925 167 319 634 199 851 143 187 149 91 42 12 109

18,737 16,122 16,317 1,745 927 7,687 4,902 2,002 6,209 1,727 1,764 3,866 1,452 6,043 1,628 977 702 497 116 53 646

two or more taxa, collections including only one taxon were not included in statistical analyses. The final data set of 474 collections includes a total of 18,737 specimens and 2,593 occurrences (Table 1). The geographic and stratigraphic distribution of collections is summarized in Table 2 for seven north-south geographic zones (Fig. 2) of about 48 km each (five townships or about 30 miles) and the five complete composite sequences. Four hundred and twenty-four collections are included in the table, leaving 50 unassigned. Seven of these came from Nebraska, thirty-eight came from the two partial composite sequences (marked 0 and VI in Fig. 1), and five came from stratigraphically floating exposures. These collections were included in ordination and cluster analyses despite uncertain external information because they still shed light on taxonomic associations. Although contingency table analysis indicates that collections are not distributed randomly (Gadj(df 5 24) 5 54.45, P 5 0.00037; Sokal and Rohlf, 1995), no stratigraphic or geographic trends are evident in Table 2. Most of the collections are small with median richness

equal to 5 and median number of specimens equal to 21 (Fig. 3). Although their small sizes suggest that many taxonomic lists may not be complete, the large number of collections reduces statistical uncertainty. Collections were taken from a wide variety of lithologies and taphonomic states. Some collections came from hard limestone, from which specimens had to be removed with chisel and hammer or examined on slab surfaces, whereas others came from soft mudrocks, which could be easily bulk sampled or surface collected. Some fossils occurred as original shell material while others were molds (sometimes in the same collection). In addition, collections most certainly represent different amounts of time-averaging (Kidwell and Bosence, 1991; Brett, 1995); some come from condensed intervals within meter-scale cycles representing 100’s to 1000’s of years, whereas others come from facies that represent relatively rapid burial. Although all these non-uniform factors increase variability, the collections are reliable as records of fossil taxa that demonstrably co-occur in specific beds at specific locations. As such, they provide a great deal of information

TABLE 2—Distribution of collections used in this study by geographic zone and composite sequence. Values are ‘‘all collections’’ with S $ 2 (Table 1). Numbers in parentheses are ‘‘new collections’’, S $ 2. The distributions of Mudge and Yochelson’s (1962) collections and ‘‘new collections’’ are significantly correlated (r 5 0.738 . r950.05 5 0.334; df 5 33). Geographic zones Composite sequences V IV III II I Column totals

1 4 2 10 3 12 31

(0) (1) (0) (0) (1) (2)

2 31 9 73 21 31 165

(14) (6) (33) (7) (6) (66)

3 16 3 25 16 18 78

(6) (0) (12) (2) (2) (22)

4 15 3 3 7 5 33

(3) (1) (0) (0) (0) (4)

5 4 7 8 3 14 36

(0) (6) (1) (0) (0) (7)

6 8 1 16 6 10 41

(0) (0) (9) (0) (0) (9)

7 14 5 12 5 4 40

(0) (1) (1) (2) (1) (5)

Row totals 92 30 147 61 94 424

(23) (15) (56) (11) (10) (115)

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the small number of specimens in many collections means that relative and rank abundances are poorly constrained. Third, different collecting methods bias samples in different ways. For example, large bulk collections yield reliable abundance data (Bennington and Rutherford, 1999), but surface collecting often results in samples with elevated diversity relative to the number of specimens because the aim in the field was to maximize the number of different taxa. Finally, presence/absence data are less sensitive to differences between collections and are, therefore, more likely to indicate a higher level of similarity between any two collections than absolute abundances or abundance rankings (Rahel, 1990). As it turns out, this bias is in opposition to our findings and strengthens the interpretation presented below. This is not to say that relative abundance data are inappropriate for paleoecological studies. In many cases, where sampling procedures are strictly controlled and taphonomy and lithology are more uniform than this study, relative abundances can reveal patterns of ecological or taphonomic significance that are obscured by presence/absence data (Olszewski and West, 1997). ANALYSES AND RESULTS

FIGURE 3—Relationship between number of specimens and number of taxa (Richness, S). Plots describe data including all genera (bivalves and brachiopods) and all collections with S $ 2. The majority of collections include fewer than 40 specimens. (A) Number of collections with a given total abundance (number of specimens). (B) Number of collections with a given richness. (C) Cross-plot of total abundance versus richness. Each cross represents a collection.

with regard to paleoecological associations. This is not to say that fossil co-occurrence proves co-occurrence during life, which is rarely demonstrable in the rock record. However, a long history of actualistic live-dead comparisons of shelly, marine macrofauna indicates that death assemblages, and ultimately fossil assemblages, faithfully record compositional differences between different environments (Kidwell and Bosence, 1991; Martin, 1999). All analyses presented here were performed using presence/absence data rather than abundance data for several reasons. First, actualistic studies and numerical models indicate that, although relative abundance data in death assemblages do reflect living abundances to some degree (Kidwell and Flessa, 1995), they also experience modification due to differences in taphonomic susceptibility among taxa and environments (Cummins et al., 1986; Staff et al., 1986; Staff and Powell, 1988; Powell et al., 1989; Miller and Cummins, 1990; Olszewski and West, 1997). Second,

Data were analyzed using a variety of techniques, each with a different purpose. Exploratory approaches included cluster analysis (R-mode, Q-mode, and two-way) and ordination (correspondence analysis). To test for changes in paleoecological associations through time, randomization and resampling approaches were applied (Crowley, 1992), here dubbed ‘‘recurrence analysis.’’ External information for collections included geographic location, stratigraphic position, and lithology. External information for genera included membership in higher taxonomic groups. In some cases, collections below a specified richness or taxa below a specified rarity were discarded (subsets listed in Table 1). This is because outliers, consisting of a few small collections or rare taxa, often obscure broader patterns when using exploratory statistical techniques. Analyses were initially performed using all data but were pared down to see if interpretable patterns became more clear; the results included here were selected for the patterns they show and presentability. The characteristics of the data used in each analysis are described in the figure captions. Cluster Analysis Clustering was conducted using the hierarchical, unweighted pair group method with arithmetic averaging (UPGMA). The aim was to examine how collections and taxa group together and whether a clear classification emerges from the data. The similarity metric used was the Dice coefficient: SD 5 2c/(Ni 1 Nj)

(1),

c 5 number of taxonomic co-occurrences between collections i and j, Ni, Nj 5 total number of occurrences in i and j, respectively. This definition is in the context of Q-mode analysis (clustering of collections), but the coefficient also can be used for R-mode analysis (clustering of taxa). Note that other names for the same metric are the Sorenson

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and Czekanowski coefficients and that equation (1) is the binary reduction of the ‘‘percentage similarity’’ and ‘‘BrayCurtis measure’’ (Sepkoski, 1974). The Dice coefficient was chosen for several reasons. First, in its fully numerical form, this metric has been found to reflect ecological differences very effectively (Faith et al., 1987). Second, it corrects for sparseness in the data matrix, thereby decreasing the influence of rare taxa and low-diversity collections in the overall result (Archer and Maples, 1989). Third, like the related Jaccard coefficient (S D 5 2Sj/(Sj11), Sj 5 Jaccard coefficient), it does not count mutual absences, which can severely skew results using sparse paleoecological data matrices (Maples and Archer, 1988). Unlike the Jaccard coefficient, however, the Dice has a wider and more symmetrical spread of expected values in randomized tests (Archer and Maples, 1987). R-mode analysis of brachiopods and bivalves together (Fig. 4), using only collections with a taxonomic richness of 4 or more, reveals three major groupings—a brachiopod cluster, a bivalve cluster, and a group of rare taxa. Both major clusters have a ‘‘chain’’ topology, suggesting that taxa were added one by one to a single, growing cluster rather than being segregated into subgroups and then agglomerated. The rare taxa are grouped at very low levels of similarity, indicating that they do not form a cluster based on strong association. Within the brachiopods, Crurithyris, Hystriculina, and Lissochonetes form a subcluster. These are all small taxa typically found in dark gray to black, pyritic mudrocks containing high organic carbon. Collections are usually numerically dominated by one species. These characteristics indicate a physiologically stressful environment due to low oxygen concentrations in the water column (Boardman et al., 1984; Kammer et al., 1986). Q-mode and two-way cluster analyses of the same data used to generate figure 4 yield very large dendrograms that could not be shown in a single journal figure; hence, the subset of the data collected as part of this study (‘‘new collections’’) is presented instead (Fig. 5). Comparison with analyses of the entire data set, which can be found in Olszewski (2000), have a similar geographic and stratigraphic distribution (Table 2), and show the same basic patterns as described here. The Q-mode analysis of collections (Fig. 5) reveals a large number of clusters. Some, but not all, show strong associations with lithology. For example, H has a high proportion of carbonate collections, and D is entirely siliciclastic. In addition, there is some correspondence between clusters and collections from particular composite sequences. For example, all the collections from composite sequence VI are included in cluster A, many collections from sequence IV occur in D, and many collections from sequence V are seen in G, H, and I. The two-way cluster analysis (Fig. 5) relates taxonomic content to collection clusters. Q-mode clusters G, H, and I clearly segregate from the other clusters because they are dominated by bivalves rather than brachiopods. The clusters of rare taxa are easily revealed as such. Within the low-diversity brachiopod clusters, a trend can be seen starting at the Derbyia-Neochonetes-Composita (taxa 9, 23, and 7) R-mode subcluster and migrating to the previously described dysoxic subcluster (Crurithyris-HystriculinaLissochonetes; taxa 8, 14, and19). As mentioned previous-

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FIGURE 4—R-mode cluster analysis of all genera using collections with S $ 4. Clusters are labeled by their dominant taxa: brachiopods, bivalves, and rare taxa. Numbers in parentheses are genus identification numbers provided for comparison with other figures (see Fig. 7 for key). ‘B’ and ‘C’ signify brachiopod and bivalve, respectively. Other numbers represent the total number of occurrences of each genus in this data set. Note the low number of occurrences in the group of rare taxa and that degree of association within the other clusters correlates to rarity. Apparent ‘‘polytomies’’ are an artifact of the software used (SPSS) and do not represent unresolved associations.

ly, this is interpreted to reflect an environmental gradient from well-to-poorly oxygenated conditions (Boardman et al., 1984), although taxa from both ends of the gradient also can be found together. Note that although bivalves and brachiopods are clearly segregated, they are not mutually exclusive—there are collections in almost all of the clusters that include representatives of both major taxa. The last cluster analysis to be presented here includes only bivalves (Fig. 6). The aim was to see if there were any patterns within this group that were being swamped by including them with the more numerous brachiopod-dom-

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inated collections. In the R-mode, taxa associate in much the same way as before, and rare taxa are still excluded. However, the two-way analysis suggests a possible gradient from Septimyalina (taxon 36) and Schizodus (taxon 35) to Edmondia (taxon 11) and Myalina (Orthomyalina) (taxon 21). Ordination Analysis

FIGURE 5—Two-way cluster analysis of ‘‘new collections’’ with S $ 2 (key to genera as in Fig. 7); B 5 brachiopod, C 5 bivalve. External data for collections includes composite sequence (Roman numerals) and lithology (s 5 siliciclastic, c 5 carbonate).

As a complement to cluster analysis, the data were ordinated using correspondence analysis. Ordination helps to reveal gradients that can be broken up artificially by clustering, and orders taxa and collections less arbitrarily than they are depicted by a dendrogram. In addition, ordination expresses multidimensional relationships more effectively than cluster analysis. Correspondence analysis was chosen for two reasons. First, Kenkel and Orlo´ci (1986) found it to be very effective at extracting known patterns in artificial ecological data compared to other ordination techniques. Second, correspondence analysis ordinates both taxa and collections in the same multivariate space (i.e., both R- and Q-mode analyses are conducted simultaneously), which allows the two to be directly related (Jongmann et al., 1995). A disadvantage of correspondence analysis is that it can produce an ‘‘arch’’ effect. This is the result of compression at the ends of ordination axes and a systematic, often quadratic, relationship between axes. These problems can be corrected by non-linear rescaling (Hill and Gauch, 1980), but we chose not to do so for several reasons. First, nonlinear detrending is a ‘‘brute force’’ re-adjustment of the pattern that often can lead to loss of ecologically meaningful information (Pielou, 1984). If patterns are readily interpretable, as is the case in the present analyses, there is no need for adjustment. Second, Minchin (1987) and Kenkel and Orlo´ci (1986) found that non-linear detrending often does not improve simulated patterns and can even exacerbate distortion of the ordination space. Ter Braak (1995) provides a more comprehensive discussion of these issues, including their mathematical basis and recommended solutions. Analyzing both brachiopods and bivalves together (Fig. 7A) reveals that they are segregated strongly in ordination space. Almost all brachiopod genera have positive values, while the bivalves are negative without exception. Demarcating the R-mode clusters of genera from figure 4 on the ordination shows that results of the two analyses are quite consistent. Note that, although the cluster marked ‘‘Rare Taxa’’ appears to sit within the brachiopod cluster, it is separated in higher ordination dimensions where it is pulled out of the plane defined by the ‘‘Bivalve Dominated’’ and ‘‘Brachiopod Dominated’’ clusters. The slight overlap of bivalve and brachiopod genera involves the bivalves Wilkingia (taxon 40) and Pteronites (taxon 3), and the brachiopod Juresania (taxon 16) (the other taxa in the region of overlap are rare and, therefore, their positions in ordination space are constrained poorly and provide limited information on their relationships). This is consistent with direct observations in the field, where Wilkingia and Pteronites are often the only bivalves in a collection otherwise dominated by brachiopods and other open-marine groups, and where Juresania seems to be characteristic of nearshore environments otherwise domi-

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FIGURE 6—Two-way cluster analysis of bivalve genera and collections with S $ 2 (key to genera as in Fig. 7). External data for collections includes composite sequence (Roman numerals) and lithology (s 5 siliciclastic, c 5 carbonate).

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FIGURE 7—Correspondence analyses of genera. (A) All genera (bivalves circled), all collections with S $ 4. Outlined regions are R-mode clusters from figure 4. Note the gap (indicated) between brachiopodand bivalve-dominated biofacies. (B) Brachiopod genera, collections with S $ 2. (C) Bivalve genera, collections with S $ 3. Percent of total inertia is shown for each axis. Units are mean standard deviations. 1 5 Anthraconeilopsis, 2 5 Aviculopecten, 3 5 Pteronites, 4 5 Beecheria, 5 5 Cancrinella, 6 5 Clavicosta, 7 5 Composita, 8 5 Crurithyris, 9 5 Derbyia, 10 5 Echinaria, 11 5 Edmondia, 12 5 Enteletes, 13 5 Hustedia, 14 5 Hystriculina, 15 5 Isogramma, 16 5 Juresania, 17 5 Leptalosia, 18 5 Linoproductus, 19 5 Lissochonetes, 20 5 Meekella, 21 5 Myalina (Orthomyalina), 22 5 Myalina (Myalinella), 23 5 Neochonetes, 24 5 Neospirifer, 25 5 Paleyoldia, 26 5 Permophorus, 27 5 Petrocrania, 28 5 Promytilus, 29 5 Pseudomonotis, 30 5 Pteria, 31 5 Punctospirifer, 32 5 Retaria, 33 5 Reticulatia, 34 5 Rhipidomella, 35 5 Schizodus, 36 5 Septimyalina, 37 5 Stroblochondria, 38 5 Volsellina, 39 5 Wellerella, 40 5 Wilkingia.

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nated by mollusks. The wide gap between most of the bivalves and the brachiopods (marked in Fig. 7A) suggests a strong discontinuity between the two main compositional groups. The first axis not only separates brachiopods from bivalves, it also strings the bivalves into a compositional gradient. Axis 2 extracts a gradient in the brachiopods perpendicular to the bivalve gradient of axis 1. This orthogonal relationship suggests that the gradients within the two groups are largely independent of one another. Ordinating the two main taxonomic groups further refines the patterns seen in the large ordination. In the brachiopods (Fig. 7B), the first axis, which is very consistent with the second axis of figure 7A, segregates Rhipidomella (34), Crurithyris (8), Wellerella (39), Lissochonetes (19), Hustedia (13), and Hystriculina (14) from the rest. As described above in the cluster analyses, these genera are all relatively small (,1.5 cm across) and often very abundant in facies interpreted as dysoxic deposits. The opposite end of the gradient is dominated primarily by Juresania (16) and some rare taxa (e.g., Echinaria [10], Cancrinella [5], Meekella [20]). The second axis further pulls out these rarities but is otherwise uninterpretable. In the bivalve ordination (Fig. 7C), the gradient along the first axis separates Pteronites (3), Wilkingia (40), and Schizodus (35) at the negative extreme, and Edmondia (11), Pseudomonotis (29), and Myalina (Orthomyalina) (21) at the other. Although not identical, this is consistent with the faunal gradient from open-marine to relatively restricted coastal or lagoonal environments interpreted in the cluster analyses. Because correspondence analysis performs both R-mode and Q-mode analyses simultaneously (Figs. 7 and 8), it is possible to examine patterns of other important variables in the same ordination space, thereby directly relating taxa to environment and time. An important difference between figures 7A and 8A (R and Q-modes of the same ordination space) is the lack of two distinct clumps in the scatter of collections (Fig. 8A). This suggests that the segregation of brachiopods and bivalves is not an artifact resulting from uneven sampling at the ends of a continuous gradient—i.e., the correspondence analysis shows the position of the intermediate collections. Also investigated was the relationship of taxa to lithology. Comparison of figures 7A and 8A indicates that both bivalves and brachiopods can be found in either siliciclastic or carbonate rocks. The contrast between these two main lithologies is one of the most prominent in the study interval, yet these analyses suggest that it does not restrict the distribution of the two main taxonomic groups. Rather, Olszewski (2000) recognized complete paralic to open marine gradients based on lithology in both siliciclastic and carbonate facies, suggesting that the benthic organisms analyzed here were more sensitive to the onshore-offshore gradient (a gradient-complex reflecting water depth, environmental energy, sediment grain size, storm frequency, salinity, etc.) than the mineral composition of the substrate. Previous work by Miller (1988, 1989) has found that by the late Paleozoic, North American bivalves do not seem to favor terrigenous over carbonate environments, as they seem to have earlier in the Paleozoic. To investigate change in communities through time, the first axis correspondence-analysis values of collections were plotted against meter-scale cycles in the study inter-

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FIGURE 8—Correspondence analysis of collections. Solid circles 5 carbonates; empty circles 5 siliciclastics; two-tone circles 5 mix of carbonates and siliciclastics. Large circles represent means for the two lithologies and brackets indicate one standard deviation on each side. These are the same ordination spaces as shown in figure 7. (A) All genera, collections with S $ 4. (B) Brachiopod genera, S $ 2. (C) Bivalve genera, S $ 3. Percentages of total inertia are shown for each axis. Units are mean standard deviations.

val. Using all taxa (Fig. 9), the average value of each cycle shifts from nearshore, bivalve-dominated assemblages at the base of each composite sequence to open marine, brachiopod-dominated assemblages through the middle of each composite sequence. The same approach using only brachiopods (Fig. 10) shows an overall trend through the entire study interval from well-oxygenated to poorly-oxygenated assemblages

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except for a brief reversal in the lower part of composite sequence V. Composite sequences I and II are dominated by well-oxygenated faunas, sequence III has equal numbers of low and high oxygen collections, whereas sequences IV and V are dominated by low oxygen faunas (despite the switchback in composite sequence V, it also contains many of the most dysoxic brachiopod assemblages). Note that dysoxic collections do not increase at the expense of welloxygenated collections; rather, increasingly low-oxygen points are added to a continuous succession of high oxygen points. Cycle 51 represents a return to well-oxygenated conditions, which is consistent with findings based on conodonts (Boardman et al., 1995). Lastly, with respect to paleocommunity recurrence, it is of interest to compare the faunal gradients of each composite sequence separately (Fig. 11). As mentioned earlier, each composite sequence represents, in effect, a naturally replicated experiment in repopulating the Midcontinent platform after subaerial exposure. In the brachiopod plots, dysoxic taxa (Rhipidomella [34], Wellerella [39], Crurithyris [8], Hystriculina [14], Lissochonetes [19]) and nearshore taxa (Juresania [16], Linoproductus [18]) are indicated. In all sequences, the dysoxic group and the nearshore group form distinct patches in the ordination space, but they do not always fall at the ends of the ordination-defined gradients. The inferred end-members of the bivalve gradient also are indicated—Wilkingia (40), Pteronites (3), and Schizodus (35) at the open-marine end, and Edmondia (11), Permophorus (26), Pseudomonotis (29), and Promytilus (28) at the restricted end (Fig. 11). The bivalve collections are far less numerous than the brachiopod collections; hence, their plots are less well constrained in terms of faunal relationships. For example, sequence IV, although it shows the gradient nicely, is based on only five collections (Table 1). Sequences I and III show the two patches segregated, but sequences II and V show them overlapping. Exploring higher axes failed to improve the pattern. Also noteworthy is the distribution of taxa within these groups, which is not consistent from sequence to sequence. This suggests that genera in this data set are not tightly restricted to particular associations. The statistical significance of this suggestion is tested using recurrence analysis. Recurrence Analysis In addition to exploratory methods, tests were also conducted for stratigraphic recurrence of paleoecologic associations using methods similar to those described by Clarke and Warwick (1994; see also Ivany and Baumiller, 1998). Taxonomic associations in a set of fossil collections can be described completely by an R-mode matrix of similarity coefficients between every pair of taxa. Such a ma-

← FIGURE 9—First axis correspondence analysis values for all collections (all genera, S $ 4) plotted against stratigraphic position. Crosses represent individual collections, dots represent mean values for each meter-scale cycle. Composite sequence boundaries are shown by dotted lines. Gray stripe shows interpreted general trend of stronger bivalve influence at the base of each composite sequence followed by increased brachiopod dominance upward.

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FIGURE 11—Correspondence analyses of brachiopod and bivalve genera by composite sequence (key to genera as in Fig. 7). Percent of total inertia is shown for each axis. Units are mean standard deviations. Outlined patches represent inferred gradient end-members (see text for discussion).

← FIGURE 10—First-axis correspondence-analysis values for all collections (brachiopod genera, S $ 2) plotted against stratigraphic position. Crosses represent individual collections, dots represent mean values for each meter-scale cycle. Composite sequence boundaries are shown by dotted lines. Gray stripe shows interpreted general trend of increasingly dysoxic faunal signatures through study interval.

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trix was built using the Dice coefficient and all the collections (S$2) from each composite sequence. These are the same data that were ordinated for each sequence (Fig. 11), so they can be generally compared with the results of the exploratory techniques. Such comparisons should not be taken too literally because correspondence analysis, although it is an effective means of visualizing complex paleoecological patterns, does not make use of the Dice coefficient. Recurrence of faunal associations was measured by comparing the Dice coefficient matrices for each pair of composite sequences using Spearman’s rank correlation coefficient (r). Note that only taxa occurring in both sequences can be included using this approach. The recurrence coefficients obtained in this manner can be tested for significance, which measures whether the r based on real data is significantly greater than if taxa were distributed randomly among collections. Standard significance tables for Spearman’s rank correlation coefficient are not valid in this case for two reasons. First, they assume a null hypothesis of r 5 0, but non-random structure (i.e., r.0) can occur in similarity matrices (i.e., the Rmode Dice matrices used here) due to differences in the number of occurrences of different taxa, regardless of whether there are any ecological associations. Second, underlying distributions are not normal (Clarke and Warwick, 1994). To deal with these issues, a randomization approach was adopted (Crowley, 1992). The occurrences of each taxon were randomized among all the collections for each of two composite sequences. By doing so, the number of occurrences of each genus did not change, just the distribution of co-occurrences between genera. Occurrences were shuffled randomly within taxa until all collections had at least one occurrence. Note that this loosens the restriction of at least two occurrences per collection in the original data matrices and makes the test conservative in recognizing recurrence by widening the calculated significance values. After both data matrices intended for comparison were randomized, their similarity matrices and correlation coefficient were calculated in the same manner as the original data. This was performed 1000 times to build a distribution of correlation coefficients, the top and bottom 2.5% of which were used to determine the 95% significance values. If the correlation coefficient from the real data lies outside this range, the statistical null hypothesis (i.e., that the degree of similarity between taxonomic associations in the two sequences being tested would be possible with just random associations of taxa) can be rejected. In other words, if the recurrence coefficient lies outside the 95% range, it is reasonably certain that there is a nonrandom degree of recurrence of taxonomic associations between sequences. According to the randomization results (Fig. 12), the degree of faunal association using all taxa (brachiopods and bivalves) is significantly recurrent (except for sequence I versus IV). In contrast, the gradients within each group are generally not recurrent. This suggests that the segregation of bivalves and brachiopods is a real aspect of the data set, while the faunal associations within each group are weak. Whether or not the correlation coefficients differ significantly from random associations, they still describe the amount of recurrence in the structure of the data, which may differ between the two taxonomic groups. In compar-

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FIGURE 12—Randomized recurrence significance. Triangles, squares, and circles indicate measured Spearman Rank Correlation Coefficient using all genera (A), brachiopods (B), and bivalves (C), respectively. I-bars indicate 95% two-sided confidence intervals based on randomized data. Roman numerals indicate composite sequences (Fig. 1). If the measured value falls outside the confidence interval, then it is outside the expected degree of recurrence if genus associations were random.

ing bivalve and brachiopod associations, the aim is to determine whether one is more recurrent than the other. To test this, a bootstrap procedure was used (Efron and Tibshirani, 1991): rather than randomize the data matrices, they were sampled with replacement by randomly picking

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Summary of Results

FIGURE 13—Bootstrapped confidence intervals (CI’s) for recurrence. Squares and circles indicate measured Spearman Rank Correlation Coefficients using brachiopod and bivalve genera, respectively. I-bars indicate 95% two-sided confidence intervals based on bootstrapped resampling. Roman numerals indicate composite sequences (Fig. 1). If any of these cases showed the measured values of each group falling outside the confidence interval of the other, then that would indicate that the degree of recurrence was significantly different. This is not the case in any of these comparisons.

entire collections from the original data set. The difference between this procedure and the randomization approach is that the bootstrapped matrix is composed of collections known to be samples reflecting real species associations in each composite sequence. (The randomized matrices shuffled occurrences; hence, any non-random species associations originally present were destroyed.) The bootstrap procedure addresses the question: if the two sequences were resampled many times over, retaining any structure of taxonomic associations present in the collections, what would be the range of correlation coefficients? Repeating the bootstrap 1000 times and using the top and bottom 2.5% of the distribution of the correlation coefficients provides 95% confidence intervals to bracket the true values. When comparing bivalves and brachiopods for differences in degree of recurrence, if either of the two true correlation coefficients falls within the 95% bracket of the other group, the two are not considered significantly different. This is a very stringent criterion, but this choice helps compensate for the tendency of bootstrapping to inherently underestimate the true range of variation. In addition, note that bootstrapped occurrence matrices were created so that every taxon occurred at least once, slightly loosening the original restrictions of two or more occurrences per taxon and making the test conservative. The results of the bootstrapped tests of whether the recurrence coefficients differ between the two groups are presented in figure 13. Although there are numerous occurrences of r for one biofacies falling outside the range of the other, because the exclusion was not mutual, they were not counted as significant. These findings indicate that given the number and nature of the collections, there is no consistently documentable difference in the strength with which bivalve and brachiopod genera adhere to their respective environmental gradients.

In the Pennsylvanian-Permian Midcontinent, two distinct biofacies can be distinguished—one dominated by bivalves and the other by brachiopods. This is the overwhelming pattern in both the cluster analyses and ordinations of these data, and is consistent with the findings of previous workers in the region (Elias, 1937; Mudge and Yochelson, 1962). Within each of these two biofacies, previously unrecognized compositional gradients can be resolved. In the brachiopods, one end of the gradient is interpreted as representing dysoxic environments (dominated by relatively small taxa like Crurithyris, Rhipidomella, Wellerella, Lissochonetes, and Hystriculina). The other end of the gradient is represented by Juresania and Linoproductus, which are interpreted to have lived in more nearshore environments. In the bivalve biofacies, Wilkingia and Pteronites are associated frequently with brachiopods, suggesting they preferred open marine conditions, while other bivalves like Edmondia occupied more restricted nearshore settings. Ordination of collections from each composite sequence suggests that these broad gradients recurred each time marine conditions were re-established on the platform, but the particular order of specific taxa along the gradients does not strictly recur. Recurrence analysis using a randomization approach confirms that bivalves and brachiopods remain segregated in each cycle, but the gradients within each biofacies do not recur to a degree significantly distinguishable from random associations. Bootstrapping recurrence coefficients indicates that the rigidity (or lack thereof) of the order of species is not significantly different between the brachiopod gradient and bivalve gradient. At first glance, the lack of gradient recurrence may seem contradictory with the results of correspondence analysis, which show interpretable environmental trends within the two groups. However, this simply indicates that taxa within the two communities are not strictly limited in their associations—they may co-occur with certain taxa more often than others, as depicted by the ordinations, but their range of tolerances relative to the amount of environmental change along the gradients allows them to occur with most other taxa in the paleocommunity. This lack of strictly limited associations means that recurrence is difficult to detect because the order of taxa observed every time the gradient is resampled will be quite variable. DISCUSSION Nature of Pennsylvanian-Permian Paleocommunities of the Midcontinent The approach taken in this investigation is related closely to gradient analysis as described by Whittaker (1967). Rather than classifying assemblages into community types, he was interested in how species assemblages change across a landscape in response to a changing environmental complex. Springer and Miller (1990) advocated adopting such an approach in paleoecological studies. Whittaker’s concept is summarized in figure 14. The ‘‘environmental gradient’’ is the sum of interrelated environmental factors that affect the organisms of the com-

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FIGURE 14—Graphical representation of ecological composition gradients. (A) Taxa showing exclusion and coadaptation. (B) Taxa showing exclusion but no coadaptation. (C) Taxa showing coadaptation but no exclusion. (D) Taxa showing neither coadaptation nor exclusion. (E) Exclusion between biofacies, but neither coadaptation nor exclusion within biofacies (after Springer and Miller, 1990; modified from Whittaker, 1975).

munity. ‘‘Species importance values’’ are typically thought of as abundances but can be any ecological variable, such as biomass or frequency of occurrence. When using presence/absence data, as in this study, the curves can be thought of as the chance that a species will occur in a collection from a certain point on the gradient. Note that although abundance and commonness (i.e., number of collections in which a taxon occurs) are often related (e.g., Fig. 3C), they need not be: some taxa occur in many collections but rarely in great abundance, and some occur in profusion but only at a few sites. There are two related means of understanding how species are distributed across an ecological gradient: direct gradient analysis and indirect gradient analysis. Direct gradient analysis involves plotting species distributions against some factor like elevation, moisture, temperature, water depth, or oxygenation. Such distributions can be fit with Gaussian curves showing overlapping species distributions in an environment (Fig. 14). Note that the measured factor need not be the actual control on species distribution—it can be a proxy for a complex of environmental factors. In marine paleoecology, biotic gradients often are associated with water depth when the main control may actually be a composite of turbidity, substrate texture, temperature, and oxygenation (Robbins and Bell, 1994). Indirect gradient analysis arranges samples based on taxonomic composition. Compositional differences typically can be related to environmental factors without strict adherence to a geographic or stratigraphic gradient. That is to say, collections can be arranged along a gradient (like

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those in Fig. 14) regardless of their geographic or stratigraphic position. The Pennsylvanian-Permian Midcontinent Platform was a complex mosaic of depositional environments disrupted by numerous stratigraphic discontinuities—the outcrop belt rarely shows a simple facies gradient vertically or laterally (Olszewski 2000). However, by using as many collections as possible, compositional gradients can be well constrained by reducing the gaps between samples. Correspondence analysis is one approach to indirect gradient analysis and it provides a maximum likelihood approximation of Gaussian curves for species distributions (ter Braak, 1985). The results presented above—i.e., two biofacies each with an interpretable but weak gradient (Fig. 7A)—can be depicted as in figure 14E. Although bivalves and brachiopods segregate, there is no pattern indicating competitive exclusion or coadaptation within either biofacies. This is more consistent with a Gleasonian model of species independence within communities than with a strong Clementsian interconnection. However, with regard to species interactions within a biotic community, Whittaker et al. (1973) very clearly warned against using the distribution of taxa along a gradient as an indicator of how they divide the habitat at a location into niches (see Schoener, 1989 for elaboration). These patterns each represent a different scale, and the question of niches (sensu Whittaker et al., 1973) cannot be addressed using data of the sort used in this study. The point is that understanding the range of conditions that a species can occupy along an environmental gradient provides only limited insight into the nature of interactions with neighboring species at a single location during life. Paleocommunity Stasis in the Pennsylvanian-Permian Midcontinent Another question of interest to paleoecologists is whether these paleocommunities are static or not. The present results indicate that the biofacies-level division into brachiopod-dominated and bivalve-dominated assemblages in these data is static—that is, it recurs consistently every time the basinal ecosystem is re-established. On the other hand, the way taxa fall along faunal gradients (i.e., how they divide up habitats) within the two biofacies is not static. In a comparison of taxonomic turnover in the basin over 12.5 Myr, analysis presented by Olszewski and Patzkowsky (in press) found that background turnover in bivalves and brachiopods was not significantly different, although their histories of first and last appearance episodes were. With regard to the relationship between ecological structure (measured using recurrence) and background turnover, the present results are equivocal—neither group differs from the other in either aspect. If ecological structure had differed but turnover had not, or vice-versa, then it could be concluded that one had little influence on the other. If both aspects were different in both groups then it could be determined whether stronger ecological structure fostered or suppressed turnover (depending on whether the two were positively or negatively correlated). In contrast to background turnover, the consistent segregation of biofacies suggests that the independence of turnover episodes (brief periods of elevated first or last ap-

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pearance) in the two groups (Olszewski and Patzkowsky, in press) may be related to the introduction or elimination of the habitat conditions required by the taxa composing each biofacies. For example, the dramatic decrease in brachiopod diversity above the Beattie Limestone Formation (Olszewski and Patzkowsky, in press) may occur because some environments favored by the brachiopods were eliminated (see the dramatic shift from dysoxic to well-oxygenated brachiopod collections near the top of the study interval in Fig. 10; the base of cycle 51 is the base of the Beattie Limestone Formation). Habitat destruction (i.e., elimination of habitable environments) is one of the most efficient extinction mechanisms in the modern world (Tilman et al., 1994), and this is consistent with the paleontological result found in this study. Comparison with Other Studies Most recent studies concerning evolution of benthic marine faunas have focused on the taxonomic composition of an entire basin over 106 to 107 years (e.g., Brett and Baird, 1995; Tang and Bottjer, 1996; Patzkowsky and Holland, 1997; Olszewski and Patzkowsky, in press), although some have examined patterns at the finer scale of biofacies (e.g., Delcourt and Delcourt, 1991; DiMichele and Phillips, 1995, 1996; Westrop, 1996). Some of these studies (Brett and Baird, 1995) have recognized ecological-evolutionary (EE) subunits (lasting 3 to 11 Myr) showing a static pattern of taxonomic composition and bounded by brief episodes of elevated turnover. Morris et al. (1995) suggested that processes governing ecological interactions might be responsible for the static patterns within EE subunits. Such processes would be expected to result in strong recurrence of biotic gradients between composite sequences due to strict limitation of the roles and interactions of individual taxa (however, see comments of Whittaker et al. [1973] discussed above). In this study, no influence of any such processes acting within biofacies has been detected. In addition, no patterns of EE subunit stasis in the faunas of the Pennsylvanian-Permian Midcontinent platform have been found (Olszewski and Patzkowsky, in press). In contrast to long-term, basinal analyses, several studies of macroinvertebrates are comparable to this one in terms of duration, resolution, and geographic scale (Bennington and Bambach, 1996; Holterhoff, 1996; Pandolfi, 1996). All of these, like the present one, were based on individual site collections rather than basinal compilations and take advantage of stratigraphic cycles to test for consistency of faunas through time. The findings of each are briefly reviewed here to search for broader similarities and differences. Bennington and Bambach (1996) examined fossil assemblages from four major marine incursions in Pennsylvanian strata of the Appalachians. These recurred every 0.4 to 2.5 Myr (about the same as the composite sequences of the Midcontinent) and contain many of the same taxa as the data presented here. The aim of their study was to determine how similar individual collections had to be before they could be considered the same. They did this by comparing collections from different locations in the same cycle, comparing collections between cycles, and resampling individual collections to constrain the range of variation. They found that there were significant differences in

FIGURE 15—Graphic explanation of difference between analysis of Bennington and Bambach (1996) and this study. Resampling of sites permitted Bennington and Bambach (1996) to constrain the range of compositional variation at points along an environmental gradient (sensu Whittaker, as in Fig. 14). The approach taken here, based on numerous collections from many points along the environmental gradient, does not allow testing of individual collections for compositional similarity, but does constrain the expected range of compositional variation along an environmental gradient.

many (but not all) collections from individual cycles, and in all comparisons between cycles. They found recurrence only at the level of ‘‘paleocommunity type’’—equivalent to the biofacies identified in this study. These results are consistent with the present study, although the scale of analysis is somewhat different. Largescale associations between cycles were compared in this work, whereas Bennington and Bambach (1996) focused on reproducibility of individual collections (Fig. 15). In both studies, biofacies or ‘‘paleocommunity types’’ recur but show a wide range of internal variation that is not structured in a recurrent manner. Holterhoff (1996) examined crinoid associations from three Upper Pennsylvanian cycles of the northern Midcontinent (just a few million years older than rocks of the present study). His cycles are similar in structure and duration to the present composite sequences. He found five paleocommunity types arrayed along an onshore-offshore gradient. Three of these paleocommunity types recur in each cycle (the two others are absent in all but one due to absence of sufficiently offshore depositional environments). One of these biofacies was unique to the transgressive phase of the cycles and absent from the regressive portions.

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These results are also consistent with the present study, although a ‘‘no-analog’’ assemblage (Overpeck et al., 1992) unique to only one portion of a composite sequence has not been recognized. Like the present results and those of Bennington and Bambach (1996), none of Holterhoff’s (1996) individual collections appear identical, although they do fall into distinct associations that recur from cycle to cycle. Lastly, Pandolfi (1996) examined Pleistocene coral-reef assemblages from Papua New Guinea. He examined nine cycles over a 95-kyr period, comparable in resolution to the meter-scale cycles of the Midcontinent, but much finer than Midcontinent composite sequences. At three different locations, he measured transects from reef crest to reef slope and compared assemblages from those two environments from place to place and through time. He found greater differences between locations than through time at any single location; this contrasts to other studies of Quaternary terrestrial and level-bottom marine communities. As a result, Pandolfi (1996) suggested that coralreef dynamics distinctly differ from these other systems. An important difference that Pandolfi (1996) points out between his work and some other studies is the difference in temporal scale—many other studies either focused on much shorter ecological time scales or much longer paleontological time scales. This led him to suggest that different patterns may be emerging at different scales of study. Although the temporal resolution used herein is significantly coarser than his, similarities are seen between Pandolfi’s (1996) results and the present investigation. Because it was not possible to resample the same point on an environmental gradient through time, results of the present study only can be compared to his individual transects through time. However, if his three sites are considered as points along an environmental gradient (not necessarily parallel to their geographic trend), then that gradient recurs very consistently from cycle to cycle just as the Midcontinent bivalve-brachiopod gradient does. Overall, these three studies are consistent with the finding of this study that biofacies or paleocommunity types, as segments of environmental gradients, do recur consistently, even when they experience severe environmental disruption and must be reassembled from their constituent taxa. Individual points on environmental gradients (collections or local paleocommunities) are never identical when resampled through time, but often do show a degree of interpretable consistency. This probably reflects the preferences and tolerances of individual taxa rather than some degree of coadaptation or evolutionary integration. CONCLUSIONS (1) Paleoecological analysis of a large data set of fossil occurrences from Pennsylvanian-Permian rocks of the northern Midcontinent indicates the presence of two biofacies, one dominated by brachiopods and the other by bivalves. (2) Within these two biofacies, compositional gradients can be recognized. The brachiopod gradient is interpreted to reflect degree of water-column oxygenation. The bivalve gradient ranges from open-marine conditions to more environmentally restricted conditions, but the controlling

factors (temperature, salinity, oxygenation, etc.) are unclear. (3) Testing for the recurrence of taxonomic associations each time marine conditions were re-established indicates that segregation of the biofacies is strongly recurrent, but the order of species along gradients within the biofacies is not. The groups of genera defining the compositional gradients described above do roughly recur, but the specific relationships among individual taxa do not. (4) With regard to stasis, a pattern of recurrent associations within biofacies that is statistically distinguishable from random taxonomic associations cannot be identified. On the other hand, the segregation of the bivalve and brachiopod biofacies is significantly recurrent, but probably reflects different environmental preferences between these two groups rather than coevolutionary integration of paleocommunities. ACKNOWLEDGMENTS This work was completed in partial fulfillment of T.D. Olszewski’s doctoral dissertation in the Department of Geosciences, The Pennsylvania State University (available through the Penn State Electronic Theses and Dissertations website at: http://etda.libraries.psu.edu/). Discussions with R.R. West and D.R. Boardman II in the field provided insights to the stratigraphy and paleoecology of the Midcontinent. Thanks to A.I. Miller and an anonymous reviewer for thoughtful and encouraging comments that helped to improve this article. Grants from the National Geographic Society, the Geological Society of America, Sigma Xi, and the Krynine Fund of the Penn State Department of Geosciences made this work possible. REFERENCES ARCHER, A.W., and MAPLES, C.G., 1987, Monte Carlo simulation of selected binomial similarity coefficients (I): Effect of number of variables: PALAIOS, v. 2, p. 609–617. ARCHER, A.W., and MAPLES, C.G., 1989, Response of selected binomial coefficients to varying degrees of matrix sparseness and to matrices with known data interrelationships: Mathematical Geology, v. 21, p. 741–753. BAARS, D.L., RITTER, S.M., MAPLES, C.G., and ROSS, C.A., 1994, Redefinition of the Upper Pennsylvanian Virgilian Series in Kansas: in BAARS, D.L., ed., Revision of stratigraphic nomenclature in Kansas: Kansas Geological Survey Bulletin 230, p. 11–16. BENNINGTON, J.B., and BAMBACH, R.K., 1996, Statistical testing for paleocommunity recurrence: are similar fossil assemblages ever the same?: Palaeogeography, Palaeoclimatology, Palaeoecology, v. 127, p. 107–133. BENNINGTON, J.B., and RUTHERFORD, S.D., 1999, Precision and reliability in paleocommunity comparisons based on cluster-confidence intervals: How to get more statistical bang for your sampling buck: PALAIOS, v. 14, p. 506–515. BOARDMAN, D.R., II, MAPES, R.H., YANCEY, T.E., and MALINKY, J.M., 1984, A new model for depth-related allogenic community succession within North American Pennsylvanian cyclothems and implications on the black shale problem: in HYNE, N.J., ed., Limestones of the Midcontinent: Tulsa Geological Society Special Publication 2, p. 141–182. BOARDMAN, D.R., II, NESTELL, M.K., and KNOX, L.W., 1995, Depth-related microfaunal biofacies model for Late Carboniferous and Early Permian cyclothemic sedimentary sequences in Mid-Continent North America: in HYNE, N.J., ed., Sequence Stratigraphy of the Mid-Continent: Tulsa Geological Society, p. 93–118. BRETT, C.E., 1995, Sequence stratigraphy, biostratigraphy, and ta-

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