gradient versus cluster analysis of fossil - cornell college

Gradient versus cluster analysis of fossil assemblages: a comparison from the Ordovician of southwestern Virginia

DALE A. SPRINGER AND RICHARD K. BAMBACH

LETHAIA Springer, D. A. & Bambach, R. K. 198507 15: Gradient versus cluster analysis of fossil assemblages: a comparison from the Ordovician of southwestern Virginia. Lethaia, Vol. 18, pp. 181-198. Oslo. ISSN 0024-1164.

Studies in modern ecology indicate that most species are distributed independently along environmental gradients according to their individual requirements. Steep gradients often produce species associations separated by discontinuities; gradual gradients produce broadly-overlapping distributions. Approaching the distribution of species populations as a continuum, using gradient analysis, avoids artificial subdivision of totally intergrading distributions, yet permits discontinuities to emerge where present. Faunas of the Martinsburg Formation (Ordovician) in southwestern Virginia offer an excellent opportunity to test the applicability of gradient analysis in a paleoecological setting. A broad spectrum of environments, from nearshore to open-marine, clastic to carbonate-dominated facies, provide both temporal and geographic variation against which to evaluate changes in species distributions. Variations of five classical, Petersen-type communities were recognized in the Martinsburg using cluster analysis: (1) Lingula, (2) bivalve, (3) Rafinesquina, (4) Onniella, and ( 5 ) Sowerbyella-dominated communities. Two gradient analysis techniques, ordination and Markov analysis, revealed the same basic associations. However, ordination and Markov analysis permit arrangement of these associations along one or more interpreted environmental gradients. Factors related to water depth and distance from clastic source areas, particularly bottom stability and disturbance frequency, appear to have been the most important of a complex of interrelated physical parameters. The high-stress, nearshore end of the Martinsburg gradient complex was occupied by a Lingula association, followed seaward by an association of bivalves adapted to less-stressed environments. Low-stress, open-shelf environments were occupied by Rafines- quina, Onniella, or Sowerbyella-dominated associations. Broad overlaps among these articulate brachiopod associations reflect variations in the open-shelf habitat. 0 Ordination, gradients, communities, cluster analysis.

Dale A. Springer, Department of Geology, Amherst College, Amherst, Massachusetts 01002, U.S.A. (Current address: Department of Geology, Smith College, Northampton, Massachusetts 01063, U.S.A.); Richard K. Bambach, Department of Geological Sciences, VPI & SU, Blacksburg, Virginia, U.S.A.: 24th February, 1984, (revised 19840904).

Paleosynecological studies have traditionally emphasized the identification of recurrent faunal assemblages, ‘communities’ in the sense of Peter- sen (Petersen 1913; Johnson 1962; Ziegler 1965; Valentine 1969). Community types are treated as discrete units with distinct temporal or geographic boundaries and described in terms of associated environmental parameters, size of species populations, or other community-wide character- istics (Ziegler et al. 1968; Bretsky 1970; Bowen et al. 1974; among others); this is a classificatory approach to the study of species distributions.

Studies in modem ecology suggest, however, that community boundaries are more diffuse (Whittaker 1975). The picture that has emerged is one of continuously overlapping ranges; each species adjusts its niche dimensions in response to the physical environment and to competitive pressures from species with similar habitat re-

quirements (Pielou 1975; Whittaker 1975). This is the ‘individualistic’ hypothesis of species distribution proposed by Gleason (1926). An assump- tion of this hypothesis is that species are distributed along environmental gradients, and. changes in species distribution (community) primarily reflect changes in physical parameters along these gradients (Whittaker 1956,1967; McIntosh 1967; Beals 1969; Johnson 1971).

Gradient analysis (Whittaker 1956, 1967) is an approach to community study that goes beyond simple classification and description of community types and integrates the study of gradients in species populations, community structure, and environment. It has enjoyed growing popularity, particularly among plant ecologists where the concept was first introduced (Curtis 1955; Bray & Curtis 1957). Gradient analysis and classitica- tory approaches to communities should not be

12 - Lethaia 3/85

182 Dale A. Springer and Richard K . Bambach LETHAIA 18 (1985)

A

B

0 so IW

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Fig. 1. DA. Martinsburg Formation correlation chart. OB. Outcrop belts of Upper Ordovician rocks in southwestern Vir- ginia. Sections: C, Catawba Mt.; N, Narrows; W, Walker Mt.; H, Hagan (after Kreisa 1980).

considered mutually exclusive. Gradient analysis can be viewed as a method of expressing relationships among classes along a continuous scale (Goff & Cottam 1967); it serves a practical pur- pose similar to that of naming certain wave- lengths of the visible spectrum 'red' or 'green'. Furthermore, changes in physical environment may be abrupt as well as gradual; the former case results in clusters of population optima separated by discontinuities. These clusters commonly can be categorized and described as communities with end results resembling those of traditional classification schemes. However, because classificatory schemes are often based on a IimiteQ number of parameters (for example, Petersen 1913; Thorson 1957; Bloom er al. 1!272), superim-

posing distinct subdivisions on a continuum of species abundance optima results in a loss of information (Goodall 1962). This becomes a particularly important consideration when choosing analytic techniques for paleoecological studies where taphonomic processes have already elimi- nated precious details.

Several recent studies have brought gradient analysis to bear on problems of paleontological interest. Miller (1981) demonstrated a relationship between environment and change in species distribution in dead (time-averaged) samples for one modern marine setting. Shaffer & Wilke (1965) found use of Bray-Curtis ordination techniques effectively demonstrated relationships between environmental parameters and species distribution in both recent and fossil marine benthic communities. Cisne & Rabe (1978) proposed 'coenocorrelation', the correlation of position in vertical section with position along an environmental gradient, as a new technique for biostratigraphy. Humphreville (1981), using ordination and other techniques, interpreted the arrangement of Mississippian faunas within a paleoenvir- onmental gradient complex. Plants (1977), in a pilot study for the present investigation, used gradient analysis to establish relative onshore- offshore position of faunal assemblages in Mar- tinsburg Formation rocks at one locality in southwestern Virginia.

The present study compares results of two gradient analysis techniques, ordination and Mar- kov analysis, to those of classical cluster analysis in the reconstruction and interpretation of paleo- communities in the Martinsburg Formation (Middle and Upper Ordovician) in southwestern Virginia. It is, to the authors' knowledge, the first gradient analysis to deal with the full spectrum of environments from nearshore to deep open shelf and clastic- to carbonate-dominated facies.

Geological setting The Martinsburg Formation (Fig. 1) forms part of a sequence of units deposited in a tectonically active foreland basin setting during the Middle and Late Ordovician (Kreisa 1980, 1981). The Martinsburg and equivalent Trenton Formation and Reedsville Shale in southwestern Virginia (Fig. 1A) represent ramp facies associated with the Martinsburg flysch (basinal) deposits of

LETHAIA 18 (1985) Analysb of fossil assemblages 183

H & m a n I J

W A I r r a niiw

400

200

N

40 0

200

C

/ /

#

L I C D r n L Y

Fig. 2. Distribution of lithologies in Martinsburg Formation measured sections. See Fig. 1 for locations. Short dashes at right of each column represent sampling locations. Changes in sample composition are tracked by curves to right of each column. Lithologies: bricks = limestone; dashes = fine clastin; dots = coarser clastics. IUT = Reedsville ShlTrenton Ls contact. Letters A- M represent Petersen ‘communities’ identified by cluster analysis. See Table 1 and text for details.

northern Virginia and Pennsylvania (McBride 1962). Rising tectonic uplands bordering the ba- sidramp complex shed clastics from the south- east into the predominantly carbonate environments of the ramp (Rodgers 1971; Kreisa 1980). Closing of the Martinsburg basin by subduction along its southeastern margin foreshadowed clo- sure of the ocean between the paleocontinents of Laurentia and Baltica (see Scotese et al. 1979; Bambach et al. 1980 for paleogeographic reconstructions).

Detailed stratigraphic and sedimentologic work by Kreisa (1980) has demonstrated a vari- ety of depositional environments within the Mar- tinsburg basin in southwestern Virginia. Vari- ability is introduced vertically by the transgres- sive-regressive nature of the Martinsburg sedimentary package. Facies vary geographically from nearshore carbonates on the western edge of the depositional basin to open-shelf clastics in the east.

Four sections, at Catawba Mt., Narrows, Walker Mt., and Hagan, Virginia, provided the data base for this study (Fig. 1B). The sections

are located over a distance of approximately 200 kilometers in several strike-belts of the Appala- chian Valley and Ridge Province. Shales dominate the lower portions of the eastern strike-belt sections (Fig. 2). Carbonates dominate approximately the lower 180 meters of the western strike-belt sections and extend as a limestone tongue into the central portions of the Catawba and Walker Mt. sections (‘limestone interval’ of Kreisa 1980, 1981).

Clastics dominate lithologies above the limestone tongue at three of the four sections; at Hagan, the interval of clastic sedimentation is brief, and carbonates predominate through much of the upper half of the section. Final basin filling is evidenced by the presence of relatively coarser clastics at the tops of all four sections: sandstones dominate at Catawba, Narrows, and Walker Mt., shales at Hagan (see Kreisa 1980). Relative amounts and stratigraphic distribution of clastics suggest each section occupied a slightly different environmental setting (Fig. 3), representing, from east to west, a decrease in both clastic influx and frequency of disturbance.

184 Dale A . Springer and Richard K . Bambach LETHAIA 18 (1985)

8. FLVSCH ” \ eC / BASIN

FLVSCM BASIN

D

Fig. 3. Reconstructed depositional environments for four time-slices during filling of Martinsburg hasin. Large arrow indicates general direction of decreasing clastic influx and decreasing disturbance frequency. 0 A. Top of S. curdwillensis zone. 0 B. Top of Kreisa’s ‘limestone interval’. O C . Top of R . alternara zone. 0 D. Top of Martinsburg Formation. Facies: bricks = limestone; dashes = fine clastics; dots = coarser clastics. Sections: C = Catawba: N = Narrows; W = Walker MI.; H = Hagan.

Biostratigraphy and fauna The Martinsburg Formation in southwestern Vir- ginia (and equivalent Trenton Limestone and Reedsville Shale) spans Upper Trenton, Eden- ian, and Maysvillian stages of the Upper Ordovi- cian (Butts 1940; Rader & Ryan 1965; Kreisa 1980, 1981). Biostratigraphic studies on Martins- burg faunas have been limited in scope and only moderately useful for correlation within the study area. Rust (1968) studied Martinsburg conodonts in a limited number of outcrops and demonstrated the Trenton through Maysville age as- signed to the unit. He suggested, however, that the upper contact might be as young as Early Richmondian. Walker (1967) and Bretsky (1970) considered the upper contact Maysvillian in age. A study currently in progress on organic-walled microfossils in these rocks (K. Colbath, personal communication 1982) may provide more control.

Walker (1967) suggested two faunal events with possible biostratigraphic significance: (1)

the disappearance of Sowerbyella curdsvillensis low in the formation and (2) the replacement of Rafinesquina alternata by Rafinesquina fracta in the upper portion of the unit. Bretsky (1970) and others have suggested the Orthorhynchula bed of Bassler (1919) represents a teilzone of Late Maysville age. Orthorhynchula linneyi occurs in abundance within the study area only in fine to very fine bioturbated sands at the top of the Walker Mt. section. Other studies have recov- ered Orthorhynchula in fine sands near the top of the formation and demonstrated facies control over the distribution of Orthorhynchula (Walker 1967; Kreisa 1980, 1981). Kreisa (1980) considered the top of his ‘limestone interval’ a time-line representing maximum transgression in the Mar- tinsburg basin. Fig. 3 presents reconstructions of the paleogeography of southwestern Virginia for four time-slices.

The Martinsburg Formation is uniquely suited to a study of ancient faunal and ecological gradients for a number of reasons. It is an abundantly

LETHAIA 18 (1985) Analysis of fossil assemblages 185

fossiliferous unit with a moderately diverse and well-described fauna (Walker 1967; Bretsky 1969, 1970). This fauna includes numerous brachiopods, bryozoans, bivalves, and trilobites; gastropods, echinoderms, and nautiloid cephalo- pods are locally important. Preservation is generally good. Fossils are preserved as internal, ex- ternal, or composite molds, and calcareous material is preserved in many brachiopod and bryozoan specimens. Fossils occur predominately in coquinites. These shell concentrations have been interpreted as basal units of storm-reworked, but essentially untransported deposits (Kreisa 1980, 1981). Species found in coquinites are identical to those found in adjacent shales (Plants 1977; Kreisa 1980; Springer 1982), where they represent thin storm lags and occasional in situ assemblages.

Two paleoecological studies have been made on Martinsburg faunas. Bretsky’s (1970) classic study of faunas collected from the upper twenty to sixty meters of the Reedsville and Martinsburg Formations in the central Appalachians demonstrated the existence of three Petersen-type ‘communities’ in these rocks. Plants (1977), working with collections from Catawba Mt., interpreted the stratigraphic sequence of faunal abundance peaks described there as the expres- sion of fluctuations in position of an onshore- offshore environmental gradient. Thus, the Mar- tinsburg offers an opportunity to document the response of a marine invertebrate fauna to both temporal and geographic changes in environment.

Sampling methods Faunal collections were made from three nearly complete, relatively undeformed sections of Martinsburg Formation: Narrows, Walker Mt., and Hagan, Virginia (Fig. 1B). Collections made by Plants (1977) at Catawba Mt. were incorpo- rated into the data base to provide a fourth section. Samples were spaced at approximately six meter intervals (Fig. 2) and collected primarily from storm-concentrated coquinas. [Adjacent shales are commonly barren as a consequence of the mode of storm-couplet generation (see Kreisa 1981)l.

Samples were split with a hydraulic press and all fossil material greater than or equal to one millimeter was identified to species level (except bryozoans, gastropods, and echinoderms) and

counted. Fragmentary material was reduced to represent a minimum possible number of indivi- duals using reduction factors described by Plants (1977). Resulting species abundances were rela- tivized to facilitate comparison of collections of various magnitudes.

Analytical techniques Cluster analysis. - Cluster analysis was applied to the Martinsburg data in order to compare results obtained with this classical community analysis technique to results obtained using gradient analysis techniques. Czekanowski’s similarity coefficient (Equation 1) was chosen for use with the Unweighted Pair Group Method (Sokal & Sneath 1963; Morrison 1976) to take full advan- tage of relative abundance data. The similarity coefficient [S (j,k)] is calculated by the formula:

S (i, k)=2[Z min (P,, Pik)lZ (PV+Pik)] (1) where j and k are two samples and P is the proportion of the ‘ith’ species in each of the pair of samples. Raw data were percent transformed to dampen effects of large variations in abundances within and between samples. Percent transformation of the data yielded higher correlation coefficients than other transformations tried (Springer 1982).

A program written for Plants (1977) was used to produce both Q- (collections) and R- (species) mode cluster dendrograms for Martinsburg faunal data. Two-way cluster diagrams (Fig. 4), in which Q- and R-mode dendrograms are set at right angles to one another and species compris- ing a minimum of five percent of a collection are marked for each sample, were produced to illustrate which species dominate each Q-mode cluster. Patterns found on two-way cluster grids can also indicate that individual species are not ran- domly distributed through Q-mode (sample) clusters.

Cluster analysis is a useful community analysis technique, but it has several drawbacks: (1) Simi- larity coefficients are derived by averaging methods. In large data sets this reduces reliability of coefficients low in the cluster hierarchy. (2) The limited dimensionality of clustering may force discontinuities on data where none exist in nature, thus overlaps in species distributions are not well illustrated. (3) Because cluster analysis forces all samples (or variables) to cluster, low similarity clusters may not be very consistent.


Markov analysis. - Five-point ' moving average curves of five numerically important Martinsburg taxa were generated using relative abundance data. Superimposed moving-average curves (Fig. 5) produce a series of abundance peaks that can be treated as a Markov chain (Davis 1973). Mar- kov analysis makes it possible to evaluate the nature of a spectrum of possible sequences from com- pletely random to totally deterministic. Transi- tion proportion matrices, which express the probability of transition from an abundance peak of one species to that of any other, were produced for all four Martinsburg sections and for the composite number of transitions (Fig. 7; see Springer 1982 for details). Transition proportions from these matrices are illustrated diagrammati- cally in Figs. 6 and 7.

Ordination. - The term ordination was first used by Goodall (1954, 1962) in reference to methods of ecological analysis that treat vegetation change as a continuum rather than as discrete units. Ordination identifies species populations or sample composition by a set of coordinates in n- dimensional space, not by membership in a cate- gory. Of the many techniques that have been developed (see for example Anderson 1971; Or- laci 1975; Phillips 1978), polar ordination is one of the least complicated mathematically (Gauch & Whittaker 1972; Gauch 1973a), and one that has been used with success in ecology (Bray & Curtis 1957.; Whittaker 1967; Gemborys 1974).

The common procedure in paleoecological studies is to compare collections of samples, thus a Q-mode form of ordination was emphasized here (Springer 1982). Ordinations in this study were performed with POLAR 11, a program written by J. J. Sepkoski and J. Shany (modified by Sepkoski in 1980 and A. Miller and T. Rounds in 1981). Percent similarity was chosen as the similarity coefficient; Gauch (1973b) has shown that this measure works well in comparison to other formulas. Tests of the Czekanowski coefficient on ecological data also produced consistently good results (Day et al. 1971; Field 1971).

Most ordinations produce a matrix of similarity (or dissimilarity) indices that are used to represent ecological distance between any pair of samples. POLAR I1 creates a second matrix based on the variance in euclidean distances between every pair of samples. The sample with the highest variance is chosen as the first endpoint of the ordination axis, on the theory that this sam-

ple most requires explanation. The sample far- thest from the first endpoint is chosen as the second reference point of the axis. If two samples are located equidistant from endpoint one, the program chooses the sample with higher variance. POLAR I1 then calculates interpoint distances along the axis for all samples. These ordination distances are subtracted from the original (observed) distances to produce a matrix of re- sidual distances. Although multiple axes can be constructed in this manner to locate each sample in n-dimensions, little additional information is gained by computing more than three axes.

It is worth emphasizing that axes produced by ordination do not directly represent environmental gradients; rather they represent gradients of change in species composition. It is hoped, of course, that compositional gradients correspond to identifiable ecological gradients.

Analytical results Cluster analysis. - The ten most abundant species in the Martinsburg can be found in nearly all samples, although in widely fluctuating abundances. R-mode (species) clusters cannot show directly the extent of this lack of fidelity. It is revealed indirectly in the consistently low coefficients of similarity (generally less than or equal to 0.30) seen in connecting branches of R-mode dendrograms (Fig. 4); further evaluation requires calculation of fidelity and constancy indices. Many Martinsburg species cluster only as an artifact of the hierarchical nature of the technique, which demands all objects in the set be clustered before the program terminates. Similar low-level coefficients can be seen in R-mode analyses of other fossil faunas (Fox 1968; McGhee & Sutton 1981).

In spite of the low level of clustering, examination of R-mode dendrograms does reveal several recumng species groups. The most persistent cluster contains the bivalves; Sowerbyella and Zygospira also form a coherent group through most of the dendrograms.

Distinct clusters are produced at higher levels in Q-mode dendrograms (Fig. 4): similarity coefficients are generally on the order of 0.40 or greater. Sub-clusters distinguished by variations in relative abundance of dominant or associated species are commonly present within major clusters. For example, Narrows cluster B (Fig. 4) can be divided into sub-cluster B,, containing sub-


C O E F F I C I E N T OF S I M I L A R I T Y 0.1 0.1 1.0

I

NARROWS 0-MODE

il

- N

I I M

Fig. 4. Two-way cluster diagram for Narrows section. Dendrograms: R-mode, species; Q-mode, collections. Note low coefficients of similarity for R-mode clusters. Small numbers on Q-mode dendrogram represent first sample number in each sub-cluster. In general, samples from higher in section are found farther down Q-mode diagram (samples numbered from bottom to top of section). Letters along right side of diagram are Petersen-type communities identified by Q-mode clustering; numbers across bottom refer to R-mode clusters. Notice gradual shift in community composition upsection. See text for details. (H) = high-spired gastropods; (L) = low-spired gastropods.

equal numbers of Onniella sp. 1 and Rafines- quina alternata, sub-cluster BZ, distinguished by a greater abundance of Rafinesquina relative to Onniella, and sub-cluster Bo, characterized by sub-equal numbers of Onniella and isotelid trilo-

bites, plus gastropods and bryozoans. Table 1 lists clusters of similar species composition found at more than one section.

Clusters tend to be stratigraphically coherent within each section: samples adjacent in outcrop

: v SMOWVN


Markov diagrams are strikingly similar, particularly those for the Narrowsmagan and Catawbd Walker Mt. diagram pairs.

The Catawba and Walker Mt. diagrams differ most notably from the NarrowdHagan diagrams with respect to the relative importance of Sower- byella transitions. Sowerbyella-bivalve transitions are a 0.40 probability at both Catawba and Walker Mts.; this transition never occurs in the western strike-belt sections.

Composite transition probabilities are illustrated in Fig. 7. The most probable sequence of species abundance peaks in the Martinsburg For- mation is: (1) Lingula, (2) bivalve, (3) Rafines- quina, (4) Onniella. The position of Sowerbyella in the sequence is less readily apparent; Sower- byella peaks follow Onniella peaks approximately 46 % of the time (0.33/0.72, where 0.72 = total of probabilities of transitions to Sowerbyella peaks), Rafinesquina peaks about 29% of the time, and bivalve peaks approximately 25 % of the time. Sowerbyella peaks also most commonly precede Onniella (0.44), Rafinesquina (0.31), and bivalve (0.25) peaks.

Ordination. - Groups produced by ordination are usually less distinct than those produced by cluster analysis: overlap often occurs in at least one direction when groups defined by cluster analysis are identified a posteriori in three-dimensional ordination space. Ordination, in con- trast to cluster analysis, does not involve averaging; it arranges all samples in their true positions relative to one another in n-dimensional ordination space. Such arrangement makes recognition of intergradational species distributions possible.

Polar ordinations of Martinsburg data confirm and extend results obtained with cluster analysis: associations of samples and species seen in the Martinsburg Formation are not products of random distribution. Samples clustered by Q-mode analyses are also closely associated in three-dimensional ordination space. This space is por- trayed as a series of two-dimensional plots com- paring (1) axis 1 with axis 2, (2) axis 1 with axis 3, and (3) axis 2 with axis 3.

Diffusion and overlap of clusters-defined groups are to be expected in ordination space: slight changes in species composition ‘pull’ a sample away from one cluster toward another. To illustrate, Catawba Mt. Q-mode cluster C (Fig. 8A, bottom center) is dominated by On- niella sp. 3. This cluster is relatively distinct in the plane formed by axes 1 and 2, but there is

WALKER CATAWBA

Fig. 6. Markov diagrams illustrating proportion of total number of transitions in abundance peak sequence (Fig. 5) represented by each pair of taxa. (L, Lingula; B, bivalves; R, Rafinesquina; S, Sowerbyella; 0, Onniella.) Heavy solid arrows indicate transition proportions greater than or equal to 0.40 and represent primary sequence. Lighter solid arrows and dashed arrows represent less common and rare transitions, respectively.

some overlap into other clusters. Collection 60 falls within the region occupied primarily by cluster H, which is dominated by samples containing R. fiacta and Z . modesta. Collection 60 contains these two species as well as Onniella sp. 3. Clus- ter samples 08 and 10 (cluster C) are closely associated on the axis llaxis 2 diagram with collections from cluster D. Cluster D is dominated by Craniops, R. alternata, and Onniella sp. 1. Samples 08 and 10 contain numerous R. alternata, as well as Onniella sp. 1, hence their affin- ity for cluster D.

Examination of Q-mode analyses from the other three sections reveals similar intergrada-

COMPOSITE

L MARKOV COMPOSITE 0

PROPORTION R S 0

Fig. 7. Markov matrices and diagram for composite Martins- burg data. Dotted arrows represent very rare abundance peak transitions. See fig. 6 for other symbols.

190 Dale A . Springer and Richard K . Bambach LETHAIA 18 (1985)

y. . . . . .%? . . . . .44. . . . ?+? ... . ..02. . . . . .”+,,,

i : A Q. i

y. . . . . .%? . . . . ?+4. . . . . ?+? . . . . .%? . . . . .’io t 1.0

A X I S 1 A X I S 1

Fig. 8. Axis l/axis 2, ordination plots for (A) Catawba and (B) Narrows section. Capital letters identify cluster-defined Petersen ‘communities’ (Table 1) as they appear in Q-mode ordination space. See text for explanation. X = samples too close together in ordination space to be represented separately on diagram.

tion of clusters in one or more planes of three- dimensional ordination space. Most clusters, however, are distinct in at least one ordination plane.

Ordination axis poles represent samples exhib- iting maximum dissimilarity. Axis 1 has endpoints with similar composition on ordination diagrams from three of the four sections: collections rich in Onniella andlor Rafinesquina are opposed on axis 1 to collections rich in Sower- byella. The one exception is Hagan, in which Sowerbyella is a less prominent member of the fauna. At Hagan, Onniella-dominated collections which form one end of axis 1 contain the majority of Sowerbyella occurrences. The second reference point for Hagan axis 1 is a Rafines- quinalzygospira-dominated collection.

Stratigraphic position also exerts an element of control on the selection of endpoints for axis 1 at Catawba and Hagan. Catawba collections from low in the section containing S. rugosa and Z . lebanonensis are opposed to samples from high in the section containing R. fracta and Z . modesta. Samples from the lower Trenton at Hagan containing Onniella sp. 1 and S. cura’svillensis are at one end of axis 1, samples rich in R. fracta and Z . modesta from the upper part of the Reedsville Shale form the other endpoint. Ordinations performed using genus-level data eliminate this stra-

tigraphic element, usually without altering the general grouping of taxa forming the endpoints of the axes.

Reference points for axis 2 are less consistent in composition. The Catawba, Narrows, and Walker Mt. sections all have samples dominated by OnniellalSowerbyella (often with R. fracta) at one endpoint, but the opposite endpoint of axis 2 is more variable. Gastropods and bivalves dominate the second endpoint at Catawba (Fig. 8A), Lingula and bivalves at Narrows (Fig. 8B), and large ramose bryozoans (with Z . lebanonensis, gastropods, or bivalves) at Walker Mt. Axis 2 reference points at Hagan are formed by a R. fractaltiebertella sinuatalPrasopora-dominated group of collections and a Z . modestalramose bryozoan group, respectively.

Least consistent in composition are reference points for axis 3. At Narrows, axis 3 ordination separates R. fractalZ. modesta collections from those containing Onniella sp. 1 and Z . lebanonensis. Ordination along axis 3 separates Lingulal bivalve-dominated samples from bivalvelnon-lin- gulid inarticulate collections (with R. alternata and/or Onniella sp. 1) at Catawba Mt. (Fig. 8A). Samples dominated by R. alternata form one endpoint of axis 3 at Walker Mt., collections rich in Z . lebanonensis form the other. Finally, On- niella sp. 3 is the major component of collections


from one end of axis 3 at Hagan, while ramose bryozoans and H. sinuata are dominant in samples from the opposite end of the axis.

Discussion Markov community sequence. - The idealized principle gradient, derived from the composite Martinsburg data set (Fig. 7), begins with a peak in Lingula abundance. This is invariably followed by a bivalve peak. Bivalve peaks are most commonly followed by Rafinesquina peaks, which, in turn, are usually followed by Onniella peaks. Onniella abundance peaks most commonly precede Rafinesquina peaks. Sowerbyella forms a side chain: no principle arrow points to a ‘most common’ transition from one of the other four taxa to Sowerbyella. Sowerbyella peaks are followed most often by peaks in abundance of On- niella. Note that, because the Martinsburg represents a shoaling (basin-filling) sequence, the gradient appears in ‘reverse’ at all sections except Catawba: the base of each section is represented by the offshore end of the faunal sequence, the tops of the sections by the nearshore, Lingula end of the sequence.

Environmentally, the basic pattern represents a complex of interrelated physical (and probably biological) parameters. Water depth, distance from shore, and frequency of disturbance are presumably the major controlling factors. Clastic influx, bottom stability, turbidity, turbulence, light intensity, and food availability are intimately, and usually complexly, related to depth and distance, although it is not possible to assess their relative importance in this study. No simple shore-parallel, depth-related ‘community zones’ (Bretsky 1969) can be recognized in the Martins- burg. Areas dominated by different species form a shifting temporal and geographic mosaic that can be related to changing influences of the physical parameters listed above.

The striking similarity of Markov patterns between the Catawba Mt. and Walker Mt. sections and between Hagan and Narrows (Fig. 6) can be explained by noting the paleogeographic locations of the section pairs. Catawba Mt. and Walker Mt. were situated near the southern margin of the Ordovician basin, Hagan and Narrows along the northern margin (Fig. 3). Principle sources of terrigenous material lay in deltas pro- grading into the basin from the south and south- east (Kreisa 1981). Fluctuations in sedimentation

rate associated with delta-building are evidenced not only by changes in lithology, but by fluctuations in species distributions, as illustrated in the Markov diagrams for the eastern strike-belt sections. Low sedimentation rates permitted colonization of shelf areas by S. rugosa. Pulses of clastic influx intermittently increased sedimentation rates and rendered the environment inhospi- table to Sowerbyella. These disturbances can be seen in the high frequency (0.40 at both Catawba and Walker Mt.) with which peaks in abundance of Sowerbyella are followed by peaks of bivalve abundance. Bivalves are morphologically better adapted than Sowerbyella to deal with increased sedimentation rates and bottom instability.

It is important to note that reappearance of bivalves does not necessarily indicate a return to nearshore environments (except at the very top of the formation); many bivalves identified at Catawba Mt. and Walker Mt. are in portions of the section that remained open shelf. The param- eter most directly controlling these changes in species distribution is disturbance rate, not abso- lute depth or distance from shore. The episodic return to higher disturbance frequencies and bivalve-dominated environments is particularly evident at Catawba Mt. Not only Sowerbyella- dominated portions of the section, but Rafines- quina- and Onniella-dominated regions are commonly succeeded by peaks in bivalve abundance, suggesting that Catawba may have been closer to areas of active delta-building for a longer period of time than Walker Mt. This scenario is support- ed by the greater total thickness of Martinsburg sediments at Catawba Mt. and the high proportion of clastics relative to the other three sections.

Markov gradient patterns from Hagan and Narrows on the northern side of the basin most closely parallel the idealized faunal gradient. Lingula is absent from the fauna at Hagan, and the portion of the gradient nearest shore is represented by bivalves. Sowerbyella peaks are never adjacent to bivalve peaks in either western strike-belt section, suggesting less rapid changes in bottom stability or disturbance frequency in areas away from major delta sources.

The complex, mosaic nature of open-shelf environments is again apparent in the strong Ra- finesquina-Onniella-Sowerbyella triangle formed by the principle gradient arrows at Hagan and Narrows (Fig. 6). Compare this pattern with Fig. 7 (composite data) and the disrupted triangles of open-shelf associations at Catawba Mt. and


Table 1. Recurrent Peterson-type communities identified by Q- mode cluster analysis and the sections in which they occur. A = Onniella sp. 1; B = R . alternata1Onniella; C = Onniella SQ. 3 ; D = Craniops; E = S . rugosa; F = Zygospira; G = bryozoans; H = R. fiactalZ. modesta; I = R. fractalHeberteNa; J = Heber- tellahryozoans; K = gastropods; L = bivalves; M = Lingula.

Hagan Walker Narrows Catawba

UM

J I H H

G F E

B B A A

M M L L K

H H G F E E

D C

B

Walker Mt. (Fig. 6). The open-shelf environments at Hagan and Narrows were less often subjected to sudden changes in bottom stability or influx of clastics than their eastern counter- parts. Minor fluctuations in sedimentation rate or disturbance frequency are recorded as changes in abundance and distribution of the three prominent articulate brachiopod genera, yet only once (at Hagan) was the influx of clastics rapid enough in a geological sense to produce a transition to bivalve-dominated conditions.

Cluster-produced communities. - It is possible to erect traditional ‘communities’ (in the sense of recurrent associations of organisms that inhabit mappable regions) in the Martinsburg faunas, based on the results of cluster analysis (Table 1 ) .

There is a distinct element of stratigraphic control on these communities at the species level: for example, species of Onniella and Rafinesquina low in a section cluster (Onniella sp. 1 with R. alternata) and different species from each genus cluster high in the section (Onniella sp. 3 with R. fracta). Re-analysis of faunal abundance data at the generic level results in the same major clusters, without the stratigraphic overprint. That is, Onniella and Rafinesquina still constitute a cluster at most sections, but the new clusters contain congeners from different portions of the sections.

A composite two-way cluster dampens local vagaries in faunal distribution and results in six major clusters: (1) Onniella sp. 11R. alternata, (2) large ramose bryozoans, (3) S. rugosalZ. leban-

onensis, (4) Onniella sp. 3lR. fracta, (5) small ramose bryozoanslH. sinuatalz. modesta, and (6) Lingulalbivalves. Note the close correspon- dence between these six clusters and those that evolve from clustering data from individual sections (see Table 1 and Fig. 4). The stratigraphic overprint already discussed is also evident in the composite diagram (see communities 1 & 4); analysis of composite data at the generic level again eliminates stratigraphic segregation of con- generic species.

The first community, dominated by Onniella sp. 1 and R. alternata, occurs in limestones and calcareous shales and siltstones through the lower portions of all four sections. Prasopora is sporadically abundant and Craniops becomes an important accessory species in some collections from Catawba Mt.

Community (2) is dominated by large ramose bryozoans. In other aspects it is a combination of elements common in community (1) , particularly R. alternata and isotelid trilobites, and community (9, particularly R. fracta and Onniella sp. 3.

The Sowerbyellalzygospira community (3) occurs in limestone-dominated (70-80 % limestone) central portions of three sections: Cataw- ba Mt., Narrows, and Walker Mt. (‘limestone interval’ of Kreisa 1981). At Hagan, S. rugosa occurs sporadically through the upper Trenton and in a few lime-rich samples from the Reeds- ville Shale. When present, S. rugosa often com- prises between twenty and sixty percent of the sample. Kreisa’s ‘limestone interval’ represents maximum transgression and lowest disturbance frequencies in the history of the Martinsburg basin (Kreisa 1981); final basin-filling is foreshadowed in the return to clastic-dominated sedimentation above the ‘limestone interval’. The S. rugosa community does not recur in these upper Martinsburg clastics.

The Onniella sp. 3lR. fracta community (4) differs significantly from community ( 1 ) only in the substitution of the new Onniella and Rafines- quina species as dominant taxa and the addition of numerous bivalves. This community alternates with community (5) in clastics in the upper portion of the Martinsburg.

The small ramose bryozoanlHebertellalZ. modesta community ( 5 ) is one of the most consistently and readily identifiable clusters in Q-mode dendrograms from the individual sections. This community always first appears above Kreisa’s ‘limestone interval’ with a return to clastic-dominated sedimentation. R. fracta, Onniella sp. 3,


and bivalves are also fairly common in this community.

The Lingulalbivalve-dominated community (6) occurs at Catawba Mt., Narrows, and Walker Mt., associated with highly bioturbated, fine to very fine-grained sandstones at the tops of the sections. This community also occurs in fine- grained clastics at the base of the Catawba section. Orthorhynchula linneyi is associated with Lingula at Walker Mt.; gastropods are rare ac- cessories at several sections. Lingula is an infaunal organism capable of adjusting burrow position to deal with sudden changes in bottom stability and unpredictable environmental conditions. Modem lingulids are at least passively tol- erant of reduced salinities (Rudwick 1970; Chems 1979; Emig 1981), and lingulids are clas- sically identified with high-stress, nearshore environments (Elias 1937; Craig 1952; Ziegler et al. 1968).

Martinsburg samples containing only abundant Lingula may represent fluctuating salinity conditions (Ferguson 1963; Bretsky 1970), but deeper than intertidal (Richards 1972). Appearance of a mixed Lingula-Orthorhynchula fauna suggests nearshore environments with near normal salinities. Few known modern or fossil articulate brachiopods have been associated with undisputedly brackish water environments (Hyman 1959; Rudwick 1970). Some Recent Terebratalia have been found living in salinities as low as 25%0 (Thayer 1974) and Fiirsich & Hurst (1980) suggest that some articulates may have (had) greater tolerances for salinity fluctuations than previous- ly accepted, but these appear to be the excep- tions. The low diversity of articulates in the Lin- gulalbivalve community and associated lithologic evidence support a marginal marine interpretation for this environment.

No Lingulalbivalve community is found at Ha- gan. There is evidence of shoaling at the top of the Reedsville Formation at Hagan, but very nearshore environments equivalent to those found at Catawba Mt., Narrows, and Walker Mt. do not occur until some distance into the overly- ing Sequatchie Formation.

Ordination-produced gradient. - Associations produced by two-way cluster analysis are repro- duced in certain views of ordination space as diffuse, often interpenetrating ‘clouds’ of points grouped about a center or stretched along an axis. Gaps between clouds may be prominent: Lingula-dominated clusters commonly plot as

distinct regions on ordination diagrams (Fig. 8B). Bivalve clusters are often segregated from other clouds in one or more views of ordination space, but may overlap slightly with Lingula- or brachiopod-dominated clouds in at least one plane. Articulate brachipod clusters exhibit the most overlap, usually penetrating bivalve or other articulate brachiopod clouds. This pattern (distinct Lingula, slight overlap of bivalve with Lingula or articulates, and broad overlap of articulate brachiopod clouds) can be predicted from Markov analysis diagrams (Fig. 7).

The order in which the associations occur in the Markov-produced sequence is also repro- duced by ordination, suggesting the gradient is real. The Martinsburg faunal gradient is distin- guishable on species-level ordination plots, but is sometimes obscured by a combination of factors, including a strong stratigraphic component. Ab- sence of Lingula and the low abundances of bivalves further obscure the species-level ordination at Hagan. The Hagan plot is principally an ordination of associations at the offshore, open- shelf end of the environmental gradient.

Narrows (Fig. 8B) best illustrates the corre- spondence between Markov and ordination-derived gradients for species-level ordinations. Axis 1 is primarily a carbonate (1eft)lclastic (right) axis ordinating the open-shelf brachiopod associations; stratigraphic position plays a secon- dary role. The gradient is most clearly exhibited on axis 2: Lingula-dominated samples form a cluster (Q-mode cluster M, see Table 1) at the top of axis 2, a bivalve-dominated cloud of samples (Q-mode cluster L) is mid-way on axis 2. The offshore end of the gradient complex is occupied by several articulate brachiopod clusters distinguished by position along axis 1. The vari- ability in both endpoint composition and arrangement of sample clusters in ordination space reflects some measure of the complexity of the environmental gradient being dealt with in the Martinsburg.

Ordinations using genus-level sample composition eliminate the stratigraphic overprint and best illustrate the gradient. Hagan and Catawba Mt . exhibit the Lingula-bivalve-brachiopod sequence along axis 1, Walker Mt. and Narrows along axis 2; the axis occupied by the primary gradient is a function of which pair of samples exhibits maximum dissimilarity.

Mean variable position. - Environmental inter- pretations of ordination axes for each section are


further substantiated by ordination plots of mean variable position (MVP). MVP diagrams plot average ordination position of variables, R (in this case, R = genus), in Q-mode space. For example, on the MVP plot for axes 1 and 2 at Narrows (Fig. 9), Lingula occupies a MVP at the upper end of axis 2; crinoids are found most often at the lower end of axis 2, along with Onniella and Sowerbyella. Crinoids, and all known echinoderms, require normal marine salinities, and do not inhabit brackish water environments. Bivalves occupy a central position on axis 2. Axis 1 is defined by Sowerbyella (left) and HebertellalRafinesquina (right). M V P thus sub- stantiates interpretation of a nearshore to open- marine-shelf gradient for axis 2, and a clastic tolerance or, perhaps, a fine-grained clastic and carbonate versus coarse clastic substrates gradient for axis 1.

Mean variable position can help clarify gradients where one taxon is particularly wide-rang- ing. Bivalves are abundant in many collections from Catawba Mt. and appear in many ordination and two-way clusters. Fig. 9 documents the ‘most common’ position of bivalves in the ordination: on the right side of axis 1, immediately to the left of the position occupied by Lingula, as would be predicted in an onshoreloffshore (high stress to normal marine) interpretation for Ca- tawba axis 1. Axis 2 on the Catawba MVP diagram separates encrusting bryozoans, Prasopora, and Onniella from bivalves, and appears to represent a substrate stability gradient: high stability at the top, more mobile substrates near the bottom of the axis.

Conclusions While it is possible to recognize classical, Peter- sen-type communities in the Martinsburg using cluster analysis (Table l ) , this ‘discrete unit’ approach to community paleoecology can impose discontinuities on the faunal data. The result is a loss of information on the true nature of interre- lationships among the species.

Studies of Recent faunas indicate that independently distributed species populations are the ecological ‘norm’. Approaching the distribution of these populations as a continuum using gradient analysis, avoids artificial subdivision of totally intergrading distributions, yet permits discontinuities to emerge were present. This is concep- tually different from defining communities a

priori. Species associations that may be identified using gradient analysis remain segments of a continuous spectrum of species distributions, they merely reflect a particular set of environmental conditions (position along gradient) to which a number of species happen to be adapted.

The subjectivity involved in arranging cluster- defined communities along a gradient is also a drawback: the investigator not only defines the gradient, but must also choose where along that gradient to place each community. Ordination techniques introduce some subjectivity, but it arises from attempts to interpret factors controlling the gradient, not from attempts to create the gradient itself.

Two gradient techniques were applied to Mar- tinsburg faunal data: ordination and Markov chain analysis. Both techniques reveal the same basic associations of organisms as those defined by traditional cluster analysis, but ordination and Markov analysis permit arrangement of these associations along one or more interpreted environmental gradients. And, because ordination does not distort intersample relationships, it becomes possible to track small-scale, sample-to- sample changes in species populations, hence in position along these gradients. This, in turn, makes it possible to seek explanation for fluctuations in species distributions in parameters to which organisms are more sensitive than sediments, such as salinity or temperature, even where there are no apparent differences in lithology among samples.

Of the two gradient techniques examined, Markov analysis is less satisfying than ordination for several reasons. Perhaps the most important is that Markov analysis requires the investigator to choose those species on which the gradient will be based. No such prejudice is necessary with ordination: all species can be considered and any gradients present emerge directly from the analysis. Markov analysis, as used here, also relies on moving average curves to produce the chain of peaks to be analyzed. Averaging data automatically results in loss of information: moving averages tend to distort information on original stratigraphic position of species. What Mar- kov analysis does do is indicate the robustness of the Martinsburg data set and provide independ- ent confirmation of the faunal gradient seen in the ordinations.

The gradient seen in ordinations of Martins- burg samples suggests that a Lingula-dominated association occupied high-stress, very nearshore


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environments on fine to very fine sand bottoms. Species found in this association include mobile forms such as Lingula, gastropods, and infaunal bivalves capable of contending with shifting substrate and environmental unpredictability. The Lingula association is not found in the Martins- burg at Hagan; final basin filling did not occur along the northern edge of the basin until deposition of the Sequatchie Formation.

The nearest approximation to a true discontinuity in the Martinsburg gradient occurs in the very nearshore end of the environmental spectrum. Lingula often composes one hundred percent of samples from high-stress, nearshore environments, and the gap between this association and the bivalve and articulate brachiopod associations from more normal marine settings is usually quite distinct, regardless of the technique

196 Dale A. Springer and Richard K. Bambach LETHAIA 18 (1985)

used to evaluate the faunas. Presence of this discontinuity is not surprising: the physical environment often changes abruptly from fluctuating conditions very near shore to the relatively stable conditions of the offshore end of the gradient.

A bivalve association occupied soft bottoms in somewhat less stressed environments, offshore of the Lingula association or less proximal to sources of sediment influx. Present lithologies include very fine sandstones and muddy siltstones; bioturbation has destroyed much of the original bedding. Ambonychia, Modiolopsis, and lschyrodonta dominate the fauna.

Brachiopod associations of typical Lower Pa- leozoic aspect occupied open-shelf settings in Martinsburg time. Rafinesquina-dominated associations occurred in areas close enough to shore or delta fronts to be subjected to low levels of disturbance and periodic episodes of clastic influx. A Sowerbyella-dominated association flour- ished in open marine areas with low disturbance frequencies and higher substrate stability, beyond the influence of terrestrial clastics. A third brachiopod-dominated association characterized by abundant Onniella, appears to have occupied both clastic and carbonate shelf bottoms wherev- er bottom stability and disturbance frequency were low to moderate. Broad overlap among the articulate brachiopod associations represents variation within the open-shelf habitat; frequency of disturbance by storms or rapid influx of clastic sediments appear to have been important factors controlling species distributions in this setting.

Results of ordination and Markov analysis suggest that no single factor controlled the distribution of Martinsburg faunas. Analysis of axes produced by ordination suggests instead a complex of interrelated physical (and perhaps biological) gradients controlling distributions of species populations. Water depth and distance from clastic source areas appear to be dominant influences; disturbance frequency, bottom stability, light intensity, and food availability are intimately related to these two factors. Biological interactions such as competition and predation undoubtedly play a role in species distribution; however, no evidence of species interdependence was seen during analysis of the Martinsburg faunas, and no attempt was made to evaluate potential importance of biological interactions among these species.

The current study supports the applicability and value of gradient analysis as a tool for evalu-

ating fluctuations in species distributions in Pa- leozoic marine benthic settings; environmental information often unavailable lithologically or distorted by classical approaches to community analysis may be accessible through use of ordination and Markov techniques. Gradient analysis is recommended as an alternative preferable to discrete community analysis whenever appropriate paleoecological data are available.

Acknowledgements. - We thank H. Frances Plants for use of her data from Catawba Mt. and J. John Sepkoski, Jr. for the Polar I1 ordination program. We also thank Ronald D. Kreisa and Marc Loiselle for many thoughtful discussions and Edward Belt and an anonymous reviewer for their helpful comments. This paper represents portions of a doctoral dissertation sub- mitted by the first author to the Department of Geological Sciences, Mrginia Polytechnic Institute and State University. Partial funding for this project was provided by the Virginia Division of Mineral Resources, a Sigma Xi Grant-in-Aid of Research, Geological Society of America grant No. 2539-79, and Amherst College. The support of these agencies and insti- tutions is gratefully acknowledged.

References Anderson, A. J. B. 1971: Ordination methods in ecology.

Journal of Ecology 59, 713-726. Bambach, R. K., Scotese C. R. & Ziegler, A. M. 1980: Before

Pangea: The Geographies of the Paleozoic World. American Scientkt 68, 2638.

Bassler, R. S . 1919: Cambrian and Ordovician Deposirs of Maryland. 424 pp. The Johns Hopkins University and Mary- land Geological Survey.

Beak. E. W. 1969: Vegetational change along altitudinal gradients. Science 165, 981-984.

Bloom, S. A., Simon, J. L. & Hunter, V. D. 1972: Animal- sediment relations and community analysis of a Florida estu- ary. Marine Biology 13, 43-56.

Bowen, Z. P., Rhoads, D. C. & McAlester, A. L. 1974: Marine benthic communities in the Upper Devonian of New York. Lerhaia 7, 93-120.

Bowin, C., Purdy, G. M., Johnston, C., Shor, G.. Lawver, L., Hartono, H. M. S. & Jezek, P. 1980: Arc-Continent colli- sion in Banda Sea region. American Association of Perrole- urn Geologists Bulletin 64, 8f%-915.

Bray, J. R. & Curtis, J. T. 1957: An ordination of the upland forest communities of southern Wisconsin. Ecological Mono- graph 27, 325-349.

Bretsky, P. W. 1969: Central Appalachian Late Ordovician Communities. Geological Society of America Bulletin 80, 193-212.

Bretsky, P. W. 1970: Upper Ordovician Ecology of the Central Appalachians. Peabody M u . Nut. H i s . Bull. 34, 1-150. Yale University.

Butts, C. 1940: Geology of the Appalachian Valley in Virginia. Virginia Geol. Sur. Bull. 52. 1-839.

Cherns, L. 1979: The environmental significance of Lingula in the Ludlow Series of the Welsh Borderlands and Wales. Lethaia 12, 35-46.

Cisne, J. L. & Rabe, B. D. 1978: Coenocorrelation: gradient analysis of fossil communities and its application in strati-


gaphy. Lethaia 11, 341-364. Craig, G. Y. 1952: A comparative study of the ecology and

paleoecology of Lingula. Trans. Edinburgh Geol. SOC. 115, 110-120.

Curtis, J. T. 1955: A prairie continuum in Wisconsin. Ecology

Davis, J. C. 1973: Stafidcs and Data Analysis in Geology. 415 pp. J. Wiley & Sons, New York.

Day, J. H., Field, J. G. & Montgomery, M. P. 1971: The use of numerical methods to determine the distribution of the benthic fauna across the Continental Shelf of North Caro- lina. Animal Ecology 40, 93-125.

Elias, M. K. 1937: Depth of deposition of the Big Blue (Paleo- zoic) sediments of Kansas. Geol. SOC. Am. Bull. 48, 403- 432.

Emig, C. C. 1981: Implications de donndes rdcentes sur les Lingules actuelles dans les interprktations palddcologiques. Lethaia 14, 151-156.

Ferguson, L. 1963: The paleoecology of a Lower Carboniferous marine transgression. 1. Paleontol. 36, low1 107.

Field, J. G. 1971: A numerical analysis of changes in the soft- bottom fauna along a transect across False Bay, South Afri- ca. 1. Exper. Mar. Biol. 7 , 215-253.

Fox, W. T. 1968: Quantitative paleoecologic analysis of fossil communities in the Richmond Group. J. Geol. 76,613-640.

Fiirsich, F. T. & Hurst, J. M. 1980: Euryhalinity of Paleozoic articulate brachiopods. Lethaia 13, 303-312.

Gauch, H. G., Jr. 1973a: A quantitative evaluation of the Bray-Curtis ordination. Ecology 54, 829-836.

Gauch, H. G. 1973b: The relationship between sample similarity and ecological distance. Ecology 54, 61rM22.

Gauch, H. G. & Whittaker, R. H. 1972: Comparison of ordination techniques. Ecology 53, 868-875.

Gemborys, S. R. 1974: The structure of hardwood forest eco- systems of Prince Edward County, Virginia. Ecology 55, 614-621.

Gleason, H. A. 1926: The individualistic concept of the plant association. Bull. Torrey Bot. Club 53, 7-26.

Goff, F. G. & Cottam, G. 1967: Gradient analysis: the use of species and synthetic indices. Ecology 48, 793-806.

Goodall, D. W. 1954: Objective methods for the classification of vegetation, 111. An essay in the use of Factor Analysis. Austral. 1. Bot. 2 , 304-324.

Goodall, D. W. 1962: The continuum and the individualistic association. Vegetatio 11, 297-316.

[Humphreville, R. G. 1981: Stratigraphy and Paleoecology of the Upper Mississippian Bluefield Formation. Unpublished Master’s Thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia. 323 pp.]

Hyman, L. 1959: The Invertebrates: Smaller Coelomate Groups. 783 pp. McGraw-Hill, New York.

Johnson, R. G. 1962: Interspecific association in Pennsylva- nian fossil assemblages. J. Geol. 70, 32-55.

Johnson, R. G. 1971: Animal-sediment relationships in shallow water benthic communities. Mar. Geol. 11, 93-104.

[Kreisa, R. D. 1980: The Martinsburg Formation (Middle and Upper Ordovician) and related facies in southwestern Vir- ginia. Unpublished Ph.D. Dissertation, Virginia Polytechnic Institute and State University, Blacksburg, Virginia. 355 pp.]

Kreisa, R. D. 1981: Storm-generated sedimentary structures in subtidal marine facies with examples from the Middle and Upper Ordovician of southwestern Virginia. J. Sediment. Petrol. 51, 823-848.

MacDonald, K. B. 1976: Quantitative community analysis: recurrent group and cluster techniques applied to the fauna of the Upper Devonian Sonyea Group, New York. 1. Geol. 83,472499.

36, 558-566.

McBride, E. F. 1%2: Flysch and associated beds of the Mar- tinsburg Formation (Ordovician), Central Appalachians. 1. Sediment. Petrol. 32, 39-91.

McGhee, G. R. & Sutton, R. G. 1981: Late Devonian marine ecology and zoogeography of the central Appalachians and New York. Lethaia 14,27-43.

Mclntosh, R. P. 1967: The continuum concept of vegetation. Botan. Revs. 33, 130-187.

[Miller, A. I. 1981: Gradients in nearshore marine mollusc assemblages, Smuggler’s Cove, St. Croix, U.S. Virgin Is- lands. Unpublished Master’s Thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia.]

Momson, D. F. 1976 Multivariate Statistical Techniques. 2nd ed., 415 pp. McGraw-Hill, New York.

Orlaci, J. 1975: Multivariate Analysis in Vegetation Research. 276 pp. Junk, The Hague.

Peterson, C. G. 1913: On the distribution of the animal communities on the sea bottom. Reports Danirh Biological Sta- tion 22:7.

Phillips, D. L. 1978: Polynomial ordination: field and comput- er simulation testing of a new method. Vegetatio 37, 129-140.

Pielou, E. C. 1975: Ecological Divers@. 165 pp. Wiley-Inter- science, New York.

[Plants, H. F. 1977: Paleoecology of the Martinsburg Forma- tion at Catawba Mountain, Virginia. Unpublished Master’s Thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia. 217 pp.]

Rader, E. K. & Ryan, J . J. 1965: Martinsburg Formation in west-central Virginia. Virginia Minerah 11, 32-34.

Richards, R. P. 1972: Autecology of Richmondian brachiopods (Late Ordovician of Indiana and Ohio). J. Paleontol. 45, 386-405.

Rodgers, J. 1971: The Taconic orogeny. Geol. SOC. Am. Bull. 82, 1141-1178.

Rudwick, R. J. S. 1970 Living and Fossil Brachiopods. 199 pp. Hutchinson, London.

[Rust, R. R. 1968: Conodonts of the Martinsburg Formation (Ordovician) of Southwestern Virginia. Unpublished Ph.D. Dissertation, The Ohio State University, Columbus. 189 pp.]

Scotese, C., Bambach, R. K., Barton, C., Van Der Voo, R. & Ziegler, A. M. 1979: Paleozoic base maps. 1. Geol. 87, 217- 277.

Shaffer, B. L. & Wilke, S. C. 1965: The ordination of fossil communities: an approach to the study of species interrela- tionship and community structure. Michigan Acad. Arrr & Letters Papers 50, 199-214.

Shanrnugam, G. & Lash, G. G. 1982: Analogous tectonic evolution of the Ordovician foredeeps, southern and central Appalachians. Geology 10, 562-566.

Sokal, R. R. & Sneath, P. H. A. 1963: Principles of Numerical Taxonomy. 359 pp. W. H. Freeman & Co., San Francisco.

[Springer, D. A. 1982: Community gradients in the Martins- burg Formation (Ordovician), southwestern Virginia. Un- published Ph.D. Dissertation, Virginia Polytechnic Institute and State University, Blacksburg, Virginia. 288 pp.]

Thayer, C. W. 1974 Salinity tolerances of articulate brachiopods. Abstr. Geol. SOC. Am. Bull. 6 , 80-81.

Thorson, G . 1957: Bottom communities (sublittoral or shallow shelf). Geol. Soc. Am. Mem. 67:l. 461-534.

Valentine, J. W. 1%9: Patterns of taxonomic and ecological structure of the shelf benthos during Phanerozoic time. Pa- laeontology 12, 684-709.

[Walker, L. G. 1967: Stratigraphy of the Ordovician Martins- burg Formation in southwestern Virginia. Unpublished Ph.D. Dissertation, Harvard University. 201 pp.]

Whittaker, R. H. 1956 Vegetation of the Great Smoky Moun- tains. Ecol. Monogr. 26, 1-80.

13 - Lethaia 3/85


Whittaker, R. H. 1%7: Gradient analysis of vegetation. Biol.

Whittaker, R. H. 1975: Communiries und Ecosystem. 2nd ed.,

Ziegler, A. M. 1965: Silurian marine communities and their environmental significance. Nurure 207. 270-272.

Ziegler, A. M., Cocks, L. R. M. & Bambach, R. K. 1968: The composition and structure of Lower Silurian marine communities. Lethaiu 1 , 1-27.

Revs. 42, 207-264.

385 pp. Maanillan, New York.

gradient versus cluster analysis of fossil - cornell college

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