STATISTICAL ANALYSIS
Multivariate Analysis: Cluster Analysis
Introduction. Cluster analysis arranges groups into a hierarchical, branching structure called a dendrogram. There are two steps in cluster analysis. First, a similarity matrix is calculated using one of numerous formulas. Then the clustering procedure is applied successively to build up a hierarchy of increasingly large clusters. (Gauch, 1982)
Analysis and Results. I performed cluster analyses on data from the C Seam of each San Miguel lignite sequence, using the CLUST program written by J.J. Sepkoski, Jr. and J. Sharry, and formatted for personal computer by W. C. Parker. Only taxa present at 1.5% (rounded to 2%) or more in at least one level were included in the analyses. This cut-off point was chosen empirically; more taxa created results that were more difficult to interpret. According to Gauch (1982), "Rare species are usually deleted from a data matrix prior to multivariate analysis...The occurrence of rare species is usually more a matter of chance than an indication of ecological conditions (p. 213-214)."
To utilize cluster analysis, data were first converted into similarity matrices for both taxa and samples. I used the [Pearson product moment] correlation coefficient option included in the SIMIL program, also written by Sepkoski and Sharry and formatted for the P.C. by W.C. Parker. This method uses a relatively complicated formula to determine the similarity matrix:
where i and j represent two columns of the data matrix, k represents the rows, and Xik represent the datum in the kth row of the ith column (Kovach, 1989).
Boulter and Hubbard (1982) used the Pearson Product method to determine similarity matrices for cluster analysis in conjunction with a paleoecological study of Eocene palynomorphs from Britain's Hampshire Basin. They explained that their results were successfully interpreted because the Pearson Product similarity matrix is based on the rank order of taxon abundance rather than on the number of specimens. The method allows the cluster dendrogram to display commonalities based on the mutuality of variation rather than the amplitude of variation. Because rank order and not raw data is used to create the matrix, no transformations are necessary. Kovach (1989) used an environmentally defined Cretaceous palynomorph sequence to compare cluster diagrams generated using a variety of similarity techniques. He found rank order methods to be superior for clustering palynological data because they minimize random variation.
I ran the CLUST program using all three available options; these included weighted and unweighted pair groups with arithmetic averaging, and complete linkage. The results from the three methods were similar, with only one or two taxa clustered in different areas of the dendrograms. Only the results of the arbitrarily chosen weighted pair group arithmetic averaging option are presented here. As an example, the cluster diagram from
Sequence C is shown in Text-Figure 21; abbreviations are given in Table 6. The remaining cluster diagrams are given in Appendix 2.
In order to discern whether taxon clusters in all seven analyses were repeated in the different palynomorph sequences, I constructed a line at the +0.5 coefficient of association level in the cluster diagram printouts; this division yielded easily compared units of one to six taxa. These resulting clusters are shown in Table 7. The most obvious common cluster includes Momipites coryloides, Nyssa, and Rhoipites angustus. These three taxa are linked above the 0.5 level in Sequence H. In sequences B, C, F, and G, M. coryloides (Momipites sp. in sequence B) clusters with either Nyssa or R. angustus above the 0.5 level, and, in the next closest cluster, with the remaining of the three taxa at a lower coefficient of association. In Sequence E, M. corlyloides links with the other two taxa in the next higher cluster. R. angustus and Nyssa cluster together above the 0.5 level in sequence A, but are negatively correlated with M. coryloides. The coefficient of association between these three taxa is zero or negative in sequence D.
Cupuliferoipollenites is not linked at the +0.5 level with any other taxon in sequences B, C, D, G, and H. In sequence A, it is linked with another small tricolporate, Siltaria, and with Cupaneidites, a relatively rare taxon. In sequence E, it is linked with Momipites microfoveolatus. In sequence F, it is linked with seven taxa, including Siltaria, and M. microfoveolatus. Cupuliferoipollenites has a negative association with Momipites coryloides in all of the sequences.
Text-Figure 21. Dendrogram for Pearson product cluster analysis, Sequence C (C Seam) taxa. Abbreviations are given in Table 6.
Table 6. Abbreviations used in reciprocal averaging plots.
A Arecipites columellus
Ag Araliaceoipollenites granulatus
Ai Ailanthipites
Al Alangiopollis
Ap Arailiaceoipollenites profundus
Cd Cupuliferoidaepollenites
Ch Chrysophyllum
Ci Cicatricosisporites
Ck Cyrillaceaepollenites kedvesii
Cm Cyrillaceaepollenites megaexactus
Cp Cupanieidites orthoteichus
Ca Caprifoliipites tantulus
Cu Cupuliferoipollenites
Cv Cyrillaceaepollenites ventosus
Cy Cyrillaceaepollenites sp.
F Foveotricolporites
Fs Fraxinoipollenites (Small)
Hs Horniella (Small)
Hl Horniella (Large)
I Ilex spp.
La Laevigatosporites
Li Liliacidites vittatus
Lt Liliacidites tritus
Ly Lygodiumsporites adriennis
Mc Momipites coryloides
Mm Momipites microfoveolatus
Mo Monocolpopollenites
N Nyssa
P Polypodiisporonites
Qi Quercoidites inamoense
Table 6. Continued.
Qm Quercoidites microhenricii
Ra Rhoipites angustus
Rl Rhoipites latus
Sa Sabal
Si Siltaria
T Tetracolporopollenites
Vt Verrutricolporites cruciatus
Table 6. Continued.
San Miguel
Sequence A Sequence C Sequence D
A1 390c C1 230c D1 10c
A2 400c C2 250c D2 20c
A3 410c C3 260c D3 30c
A4 420c C4 330c D4 40c
A5 440c C5 340c D5 50c
A6 450c C6 350c D6 60c
A7 460c C7 360c D7 80c
A8 470c D8 90c D9 100c
D10 110c
Sequence E Sequence F Sequence G Sequence H
E1 210c F1 0c G1 0c H1 40c
E2 230c F2 30c G2 10c H2 30c
E3 240c F3 40c G3 40c H3 20c
E4 250c F4 50c G4 50c H4 10c
E5 260c F5 60c G5 60c H5 0c
E6 270c G6 70c
E7 280c G7 80c
E8 290c G8 90c
G9 100c
Table 6. Continued.
Lake Somerville
Lower Seam O "Overburden Upper Seam
0l 0 1u 10
1l 10 2u 20
2l 20 3u 30
3l 30 4u 40
4l 40 5u 50
5l 50 6u 60
6l 60 7u 70
7l 70 8u 80
8l 80 10u 100
9l 90
Highwall Sequences
M1 Mini 10 S1 Seambase 1 A1 Ash 1 H0 Sequence H 0
M2 Mini 20 S2 Seambase 2 A3 Ash 3 H1 Sequence H 10
M3 Mini 30 S3 Seambase 3 A4 Ash 4 H2 Sequence H 20
M4 Mini 40 S4 Seambase 4 A5 Ash 5 H3 Sequence H 30
M5 Mini 50 S6 Seambase 6 A6 Ash 6 H4 Sequence H 40
M6 Mini 60 S8 Seambase 8
M7 Mini 70 S10 Seambase 10
M9 Mini 90
M10 Mini 100
Table 7. Clusters at the .5 level of association in the San Miguel sequences. Taxon groups are numbered from the top of the cluster dendrograms.
Sequence A; r2=.65
1. Sabal, Cicatricosisporites, Laevigatosporites
2. Liliacidites, Momipites coryloides, Arecipites
3. Cyrillaceaepollenites megaexactus, C. kedvessii, Chrysophyllum, Quercoidites inamoense, Monocolpopollenites
4. Cupaniedites, Siltaria, Cupuliferoipollenites
5. Araliaceoipollenites granulatus
6. Araliaceoipollenites profundus, Nyssa, Rhoipites latus, R. angustus, Foveotricolpites
7. Quercoidites microhenricii, small Fraxinoipollenites,
Cupuliferoidaepollenites, Liliacidites tritus, Momipites microfoveolatus
Sequence B; r2=.73
1. Rhoipites angustus, Momipites sp.
2. Nyssa, Cyrillaceaepollenites sp.
3. Cupuliferoipollenites
4. Cupuliferoidaepollenites
5. Caprifoliipites, small Horniella, Siltaria, Arecipites
Table 7. Continued.
Sequence C; r2=.43
1. Nyssa, Quercoidites inamoense, Momipites coryloides
2. Rhoipites angustus, Araliaceoipollenites granulatus
3. Tetracolporopollenites
4. Siltaria, Cupuliferoidaepollenites
5. Momipites microfoveolatus
6. Chrysophyllum, Caprifoliipites tantulus
7. Cupuliferoipollenites
8. Quercoidites microhenricii, Cyrillaceaepollenites kedvessii
9. Cyrillaceaepollenites megaexactus, Ailanthipites, Alangiopollis, Arecipites
Sequence D; r2=.47
1. Ailanthipites, Liliacidites, Laevigatosporites
2. Arecipites
3. Lygodiumsporites adriennis
4. Momipites coryloides, Cicatricosisporites, Chrysophyllum, Cyrillaceapollenites kedvesii
5. Cupaneidites, Monocolpopollenites, small Fraxinoipollenites, Rhoipites latus, Cyrillaceaepollenites ventosus
Table 7. Continued.
6. Nyssa, Verrutricolporites, Momipites microfoveolatus
7. Quercoidites microhenricii, Sabal, Cyrillaceaepollenites megaexactus
8. Quercoidites inamoense, Cupuliferoidaepollenites
9. Arailiaceoipollenites granulatus, Siltaria
10. Caprifoliipites tantulus, Rhoipites angustus
11. Cupuliferoipollenites
Sequence E; r2=.59
1. Arecipites, Lygodiumsporites adriennis
2. Cupuliferoipollenites, Momipites microfoveolatus
3. Siltaria, Cyrillaceapollenites sp., Tetracolporopollenites
4. large and small Horniella, Ilex media, Caprifoliipites tantulus, small Fraxinoipollenites, Cyrillaceaepollenites? ventosus, Cupuliferoidaepollenites
5. Chrysophyllum, Araliaceoipollenites granulatus,
Quercoidites inamoense
6. Araliaceoipollenites sp., Rhoipites angustus, Nyssa
7. Momipites coryloides
Sequence F; r2=.61
1. Rhoipites, Momipites coryloides
2. Nyssa, Quercoidites inamoense
3. small Fraxinoipollenites,
4. Quercoidites microhenricii, Cupuliferoidaepollenites
Cyrillaceapollenites sp., Liliacidites, Arecipites, Sabal
5. Ailanthipites, Siltaria, Tetracolporopollenites,
Table 7. Continued.
Chrysophyllum, Araliaceoipollenites granulatus, Caprifoliipites tantulus, Cupuliferoipollenites, Momipites microfoveolatus
Sequence G; r2=.39
1. small Fraxinoipollenites, Polypodiisporonites,
Caprifoliipollenites tantulus
2. Cyrillaceaepollenites sp.
3. Cupuliferoipollenites
4. Tetracolporopollenites, Cupuliferoidaepollenites
5. Araliaceaepollenites granulatus
6. Chrysophyllum
7. Cyrillaceaepollenites? ventosus
8. Arecipites
9. Rhoipites angustus, Quercoidites inamoense, small Horniella, Momipites coryloides
10. Nyssa
11. Siltaria, Quercoidites microhenricii, Momipites
microfoveolatus, Liliacidites, Cicatricosisporites
Sequence H; r2=.53
1. Nyssa, Momipites coryloides, Rhoipites angustus, Quercoidites microhenricii, Momipites microfoveolatus
2. Cupuliferoidaepollenites, Liliacidites
3. Chrysophyllum, Araliaceoipollenites granulatus, Siltaria, Quercoidites microhenricii
4. Arecipites
5. Cupuliferoipollenites
Table 7. Continued.
Lake Somerville; r2=.64
1. Laevigatosporites
2. Cyrillaceapollenites sp.
3. Chrysophyllum brevisulcatum
4. Caprifoliipites tantulus, Salixipollenites parvus
5. Cupuliferoipollenites, Cupuliferoidaepollenites
6. Rhoipites angustus, Nyssa
7. Momipites coryloides
8. Arecipites columellus
9. Rhoipites latus, Liliacidites vittatus
10. Momipites microfoveolatus, Polypodiisporonites
In most cases, where spores are present in adequate quantities for analysis, they are associated with monolete ("palm") pollen. The exception to this phenomenon is sequence D where, although Laevigatosporites is linked to Liliacidites, no palms or other spores are linked closely to Cicatricosisporites. "Palms" and spores are never closely linked to Cupuliferoipollenites or Nyssa, but in core D, Cicatricosisporites is linked to Momipites coryloides, and Monocolpopollenites is linked to Rhoipites angustus.
No other relationships seem to be consistently present and discernable using the clustering technique.
I also analyzed the lignite samples from Lake Somerville using the same methods. In order to decrease the larger taxon list, I included only taxa with five or more levels with over 2% (rounded). The results are shown in a cluster diagram (Text-Figure 22) and in Table 7. Nyssa and Rhoipites angustus form a cluster, but Momipites coryloides is negatively correlated with this cluster. Cupuliferoipollenites, which is linked above the 0.5 level to Cupuliferoidaepollenites, is negatively linked to both Nyssa-R. angustus and M. coryloides. The spore Laevigatosporites is negatively correlated to all other taxa, but clusters with Cicatricosisporites and Microfoveolatus when more taxa are added to the analysis. There is no link between spores and monocolpates. Polypodiisporonites is linked to Momipites microfoveolatus.
The square of the cophenetic correlation coefficient (r2) is listed for each sequence in Table 7. The r2 gives a rough estimation of the amount of variation in the similarity matrix that is reflected in the cluster diagram. An r2 of less than 0.5, which
Text-Figure 22. Dendrogram for Pearson product cluster analysis, Lake Somerville taxa. Abbreviations are given in Table 6.
occurs for sequences C (.43), D (.47) and G (.39), suggests that much of the relationship between taxa does not appear in the clusters. This suggestion implies that the results of cluster analysis for these sequences reflects only a small proportion of the information present in the similarity matrix. When cluster analyses were performed using unweighted pair-group with arithmetic averaging and complete linkage techniques included in the CLUST program, the r2 was not increased.
Multivariate Analysis: Reciprocal Averaging (Correspondence Analysis)
Introduction. Reciprocal averaging (RA) was developed by Hirschfield (1935) and Fisher (1940); Hill
(1973; 1974) introduced the method to ecologists. RA ordinates samples and species simultaneously. Initially, species ordination scores are assigned arbitrarily. Sample scores are obtained from these species scores using weighted averages. New species scores are then produced using weighted averages of the sample scores. (Weighted averages are discussed by Gauch (1982, p. 120-126.) The process is continued until the scores stabilize. The first RA axis has the property of maximizing the correlation of samples and species, so usually one or a few RA axes are adequate. Gauch (1982) and Kovach (1989) believed RA to be superior to PCA (Principal Component Analysis) in the analysis of community data sets.
According to Gauch (1982), "Ordination primarily endeavors to represent sample and species relationships as faithfully as possible in a low-dimensional space...The end product is a graph, usually two-dimensional, in which similar samples or species or both are near each other and dissimilar entities are far apart." He added: "The advantage of low-dimensionality is workability for contemplation and communication; the disadvantage is that some degree of fidelity to the data structure must be frequently sacrificed..." (p. 15).
Both PCA and RA are subject to an "arching problem." This means that, instead of a continuum of related species or sites being situated in a straight line on the graph, it forms an arch. In PCA, the arch may become involuted, so that entities which are at opposite ecological poles are brought into juxtaposition. This does not occur in RA. Gauch cited three additional faults of RA. The second axis may be a quadratic distortion of the first axis, which implies that a graph of the first vs. second axis may reflect only one axis. A second fault is that the first axis ends tend to be compressed, leading to the false interpretation that end members are closer to each other ecologically than they actually are. This latter fault would be more important to ecologists with data sets which represent individuals living in definite niches. Pollen and spore data sets consist of gametophytes which, like paleontological death assemblages, may be dispersed beyond the niche of the parent plant, and relative distances on a plot may be irrelevant considering the amount of ecological error inherent in the data. Thirdly, rare species are treated as extremely distinctive and are placed at the ends of axes.
Gauch added that points interior to the arch may represent broadly ranging species or samples with a wide range of taxa. Peripheral points may represent species with narrow distributions, or samples with only a few species.
Kovach (1988), in his study of a Cenomanian megaspore flora, stated that RA is "...particularly well suited for distinguishing single, major gradients on the first axis, although they are susceptible to domination by outlying samples..." (p. 268). He found that the use of RA on his data yielded a "...clear ecological gradient along the first axis, ranging from algal cysts, which are restricted to marine deposits, to the bilobed cuticular structures, which are only found in terrestrial deposits." (p. 256)
Analysis and Results. RA values were computed for all sequences and for the Lake Somerville lignites using the MVSP program developed by Warren Kovach. I also computed RA values for a "composite" C seam, containing all sequences except B. B was omitted because several of the taxa were lumped for counting. All RA plots are presented in Appendix 2. As was done in the cluster analysis of Lake Somerville, in order to limit the number of taxa in the composite analysis and thereby avoid confusion, only taxa with 5 or more occurrences of 2% or greater (rounded) were included.
RA values were computed using raw data, transformed data, and raw data with rare species weighted. When the two latter types were plotted using the MVSP program, the most common taxa, Cupuliferoipollenites and Momipites coryloides invariably were grouped together. Consequently, only the diagrams of RA's using raw data are presented here. Plots given are of axis 1 vs. axis 2 only. Taxon names are abbreviated on the RA plots, and these abbreviations are given in Table 6.
No clear pattern emerges from the sequence diagrams; the species are scattered and do not seem to indicate a well-defined environmental gradient. The graph for Sequence C is shown in Text-Figure 23 as an example. Table 8 describes the position of several important taxa on these graphs. In most cases, Cupuliferoipollenites lies fairly distant from Rhoipites angustus and Nyssa, with Momipites more toward the center.
In contrast, the graph from Lake Somerville exhibits a strong gradient on axis 2, with Cupuliferoipollenites and Rhoipites angustus acting as positive and negative end members respectively. Besides Cupuliferoipollenites (+2.2), Cupuliferoidaepollenites
(+1.88) scores high on this axis; most taxa score relatively low. These include Momipites coryloides
(-.47), Nyssa (-.73), and Rhoipites angustus (-.88). The monocotyledons Arecipites (-.30) and Liliacidites vittatus (-.50) also score negatively on Axis 2. Additionally, the spore taxon Laevigatosporites (+4.51) occurs outside this "gradient" and has a relatively highscore on axis 1. Cicatricosisporites and Microfoveolatosporites also score high on this axis when more taxa are included in the analysis.
The graph of the C Seam composite shows a similar gradient (Text-Figure 24). In this case, Siltaria and Rhoipites angustus are the end members of axis 2. Momipites coryloides (+0.87) and Nyssa (+1.82), in addition to R. angustus (+2.14) score high on axis 2. (Positiveness and negativeness are assigned arbitrarily to any given set of results.) Cupuliferoipollenites scores low (-.83). The monocotyledonous taxon Arecipites, however, scores low (-.60), with Cupuliferoipollenites instead of the Momipites association. Both Laevigatosporites (+4.25) and
Text-Figure 23. Reciprocal averaging (RA) plot, Sequence C (C Seam) taxa. Abbreviations are given in Table 6.
Table 8. Synopsis of untransformed RA plots.
Sequence Nyssa, Rhoipites, Cupuliferoipollenites
Momipites
A Low on axis 2, Near center on both
Nyssa with axes
R. angustus,
Momipites near
center.
B Nyssa and Low on axis 1,
R. angustus high on centered on axis 2
axis 1, widely
separated on axis 2,
Momipites near center.
C Continuum on axis 1, Very high on axis 1.
with R. angustus very
negative, Momipites
near center.
D R. angustus very low Very low on axis 1,
on axis 1, Nyssa and near R. angustus.
Momipites at positive
middle positions on
both axes.
E Nyssa and R. angustus Near center on both high on axis 1, axes.
centered on axis 2,
Momipites near center.
F Grouped together, high Relatively low on on both axes. axis 2; high on axis 1. G Nyssa and R. angustus Moderately low on
grouped together, very both axes.
low on axis 2. Momipites
Table 8. Continued.
Sequence Nyssa, Rhoipites, Cupuliferoipollenites
Momipites
at center on axis 2,
moderately high on axis 1.
H All negative on axis 1, Positive on axis 1.
Momipites closest to
center.
Somer- All low on axis 2, Very high on axis ville Momipites most towards 2.
center.
(spores form axis 1)
Compound All high on axis 1, Low on axis 2.
Momipites most toward
center.
(spores and some palms
form axis 1)
Text-Figure 24. Reciprocal averaging (RA) plot, Composite C Seam samples. Abbreviations are given in Table 6.
Cicatricosisporites (+4.22) score high on axis 1 and are not included in the "gradient."
Examining these graphs together suggests an environmental gradient with this approximate floral sequence: Cupuliferoipollenites, Cupuliferoidaepollenites, Quercoidites microhenricii-Chrysophyllum-small Fraxinoipollenites,
Araliaceoipollenites granulatus, Momipites coryloides, Nyssa, Rhoipites angustus.
Comparison of Reciprocal Averaging with Cluster Analysis
One test of whether a multivariate method yields a valid discriminate of floral associations is to compare the results of those methods used. I transferred cluster analysis groupings from the Pearson product method onto the RA analysis graph of the Lake Somerville lignite samples by drawing curved lines on the RA plot around taxa which successively clustered together (Text-Figure 25). The Pearson Product method separates out Laevigatosporites, also evident in the RA analysis. Cluster analysis is not completely successful at defining the Axis 2 continuum delineated by RA analysis; the Pearson product method separates the species which are high on RA axis two from the majority of taxa, but includes several taxa which scored around zero on Axis 2. Within the large group of taxa which have relatively similar scores low on axis 2, cluster methods pick out some taxa which were adjacent on the RA graph. Several of the cluster diagram pairings join taxa which were relatively widely separated on the RA graph, and larger order pairings do not necessarily join adjacent clusters.
Text-Figure 25. Pearson product cluster analysis groupings superimposed on RA plot of Lake Somerville taxa.
I also compared results of the two cluster analyses of the composite C seam with the RA graph (Text-Figure 26). The cluster diagram is again successful at separating the spore group and at delineating groups which score high on the second RA axis. Within the large group of taxa ranking low on the second RA axis, cluster methods often pick out taxa which are near each other on the RA graph, but larger order associations group taxa which are moderately distant on the RA plot. Cluster analysis splits off a subgroup, defined on the RA graph by adjacent taxa, containing Cyrillaceapollenites sp., C. ventosus and Sabal. Cluster analysis solidly delineates three groups which may have environmental significance: spores, a Cupuliferoipollenites-group, and a group which includes Nyssa, Rhoipites angustus, and Momipites coryloides.
Multivariate analysis of Levels (Seam C)
San Miguel Sequences. I ran both Pearson Product Cluster and Reciprocal Averaging Analyses on samples from the C seam of all San Miguel lignite sequences. A composite diagram of the methods was constructed for each sequence. Cluster dendrograms and RA plots are shown in Appendix B.
Both RA and cluster analysis of sequence A split the Cupuliferoidaepollenites-dominated basal sample off from the rest of the C seam. Multivariate techniques further divide the large group of samples from the upperpart of the seam into two parts: the two samples from the top of the seam are separated from the middle four samples which have higher Cupuliferoipollenites percentages.
Text-Figure 26. Pearson product cluster analysis groupings superimposed on RA plot of Composite C Seam taxa.
Both multivariate techniques separate the lower two samples in seam C of sequence B from the top three Cupuliferoipollenites-dominated samples. The two lower samples, one with high Nyssa percentages and the other with high Rhoipites angustus values, lie at opposite ends of axis one of the RA plot.
RA and cluster analysis of the C seam of sequence C both separate out a group consisting of the upper three Cupuliferoipollenites-dominated samples. The lower four samples are grouped into a cluster which has lower Cupuliferoipollenites percentages. Reciprocal averaging further segregates this group into subgroups on the basis of Rhoipites angustus content.
In Sequence D, the uppermost five Cupuliferoipollenites-dominated samples are grouped together by both RA and cluster analysis; sample 250 is only loosely bound to this cluster because of its large percentage of Laevigatosporites. The Momipites coryloides-dominated lower samples also cluster together, although again the Laevigatosporites-Liliacidites dominated sample 280 is only loosely associated with the others.
Values from analysis of the C seam of the E sequence do not form groups, but rather a continuum; the cluster analysis grouping generally follows a transect along the RA plot. This transect follows a dominance sequence of Siltaria-Cupuliferoipollenites-degraded small tricolporates-Araliaceoipollenites granulatus-Rhoipites angustus. The positions of Siltaria and Cupuliferoipollenites are switched in the cluster analysis sequence. In general, the basal samples are at the low Cupuliferoipollenites end of the transect. Samples with higher Cupuliferoipollenites values from the upper part of the seam are at the opposite end.
Multivariate analysis separates the uppermost Cupuliferoipollenites-dominated sample of the C seam of sequence F from the rest of the samples. Within the larger group, both methods define a group from the middle of the seam with a moderate amount of Cupuliferoipollenites and a basal group with relatively low Cupuliferoipollenites as well as higher Momipites and Rhoipites angustus percentages. Cluster analysis places the two lowest samples in the latter group, whereas RA places only the lowermost sample in that group.
Samples from the C seam of the G sequence are also segregated into two groups. The lower two samples, dominated by a mixture of Quercoidites microhenricii, Rhoipites angustus, and Momipites coryloides, are loosely connected. The other group generally has a higher dominance by Cupuliferoipollenites. Samples at 40 and 60 cm. have the highest percentage of this taxon and cluster tightly; samples at 10 and 50 cm also cluster in this group. Sample 0 with relatively large numbers of Q. microhenricii and Siltaria clusters with neither subgroup. Another subgroup, composed of samples 70 and 80 from lower in the seam, is set off by intermediate amounts of Momipites coryloides, Quercoidites inamoense, and Rhoipites angustus.
Samples from the highwall (H) sequence also cluster on the basis of Cupuliferoipollenites percentages, but the groupings are not stratigraphically continuous.
Composite Diagram. Both cluster analysis and reciprocal averaging were run for the composite sample group composed of all C seam samples, except for those from sequence B (Text-Figure 27). Many of the samples from the D sequence are strewn along RA axis 1, otherwise, the composite set forms an "ecological"
Text-Figure 27. Pearson product cluster analysis groupings superimposed on RA plot of Composite C Seam samples.
continuum along axis two. The D samples differ in that they contain significant amounts of spores as well as Liliacidites.
Cluster analysis splits the composite set into two groups. On the right side of the composite diagram, the lower D sequence samples cluster in a small group with basal samples from sequences F and G and from the top of sequence A. A larger group to the left consists mostly of samples spread along the second RA axis. At the positive end lies a cluster formed from samples from the lower parts of sequences C and E, and two sequence H samples. These samples have fairly high levels of Rhoipites angustus. Two cluster groups lie at the negative end of axis two. One group contains several samples from the upper parts of sequences C and D. These samples are dominated by Cupuliferoipollenites. The other group contains most of the non basal samples from sequence G as well as some samples from sequence H. Cupuliferoipollenites also dominates these samples, but Siltaria percentages are higher. The sample at the base of sequence A, highly dominated by Cupuliferoidaepollenites, clusters in neither group.
Lake Somerville. The spore dominated 10U (1u) sample (Text-Figure 28) is segregated both by reciprocal averaging, where it appears alone at one end of the first axis, and by cluster analysis, which "clusters" the sample alone. A well-defined continuum occurs along RA axis two between Cupuliferoipollenites dominated samples, and levels with a mixed flora.
Cluster analysis further separates a cluster with relatively high percentages of Liliacidites, including samples 0L, 50L, and 30U within a cluster of many samples at the "mixed flora" end of axis 2. All these
Text-Figure 28. Pearson product cluster analysis groupings superimposed on RA plot of Lake Somerville samples.
"mixed flora" samples have relatively high Momipites coryloides percentages.
Discussion. Most of the multivariate diagrams of individual C seams split the samples into an upper and lower group on the basis of Cupuliferoipollenites percentages. Two sequences are without definite clusters, but a continuum with high Cupuliferoipollenites percentages nevertheless exists.
The composite C seam multivariate diagram (Text-Figure 27) indicates that there are three types of seam base floras. One group contains spectra from sequence D, F and G; another from A; and the third from C and E. Slightly to conspicuously higher Momipites coryloides percentages is the most obvious delineator of the first group. The unusually high basal percentage of Cupuliferoipollenites sets apart the second. The third group consists of samples with higher Rhoipites angustus percentages.
The continuum along RA axis one indicates that an environmental gradient may be represented within the samples. There is no reason to believe that all palynomorph sequences would travel the same temporal path through the gradient. The multivariate plot indicates that they did not do so: some seamtops and seambases are positioned at the ends of axes, but others are not. In any case, two basic continuums are suggested. One continuum features high Cupuliferoipollenites grading to high Rhoipites angustus or Momipites coryloides percentages. The other continuum changes gradually from this R. angustus- Cupuliferoipollenites based assemblage to one dominated by spores and Liliacidites.
This same scheme is present in the Lake Somerville sequence. Samples with high Cupuliferoipollenites percentages lie at one end of axis two, with samples high in Momipites coryloides and other taxa at the other end. One sample high in spores clusters at the other end of axis one.
Efficacy of the Multivariate Technique
Multivariate techniques tended to substantiate and reinforce the floral and sample relations which I noticed in the samples. Both observation and multivariate techniques found the oppositional relationship in the San Miguel lignites and at Lake Somerville of samples high in Cupuliferoipollenites and samples high in Rhoipites angustus and Nyssa. Observation showed a strong difference between basal samples with high M. coryloides and those with high R. angustus percentages. Observation did not show the importance of Cupuliferoipollenites-dominated samples with high percentages of Siltaria. Neither did it indicate the importance of Liliacidites and spores as an oppositional assemblage.
Because both methods indicated the same end member taxa, however, observation and multivariate analysis divided individual C seam sequences in the same general manner.
Horizontal Sequences
Few experienced palynologists interpret "pollen" diagrams literally. The factors which potentially lead even Quaternary palynologists astray are many, and are described by Moore and Webb (1978). For a palynologist interested in generalized or regional interpretations, one of the pitfalls is the lateral, local variations in pollen spectra. These variations are particularly evident in wetlands where much of the pollen rain is local: modern pollen percentages vary considerably within a few meters in surface samples from wetlands. For example, Griffin's (1975) study of the Red Lake peatlands of Minnesota shows differences of 30 and 42% for Acer and 30 and 312% for Betula (not included in Griffin's pollen sum) in samples taken about 12 m apart in larch forest.
For a palynologist interested in microenvironmental change, however, these lateral changes are advantageous. Birks and Gordon (1985) comment:
Answers to the question of where particular plant communities grew in the past are critically dependant on our knowledge and understanding of the complex processes of plant transport and dispersal and on the choice of site, particularly in size and potential pollen source area...Pollen sequences from several sites within a small geographical area are required to detect patterns of vegetational differentiation related, for example, to altitude,...and to climate and topography...
Alternatively, transect of pollen diagrams across a site either in one...or two...dimensions may permit the detection of spatial differentiation in the occurrence of particular pollen assemblages and hence particular plant communities...(p. 9).
The vertical palynomorph sequences from San Miguel are fortunately representative of a paleotransect, and the palynomorph diagrams do show some striking differences. This opportunity for interpretation of local paleoenvironments will be exploited in the chapter entitled "Paleoecology."
Sampling Methods. In order to estimate of the amount of lateral variability in the San Miguel lignite, I collected horizontally spaced samples from the highwall section in addition to those vertical samples designated as Sequence H (Text-Figure 11). Ten "Mini" samples from the base of the C seam were collected at 10 cm intervals beginning with the basal sample of sequence H. Additional basal samples ("Seambase") were taken at points coinciding with Sam Gowan's "flags," representing intervals of approximately 6 m. A third sample set ("Ash") was taken from lignite immediately above the ash layer pictured by Gowan (1985), also taken at approximately 6 m intervals coinciding with Gowan's "flags." The samples were processed and counted according to procedures outlined in the Methods chapter. Some samples had statistically inadequate pollen counts; these data were not used.
Methods and Results: Introduction. Palynomorph diagrams of the three horizontal sequences are shown, with confidence intervals, in Text-Figures 29-32. These diagrams indicate that percentage values vary systematically rather than randomly along the traverse. There is some indication from these curves that Momipites varies conversely with Rhoipites angustus. The variation may be due, as suggested by Turner et al. (1989), to differential pollen preservation, or to systematic differences in pollen deposition within microenvironments. In any case, the large horizontal variations in percentages in the closely-spaced San Miguel lignite samples imply that many vertical changes in the palynomorph curves are likely to be meaningless.
I used several different statistical methods to determine whether taxon proportions in these horizontal samples varied more or less than the percentages in the vertical sequences.
Methods and Results: Confidence Intervals. The concept behind confidence intervals is discussed by Moore and Webb (1978) and by Birks and Gordon (1985).
Text-Figure 29. 95% confidence intervals, Mini samples.
Text-Figure 30. 95% confidence intervals, Seambase samples.
Text-Figure 31. 95% confidence intervals, Ash samples.
Text-Figure 32. 95% confidence intervals, Sequence H.
By necessity, only a small proportion of the palynomorphs in a given sediment sample can be counted. The percentages derived from these counts are in reality estimates of the true proportion of each taxon present in the sample. A 95% confidence interval is constructed around the counted, or "estimated" value; there is a 95% chance of the "true" value being included within this interval. A "true" value would have a 99% chance of being included within a 99% confidence interval, which is much wider than a 95% confidence interval. Sample size is an important component of these equations; the confidence limit narrows as sample size increases.
Confidence intervals have been used by a number of palynologists to evaluate the statistical validity of the variations in pollen curves. In a pioneering work, Maher (1972) included confidence intervals for every taxon present in his pollen diagram of Quaternary sediments from Colorado. Maher explained how to interpret his diagrams: "In general, if the point estimate or estimate of either sample is included in the 95% confidence interval of the other, the two samples will not be found to differ significantly at the 0.05 level. But if the point estimate of neither of the samples is included in the 0.95 confidence interval of the other, the two samples will be found to differ significantly at the 0.05 level." This differs from Moore and Webb's (1978) explanation, which implies that taxon percentages with confidence intervals that do not overlap are statistically different at that level of confidence.
Maher unfortunately did not interpret his profiles in the light of confidence intervals, but his superpositions of confidence intervals on pollen profiles imply that many of his intrazonal variations are not statistically significant. Since then, only a few authors have included confidence intervals in pollen diagrams. It remains, however, a useful technique for comparing counts of different sizes and for discerning the importance of percentage fluctuations.
p is the proportion of grains counted and n is the pollen sum.
This equation is used for taxa within the palynomorph sum.
Confidence intervals have been superimposed on the diagrams for the three horizontal sample sequences and the vertical sequence (Text-Figures 29-32). These diagrams are not particularly helpful in determining whether the vertical changes in Sequence H are valid. In each of the highwall horizontal traverses, no major taxon emerges statistically equal in all samples. In the Mini sequence, where samples are only 10 cm. apart, palynomorph spectra seem no more likely to be statistically the same than in the Seambase sequence where the samples are 6 m apart. When 95% confidence intervals for the vertical highwall sequence are plotted, most major taxa are likely to have some statistically different data points; conversely, other taxa such as Nyssa have percentages which are statistically the same through the sequence H diagram. The use of 95% confidence intervals indicates that there are statistically significant differences between samples in both the vertical and horizontal sequences, but does not indicate the relative importance of these differences.
Methods and Results: Multivariate Analysis. One of the few papers which examines variability over a short distance is by Turner et al. (1989). These authors compared pollen spectra from two Holocene blanket peat sections from the North York Moors of England. The sections were dug 30 cm. apart, and samples were removed every cm. After pollen analysis, Turner and her colleagues separated the profiles into zones, figured taxon averages for each zone, and grouped these averages using DECORANA (detrended correspondence analysis), a multivariate technique similar to reciprocal averaging. They found that "...the differences between the two diagrams are small relative to the differences between zones." (p. 416)
I ran both reciprocal averaging (correspondence analysis) and Pearson product moment cluster analysis for all the highwall samples. A composite diagram of these two methods is shown in Text-Figure 33.
There are basically two groups in the composite diagram. One large group contains mostly samples from the two basal sequences as well as from the lower part of the vertical highwall sequence (H). The other much smaller group contains samples from the ash layer and two vertical sequence samples, as well as one sample from the Seambase series. The latter group is defined by higher levels of Cupuliferoipollenites. Within the larger group, most of the Mini (10 cm.) samples are located close together on the RA plot, as are most of the Seambase samples. Cluster analysis groups some Mini samples closer to Seambase samples. Both methods cluster one Ash sample with the Mini samples. These changes include not only fluctuations between two
Text-Figure 33. Results of Pearson product cluster analysis superimposed on Reciprocal Averaging plot, Highwall samples.
statistically equivalent percentages, but also changes of larger magnitude. Conversely, the successful grouping of horizontal sequences, as well as the results of Turner et al, suggests that changes which occur in the vertical sequences and which are consistent between sequences can be interpreted as "real." Larger scale percentage changes which occur in only one sequence likely represent "real" changes in the local vegetation. Grouping the samples of a given sequence using multivariate techniques may prove useful for determining valid large scale vegetational events (see the chapter on Multivariate Analysis of Samples).
Methods and Results: Running Averages. "Running averages" is a simple statistical procedure which smooths data and removes "noise" (and possibly some of the data as well) by averaging data from several adjacent levels. The formula for a three sample unweighted running average is:
P is the percent counted for sample i, k.
Running averages are not often used by palynologists. Birks and Gordon (1985) recommend against the method because they believe an a priori knowledge of the structure of the data is necessary to use this technique for primary data. Nevertheless, running averages have been used by a few palynologists; for example, Ritchie (1982) used the technique to cut out excessive noise in Quaternary pollen concentration data from the Yukon.
In this study, I have used confidence intervals of running averages of three taxa, Momipites coryloides, Cupuliferoipollenites, and Rhoipites angustus, to graphically compare palynomorph variability in the eight vertical sequences through the C and D seams and through the overburden of sequence E, as well as in the closely spaced vertical "Mini" samples from the San Miguel highwall. Several types of running averages exist. I used a three sample running average because it provides the minimal amount of "smoothing" necessary for the confidence intervals of all three taxa in samples from the horizontal "Mini" sequence to at least touch one another and be considered identical. I also averaged the sums used in the calculation of confidence intervals. Results of the averaging of the C seam of the sample sequences are summed up in Table 9.
Within the horizontal sequence (Text-Figures 34-36), averaged percentages of Rhoipites angustus exhibit the most variability; the 95% confidence intervals of samples "60" and "90" barely coincide with one another (Text-Figure 36). Larger segments of the confidence intervals of the other two taxa coincide with those from all other samples. Percentages of R. angustus are unusually high in these seam base samples.
The 95% confidence intervals for taxa in the clastic overburden samples are most uniform (Text-Figures 37-39), more so than for taxa in the horizontal samples. Overlap of confidence intervals is substantial for all three taxa, but is greater for Cupuliferoipollenites and Momipites coryloides than for Rhoipites angustus. For all three taxa, there are no samples which cannot be considered "statistically the same" as any other sample.
In contrast, variability is greater for the vertical sequence (Text-Figures 40-63) in all the lignite seams analyzed than for the Highwall horizontal sequence. The variability is most noticeable for
Table 9. Synopsis of confidence intervals of running averages, vertical sequences.
Seam Momipites Cupuliferoipollenites Rhoipites A S S
B S S
C S S
D S S
E S S S
F S
G S S S
H S
B S S S
C S S S
D S S
E S S
F S S S
G S S S
S="Statistically Significant"
Text-Figure 34. 95% confidence intervals for running averages of Cupuliferoipollenites percentages, horizontal highwall "Mini" samples.
Text-Figure 35. 95% confidence intervals for running averages of Momipites coryloides percentages, horizontal highwall "Mini" samples.
Text-Figure 36. 95% confidence intervals for running averages of Rhoipites angustus percentages, horizontal highwall "Mini" samples.
Text-Figure 37. 95% confidence intervals for running averages of Cupuliferoipollenites percentages, overburden of Sequence E.
Text-Figure 38. 95% confidence intervals for running averages of Momipites coryloides percentages, overburden of Sequence E.
Text-Figure 39. 95% confidence intervals for running averages of Rhoipites angustus percentages, overburden of Sequence E.
Text-Figure 40. 95% confidence intervals for running averages of Cupuliferoipollenites percentages, C seam of Sequence A.
Text-Figure 41. 95% confidence intervals for running averages of Momipites coryloides percentages, C seam of Sequence A.
Text-Figure 42. 95% confidence intervals for running averages of Rhoipites angustus percentages, C seam of Sequence A.
Text-Figure 43. 95% confidence intervals for running averages of Cupuliferoipollenites percentages, C seam of Sequence B.
Text-Figure 44. 95% confidence intervals for running averages of Momipites coryloides percentages, C seam of Sequence B.
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Text-Figure 45. 95% confidence intervals for running averages of Rhoipites angustus percentages, C seam of Sequence B.
Text-Figure 46. 95% confidence intervals for running averages of Cupuliferoipollenites percentages, C seam of Sequence C.
Text-Figure 47. 95% confidence intervals for running averages of Momipites coryloides percentages, C seam of Sequence C.
Text-Figure 48. 95% confidence intervals for running averages of Rhoipites angustus percentages, C seam of Sequence C.
Text-Figure 49. 95% confidence intervals for running averages of Cupuliferoipollenites percentages, C seam of Sequence D.
Text-Figure 50. 95% confidence intervals for running averages of Momipites coryloides percentages, C seam of Sequence D.
Text-Figure 51. 95% confidence intervals for running averages of Rhoipites angustus percentages, C seam of Sequence D.
Text-Figure 52. 95% confidence intervals for running averages of Cupuliferoipollenites percentages, C seam of Sequence E.
Text-Figure 53. 95% confidence intervals for running averages of Momipites coryloides percentages, C seam of Sequence E.
Text-Figure 54. 95% confidence intervals for running averages of Rhoipites angustus percentages, C seam of Sequence E.
Text-Figure 55. 95% confidence intervals for running averages of Cupuliferoipollenites percentages, C seam of Sequence F.
Text-Figure 56. 95% confidence intervals for running averages of Momipites coryloides percentages, C seam of Sequence F.
Text-Figure 57. 95% confidence intervals for running averages of Rhoipites angustus percentages, C seam of Sequence F.
Text-Figure 58. 95% confidence intervals for running averages of Cupuliferoipollenites percentages, C seam of Sequence G.
Text-Figure 59. 95% confidence intervals for running averages of Momipites coryloides percentages, C seam of Sequence G.
Text-Figure 60. 95% confidence intervals for running averages of Rhoipites angustus percentages, C seam of Sequence G.
Text-Figure 61. 95% confidence intervals for running averages of Cupuliferoipollenites percentages, C seam of Sequence H.
Text-Figure 62. 95% confidence intervals for running averages of Momipites coryloides percentages, C seam of Sequence H.
Text-Figure 63. 95% confidence intervals for running averages of Rhoipites angustus percentages, C seam of Sequence H.
Cupuliferoipollenites. In graphs from each of the seams analyzed for variability, at least two samples exist for which the confidence intervals of Cupuliferoipollenites do not coincide. This means that all values of Cupuliferoipollenites cannot be considered statistically identical throughout any vertical sequence through any seam examined palynologically at San Miguel. In three of the C seam sequences and five of the D seam sequences averaged Momipites coryloides percentages are not statistically identical at all levels. Conversely, in five sequences from the C seam and one sequence from the D Seam, all M. coryloides values are statistically the same. Likewise, averaged Rhoipites angustus percentages are not all statistically identical in five of eight C seam sequences and in five out of six D seam levels.
For these two taxa, the more complete sequences with their greater number of samples are more variable and confidence intervals are less likely to overlap in all samples. The relatively complete C seam of sequence D, in which all Rhoipites angustus averages can be considered statistically the same, has a very low percentage of that taxon at all levels, and no R. angustus peak at the base. Instead, there is a Momipites coryloides peak; this is one of the few C seam sequences in which M. coryloides variation is statistically significant using this method.
Discussion. The confidence interval analysis of running averages underlines the extreme variability of palynological samples, and the need to consider confidence intervals in assessing trends within a vertical sequence. Assuming that the variability revealed in the closely-spaced horizontal samples reflects the effects of sampling rather than a vegetational gradient, the variability of vertical sequences must be evaluated against this standard. These results do suggest that some groups of samples and taxa are more variable than others: the vertical overburden sequences are less variable than either the horizontal or vertical lignite sequences and the vertical lignite sequences are the most variable of all three sequence types, supporting the interpretation of a replacement of lignite-forming communities through time.
The palynological input into the overburden was largely regional, whereas the input into the lignite samples contained more palynomorphs with a local origin (Darrell, 1973). This contrast in variability between the clastic overburden samples suggests that palynomorphs deposited in water are more thoroughly mixed before deposition than palynomorphs deposited in peats. Jones and Gennett (1991) presented a clastic palynomorph flora from the Claiborne Group which, like the overburden sequence, exhibited very few substantial changes throughout the extent of the formation. The palynological uniformity of these two Eocene clastic sequences suggests that no significant climatic changes took place during their depositions. It is, consequently, easy to rationalize a regionally derived palynoflora with no statistically significant changes throughout a hundred or so meters of overburden.
The statistically significant changes in the three taxa which occur in the lignite are probably "real" and were caused by changes in the lignite flora, and not by regional floral variations. Because the percentages of all taxa are affected by the influx of all other pollen taxa, and because it is impossible to measure palynomorph influx without dating the lignites, it is difficult to determine what proportion of each palynomorph taxon is local. It should, however, be reasonable to assume that the statistically significant changes in the vertical sequences are representative of actual changes which occurred in the local vegetation.
Diversity
Introduction. Nichols and Traverse (1971) indicated that the number of palynomorph taxa present in a given sample, represented by the Simpson Diversity Index, may differ with depositional environment. Simpson diversity measures both the number of taxa in a sample (richness) and the relative abundance of these taxa. The index "...expresses the probability that two specimens taken at random belong to the same species." (Margalef, 1978, p. 252.) It has the disadvantage of deleting taxa which have a single occurrence a given sample (Nichols and Traverse, 1971).
The formula for the Simpson Diversity Index is:
where Ni is the number of individuals in species i, N is the total number of individuals in the sample, and s is the number of species (Margalef, 1978).
Methods and Results. I calculated Simpson Diversity Indices for each sequence from the San Miguel lignites, as well as for Lake Somerville, with the MVSP program developed by Warren Kovach at the University College of Wales using the option which transformed the species data using log base 10, in order to emphasize rare taxa. These indices, plotted against depth, are shown in Text-Figures 64-82.
Text-Figure 64. Simpson diversities for Sequence A.
Text-Figure 65. Simpson diversities for Sequence B, A to B seams.
Text-Figure 66. Simpson diversities for Sequence B, C seam.
Text-Figure 67. Simpson diversities for Sequence B, D seam.
Text-Figure 68. Simpson diversities for Sequence C, C seam.
Text-Figure 69. Simpson diversities for Sequence C, D seam.
Text-Figure 70. Simpson diversities for Sequence D.
Text-Figure 71. Simpson diversities for Sequence E, overburden.
Text-Figure 72. Simpson diversities for Sequence E, seams A and B.
Text-figure 73. Simpson diversities for Sequence E, C seam.
Text-Figure 74. Simpson diversities for Sequence E, D seam.
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Text-Figure 75. Simpson diversities for Sequence E, E seam.
Text-Figure 76. Simpson diversities for Sequence F, C seam.
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Text-Figure 77. Simpson diversities for Sequence F, D to E seam.
Text-Figure 78. Simpson diversities for Sequence G, C seam.
Text-Figure 79. Simpson diversities for Sequence G, D seam.
Text-Figure 80. Simpson diversities for Sequence H.
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Text-Figure 81. Simpson diversities for Lake Somerville, upper seam.
Text-Figure 82. Simpson diversities for Lake Somerville, lower seam.
In Sequences B, C and D, diversity decreases conspicuously in the top half of the C Seam. In other sequences, this decrease is not as clear, but, in all sequences, low diversities in the seam correlate with high Cupuliferoipollenites percentages. Plots from the D seam show several diversity dips, which correspond to
high values of dominant taxa, including Cupuliferoipollenites.
Text-Figures 83 and 84 show the relationship between the maximum palynomorph percentage per level and Simpson diversity in the San Miguel sequences and at Lake Somerville. Sequence B is omitted because the castolite mounting medium may have affected pollen identification, and because small tricolporates were lumped together for counting in some levels. Regression analysis shows an adjusted coefficient of determination (r2) of .92 for the San Miguel samples and .96 for Lake Somerville samples. This indicates that over 90% of the variation in the diversity index is explained by variation in maximum palynomorph percentage. and suggests that these variables are closely related.
I have also compared diversity to ash and sulfur data where it is available. The San Miguel and Lake
Somerville lignites show a different relationship between palynomorph diversity and percent ash (Text-Figures 85 and 86). In the Lake Somerville samples (Text-Figure 86), diversity is weakly dependent (r2=.43) on ash content. It is clear, however, from the graphs that the two samples with high percentages (over 50%) of ash have relatively low diversities. Samples with less than 50% ash content have both relatively high and low diversities. The regression line relating ash percentage and diversity in the San Miguel samples (Text-Figure 85) has an r2 of .13. This low figure
Text-Figure 83. Simpson diversity vs. maximum palynomorph percent in the San Miguel lignites.
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Text-Figure 84. Simpson diversity vs. maximum palynomorph percent in the Lake Somerville lignites.
Text-Figure 85. Ash vs. Simpson diversity in Sequence E of the San Miguel lignites.
Text-Figure 86. Ash vs. Simpson diversity in the Lake
Somerville lignites.
indicates that there is very little dependency between these variables, but regression is not always the best method of defining ecological relationships (Gauch, 1982). In the San Miguel samples, levels with relatively high (>30%) ash percentages have uniformly high content diversities, whereas diversities in samples with low (<30%) ash percentages are both high and low. These disparities may reflect different sources for the ash in the lignites; a high ash from a clastic source would introduce a greater variety of palynomorphs than a high ash contact from a volcanic source. This would imply that the source of ash in the San Miguel lignites was largely clastic. Unfortunately, there is insufficient data on which to base this conclusion.
The plot of sulfur percentage against diversity for Sequence E of the San Miguel lignite (Text-Figure 87) suggests that there is little or no relationship between these two variables, yielding a "statistically insignificant" r2 of .2. In this sequence, samples with low total sulfur have relatively high diversities; samples with sulfur values of >2% have either high or low diversities. In the sulfur vs. diversity plot for Sequence E, the r2 is again statistically insignificant at -.12. The only low diversity values occur in the interval between 1.5 and 2.5 % sulfur. In the sulfur vs. diversity plot for Sequence E, the r2 is also statistically insignificant at -.14, and no segregation of low and high values is visible.
Text-Figure 88 shows palynomorph diversities from other Gulf Coast Eocene sites. In each case, many fewer samples were analyzed than at San Miguel. Samples from the marine Middle Eocene Stone City Formation (Jones and Gennett, 1991) yield uniformly high diversities, as do clastics from the Middle Eocene (?) section at Wittsburg Quarry in Arkansas (Gennett, 1990). These clastic sites also have a comparatively low range of diversities. Upper Eocene lignite samples from the Gibbons Creek Mine (Gennett et al., 1986) have lower and more variable diversities than the clastics. The one Yegua (Uppermost Middle Eocene) lignite sample, mentioned in this study,
Text-Figure 87. Sulfur vs. Simpson diversity in Sequence E of the San Miguel lignites.
Text-Figure 88. Simpson diversities of samples from some Eocene Gulf Coast sites.
has a diversity within the range of the clastic samples from San Miguel.
The clastic overburden samples from Sequence E of the San Miguel lignites have an average diversity of .822; if the lowermost sample at 130 cm, which is adjacent to the A seam, is removed from consideration, the average diversity is .843. The average diversity for four parting samples is .835. These averages are lower those than the .898 value for estuarine samples from Wittsburg Quarry. The San Miguel clastic averages are also lower than the .892 average from the marginal marine Stone City Fm.
The average diversity of all samples from Lake Somerville is .740; the average for C seam lignites from San Miguel is .769; and for D seam lignites from San Miguel, the average is .748. These average diversities are lower than those of these clastics from San Miguel, although the diversities for some lignite samples are as high as for the clastic samples.
Diversity indices, although commonly used by paleozoologists, have not been regularly employed by palynologists. Birks and Gordon's (1985) text on the use of statistics in Quaternary pollen analysis makes no mention of diversity indices. Some qualitative information on diversity is available for modern environments. Darrell (1973) pointed out that there were "more morphotypes" deposited in the bay sedimentary environments of the Mississippi Delta than in the marsh environments. Both environments have "fewer morphotypes with more individuals per morphotype" than channel, levee, distributary mouth bar, delta front, and prodelta environments. I computed the Simpson diversity for the uppermost, probably modern, sample from a peat in a small pond in Wyoming (Gennett, 1977) surrounded by douglas fir steppe to be only .07, with only 7 taxa. Jacobs (1982), counting at least 200 grains per sample, found as few as 8 taxa in soil samples from pine forest and as many as 20 taxa in mangrove swamp in Northern Mexico.
Biological diversity is dependent on numerous factors such as environmental stability and resource availability (Dodd and Stanton, 1981). Additionally, transport has a substantial effect on fossil palynomorph diversity because pollen and spores act as silt size particles. By consequence, diversity for a given site may be further determined during the depositional process by the relative input from the various transport agents: wind, water, and gravity. A sedimentary site receiving clastic input from a large river would theoretically have a higher diversity than one with no stream input. A large, open site such as a marsh, receiving input both from the local marsh communities and from the forests in the region, would have a higher diversity palynomorph assemblage than a small pool within a closed forest (Moore and Webb, 1978).
Because numerical diversity has not been well studied for palynomorphs, it is difficult to make significant conclusions from the figures given here. However, within the samples for which data are available, ash and sulfur have little influence on diversity. A high ash content due to clastic influx from fluvial systems would hypothetically imply a higher diversity of fluvially transported palynomorphs. This is not the case at either San Miguel or Lake Somerville, and this fact suggests that volcanic ash may comprise at least some of the ash in the lignites.
Palynomorph Concentration
Introduction. Palynomorph concentration is often used by Quaternary palynologists to estimate the actual number of palynomorphs present in a given amount of sediment. If the sedimentation rate is constant or if the sequence is well-dated, palynomorph concentration provides palynomorph spectra in which the quantity of each taxon is calculated independently in relation to other taxa. If preservation is good, each spectrum in an approximation of palynomorph input at the sample site at the time of deposition.
Concentration is rarely used by Pre-Quaternary palynologists because it is cumbersome (Frederiksen, 1985; Farley and Traverse, 1990) and difficult to interpret. To compare concentration spectra, it is necessary to know, at least in relative terms, how much time was necessary to accumulate the sediment in each sample. Time references are rare in Pre-Quaternary palynomorph sequences, and deposition rates commonly vary even when sediment type does not (Moore and Webb, 1978). In fact, a recent paper by Farley and Traverse (1990) suggested that higher concentrations of specific taxa in different parts of a sediment sequence might be used to indicate clastic depositional environments.
Methods and Results. Palynomorph concentration was calculated using the formula given by Maher (1972):
11,300 + 400 Grains Palynomorph Sum
C= __________________________ X _____________________
Lycopodium Grains Counted Volume of Sediment C represents the palynomorph concentration. 11,300 + 400 grains is the average number of grains in a Lycopodium tablet.
Palynomorph concentration for Cupuliferoipollenites, Momipites coryloides, Nyssa, and Rhoipites angustus were then determined by substituting the taxon count for Palynomorph Sum in the formula.
Histograms for Sequences C and F are shown in Text-Figures 89 and 90). Histograms were also constructed for four important taxa: Cupuliferoipollenites, Momipites coryloides, Nyssa, and Rhoipites angustus (Text-Figures 91-98). In both cores, total concentrations range up to 8,000,000 grains/cc, although, especially in the F sequence, many levels have total concentrations of less than 1,000,000. Concentration levels are variable. Except for higher concentrations in the upper part of the C seam of Sequence C, no pattern is apparent.
Cupuliferoipollenites concentrations are highest and most variable in both sequences, and values in general follow the pattern of total concentration. These concentration values are much higher (over 500,000 grains/cc) in the upper portion of the C seam of the C sequence than in the lower portion (less than 250,000 grains/cc); these concentrations correspond to percentages that rise to almost 65%. In the F sequence, Cupuliferoipollenites concentration values are less than 250,000 grains/cc throughout the seam, corresponding to maximum percentage values of around 40%. In the D seam, Cupuliferoipollenites concentrations are also tied to percentages. In the C sequence, maximum concentrations corresponding to higher percentages are much greater (over 500,000 grains/cc) than for the F sequence (less than 500,000 grains/cc except in one sample).
Momipites coryloides concentrations are on the average lower than Cupuliferoipollenites concentrations. M. coryloides concentrations are lower in the F sequence, which has higher M. coryloides percentages (to 55%) than the C sequence (to 20%).
Text-Figure 89. Total palynomorph concentrations for Sequence C.
Text-Figure 90. Total palynomorph concentrations for Sequence F.
Text-Figure 91. Cupuliferoipollenites concentrations for Sequence C.
Text-Figure 92. Cupuliferoipollenites concentrations for Sequence G.
Text-figure 93. Momipites coryloides concentrations for Sequence C.
Text-Figure 94. Momipites coryloides concentrations for Sequence F.
Text-Figure 95. Nyssa concentrations for Sequence C.
Text-Figure 96. Nyssa concentrations for Sequence F.
Text-Figure 97. Rhoipites angustus concentrations for Sequence C.
Text-Figure 98. Rhoipites angustus concentrations for Sequence F.
Rhoipites angustus concentrations are also low, but spike to high values in two samples, 330C in Sequence C and 50D in Sequence F. The R. angustus percentages for these two samples are higher than for adjacent samples but cannot be described as spikes.
Concentration values for Nyssa are on the average the lowest of the four, and are especially low for Sequence F. Small peaks in concentration occur in sample 310D of sequence C and at 50D in sequence F.
The likelihood of a variable rate of sediment deposition (Moore and Webb, 1978) make these concentration sequences difficult to interpret. The higher concentrations in Sequence C, however, may indicate an overall slower rate of deposition in that part of the swamp than in the area where Sequence F was deposited. Concentrations are higher in the levels that are dominated by Cupuliferoipollenites than in those dominated by Nyssa, Rhoipites angustus, and Momipites coryloides. These high, variable concentrations suggest that Cupuliferoipollenites produced relatively large numbers of pollen grains and was present near the site of peat deposition. The lower, less variable concentrations of M. coryloides may indicate that this palynomorph came from outside the swamp.