Principal components and correspondence analyses of quantitative data from a Jurassic plant bed

Review of Palaeobotany and Palynology, 28 (1979): 273--299

273

© Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands

PRINCIPAL COMPONENTS A N D CORRESPONDENCE A N A L Y S E S OF QUANTITATIVE D A T A FROM A JURASSIC PLANT BED

ROBERT A. SPICER ' and CHRISTOPHER R. HILL

Department of Botany, Imperial College, London SW7 2AZ (Great Britain) Department of Palaeontology, British Museum (Natural History), Cromwell Road, London SW7 5BD (Great Britain) (Received April 27, 1978; revised version accepted March 14, 1979)

ABSTRACT Spicer, R.A. and Hill, C.R., 1979. Principal Components and Correspondence Analyses of quantitative data from a Jurassic plant bed. Rev. Palaeobot. Palynol., 28: 273--299. Quantitative data on species abundance of plant fossil remains were collected from a plant bed of Middle Jurassic age exposed at Hasty Bank in North Yorkshire, England. A histogram of the data is compared with the results of two methods of multivariate ordination analysis: Correspondence Analysis (= Reciprocal Averaging or Reciprocal Ordering) and Principal Components Analysis. A main component of the pattern of distribution of the plant remains is an apparent control by lithology, though more data are required for interpretation of this in terms of individual depositional or ecological factors. Pattern was also detected in terms of associations between detached organs originally belonging to the same kind of whole plant, but only when the data were appropriately restricted. Because of the complexity of factors governing deposition and sampling of allochthonous plant remains, there is a good deal of apparently meaningless variation in the data, and "useful" pattern was detected more readily when the counts were transformed logarithmically. This suggests that the field use of simple, essentially logarithmic, scales for estimating density may sometimes be preferable to counting, besides being relatively quick and easy in practice. INTRODUCTION

Analysis o f quantitative data for ecological purposes is now a firmly established practice in palaeobotany, particularly in studies of Quaternary pollen and certain other microfossils. There have, however, been few palaeoecological analyses o f plant megafossil material, perhaps partly because quantitative sampling o f megafossils is relatively laborious -- requiring excavation and counting of numerous plant fragments within large volumes of rock. Secondly, except for a u t o c h t h o n o u s floras -- in which the plants were deposited where t h e y grew -- there is often uncertainty about the quality of the evidence. This is because in m o s t fossil floras -- termed allochthonous -the uprooted plants, or organs abscissed or broken off from them, were transported and finally deposited some distance away from their place of ' The sequence of authors was determined by the toss of a coin.

274 growth. Numerous processes were involved in this transport, for example fragmentation followed b y sorting and mixing of the plant fragments according to their size and density. These processes tended to obscure the original (community) composition of the vegetation, often imposing a pattern of their own {Hill, 1974b; Krassilov, 1975; Spicer, 1975). Thus the depositional assemblages of fossils actually excavated in the field may bear scant resemblance to the original communities as they existed in the once living vegetation. Despite this uncertainty a number of pioneering quantitative studies on plant macrofossils were published in the early part of the present century (e.g. Davies, 1908, 1920, 1921, 1929; Dix, 1933; Chaney, 1924; Thomas, 1925). There are also more recent studies, notably by Gordon and Birks (1972), H.H. Birks (1973), H.J.B. Birks (1976), and Watts and Winter (1966), and also b y Scott (1977) who gives a useful summary of the literature. Rather superficial assessments in terms of " c o m m u n i t i e s " were frequently reached b y the earlier workers, b u t their contribution nevertheless was highly significant: they showed for the first time that numerical variation -at least potentially of ecological interest -- can occur within plant deposits. Our current work attempts to revive the optimistic approach of these pioneers though the aims of the present paper are limited. Based on detailed sampling from one locality we aim firstly to re-establish that statistical pattern, potentially of ecological interest, can be exhibited by a pre-Quaternary fossil plant deposit. Secondly we examine two methods of multivariate analysis which m a y be used for illustrating this kind of pattern, and the results are compared on an empirical basis with a histogram. We do not a t t e m p t at this stage fully to interpret the results in ecological terms as this complex problem deserves separate treatment and further data will be needed. The m e t h o d s chosen are applied to data collected from the allochthonous components of the Middle Jurassic plant bed exposed at Hasty Bank in the North Yorkshire Moors National Park, England. To our knowledge this is the first detailed quantified sampling of a plant deposit of Mesozoic age. CHOICE OF STATISTICAL METHODS The range of multivariate m e t h o d s currently used by ecologists provides two main approaches, classification and ordination, and the relative merits of these have been much discussed in the literature (e.g. Greig-Smith, 1964; Lambert and Dale, 1964). Classification involves arranging stands or observations into groups, the members of which share certain characteristics setting them apart from the members of other groups. The application of this approach to allochthonous fossil assemblages is debatable, because the continuous nature of pattern in such assemblages is likely to be strongly marked, owing to complex interactions between the various factors involved in their transport and deposition. Blackith and R e y m e n t {1971, p. 236) note that comparable sedimentological data often contain a strong element

275

of apparently random variation ("noise"), and Hill (1974b) has shown similarly, from work on an allochthonous plant assemblage, that a large variation in species abundance is to be expected between adjacent stands at a single horizon. The use of classification techniques under these circumstances, where the m e t h o d would inherently force the data into discontinuous groupings, could lead to erroneous conclusions. Alternatively, ordination techniques, such as the two methods used in the present work, do not assume discontinuities in the data. They attempt instead to order the stands relative to one or more axes, so that the position of a stand conveys the maximum a m o u n t of information a b o u t its species composition (Greig-Smith, 1964). Thus a continuum is implied b u t this does n o t preclude the existence of discontinuities within the sample population. If present they will be displayed by the technique. Ordination therefore seems more suited than classification for displaying the distributional pattern of plant remains within fossil assemblages. DETAILS OF THE ORDINATION METHODS USED

Principal Components Analysis (PCA ) Principal Components Analysis has been used for some time in studies of living vegetation (e.g. Gittins, 1965). It has proved particularly suitable for detecting the occurrence of environmentally dependent pattern when n o t previously suspected. Although normally presenting a continuum that may sometimes be assigned to an environmental gradient, it will also detect discontinuities, and thereby group the data, if this is justified. The clustering may then be used as a basis for dividing the sampled vegetation into communities, each exhibiting a more homogeneous structure. Despite a theoretical requirem e n t for linearity of data structure (Orloci, 1975), like many other multivariate methods, PCA is remarkably robust and will still give a fair result on data not fulfilling this requirement. Indeed it is this robustness which commends its application to the analysis of plant fossil assemblages, where sampling is likely to be subject to constraints of exposure and lithology and where the statistical distribution of the abundances of individuals may depart from normality. In simple terms, the rationale of PCA may be thought of as follows. If only two species were present in the sample their occurrence within a stand (quadrat) would define its position on a two-dimensional graph, with the axes representing some kind of quantification of the two species. Similarly, if three species occurred then a three-dimensional graph could be constructed. The same procedure can be mathematically expressed for any number of stands and any number of species, with the result that a swarm of stands (or if stands are used as the axes, species) exist in multi-dimensional hyperspace. Clearly this can only be grasped conceptually if the distribution of stands or species can be summarised b y projection on to three dimensions or less. This unfortunately introduces distortion, b u t the distortion can be reduced if the

276

projected axes are aligned with the principal axes of variation within the multi
Correspondence Analysis (CA) Correspondence Analysis (Benzecri, 1973; M.O. Hill, 1974), also referred to as Reciprocal Ordering (Orloci, 1975) and Reciprocal Averaging (M.O. Hill, 1973), is an eigenvector m e t h o d of ordination very closely related to PCA (M.O. Hill, 1973, 1974; David et al., 1974) b u t which overcomes some of its limitations since the rationale is developed differently. In simple terms CA may be thought of as follows (based on Hill, 1973). A species (row) by stand (column) data matrix is constructed and an arbitrary set of species starting scores between 0 and 100 is allocated. The allocated scores should in practice preferably reflect what is suspected as being the main gradient of change, as a good initial choice reduces the a m o u n t of calculation required. Using this set of starting scores, a set of stand scores is obtained by averaging stand data in terms of the estimated species scores. These scores are then rescaied between 0 and 100. From this set of stand scores a new set of species scores is again derived, b y averaging, and also rescaled between 0 and 100. This procedure continues until, after a certain number of iterations (dependent on the initial species scores), the species and stand scores stabilise. The resulting vectors are a uni-dimensional ordering of the stands and species derived simultaneously from the data matrix. The second axis may be obtained by using a set of scores which were fairly near to the final scores of the first axis. These scores are then adjusted b y subtracting a multiple

277 of the first axis and the iterations continued until a new set of scores stabilise. These become the second axis. The third and subsequent axes are similarly derived. Strictly speaking, Correspondence Analysis should only be used with contingency table data, but continuous data can be analysed by dividing the ranges of the variates into a number o f discrete pieces. If the pieces are small enough, an approximation to the continuous case is achieved (Naouri, 1970; M.O. Hill, 1974). David et al. (1974) and JSreskog et al. (1976) suggest dividing the elements o f the data matrix by the sum of all the elements in the matrix. The resulting proportions may be interpreted as probability values and the matrix becomes a contingency table in the sense of Fisher (1940). Unlike PCA the simultaneous derivation of stand and species scores results in ordinations which are directly comparable. The species score is equal to the average stand score for those stands in which the species occur (but rescaling so t h a t the total range is 0 to 100) and the stand score is equal to the average species score for those species which occur in the stand (again rescaling between 0 and 100). This duality leads to a generally more straightforward interpretation than is possible with PCA, in terms of the relative abundance o f species within the stands, by simply overlaying the species plot on the stand plot. Although there is a risk of the argument becoming circular the species would n o t be used to interpret the stand plot in terms of causes of variation but only to characterise clusters of floristic gradients if they arise from the ordination. M.O. Hill (1973) makes the point that where there is a long floristic gradient it will always be presented linearly along the first axis of an ordination using CA, whereas with PCA, "where there is a long and strong floristic gradient, stands which are extreme on the first axis of the ordination need not be extreme on the floristic gradient, and vice versa". The species scores derived by CA are also corrected for species abundance, unlike unstandardised PCA ordinations. In view of these theoretical considerations CA might be expected to be a rather more effective m e t h o d than PCA for the analysis of plant fossil assemblages. It should be noted that the eigenvalue quoted for the axes on a CA ordination is n o t a measure of the variance extracted by the axes (as it is in PCA). It is a measure of the relationship between the stand and the attribute ordinations (M.O. Hill, 1974). Orloci (1975) considers it as "an indication of the conceptual difficulty with which the quadrats (stands) can be ordered based on the species (attribute) scores." A Fortran IV computer program to carry out CA was written by Dr. A.J. Morton, Imperial College, London, based on the hand calculation m e t h o d of M.O. Hill (1973). This program was modified to generate three axes. Presentation of the plots follows that of Pemadasa et al. (1974). COLLECTION OF THE DATA (Fig.l) The field data were collected from the Hasty Bank main plant bed (NZ 567 037), which outcrops at the base of the Lower Deltaic (= Saltwick

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279 Formation) rocks of the Yorkshire Middle Jurassic, England. This plant bed, a b o u t 7 m thick, has yielded a diverse flora of 90 species and is composed of two main lithologies: siltstones and claystones. The siltstones form the upper part of the bed and grade laterally into a sandstone-filled stream channel (Fig.l), they u n d o u b t e d l y themselves represent part of the same channel (Hill, 1974b). They lie disconformably on the dark-coloured claystones which form the lower part of the bed. A vertical section, section 1, through the main plant bed was sampled quantitatively by C.R. Hill in 1972, and the data from this section are here summarised in the form o f a histogram (Fig. 2). The section was excavated from t o p to b o t t o m to give a contiguous series of sample volumes (stands), and the plant remains in each volume were uncovered (and their species abundances thus counted) b y splitting along the bedding planes with a knife. The volumes excavated in the siltstone were (50 × 50) cm 2 in area, plane to the bedding, X 10 or 20 cm in depth, perpendicular to the bedding, whilst in the claystone smaller volumes were sampled, 25 × 25, × 10 or 20 cm, owing to the great abundance of plant fossils there. The sample volume sizes were based on a preliminary study to determine minimal representative size. The numerous limitations of the sampling procedures are discussed in detail by C.R. Hill (1974b). In the preparation o f the histogram and ordination data the counts from the sample volumes were multiplied X 1, × 2, × 4, or X 8, thus referring them uniformly to volumes of (50 × 50 X 20) cm 3. To test the results from section 1, t w o other sections, sections 2 and 3, were also examined quantitatively, b u t in these the abundance was visually estimated on a scale of ten points (1--10) (Table I). The sample volumes excavated were kept uniformly at 50 × 50 cm in area regardless of lithology. RESULTS T h e histogram (Fig.2)

C.R. Hill (1974b) recognised three main assemblages at Hasty Bank, based on histograms of data from the three sampled sections. These assemblages reflect the similarities of sections 2 and 3 with section 1 and for this reason only the section 1 histogram is presented here. The assemblages were defined as follows, the numbers given next to the species names being the identification numbers used in the ordination. Siltstone Assemblage. This is limited to the siltstone and is characterised by the following species: 4 Marattia anglica (Thomas) Harris 18 N ilsso n ia s y llis Harris 39 Nilssoniopteris vittata (Brongniart) Florin

280

TABLE I Comparison of the abundance/dominance scale of Hill (1974b) with the equivalent solely abundance scale used here Description of abundance and d o m i n a n c e

S c a l e of Hill

No. of f r a g m e n t s ~300

A b u n d a n t : easily the m o s t a b u n d a n t s p e c i e s in the s a m p l e

300

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100--300

V e r y c o m m o n : w i t h o t h e r s p e c i e s of similar a b u n d a n c e

100--300

C o m m o n : t h e o n l y s p e c i e s o f this a b u n d a n c e in the s a m p l e

50--100

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Claystone Assemblage. This is limited to the claystone where it is characterised by:

7 Clathropteris obovata Oishi Cladophlebis harrisii van Cittert Nilssonia tenuinervis Seward Pseudoctenis lanei Thomas Ctenozamites cycadea (Berger) Schenk Sphenobaiera gyron Harris et Millington Brachyphyllum crucis Kendall B. mamillare Brongniart Hirmerella sp. nov. Hill (in prep. -- female cone of Brachyphyllum crucis)

12 17 22 24 45 48 49 53

As the histogram results are compared below with those from the ordinations, it is worth considering in some detail the way in which Hill's assemblages were defined. He was attempting to make general divisions of the histogram pattern by eye. From Fig. 2, however, it may be seen that

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285 there is no clear division which is uniform for all species, and that for some, for example Sagenopteris colpodes and Nilssonia kendalliae, there is little or only gradual change in abundance throughout the section. Hill was able to make a general division only b y being selective, particularly b y emphasising qualitative presence and absence of species in the siltstone versus claystone, e.g. of Marattia anglica. This qualitative difference is also associated with a quantitative one, for there is a generally lower abundance and diversity in the siltstone compared to the claystone (for example the abundances of Pachypteris papillosa and Ptilophyllum pectinoides). Such quantitative change may be caused by differing rates of sedimentation and extents of compaction in the two lithologies, much as might be expected in any siltstone contrasted with a claystone, simply reflecting their grain sizes. It is unlikely therefore to be of ecological interest. The point of relevance to the present discussion is that it is an arithmetical pattern in the data which corroborates Hill's division into two main assemblages. A different way of summarising the data is to recognise a continuum of decline in diversity and abundance from the b o t t o m of the section upwards, for example in the abundance of Nilssonia kendalliae and Ptilophyllum pectinoides. Like Hill's a t t e m p t to divide the data into assemblages, such a conclusion is selective of the evidence, ignoring species limited to the siltstone. We therefore believe that the balanced view of Fig.2 is that it shows two kinds o f pattern depending on the species considered. Firstly there is the qualitative limitation of certain species to the siltstone, which correlates with a generally lower abundance and diversity in this lithology compared to the claystone, and secondly there is a continuum of decline in abundance and diversity from the b o t t o m of the section to the top. Fig. 2 also shows that there is a strongly marked sub-pattern in section 1, occurring within the main assemblages. Hill made no a t t e m p t to base subassemblages on this since, unlike the main pattern, it did not prove consistent with the sub-pattern of sections 2 and 3.

Principal Components Analysis (Figs.3--5, 11) In an unstandardised PCA ordination (Fig.3A), the variance accounted for by the first two axes is high, 74% of the total, and this suggests that the data are well represented in two dimensions. The plot shows a grouping of the siltstone stands distinct from the claystone ones whilst the subpattern in the claystone is illustrated spectacularly. However, there is little indication of gradual change through the section, or that the claystone can in any w a y be considered a discrete assemblage comparable with the siltstone. Orloci (1966) has noted that species-poor stands in PCA ordinations tend to ordinate in a tight bunch compared to species-rich ones, and this appears to be the case in Fig.3A. The species-poor siltstone stands ordinate in a bunch whilst the species-rich claystone stands are widely dispersed. Thus the plot appears to be dominated by the diversity of the claystone flora and fails to give a

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Fig.3. Axes I and II of PCA stand plots based on species abundance counts from Hasty Bank, section 1. The stands (sample volumes) are numbered consecutively 1--25 from top to bottom of the section (Fig.l). A. Unstandardised counts, percent variance axis I, 42%; axis II, 32%. B. Standardised to zero mean and unit variance, percent variance axis I, 18%; axis II, 10%. Open circles represent stands from the siltstone and the solid circles stands from the claystone.

balanced illustration o f the pattern. This is n o t to say, o f course, that it fails to give a useful insight into the structure of the data. To compensate for response o f PCA to large variations in species diversity, the data can be standardised. This is achieved by subtracting from each observation the mean o f the set o f data and then dividing by the standard deviation. In this way a new data matrix is derived in which the variables have a mean o f zero and a variance = 1 (unit variance). Such a procedure reduces the overall variance in a set of observations and gives equal weighting to all variables. Standardisation thus "adjusts" certain c o m p o n e n t s of the data more than others, for example those species with a high variance are divided by a correspondingly high standard deviation, and under certain circumstances such adjustment clearly may n o t be desirable. It may be acceptable, however, w h e n differences in abundance between stands are brought about by factors other than those o f direct palaeoecological significance - - for example, by differing rates o f c o m p a c t i o n o f sediment both during and after deposition.

287

When the Hasty Bank data are standardised (Fig.3B) the stands plotting positively on axis I have comparatively high abundances of otherwise rare species, such as Clathropteris obovata, Nilssonia tenuinervis, Pseudoctenis oleosa Harris, Ctenis kaneharai Yokoyama, and Cycadolepis hypene Harris. They also include the more ubiquitous species such as Pachypteris papillosa (Thomas et Bose) Harris, Nilssonia kendalliae Harris, Ptilophyllum pectinoides (Phillips) Morris and Elatides thomasii Harris (1979). Stands 22--25 are separated from the rest, as are 15, 16 and 18, representing the strong subpattern in the claystone. As in Fig. 3A, however, there is again a bunching of the siltstone stands, as a result of the wide dispersion of those from the claystone, and in this case even the siltstone/claystone discontinuity is lost. In addition the variance accounted for by the first two axes is low, 28%. This result suggests that high species diversity in the claystone is not the main cause of bunching o f siltstone stands in the present data. It is known that wide variations in species abundance can have a similar effect on PCA, and considering the high abundances in the claystone, seen in Fig.2, this seems a reasonable causal factor in the Hasty Bank data. Such variations in abundance can be moderated by transforming the data logarithmically. This condenses the differences in scores between abundant and rare species, compressing the range of data as well as the variance of the abundant species from stand to stand. In this way also, much of the random variation -- Blackith and R e y m e n t ' s noise -- is reduced, and unlike standardisation this is achieved w i t h o u t distorting species relationships. Fig. 4A shows that the scatter of points after logarithmic treatment is fairly evenly spread and the main effect is one of an ordering of stands in the axis I direction, in which there is a gradual change from top to b o t t o m of the section. There is also however a discontinuity between the siltstone and the claystone groups. Stands 1--3, 4--6 and 7--10 of the siltstone, and 22--25 of the claystone are clearly separated off from the rest, representing the subpattern t h r o u g h o u t the section. If our interpretations of the histogram are correct this suggests that logarithmic transformation is particularly useful in producing a PCA plot which corresponds in a balanced way both with Hill's assemblages and also with the idea o f gradual change. Furthermore this information is conveyed in a more graphic way than by visual inspection of the histogram. Reference to the histogram (Fig.2) indicates that there does seem to be sub-pattern in the siltstone, e.g. of stands 1--3, but it is of minor magnitude in terms of both abundance and diversity compared with the claystone subpattern. Thus this pattern was scarcely evident in Fig.3A, a little more so in 3B, but owing to the log transformation it is plainly shown in Fig.4A whilst the claystone sub-pattern remains well marked. The fact is instructive that even after logarithmic transformation stands 22--25 are separated to the same extent as is the claystone as a whole from the siltstone: it suggests t h a t the pattern at the base of the claystone in section 1 is at least as different from the rest of the claystone as is the claystone from the siltstone.

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Fig.4. Axes I and II of PCA ordinations based on logarithmically transformed species abundance counts from Hasty Bank, section 1. A. Stand plot, percent variance axis I, 37%; axis II, 13%. B. Species plot, percent variance axis I, 61%; axis II, 9%; species indicated by open squares.

Fig.4B, a species plot o f the same data, shows that the stand-plot and species-plot PCA ordinations are n o t directly comparable. By inspection of the histogram it can be seen that axis I reflects a gradient of species abundance; those species that are both ubiquitous and have high density counts plot positively, whilst the rarer species plot negatively in a tight bunch. On axis II the species identified as being characteristic of the claystone (nos. 7, 12, 17, 22, 24, 47, 48, 49 and 53) can be seen to plot negatively, whilst those characteristic of the siltstone (4, 18, and 39) plot on the positive side. The total variation extracted b y the first two axes of these ordinations is 50% and 70%, respectively. Logarithmic transformation of the Hasty Bank data, therefore, resulted in an ordination that could be summarised on two axes with considerably less distortion than an ordination using standardised data, and with n o t much less distortion than the ordination o f raw data. When the logarithmically transformed data are subsequently standardised, with the aim of reducing the effects o f b o t h species diversity and species

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Fig.5. Axes I and II of a PCA stand plot based on logarithmically transformed counts from Hasty Bank, section 1, subsequently standardised to unit variance. Percent variance axis 1, 22%; axis 2, 11%.

abundance, the resulting ordination (Fig.5) shows some bunching of the stands having low species abundance, though the effect of the logarithmic transform in spreading o u t the scatter is largely preserved. Stands 15, 16, 18, and 22--25 of the claystone are separated off from the rest. However, the low variance of 33% accounted for by the first two axes indicates that such an ordination m a y be rather poorly summarised in t w o dimensions. A species plot ordination o f the data proved to be very similar to Fig. 4B and is therefore not illustrated.

Summary of PCA results The most conformable PCA results to our understanding o f pattern in the histogram of section 1 are those based on logarithmically transformed data (Fig.4A). These also have a reasonably high percentage variance displayed on the first two axes. The detection of sub-pattern within section 1 varied widely according to the transformation treatment, except for consistent separation of stands 22--25. Analyses of the other two sections yielded different subpatterns, as had been indicated b y visual inspection of the relevant histograms, whilst the siltstone and claystone stands were consistently separated. The results demonstrate that PCA o f the raw Hasty Bank data is apparently susceptible to the effects of wide variations in species abundance. Furthermore, even with logarithmically transformed data the effects of species abundance result in stand plots and species plots which cannot be directly compared.

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Correspondence Analysis (Figs.6--10) A CA ordination of abundance counts from section 1 (Fig.6) shows some degree of ordering b u t no separation of stands or species according to lithology on any of the axes shown. It resembles the PCA results from standardised data and does n o t appear to be useful compared to our understanding of pattern in the histogram. After logarithmically transforming the data (Fig. 7), however, axis 1 clarifies the ordering and also clearly separates the siltstone stands from the claystone ones, positioning the stands from the lithological boundary in the central region o f the axis 1/axis 2 face of the plot. Axis 2 displays the variation within the siltstone group and separates stands 1--3 and 5--6 as being somewhat different from the others, whilst the claystone continuum displayed along axis 3 m a y be divided into three or four groups of stands more or less comparable with the PCA results in Fig.4A. From the corresponding species plot (Fig.7B) it may be seen that variations in the abundance of the ordinated species along the axis 3 continuum suggest that these groups can be weakly defined in terms of species. Axis 1 of the species plot shows that the species characteristic of Hill's intermediate assemblage, Otozamites penna (37), plots midway between the siltstone and claystone assemblages.

291

It is notable that the CA results, being affected less than PCA by species abundance, give more weight to sub-pattern in the siltstone than that in the claystone, the latter sub-pattern only becoming apparent from the third axis. Reference to the histogram indicates that this seems to be a less faithful representation than is given by log. transformed PCA on the first two axes (Fig.4A). The advantage of CA over PCA in the present study seems therefore to be mainly the facility to characterise such sub-pattern of stands in terms of species.

Logarithmic treatment o f the data (Figs. 7--9) The foregoing results indicate that logarithmic transformation was an apparently useful way of handling the Hasty Bank data for both PCA and CA ordination. It reduced the wide variations in species abundances, the "noise" of Blackith and R e y m e n t (1971), whilst n o t obscuring the pattern definable by eye from the histogram. This is specially interesting in relation to the use by Hill of an approximately logarithmic scale of ten points, 1--10, for estimating (rather than counting) species abundances in sections 2 and 3. When Hill first employed this scale it was conceived of as a dominance/abundance scale, b u t he later realised (1974b) that the concept of dominance in the ecological sense is meaningless in its application to fossil assemblages. Thus an equivalent scale of 1--6 points, based solely on abundance, was adopted for the analyses presented here (Table I). 2

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292

The reasoning behind the use of such logarithmic scales, and also logarithmic transformation, derives from the simple assumption that a difference between, say, 5 and 10 individuals per stand is more significant than, for example, between 1,000 and 1,005. However, an ordination based on scale estimates m a y be bogus if valuable information is lost by a bad choice of intervals in the particular scale used, and ideally Hill would have used a truly logarithmic scale. To test for the 1--10 scale actually used at Hasty Bank, the section 1 abundance counts were converted to their equivalent points on the 1--6 scale (Table I) and subsequently ordinated (Fig.8). As can be seen by comparison with Fig.7 the plots are essentially similar to those obtained from logarithmically transformed counts, apart from the inversion of axis 2, owing to randomised allocation of initial scores by the computer program. This indicates that the choice of abundance classes in Hill's scale was suitable, and assuming the estimates in sections 2 and 3 are sufficiently accurate, one would expect little significant information to have been lost by use of the scale for these sections. Clearly however there is a strong case for using in the field a simpler, truly logarithmic, scale. Plots of the section 2 and section 3 estimates do seem to confirm the lithological separation seen in section 1, and for reasons of space are therefore omitted. As with the histogram and PCA results, they also show some subpattern, particularly in the claystone, but neither as clearly as in section 1

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293

nor consistently with it. A plot of the combined data from all three sections illustrates the extent o f the lithological separation and also the somewhat obscure sub-pattern for Hasty Bank as a whole (Fig.9).

Associations of morphological significance (Figs.9--11) During the transport o f terrestrial plants into environments suitable for their preservation, they usually become broken up. Because of this the separate organs originally belonging to any one kind of whole plant are rarely seen attached to one another in allochthonous plant beds, though they frequently occur together in association. The reconstruction of fossil plants depends largely on detecting consistent association of this kind in the field, coupled with laboratory work aimed at detecting any structural agreement between the organs (for example in microscopic details of the cuticle). In the past the detection of associations has depended on the eye and experience of the field collector, though this may be criticised as some of the associations so detected may be imaginary whilst real ones m a y be overlooked. Certainly, as C.R. Hill (1974b) has pointed out, associations tend in general to be poorly documented. By ordinating the data from Hasty Bank, we hoped associations might be detected on a more objective basis, b u t the data from all three sections (Fig.9) lead to a highly complex plot which is dominated by lithology. By 2

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reducing the input data to that of just one taxonomic group, however, such complications m a y be overcome. Fig.10, for example,shows the CA ordination of the Bennettitales, for which a n u m b e r of relatively well-documented reconstructions have been proposed in the literature. One of the reconstructions, the "Williamsonia hildae" plant, was given by Harris (1969). It is composed of the following fossil organs which, because they are normally found detached, are given separate names: 38 40 42 43 44

Ptilophyllum pectinoides (Phillips) Morris (leaf) Cycadolepis hypene Harris (perianth scales) Williamsonia hildae Harris (female flower) Weltrichia whitbiensis (Nathorst) Harris {male flower) Bucklandia pustulosa Harris (stem)

Evidence for reconstruction is provided by the intimate association of the detached organs with one another, seen repeatedly in many plant localities. Association between the leaves and female flowers has also been recorded in fossil dung (C.R. Hill, 1976). Clinching evidence is provided b y rare organic continuity noted between the organs: Bucklandia pustulosa with Ptilophyllum

pectinoides, Williamsonia hildae and Cycadolepis hypene. As can be seen from Fig.10, particularly on the axis 1/axis 2 face of the plot, all the c o m p o n e n t species as they occur at Hasty Bank plot close to one another except for Williamsonia hildae (42), the female flower, and since these flowers are rare (occurring in only three stands from all three sections) there is likely to be a significant error in their positioning in the ordination. Cycad2

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295

olepis hypene (40), the perianth scale of the flower, does however occur far more frequently and its ordinated position lies within the "Williamsonia hildae" group. The ordination would probably be more effective in placing the flowers themselves if a greater number of samples had been available. Cycadolepis spheniscus Harris (present in section 2 only) and Otozamites penna Harris [syn. O. grarnineus (Phillips)], identification numbers 60 and 37 respectively, also show a degree of mutual association. Like the "Williamsonia '" association this had already been noted by Harris (1969), though only in other localities and with less certainty. The additional evidence from Hasty Bank is clearly in support. The leaf Nilssoniopteris vittata (39) occurs well separated from these groupings on the axis 1/axis 2 face of the plot. This too is to be expected as its fructification different (and u n k n o w n at Hasty Bank). When larger taxonomic groups were ordinated, such as a combination of cycads and pteridosperms, the lithological control again became apparent and dominated the plots. These results based on CA ordination correspond with those based on visual inspection of the histogram (Fig.2). As with CA, the associations are most readily detected from the histogram when the plant groups are considered separately. This emphasises and clarifies the need when reconstructing fossil plants for attention to structural details as well as to association. PCA proved weak at resolving associations. F i g . l l A , a PCA species plot ordination o f the Bennettitales, presents an ordination very different from the CA plot of Fig.10. Axis I reflects an ordering of the species along a gradient of increasing abundance towards the more positive values. Species no. 38, the leaf of the "Williamsonia hildae'? plant, is the most abundant whilst nos. 42 and 43 represent the rare female and male flowers. Species nos. 37 and 60 plot close together mainly because t h e y are comparatively rare. Thus the powerful effect on ordering o f species abundance masks any pattern of associations. As can be seen from F i g . l l B the situation is in no way improved by standardisation. DISCUSSION Assessing the effectiveness of ordinations of plant megafossil data by comparison with an understanding o f pattern as illustrated by histograms is a pragmatic and to that extent a limited approach. The occurrence of two main assemblages at Hasty Bank was nevertheless confirmed by the ordinations, as was the occurrence of a general change in the data through the section. So too was the occurrence of sub-pattern and of associations between botanically related but physically separated organs. The graphical presentation by the ordinations was considered preferable to the histogram in t h a t the relationships in the pattern were balanced by being precisely indicated arithmetically. Furthermore, with an increasing body of data from other localities, visual comparison of histograms is likely to become difficult, and under such circumstances ordination m a y well prove particularly useful as a rapid m e t h o d o f analysis.

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297

over-emphasise sub-pattern in the siltstone at the expense of that in the claystone. Nevertheless, we do n o t feel that the relative merits of the two m e t h o d s can be fully tested either on a pragmatic basis or on data from a single locality. There are certain points which are likely to be clarified empirically from additional data, for example whether associations of organs will uniformly be best demonstrated b y the first two axes of CA plots. Equally there is a need to define the o p t i m u m structure of data required for such examination of associations and also the limits b e y o n d which, as for the Hasty Bank cycads and pteridosperms, such analysis is ineffective. The actual pattern detected at Hasty Bank presumably represents some kind of control, either depositionally or ecologically. For those species which show an upwards decline in abundance at the boundary of the siltstone with the claystone, e.g. Pachypteris papillosa, the control may well be depositional the reduced abundance being caused b y faster rates of sedimentation and/ or reduced compaction. This t o o could explain the lower diversity in the siltstone compared with the claystone. However, it cannot explain away the limitation of some species to the siltstone and their absences from the claystone. There are t o o many unquantifiable factors involved in transport and deposition o f plant fragments for there to be any certainty a b o u t generalised conclusions based on Hasty Bank alone (C.R. Hill, 1974b). As with subpattern and with botanically related detached organs, comparative data are needed from other localities, and to this end a study of the Roseberry Topping plant bed is currently in progress. This locality is stratigraphically equivalent and has a similar flora and lithologies to Hasty Bank, but the flora has a somewhat different distribution. Preliminary results indicate that at least one species, Marattia anglica, which is characteristic of the siltstone assemblage at Hasty Bank can occur with equal abundance in both the siltstone and the claystone at Roseberry: implying that the control, at least for this species, perhaps was ecological. -

-

ACKNOWLEDGEMENTS

The work by R.A. Spicer was supported by a NERC studentship and a Lindemann fellowship, that of C.R. Hill by a Parkinson scholarship held at the University of Leeds. We are grateful to Dr. A.J. Morton, Imperial College, and Dr. M.E. Collinson, British Museum (Natural History), for their helpful criticisms of the manuscript. REFERENCES Benzecri, J.P., 1973. L'analyse des donn~es: 2, L'analyse des correspondences. Dunod, Paris, 619 pp. Birks, H.H., 1973. Modern macrofossil assemblages in lake sediments in Minnesota. In: H.J.B. Birks and R.G. West (Editors), Quaternary Plant Ecology. Blackwell, Oxford, pp. 173--189. Birks, H.J.B., 1976. Late-Wisconsian vegetational history at Wolf Creek, Central Minnesota. Ecol. Monogr., 46: 395--429.

298 Blackith, R.E. and Reyment, R.A., 1971. Multivariate Morphometrics. Academic Press, London and New York, 411 pp. Chaney, R.W., 1924. Quantitative studies of the Bridge Creek Flora. Am. J. Sci., 8: 127--144. David, M., Campiglio, C. and Darling, R., 1974. Progresses in R- and Q-mode Analysis: Correspondence Analysis and its application to the study of geological processes. Can. J. Earth Sci. 11: 131--146. Davies, D., 1908. Geological features of the Red seam at Clydach Vale. J. Proc. South Wales Colliery Officers Assoc., 75: 4--16. Davies, D., 1920. Distribution of the different species of flora and fauna from the Westphalian and part of the Staffordian Series of Clydach Vale and Gilfach Goch, East Glamorganshire. Trans. Inst. Min. Eng., 59: 183--221. Davies, D., 1921. Ecology of the Westphalian and lower part of the Staffordian Series of Clydach Vale and Gilfach Goch. Q. J. Geol. Soc. Lond., 77 : 30--74. Davies, D., 1929. Correlation and palaeontology of the Coal Measures in East Glamorganshire. Philos. Trans. R. Soc., (B), 217: 91--154. Dix, E., 1932--1933. The sequence of floras in the Upper Carboniferous, with special reference to South Wales. Trans. R. Soc. Edinb., 57(33): 789--838. Fisher, R.A., 1940. The precision of discriminant functions. Ann. Eugen., Lond., 10: 422--429. Gittins, R., 1965. Multivariate approaches to a limestone grassland community, III. A comparative study of ordination and association analysis. J. Ecol., 53: 411--425. Gordon, A.D. and Birks, H.J.B., 1972. Numerical methods in Quaternary paleoecology. I. Zonation of pollen diagrams. New Phytol., 71: 961--979. Greig-Smith, P., 1964. Quantitative Plant Ecology. Butterworths, London, 2nd ed., 256 pp. Harris, T.M., 1969. The Yorkshire Jurassic Flora, III: Bennettitales. British Museum (Natural History), London, 186 pp., (7 pls.). Harris, T.M., 1979. The Yorkshire Jurassic Flora, V: Coniferales. British Museum (Natural History), London, 166 pp. (7 pls.). Hill, C.R., 1974a. Further plant fossils from the Hasty Bank locality, Naturalist, Lond., 929: 55--56. Hill, C.R., 1974b. Palaeobotanical and Sedimentological Studies on the Lower Bajocian (Middle Jurassic) Flora of Yorkshire. Thesis, University of Leeds, Leeds, 281 pp. Hill, C.R., 1976. Coprolites of PtilophyUum cuticles from the Middle Jurassic of North Yorkshire. Bull. Br. Mus. (Nat. Hist.), Geol. 27(4): 289--294. Hill, C.R. and Van Konijnenburg, J.H.A., 1973. Species of plant fossils collected from the Middle Jurassic plant bed at Hasty Bank, Yorkshire. Naturalist, Lond., 925: 59--63. Hill, M.O., 1973. Reciprocal Averaging: an eigenvector method of ordination. J. Ecol., 61: 237--249. Hill, M.O. 1974. Correspondence Analysis: a neglected multivariate method. Appl. Statist., 23(3): 340--354. JSreskog, K.G., Klovan, J.E. and Reyment, R.A., 1976. Geological Factor Analysis. Elsevier, Amsterdam, 178 pp. Krassilov, V.A., 1975. Paleoecology of Terrestrial Plants (Translated from Russian). John Wiley, New York, N.Y., 283 pp. Lambert, J.M. and Dale, M.B. 1964. The use of statistics in phytosociology. Adv. Ecol. Res., 2: 59--99. Naouri, J.C., 1970. Analyse factorielle des correspondences continu(~s. Publ. Inst. Statist. Univ. Paris, 19: 1--100. Orloci, L., 1966. Geometric models in Ecology, I. The theory and application of some ordination methods. J. Ecol., 54: 193--215. Orloci, L., 1968. Definitions of structure in multivariate phytosociological samples. Vegetatio, 15: 281--291. Orloci, L., 1975. Multivariate Analysis in Vegetation Research. Junk, The Hague, 276 pp.

299 Pemadasa, M.A., Greig-Smith, P., and Lovell, P.H., 1974. A quantitative description of the distribution of annuals in the dune system at Aberffraw, Anglesey. J. Ecol., 62(2): 379402. Scott, A.C., 1977. A review of the ecology of upper Carboniferous plant assemblages, with new data from Strathclyde. Palaeontology, 20(2): 447--473. Spieer, R.A., 1975. The Sorting of Plant Remains in a Recent Depositional Environment. Thesis, Imperial College, University of London, London, 309 pp. Thomas, H. H., 1925. The Caytoniales, a new group of angiospermous plants from the Jurassic rocks of Yorkshire. Philos. Trans. R. Soc. (B), 213(407):299--363. Watts, W.A. and Winter, T.C., 1966. Plant macrofossils from Kirchner Marsh, Minnesota -- a paleoecological study. Bull. Geol. Soc. Am., 77: 1 3 3 9 - 1 3 6 0 .