Precambrian Stromatolites_ Image Analysis

PRECAMBRIAN STROMATOLITES: IMAGE ANALYSIS OF LAMINA SHAPE1

ZHANG2 YUN AND H. J. HOFMANN

Department of Geology, University of Montreal, Montreal, Que., Canada H3C 3J7

ABSTRACT

A morphometric study of 808 lamina profiles of 18 previously published stromatolite taxa was performed using an image analyser. The data were plotted using different shape factors as coordinates and were subjected to multivariate statistical analysis. Visual inspection of the scatter diagrams allows similarities and differences to be readily perceived. Cluster analysis yielded similarity coefficients and dendrograms based thereon, providing quantitative statements of resemblance of lamina profiles. Three major groupings of lamina shape are recognized: (1) those with comparatively uniform, flattened convex profiles, associated with unbranching stromatolites or those with essentially parallel branches, (2) those with variable convex profiles, associated with divergent branches, and (3) those with conical laminae. Subsidiary groupings of more closely related taxa occur in each of the three groupings. The combination of image analysis and multivariate statistical analysis offers a practical and objective adjunct, if not an alternative, to traditional stromatolite systematics.

INTRODUCTION

A major problem in the identification and classification of stromatolites has been the method of comparing the morphological attributes. Taxonomically oriented stromato- litologists convey these characteristics verbally by descriptive adjectives and nouns. This does not necessarily lend itself to precision, and at times even hinders communication because exactly equivalent words in different languages may not be found. Moreover, some words may have different meanings for individuals using the same language. Furthermore, when comparing data for several taxa, the degree of similarity or difference among them may not be clearly perceived.

To present and treat the data more objec- tively and quantitatively, a morphometric approach using image-analysis computers was developed (Hofmann 1976). The philosophy of this approach, its need, and the basic equipment and parameters, are explained in Hofmann (1977), and an application to the erection of new taxa is illustrated in Hofmann (1978). The numerical data allow statistical

1 Manuscript received October 16, 1981; revised February 1, 1982.

2 Permanent address: Department of Geology, Beijing University, Beijing, China (P.R.C.) [JOURNAL OF GEOLOGY, 1982, vol. 90, p. 253-268]

© 1982 by The University of Chicago. All rights reserved. 0022-1376/82/9003-009$1.00

treatment, and these can be presented in a way that should facilitate inter-language communication.

In this explorative study we present the first morphometric analysis of morphological data that others have provided in the literature in photographic form, with the objective of determining the degrees of similarity and difference of lamina shape of various selected taxa. The application of image-analysis per- mits the quantitative evaluation of several parameters not utilized by previous inves- tigators in the statistical study of lamina attributes.

ATTRIBUTES STUDIED

The study of stromatolites involves the gross morphology and lamina shape which make up the stromatolite (group or "genus"), and the microstructural and textural (fabric) features that compose the spongiostrome (form or "species").

In the initial stages of our study we ex- pected to be able to quantitatively analyse both gross morphology and lamina shape from photographic images published in the literature. We did not attempt to analyse mi- crostructures, because of the difficulty in distinguishing primary from diagenetic or secondary features. After consulting a large number of publications in which new taxa were erected, we found that too many of them were insufficiently illustrated to allow a statistical analysis of the geometric attributes. The most common problem encoun-

253

ZHANG YUN AND H. J. HOFMANN

tered was the incompleteness of specimens, which prevented us from quantifying the sil- houette shape (longitudinal section) and plan view (cross section). The only attribute suffi- ciently illustrated to suit our purpose was lamina profile. In a way, this was fortunate because the lamina is the most fundamental characteristic, or template, of stromatolites. It is the active interface in the construction of the structures (synoptic profile), and reflects the balance between biotic activity and envi- ronmental conditions. Studies on modem microbial stromatolitic mats indicate that lamina shape can be substantially controlled by biological factors, and fossil counterparts exist showing that this may also have been so in the past (Hofmann 1975; Awramik and Semikhatov 1979). There is little doubt now that microstructure was greatly influenced by the microbiota, but diagenetic and secondary effects often are superimposed.

MATERIAL

We searched for published photographs and line-drawings of Precambrian taxa from a variety of geographic and stratigraphic occur- rences, but concentrated on those that were most profusely and most clearly illustrated. Eventually 18 taxa (one of which is com- pound) were selected, none of whose illustrations were ideal (table 1). This selection therefore represents a severely biased sample of Precambrian stromatolites insofar as it was governed by the choice of the field geologist who collected a "good" specimen in the field, the choice of the author in selecting a "good" photograph, the choice by us (users of published information) of "suitable" available illustrations, and the choice of particular lamina in an illustration. Moreover, the size of the sample was quite variable, ranging from 12 to 135 laminae, and averaging 42 per sample. Nevertheless, this material allows us to attempt making some comparisons between profiles of different taxa, and to make statements about the degrees of similarity or difference. It would be most useful if, in fu- ture, scaled line drawings of 30-50 laminae were to be provided by authors, in addition to photographs of columns, so as to permit more accurate quantification of data. In the same vein, line drawings of microstructure, sil- houettes of columns, and plan views would

be necessary adjuncts for a more complete quantitative evaluation of stromatolite morphology.

EQUIPMENT AND METHOD

The equipment (QUANTIMET Model 720) is the same as that described by Hofmann (1976, p. 48), but, in addition, a desk-top cal- culator (HEWLETT-PACKARD Model 9825A) and an x-y plotter (HEWLETT- PACKARD Model 9862A) were now available for more efficient treatment of the data. A digital computer (IBM Model 360) was used to calculate the various similarity indices.

After selection of samples from the literature for study, suitable lamina profiles were traced on polyester drafting film (KEUFFEL & ESSER, Herculene 0.05 mm thick, matte on one side) with black ink, using a Rapido- graph pen size 00. This involved drawing only the upper boundary of a lamina with a uniform line 0.3 mm wide irrespective of the ac- tual lamina thickness. The orientation of the profile coincides with its natural orientation within the column in the bed, as far as can be deduced from the information provided in the publication. The laminae are drawn in such a way that each falls within an imaginary plumbed tangential rectangle that does not overlap with that of another lamina. Each lamina is numbered for reference in such a way that the numbers do not fall within the imaginary circumscribed rectangle containing the lamina. The laminae for different taxa are drawn on separate sheets, each sheet is identified and is provided with vertically or horizontally arranged graphic scale that serves as a reference for size and orientation during the computer analysis. The end points of each profile are then connected by a straight line in red ink so as to enclose an area below each lamina profile (fig. 1). Because this closure line is in red and the profile line in black ink, the two lines have different optical densities, and the contrast on the image- analysis computer can accordingly be ad- justed so as to alternatively display and analyse either the black profile line alone, or together with the red line connecting its ends (a closed figure); this essential feature allows us to obtain the measurements necessary for morphometric analysis.

254

PRECAMBRIAN STROMATOLITES: IMAGE ANALYSIS

The tracings are then subjected to automated image-analysis. (All parameters can also be determined manually, without a computer, by using a ruler, protractor, curvometer, and planimeter (Hofmann 1976, p. 46)).

The functions A, Iv, and Fv are measured directly, using instrument settings for AREA, INTERCEPT, and FERET's diameter. S is obtained using the instrument setting for PERIMETER and halving the value (S = perimeter/2). Fh is determined indirectly by electronically dilating A in the vertical direction by a 1-point thickness and automatically subtracting A from this value. Ih is the residual obtained by measuring the area of the black profile line, electronically dilating this line by a 1 point-thickness in the vertical direction, determining this new area, and obtaining the difference between the two values. These measurements serve as a basis for deriving parameters that are descriptive of lamina shape.

BASIC PARAMETERS

An effective method of categorizing the shape of lamina profiles is the laminosity plot (Hofmann 1977, fig. 14), which graphically combines three of the basic geometric elements of a lamina-its length (S), its height (Fv), and its width (Fh)-in the form of three dimensionless ratios. Fv and Fh represent the smallest plumbed rectangle tangent to the profile; their ratio expresses the relative flatness or steepness of the profile and is de- pendent on the orientation of the lamina. S, which is independent of orientation, gives an idea of the quantity of populated surface crowded into this rectangle: the more corru- gated or more globoidal the lamina, the greater S for the same rectangle. A high value for the horizontal laminosity ratio, Fh/S, expresses predominantly horizontal develop- ment of the microbial surface, and a high value for the vertical laminosity, Fv/S, indicates that the laminae have a steep orientation.

We now have used two additional dimensionless parameters for characterizing stromatolite laminae quantitatively (fig. 1). These involve the angle a subtended by the red closure line joining the termini of the profile, and the area (A) enveloped by this line and the profile line. The angle can be ob-

tained with the contrast adjustment on the instrument set so that only the profile in black ink is analysed, and obtaining measurements of the total projection lengths in the vertical (Iv) and horizontal (Ih) directions, and automatically calculating the quantity tan a = (2Fv - Iv)/(2Fh - Ih), or the corresponding angle itself. This ratio, which can also be obtained by direct manual measurement of the angle and trigonometric tables, is a measure of the profile inclination.

The area A subtended by the profile is measured by readjusting the contrast setting on the instrument so as to be able to analyse the closed figure composed of the black profile line and the red closure line connecting its termini.

The dimensionless ratio A/S2 is an alternative measure of profile shape; it is particularly useful in distinguishing inflexed conical or dentate configurations (with low values) from convex or crinkled ones (with higher values), as well as flat ones from globoidal ones. The ratio is independent of the orientation (inclination) of the lamina and can be designated the "outline index" of the profile. It is similar to the circularity index of Hofmann (1976, p. 50) and has a maximum value of 27r for semicircles and a minimum for flat, stratiform layers. This index is a measure of the surface extent of the active microbial mat (synoptic surface) with respect to the volume of the interior enclosed by it and may have biologic significance, inasmuch as the mode of construction of conical laminae is fundamentally different from that of convex laminae requir- ing the presence of filamentous, phototactic, gliding microbes (e.g., Walter et al. 1976).

RESULTS

The results of our study of the seven basic attributes and five derived shape parameters are presented in table 2 and figures 2-9. Fig- ure 2 illustrates "typical" profiles, those that are closest to the mean value of each taxon shown in figure 4. Figure 3 shows a laminosity plot of all 808 laminae, while figure 4 shows an alternative plot of lamina shape, using outline index and profile steepness ratio as coordinates.

Inspection of figure 3 reveals the wide scatter of points for each taxon, but also similarities between the clusters of certain

255

TABLE

1

STROMATOLITE

TAXA

ANALYSED

No.

Taxon

1

Colonnella

cormosa

Komar

2

Gymnosolen

ramsayi

Stein-

mann

3

Gymnosolen

furcatus

Komar

4

Baicalia

capricornia

Walter

5

Baicalia

kirgisica

Krylov

6

Inzeria

tjomusi

Krylov

7

Inzeria

toctogulli

Krylov

8

Inzeria

intia

Walter

9

Alcheringa

narrina

Walter

Reference

Komar

1966,

PI.

3, fig.

1

Krylov

1963,

PI.

25,

figs.

5, 6

Komar

1966,

P1.

11,

fig.

1

Walter

1972,

P1.

18,

fig.

2

Krylov

1963,

P1.

7, fig.

3

Krylov

1963,

PI.

13

Krylov

1967,

P1.

1, figs.

1-2

Walter

1972,

P1.

22,

figs.

4-5

Walter

1972,

P1.

16,

figs.

2-3

Stratigraphic

unit

Yusmastakh

Fm.

Not

given

U. Yusmastakh Fm.

Irregully

Fm.

Ovv

Fm.

Katav

Fm.

Chatkaragai

Fm.

Bitter

Springs

Fm.

Pillingini

Tuff

Age

Locality

M. Riphean

Anabar

Mas-

sif,

USSR

U. Riphean

Western USSR

U.

Riphean

Anabar

Mas-

sif,

USSR

M. Riphean

Bangemall Basin,

W

Australia

M. Riphean

Tien

Shan, USSR

U. Riphean

S. Urals, USSR

U.

Riphean

Tien

Shan, USSR

U. Riphean

Amadeus Basin,

Aus-

tralia

2500

Ma

±

Hamersley Basin,

Aus-

tralia

No.

of

laminae

20 32 30 53 30 62 43 55 30

10

Linella

simica

Krylov

11

Katavia

karatavica

Krylov

12

Jurusania

cylindrica

Krylov

13

Madiganites

mawsoni

Walter

14

Jacutophyton

f. (central

col-

umn)

15

Jacutophyton

f. (branches)

16

Vertexa

termina

Semikhatov

17

Kussiella

kussiensis

(Maslov)

18

Acaciella

australica

Walter

19

Conophyton

gaubitza

Krylov

Krylov

1967,

P1.

5, fig.

3

Krylov

1963,

P1.

33

Krylov

1963,

PI.

25,

figs.

1-4

Walter

1972,

PI.

28,

fig.

1

Bertrand-Sarfati

1972,

fig.

35f

Bertrand-Sarfati

1972,

fig.

35f

Semikhatov

1978,

Pl.

24,

figs.

1 and

3

Krylov

1963,

PI.

3

Walter

1972,

Pl.

15,

fig.

1

Krylov

1967,

Pl.

7, fig.

1

Uk

Fm.

Katav

Fm.

(upper)

Katav

Fm.

(lower)

Jay

Creek

Lime-

stone Atar

Gp.

15

Atar

Gp.

Is

Utsingi

Fm.

Satka

Fm.

Bitter

Springs

Fm.

Malokaroi

Fm.

U. Riphean

S. Urals, USSR

U. Riphean

S. Urals, USSR

U. Riphean

S. Urals, USSR

U. Riphean

Amadeus Basin,

Aus-

tralia

U. Protero-

Atar,

zoic

Mauritania

U. Protero-

Atar,

zoic

Mauritania

Aphebian

Great

Slave

Lake, Canada

L. Riphean

S. Urals

U. Riphean

Amadeus Basin,

Aus-

tralia

U. Protero-

Karatau,

zoic

USSR

23 50 77 17 12 27 40 135 56 16


plumbed tangential rectangle

IFh reference number

cm

scale

lamina profile (black)

"closure line (red)

FIG. 1.-Basic parameters of lamina profile. Note that all functions can be obtained manually, using a ruler, protractor, curvometer, and planimeter (Hofmann 1976, p. 46). Functions measured in oriented specimen: Fv-Profile height (vertical Feret diameter). Fh-Profile width (horizontal Feret diameter). S- Profile length (=perimeter/2). Iv-Vertical intercept (projection) length = Fv + a + b. Ih-Horizontal intercept (projection) length = Fh + c + d. tan a-Profile inclination = (2Fv - Iv)/(2Fh - Ih) = (Fv - a - b)/(Fh - c - d). A-Subtended area of profile. Parameters calculated: Fv/S-Vertical laminosity. Fh/S-Horizontal laminosity. Fv/Fh-Profile steepness; or Fh/Fv-Profile flatness. A/S2-Profile outline. (or2/X)tan a-Variability of profile inclination (Variance divided by mean of tan a).

taxa. For instance, samples 4, 5, and 15 have comparable great dispersion of points, which represents the greatly variable inclination and shape characteristic of laminae in the Group Baicalia and in the branches of Jacutophy- ton. Close clustering to the left is shown in samples 14 and 19, representing conical laminae in Conophyton and Jacutophyton. Small dispersion in samples 7, 8 and 18 con- forms to uniform, somewhat flattened profiles in Inzeria and Acaciella. The cumulative plot for all samples shows a bifurcating curvilinear trend and a concentration of points towards the lower right; the density of points is shown quantitatively in figures 5 and 6.

Figure 4 exhibits a scattering similar to that in figure 3 for the same taxa. Low values for outline index with high values for profile steepness are characteristic for conical laminae. The cumulative curves show the trend from flattened convex profiles at the lower left, rising curvilinearly to a maximum theoretical value of 0.159 for a semicircle whose chord is horizontal (the A/S2 values exceeding 0.159 are due to imprecision, generally associated with measuring profiles of small size, the errors amounting to as much

as 8%). The descending trend of points for steepness values higher than 0.5 mainly includes variably inclined convex profiles.

The data of figures 3 and 4 are replotted in the form of contoured diagrams as figures 5-8. Figure 5 shows the highest relative density of points (more than 30 per 0.05 laminosity interval) in the lower right, representing laminae with flattened convex laminae (compare with Hofmann 1977, fig. 14). It is also the region of the laminosity plot where the taxonomic overlap is greatest (fig. 6), up to 10 taxa having laminae with the same general shape.

Figures 7 and 8 are based on figure 4, but plotted using a logarithmic scale for the abscissa so as to equalize the intervals between ratios, and to accommodate samples 14, 15 and 19 on the same graph as all other samples (interval for A/S2 = 0.1, for Fv/Fh = 0.1). The highest concentration of points (more than 30 per contoured interval) is slightly below the value for semicircles. Fig- ure 8 shows the taxonomic overlap, with as many as 10 taxa having some laminae of common shape. A tabular summary of the numerical data is given in table 2.

258

TABLE

2

SUMMARY

OF

NUMERICAL

DATA

Measurements

Taxa

A

S

cm2

cm

F cm

Fh cm

A S2

I vcm cm

cm rm

F v Fh

F v S

Fh S

tan

a

(a)

X

a

X

a

X

x

a

X

a

X

o

X

o

X ax

oa

a X

X

1 Colonnella

cormosa

20

17.77

2.46

11.24

.63

3.10

.39

8.68

.43

5.73

.37

8.92

.62

.140

.009

.36

.05

.28

.02

.77

.05

.06

.05

.04

(3.4)

(2.9)

2 Gymnosolen

ramsayi

32

1.09

.66

2.89

1.07

.75

.27

2.38

.93

1.25

.49

2.41

.88

.120

.017

32

.07

.27

.05

.84

.07

.13

.11

.08

(7.4)

(6.3)

3 Gymnosolen

furcatus

30

.77

.53

2.25

.75

.41

.11

.67

.22

.63

.20

.68

.20

.145

.010

.63

.17

.37

.06

.60

.10

.42

.24

.18

(22.8)

(12.4)

4 Baicalia

capricornia

53

7.80

5.11

6.93

2.65

3.31

1.77

4.28

1.31

4.62

2.23

4.28

1.28

.142

.017

.75

.35

.45

.13

.66

.14

.49

.44

.39

(26.1)

(23.8)

5 Baicalia

kirgisica

30

2.57

2.50

4.04

1.86

1.83

.98

3.02

1.27

2.49

1.94

3.02

1.29

.117

.023

.63

.28

.46

.13

.76

.11

.55

.33

.20

(28.8)

(18.3)

6 Inzeria

tjomusi

62

2.97

1.42

5.14

1.52

1.55

.58

4.09

1.23

2.48

.88

4.06

1.17

.110

.026

.38

.12

.30

.06

.80

.10

.16

.12

.09

(9.1)

(7.0)

7 Inzeria

toctogulli

43

.51

.46

1.94

1.09

.41

.22

1.68

.94

.65

.40

1.68

.93

.117

.020

.25

.06

.23

.05

.88

.04

.13

.10

.04

(7.4)

(5.7)

8 Inzeria

intia

55

3.29

2.12

5.46

2.15

1.19

.49

4.68

1.78

2.20

.93

4.77

1.73

.102

.024

.27

.07

.23

.06

.85

.05

.09

.09

.09

(5.1)

(5.1)

9 Alcheringa

narrina

30

.03

.02

.41

.15

.18

.06

.22

.11

.27

.10

.24

.10

.147

.016

.90

.36

.46

.10

.55

.11

.61

.57

.51

(31.4)

(29.7)

10 Linella

simica

23

.12

.06

1.00

.29

.44

.13

.54

.17

.72

.22

.54

.18

.114

.022

.85

.27

.44

.09

.57

.09

.37

.28

.19

(20.3)

(15.6)

1 Katavia

karatavica

50

1.52

.73

3.29

.77

1.38

.41

1.93

.44

2.30

.61

1.98

.43

.134

.009

.70

.12

.41

05

60

.08

.23

.15

.09

(13.0)

(8.5)

2 Jurusania

cylindrica

77

1.14

.53

2.75

.62

1.00

.30

1.90

.39

1.71

.48

1.87

.34

.147

.011

.53

.13

.36

.05

.69

.05

.14

.10

.07

(8.0)

(5.7)

3 Madiganites

mawsoni

17

.65

.39

2.18

.69

.91

.37

1.37

.44

1.34

.49

1.38

.45

.125

.177

.68

.22

.42

.11

.64

.09

.38

.28

.21

(20.8)

(15.6)

4 Jacutophyton

f.

12

i26.66

272.5

101.72

28.17

47.58

13.98

18.92

7.79

93.83

28.15

19.10

8.03

.048

.019

3.33

1.92

.46

.02

.19

.09

.11

.10

.09

(central

column)

(6.3)

(5.7)

5 Jacutophyton

f.

27

90.55

80.54

22.58

11.05

10.45

3.95

13.01

8.82

15.56

7.11

13.25

8.85

.141

.016

1.15

.74

.51

.17

.53

.15

.88

1.04

1.19

(branches)

(41.4)

(46.1)

6 Vertexa

termina

40

.97

.53

2.65

.78

1.23

.53

1.84

.51

1.53

.49

1.85

.53

.132

.017

.67

.17

.46

.09

.70

.06

.51

.28

.16

(27.0)

(15.6)

7 Kussiella

kussiensis

135

1.95

1.96

3.13

1.95

1.22

.83

2.08

1.17

1.96

1.40

2.06

1.16

.150

.040

.57

.15

.38

.06

.69

.10

.24

.14

.08

(13.5)

(8.0)

8 Acaciella

australica

56

.43

.20

1.98

.42

.43

.15

1.74

.38

.66

.19

1.73

.41

.102

.023

.24

.06

.21

.05

.87

.04

.11

.07

.04

(6.3)

(4.0)

9 Conophyton

gaubitza

16

8.32

2.29

12.18

2.18

6.18

1.04

2.44

.41

11.09

2.06

2.88

.56

.056

.008

2.76

.40

.51

.02

.19

.04

.72

.30

.13

(35.7)

(16.7)


FIG. 2.-Typical profile shape for each of the 18 taxa. The laminae illustrated are those closest to the mean value of each taxon of figure 4. Numbering is same as in table 1. Length of bar below each profile equals 1 cm.

ANALYSIS

The basic data obtained were subjected to computerized analysis. A data matrix for taxa and parameters was set up, and the values of the means and standard deviations for each sample were obtained. Because the data have different dimensional units, they were standardized (mean of zero, standard devia- tion of unity).

Different methods have been proposed for cluster analysis (e.g., Sokal and Sneath 1963; Boyce 1969; Klovan 1975). The weighted pair-group method was used in the computa- tion of the pairwise similarity between all elements in the matrix. The two mutually most highly correlated values are clustered to form a new matrix element that is used in the next clustering cycle, being of equal weight with respect to the other elements already in

the matrix. Successive clustering cycles re- duce the number of elements in the matrix until the matrix is depleted.

To check the correlation among parameters in the R-mode we calculated the correlation coefficients between the 12 parameters, using the weighted pair-group method. These are given in table 3. Inasmuch as highly correlated parameters do not give extra weight in the discrimination of samples, we eliminated 3 of the highly correlated parameters in our Q-mode analysis, leaving a 19 x 9 data matrix comprised of the 19 taxonomic entities, and the attributes A, S, Fv, Fh, Iv, A/S2, Fv/Fh, Fh/S, and tan a.

Q-mode analyses were made using two different similarity functions (Sokal and Sneath 1963, p. 296; Boyce 1969, p. 7; Klovan 1975, p. 47):

260


(1) Correlation coefficient, defined as

Xii X ( ) ; X X

rjk =

i=1 I I

(2) Cosine of angle, defined as

X Xj Xik i=l

cosOjk -

where X, is the value of attribute i for formj, and Xik is the value of attribute i for form k; n is the number of attributes used in a particular comparison.

The results are presented as dendrograms in figure 9. Calculations using the correlation coefficient and the cosine 0 functions give quite similar patterns.

The dendrograms in figure 9 define three major groupings of laminae but the composi- tion of each grouping varies slightly, de- pending on the function used. For the method using the correlation coefficient, the first grouping includes nine samples belonging to Inzeria (nos. 6, 7, 8), Gymnosolen (2), Acaciella (18), Colonnella (1), Jurusania (12), Katavia (11), and Kussiella (17). The second grouping comprises eight samples belonging to Baicalia, Gymnosolen, Alcheringa, Vertexa, Linella, Madiganites, and branches of Jacutophyton. A well defined third grouping comprises the conical laminae of Conophyton and Jacutophyton.

In the dendrogram based on the cosine 0 function, samples 11, 12, and 17 fall into the second group rather than the first and the branches of Jacutophyton (15) plot with the third grouping, instead of the second.

Internal subgroupings defined by succes- sively higher similarity levels are comparable for both the correlation coefficient and cosine 0 function; only the positions of Linella (10), Madiganites (13), and one form of Gym- nosolen (3) are different in these two dendrograms. In both dendrograms samples 2 and 7, 3 and 9, 6 and 8, and 12 and 17 exhibit the highest pairwise correlation.

DISCUSSION

The results presented in figures 3-8 pro- vide not only a visual means of appreciating similarities and differences between the lamina belonging to different taxa, but also dem- onstrate the great abundance of laminae of common shape among many different taxa. The predominance of somewhat flattened, convex laminae among most of the taxa analysed reveals a common trait among stromatolites. Deviations from this dominant shape reflect particularities of individual taxa which may be controlled biologically or en- vironmentally, or by a combination of both. The exact methods of generating lamina shape are still not understood for fossil forms.

The degree of similarity or dissimilarity of lamina shape is shown graphically in figure 9, for which two of the many possible similarity indices were selected. The choice of a particular index is arbitrary; each has its own advantages as well as drawbacks (e.g., see Sokal and Sneath 1963; Klovan 1975). The two similar dendrograms clearly show three major groupings, groupings that are also evi- dent in the cumulative clustering in figures 3 and 4. The first grouping of rather uniform slightly flattened convex laminae reflects stromatolite columns that are erect and un- branched, or that have branches that are generally parallel.

The second grouping comprises stromatolites with more or less irregular, inclined convex laminae which are generally associated with variably divergent branching resulting from the obliquely directed accretion. The third grouping is for conical laminae, readily distinguishable without statistics even by the casual observer.

To some extent the results obtained by cluster analysis coincide with the taxonomic grouping determined by the traditional morphological classification. For instance, it is noteworthy that all three forms of Inzeria

261

1 Colonnella cormosa

5 Baialia kirgisica

9 Alcheringa narrina

13 Madiganites mawsoni

18 Acaciella australica

2 3 Gymnosolen ramsayi Gymnosolen fureatus

6 Inzeria tjomusi

10 Linella simica

14 +15 Jacutophyton f.

19 Conophyton gaubitza

7 Inzeria toctogulli

11 Katavia karatavica

16 Vertexa termina

all samples 1-19

0 0.5 1.0

FIG. 3.-Laminosity plot for each of the 18 taxa sele,..d from the literature. Field of sample 14 is outlined by dashed contour. A cumulative plot for all 808 laminae representing the 18 taxa (19 samples) is given at the bottom; the scales for all graphs are identical and are shown at the bottom right. For each sample, note the location of the cluster, its trend and the variable scattering; in the cumulative graph note the bifurcating trend and concentration of points towards the bottom right.

4 Baicalia capriconuia

8 Inaeria intia

12 Jurusania cylindrica

17 KussieUla kussiensis

1.0

0.5

2 3 (;ymnsolenl ramnsavi vGymruolen furnatuls

7 Ineria tctogulli

11 Kata'ia karaticu'a

16 Verttxa thrmnina

4 aiucalia caprirnia

8 Inazria intia

12 Jurusania cylindrica

17 Kulsiella huss.nsi

19 (bip/zi~.\loi gahctza~

all samples except 14. 15. and 19 samples 14, 15, and 19

0.2 0.2 A A_ S2

0.1 0.1

0 1.0 F 20 0 Fh

2 4 F 6 Fh

FIG. 4.-Profile shape of each of the 18 taxa (19 samples), based on plot of outline index (A/S2) vs. profile steepness (Fv/Fh). Field of sample 14 is outlined by dashed contour. The horizontal scale for samples 14, 15, and 19 is one fourth of that for the rest of the samples. Two cumulative plots are shown at the bottom right. For each sample, note the location of the cluster, its attitude, and the variable scattering and, in the cumulative curves, the arcuate trend for the taxa with convex lamina profiles, and the slightly sloping trend for conical profiles in samples 14 and 19.

1 ( ilunmwlla ormmn a

5 iHkicalia kirgisia

9 Aic'heringa narrina

13 A.l<idianit's mn o.sni

6 Inzeria tjomu.si

10 Linella simica

14+15 *Jaulph \yton [

18 Acadul'a ti.lriluic

264 ZHANG YUN AND H. J. HOFMANN

PROFILE STEEPNESS -F Fh Fh

PROFILE FLATNESS -

LAMINA SHAPE

Fh HORIZONTAL LAMINOSITY -

FIG. 5.-Synopsis of profile shape (laminosity plot). The contours are drawn around the 808 points in the cumulative graph at the bottom of figure 3, and show the relative density of profiles for given laminosity ratios. Contoured values based on grid of laminosity interval of 0.05. The concentration of points towards the bottom right reflects the dominance of flattened, semi-elliptical lamina profiles among the stromatolites analysed (compare with figure 14 of Hofmann 1977).

(6,7,8) are in the same subcluster at high values for both the correlation coefficient and the cosine 0 function. The two forms of Baicalia (4,5) belong to a second cluster. However, the two forms ascribed to Gym- nosolen (2,3) are widely separated, belonging to two entirely different stems. This suggests that lamina shape was not one of the attributes used to assign the form Gymnosolen furcatus to the group Gymnosolen. Based on traditional morphologic criteria, this form actually appears to be closer to Pseudogym- nosolen.

It is also interesting to note that the shape of the laminae of Acaciella australica (18) is close to that for Inzeria intia (8), two taxa that co-occur in the same formation in central Australia, and reconstructions of which suggest that these two may be two variants of the same stromatolite taxon.

CONCLUSION

Our study indicates that it is feasible to ex- press differences between profile shapes of different stromatolite taxa quantitatively. The data can also be presented graphically. The


PROFILE STEEPNESS - Fh

Fh PROFILE FLATNESS

OVERLAP OF TAXA

Fh HORIZONTAL LAMINOSITY - S

FIG. 6.-Synopsis of taxonomic overlap: Summary of laminosity plots, showing number of taxa with profiles of given laminosity ratios, based on data in figure 2. Contoured values based on grid of laminosity interval of 0.05. The taxonomic overlap is greatest (10 taxa) towards the bottom right of the graph.

use of automated image-analysis and computerized multivariate statistical analysis offers an objective adjunct, if not an alternative, to stromatolite systematics, whose use should be further explored and encouraged. It is recommended that several similarity indices be employed so as to allow comparison of dendrograms based on different formulae. Our analysis, though based on a severely limited sample, affirms several taxonomic groupings set up by traditional classifications, while suggesting new groupings for some others.

ACKNOWLEDGMENTS.-The project was

carried out at the University of Montreal while Zhang was on sabbatical leave from Beijing University. We thank Jacques Masounave for writing the computer program for the automated image-analysis, and Li Shi-he for writing the computer program for the Q- and R-mode analyses. Gerard Guerin operated the image analyser. Financial sup- port for this project from the Natural Sci- ences and Engineering Research Council of Canada (Grant A7484) is gratefully acknowl- edged. We thank F. P. Agterberg, S. M. Aw- ramik, J. A. Donaldson, R. H. Horodyski, and W. V. Preiss for helpful criticisms of our manuscript.

265

0.18

0.16

014 n=808 A 0.14 0 15

S10 0 12 -

x o.o10 -

O 0.08

.

0.06

0 0.04

0.02 LAMINA SHAPE 0 I

I

I

a

i

m i

i

I a

mIIi I 11II 1/8 1/4 1/2 1 F 2 4 8

PROFILE STEEPNESS - Fh

FIG. 7.-Synopsis of profile shape, using outline index and profile steepness ratio (logarithmic scale) as coordinates. The contours indicate the relative prevalence of laminae with particular shape factors. The maximum value theoretically attainable for A/S2 is qir (=0. 159), for semicircles; values exceeding this limit in the graph are mainly for very small profiles, for which the accuracy and precision of the method are not high, the error amounting to as much as 8%. The concentration of points trending from the top middle to the bottom left reflects the predominance of flattened, convex profiles; the group combining great steepness with low values for outline index represents conical profiles.

0.18

0.16

8 "2

A 0.'4 6 n=18

0.12 - 4

X 0.102

z 0.08

z " 0.06 1

0 0.04

0.02- OVERLAP OF TAXA

0 L I a . .

I aI.I.aIa

I -

|I

1

I- II-II

IAi

1/8 1/4 1/2 1 Fv

2 4 8 PROFILE STEEPNESS

Fh FIG. 8.-Synopsis of taxonomic overlap, based on outline index and profile steepness. Contours indicate

the number of taxa having laminae of a given shape.

TABLE

3

CORRELATION

COEFFICIENTS

BETWEEN

THE

12 MORPHOLOGICAL

ATTRIBUTES

A/S2

Fv/Fh

Fv/S

Fh/S

tan

a

(o2/X)tan

a

1.000 266

1.000

027

943

1.000

146

707

756

1.000

076

883

941

632

1.000

421

659

805

460

903

737

537

356

691

274

034

158

155

058

188

249

439

609

771

558

267

637

670

102

707

436

197

441

588

470

270

632

669

104

701

1.000 .024 .151 585 665 565 656

A

S

Fv

Fh

Ih

1.000 146

1.000

293

092

1.000

212

310

028

1.000

026

059

903

034

1.000

222

322

028

999

-.030

1.000

A/S2 Fv/Fh Fv/S Fh/S tan

a

(o2/X)tan

a.

A S Fv Fh Iv Ih


REFERENCES CITED

AWRAMIK, S. M., and SEMIKHATOV, M. A., 1979, The relationship between morphology, microstructure, and microbiota in three vertically in- tergrading stromatolites from the Gunflint Iron Formation: Can. Jour. Earth Sci., v. 16, part 1, p. 484-495.

BERTRAND-SARFATI, J., 1972, Stromatolites col- umnaires du Precambrien Superieur du Sahara nord-occidental: Centre Nat. Rech. Scientif., Paris, Ser. G6ol. 14, 245 p.

BOYCE, A. J., 1969, Mapping diversity: a compara- tive study of some numerical methods, in COLE, A. J., ed., Numerical Taxonomy: New York, Academic Press, p. 1-31.

HOFMANN, H. J., 1975, Stratiform Precambrian stromatolites, Belcher Islands, Canada: relations between silicified microfossils and microstructure: Am. Jour. Sci., v. 275, p. 1121-1132.

--- 1976, Stromatoid morphometrics, in WAL- TER, M. R., ed., Stromatolites: Amsterdam, Elsevier, p. 45-54.

--- 1977, On Aphebian stromatolites and Riph- ean stromatolite stratigraphy: Precamb. Res., v. 5, p. 175-205.

--- 1978, New stromatolites from the Aphebian Mistassini Group, Quebec: Can. Jour. Earth Sci., v. 15, p. 571-585.

KLOVAN, J. E., 1975, R- and Q-mode factor analysis, in MCCAMMON, R. G., ed., Concepts in Geostatistics: New York, Springer-Verlag, p. 21-69.

KOMAR, V. A., 1966, Upper Precambrian stromatolites in the northern part of the Siberian Platform and their stratigraphic significance: Tr. Geol. Inst., Akad. Nauk SSSR, v. 154, 122 p. (in Russian).

KRYLOV, I. N., 1963, Columnar branching stromatolites of the Riphean deposits of the South- ern Ural and their significance for the stratigraphy of the Upper Precambrian: Tr. Geoi. Inst. Akad. Nauk SSSR, v. 69, 133 p. (in Russian).

1967, Riphean and Lower Cambrian stromatolites of Tien-Shan and Karatau: Tr. Geol. Inst. Akad. Nauk SSSR, v. 171, 88 p. (in Russian).

SEMIKHATOV, M. A., 1978, Some Aphebian car- bonate stromatolites of the Canadian Shield, in RAABEN, M. E., ed., Lower Boundary of the Riphean and stromatolites of the Aphebian: Tr. Geol. Inst. Akad. Nauk SSSR, v. 312, p. 111-147.

SOKAL, R. R., and SNEATH, P. H. A., 1963, Princi- ples of Numerical Taxonomy: San Francisco, W. H. Freeman, 359 p.

WALTER, M. R., 1972, Stromatolites and the bio- stratigraphy of the Australian Precambrian and Cambrian: Palaeont. Assoc., London. Special Papers in Palaeont. 11, 190 p. --; BAULD, J.; and BROCK, T. D., 1976, Mi-

crobiology and morphogenesis of columnar stromatolites (Conophyton, Vacerilla) from hot springs in Yellowstone National Park, in WAL- TER M. R., ed., Stromatolites: Amsterdam, Elsevier, p. 273-310.

267

268 ZHANG YUN AND H. J. HOFMANN

2 Gymnosolen ramsayi 7 Inzeria toctogulli

18 Acaciella australica 6 Inzeria tjomusi 8 Inzeria intia 1 Colonnella cormosa

12 Jurusania cylindrica 17 Kussiella kussiensis 11 Katavia karatavica

3 Gymnosolen furcatus 9 Alcheringa narrina

13 Madiganites mawsoni 16 Vertexa termina

4 Baicalia capricornia 10 Linella simica

5 Baicalia kirgisica 15 Jacutophyton f. (branches) 14 Jacutophyton f. (central column) 19 Conophyton gaubitza

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

CORRELATION COEFFICIENT

2 Gymnosolen ramsayi 7 Inzeria toctogulli

18 Acaciella australica 6 Inzeria tjomusi 8 Inzeria intia 1 Colonnella cormosa

12 Jurusania cylindrica 17 Kussiella kussiensis 11 Katavia karatavica 10 Linella simica 13 Madiganites mawsoni 3 Gymnosolen furcatus 9 Alcheringa narrina

16 Vertexa termina 4 Baicalia capricornia 5 Baicalia kirgisica

15 Jacutophyton f. (branches) 14 Jacutophyton f. (central column) 19 Conophyton gaubitza

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

COSINE OF ANGLE

FIG. 9.-Q-mode cluster analysis of lamina profiles of 18 taxa, using standardized data with 9 parameters; comparison of dendograms produced by weighted pair-group method, using correlation coefficient (top) and cosine 0 functions (bottom).

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Precambrian Stromatolites_ Image Analysis