A new method to determine volume of bromalites: morphometrics of Lower Permian (Archer City Formation) heteropolar bromalites


Lower Permian vertebrates from both terrestrial and aquatic organisms have been collected from Archer County, Texas, for over a century. These include preserved shark cartilage and spiral bromalites presumed to have been produced by freshwater sharks of the genus Orthacanthus. Specimens were collected in the newly named Archer City Bonebed V occurring in the Archer City Formation. Physical characteristics (length, width, height, mass, eccentricity, volume, and density) were measured and recorded for 300 spiral bromalites and compared by linear regression analysis. The spiral bromalites had an average length of 31.74 mm; width 14.43 mm; height 10.51 mm, and mass 7.971 g. Eccentricity ranged from 0.9 to 0.06. All of these values follow a normal distribution. In addition to the collection of this statistical data, a new formula is proposed to help determine the volume of these elliptical fossils when volume determination by water displacement is not an option. The percent difference between the observed volumes obtained by water displacement and calculated volumes ranged from 0.04 to 56 %. Ninety-five percent of the statistical sample had a percentage difference of <30. This data, if compiled with data from the analysis of specimens from other localities, may ultimately reveal size groupings that could reflect the presence of previously unknown taxa that possessed a spiral valve and coexisted with the Orthacanthus sharks.


Classically, the term “coprolite” has been applied to any type of fossilized digestive material, regardless of its origin, since Rev. William Buckland coined the term in 1829. Hunt (1992) has proposed the term “bromalite” as an alternative to using the word coprolite. Bromalite means “food stone” and is defined as any fossilized digestive matter originating from animals. This encompasses true coprolites, cololites, regurgitalites, and gastrolites (Hunt 1992; Northwood 2005; Hunt et al. 2012), which are present in sedimentary rocks formed in aquatic and terrestrial environments (Amstutz 1958; Häntzschel et al. 1968; Thulborn 1991). This term has been chosen because of the controversy surrounding the true origin of spiral bromalites and to circumvent the terminology associated with these differing hypotheses about these fossils. Many authors have debated whether or not they were preserved after being expelled from the body as feces, or if they were actually retained in the body after death either in the colon or being the actual preserved spiral valve itself (Fritsch 1907; Williams 1972; Stewart 1978; Duffin 1979; Jain 1983; McAllister 1985, 1987; Chin 1996; Holmgren et al. 1999). As observed, fecal pellets from fish tend to unwind as ribbons, and dissipate into the water within hours of expulsion (Jain 1983; McAllister 1985). With the exception of the true coprolite hypothesis, each spiral bromalite would represent a death (Stewart 1978), and retention of the bromalite in the body could provide an ideal taphonomic situation for preservation.

Williams (1972) compared the length to width ratio of 38 spiral bromalites from Kansas and found a 2:1 ratio. He suggested this could be misleading due to the crushing or deformation of the specimens. Williams (1972) suggested that a comparison to uncrushed spiral bromalites from Texas could reveal the length to width ratio is closer to 2.5:1. If one observes the eccentricity of the cross section of spiral bromalites, an appreciation of what Williams (1972) referred to as the “crushing” can be better understood (Fig. 1b). In general, the few studies that have mentioned “coprolite” or bromalite morphometrics have only focused on a small sample or a single specimen and even then only giving a few physical aspects of the specimen(s). This is the first study to focus on what can be learned from the analysis of a larger sampling size when taking morphometrics into account. This study derives a new formula for calculating the volume of spiral bromalites by incorporating three linear measurements from each of the specimens (Fig. 1a). This formula has the potential for use when volume measurement by water displacement is not a viable option for reasons such as time constraints, quick field analysis, samples encased in matrix, calculating volume from published information without having the specimen, or the specimen may be too large or too fragile to submerge. The latter might apply to more recent Pleistocene cave deposits or bromalites from archeological sites, if this formula proves applicable to these areas of research.

Fig. 1

The measurements taken from each of the 300 spiral bromalites and how they were used in the calculation of the volume and eccentricity. a Physical measurements (l length, t thickness, w width) taken from the spiral bromalites and used as variables in the proposed volume formula. The constant 1.7088 was found as a slope after regressing the preliminary volumes and the observed water displacement volumes. Orientation is based on Hunt and Lucas (2012). b Spiral heteropolar bromalite shown in cross-section indicating the measurements (t thickness, w width) used to calculate eccentricity in the formula below. The closer the value is to 1 the more crushed the specimen is

It should be noted that a recent attempt has been made to categorize spiral bromalites of Permian and Triassic age by assigning them ichnotaxonomic nomenclature based on their morphologies, related geographical origin, and unsubstantiated hypothesized producers (Hunt and Lucas 2005a, b; Hunt et al. 1998, 2005a, b, 2007). This study does not follow this scheme to avoid adding confusion stemming from the current debate over their origin. Instead, Neumayer’s (1904) bimorphological scheme for identifying spiral bromalites will suffice (Fig. 2). His classification of spiral bromalites, collected in Baylor Co., Texas, USA, is based on external morphology and remains the standard for describing spiral bromalites. Heteropolar bromalites are those with relatively closely spaced turns concentrated towards one end (Fig. 2a). Amphipolar bromalites have blunt ends with wider and regularly spaced turns running along the entire length (Fig. 2b). Some experts have stated that these morphologies may ultimately provide little taxonomic information (Zidek 1980; McAllister 1985; Chin 1996), but this is not their only significance.

Fig. 2

a Spiral heteropolar bromalite morphololgy, relatively closely spaced turns concentrated towards one end. b Spiral amphipolar bromalite morphology, blunt ends with wider and regularly spaced turns running along the entire length (redrawn from Hunt et al. 1994). Orientation is based on Hunt and Lucas (2012)

Geological setting

One of the localities which yielded the study material has not yet been described in the literature and is here named “Archer City Bonebed (ACBB) V” (TMM-45923, coordinates on file at the J.J. Pickle Lab Vertebrate Paleontology Department of the Univesity of Texas in Austin, Texas). The second locality is known as ACBB III (Sander 1989), and a general description is on file at the Texas Memorial Museum at UT Austin (Fig. 3). ACBB V is very similar to ACBB III as described by Sander (1989). Both localities are located on the property of the Circle A Ranch within a few hundred meters of each other. The site is in Archer County approximately 4 km southwest of Archer City, Texas, USA (Fig. 3). The bonebed is situated in the Archer City Formation, the uppermost formation of the Bowie Group in the Texas Lower Permian (Hentz 1988; Wardlaw et al. 2004). This is one of many bonebeds that occur locally (Romer and Price 1940; Sander 1987, 1989); the overall lithology, which is mostly gray mudstone, is again identical to that of ACBB III (Sander 1989). Stratigraphy follows that of Hentz (1988).

Fig. 3

a Map of Archer County, Texas, USA, showing the location of the Archer City Bone Beds (ACBB). b Geologic map showing the ACBBs set in the Lower Permian Archer City Formation (modified from Hentz 1988; Labandeira and Allen 2007). c Photograph of ACBB V in the foreground facing southwest (arrow indicates southwestern boundary of ACBB III)

Evidence of Lower Permian vertebrates from both terrestrial and aquatic organisms have been collected from these and surrounding localities in Archer County, Texas, for over a century (Case 1915; Romer 1928; Cope 1878). Spiral bromalites are of the most distinctive fossilized remains found of vertebrates from the Lower Permian in this area (Amstutz 1958; Olson 1966; Häntzschel et al. 1968; Sander 1989). Presently, spiral bromalites are attributed to marine and freshwater fish that retained the spiral intestinal valve (Parker 1885; Bertin 1958; McAllister 1987; Holmgren et al. 1999). It is a pliesiomorphic condition of present day sharks. However, agnathans, lungfish, gars, and bowfins possess it as well (Gilmore 1992). Spiral intestinal valves may have been secondarily lost during the evolution of tetrapods, if they ever possessed them at all (Romer and Parsons 1986).

In addition to the spiral bromalites found at the ACBBs, other remains found in abundance at these sites presumed to be from the extinct freshwater xenacanth shark Orthacanthus, included vertebrae, fossilized cartilage, scales, and teeth (Schneider 1996). Not only are O. texensis teeth found at the ACBBs but also the teeth of O. compresus, which are both very similar in appearance (Gary Johnson, personal communication 2005).

ACBB V yielded additional vertebrate material from reptiles and amphibians including pelycosaur neural spines, Archeria vertebrae, and fragmented dermal skull bones of Eryops. Fossil flora observed at the site consisted of Walchia impressions preserved in hematitic nodules, a plant indicative of Permian delta margins (Read and Mamay 1964; DiMichele et al. 2001). Invertebrate fossils were not found.

Materials and methods

In the North Texas Lower Permian, spiral bromalites most often erode out of their encasing sediments and are collected as float. However, the informative value of bromalites is greatly enhanced when they are collected in situ and can be correctly placed within a detailed stratigraphic column (Chin 2002). All 1,070 spiral bromalites found during this study were surface collected between 2003 and 2006. Of these, 300 heteropolar specimens were used for statistical analysis. <20 amphipolar spiral bromalites were found, but they were not used because of their incompleteness. In the lab, all specimens were cleaned in a soap and water solution to remove excess dirt and allowed to dry for several hours at room temperature. Each spiral bromalite was numbered using a personal field catalog system (CDS-#) at the time of collection. All fossil material used for this study is housed in the vertebrate fossil collection of the J.J. Pickle Lab Vertebrate Paleontology Department of UT AUSTIN (TMM 45923-#) Austin, Texas, USA (see “Appendix”).

Table 1 Physical characteristics of 300 spiral heteropolar bromalites from Archer City Bonebeds III and V


The study set of 300 near complete, heteropolar spiral bromalites was chosen at random for use as a representative sample of the specimens found at the bonebed. Each bromalite was weighed on a Mettler Toledo PB303-S digital weight scale to the nearest 0.001 g. Length, greatest width, and thickness (which was taken at 90° from the greatest width) (Fig. 1a) were measured with Mitutoyo Digimatic 500-133 CD-6”B calipers to the nearest 0.01 mm (see “Appendix”). The length is considered the longest linear measurement available. The width is recorded as the longest measurement perpendicular to length. Last, thickness was taken at 90° from where the width is recorded, which is essentially the shortest measurement. The degree of flatness was calculated for each spiral bromalite using the Euclidean geometric formula for finding the eccentricity of an ellipse. Eccentricity (e) is mathematically defined as the deviation of an ellipse from the true circular form, determined by utilizing the ratio of the major and minor diameter, which is the width (w) and thickness (t), respectively (Fig. 1b).

$$ e = \sqrt {1 - \left( {\frac{{\mathop t\nolimits^{2} }}{{\mathop w\nolimits^{2} }}} \right)} $$

The closer the eccentricity value is to zero the more round the ellipse is, and the closer it is to a perfect circle. When the value is closer to one, the specimen is flatter or more “crushed”.

Volume was first determined by placing each spiral bromalite in a water-filled graduated cylinder to measure displacement. A variety of graduated cylinders (10, 100, and 200 ml) were needed to accommodate the varying sizes of the bromalites. These measurements are referred to as the “observed” volume (see “Appendix”). Density was also calculated for each spiral bromalite utilizing each specimen’s calculated and observed volume measurements (see “Appendix”).

New volume formula

Using the three linear measurements, volume (V) was also calculated using the new formula (Fig. 1a). Length (l), width (w), and thickness (t) are multiplied together. The resulting product is then multiplied by Pi (π) and divided by 12,000 to convert the measured units.

$$ V = \int\limits_{0}^{l} {\pi \left( \frac{w}{2l} \right)x\left( \frac{t}{2l} \right)xdx} = \left( {\frac{\pi lwt}{12}} \right)\left( {\frac{1}{1{,}000}} \right) = \frac{{\pi \left( {lwt} \right)}}{12{,}000}\left( {1.7088} \right) $$

The “preliminary” volumes were compared with the observed volumes by linear regression. These data were analyzed with the Number Cruncher Statistical Systems (NCSS) 2001 software. A slope of 1.7088 and an R 2 value of 0.9836 were found (Fig. 4). The slope (1.7088) was used as a constant (Fig. 5) and every “preliminary” volume was multiplied by this number. These results are referred to as the “calculated” volumes (see “Appendix”).

Fig. 4

Linear relationship between the calculated preliminary volumes and observed volumes. The calculations were done with the proposed volume formula. Observed volumes were obtained by recording water displacement using a graduated cylinder. The slope of the regression line (1.7088) is used as a constant in the proposed volume formula

Fig. 5

Sample distribution of the spiral heteropolar bromalites from Archer City Bonebed III and V, n = 300. The a observed volume and the b calculated volume show a similar distribution pattern both indicating a decrease in specimens with large volumes. c Length shows a bell curve distribution giving to the possibility that a single species is present in the sample set. d Eccentricity, there is a bell cure distribution on the degree of flatness preserved in these specimens. There is a trend towards the more crushed state

Histograms and linear regressions

Histograms were produced using Microsoft Excel 2010 to show the grouping and distribution of values for the observed and calculated volumes, length, and eccentricity of the 300 spiral bromalites (Fig. 5). The three linear measurements were each regressed against both the observed and calculated volumes (Fig. 6).

Fig. 6

Linear relationship between the three physical measurements of each of the spiral heteropolar bromalites with respect to the observed water displacement and calculated volumes, n = 300. Comparison of the two regressions shows similar results between the respected volumes. a Linear relationship between the lengths and the observed water displacement volumes (R 2 = 0.75). b Linear relationship between the lengths and the calculated volumes (R 2 = 0.75). c Linear relationship between the widths and the observed water displacement volumes (R 2 = 0.8). d Linear relationship between the widths and the calculated volumes. (R 2 = 0.8) e Linear relationship between the thickness and the observed water displacement volumes (R 2 = 0.63). f Linear relationship between the thickness and the calculated volumes (R 2 = 0.63)


Linear dimensions and volumes

Overall length of the 300 spiral bromalites ranged from 11.77 to 71.98 mm with a mean of 31.74 mm, and greatest width was between 5.07 and 44.52 mm with a mean of 14.43 mm. Height ranged from 4.00 to 23.04 mm with a mean of 10.51 mm, and eccentricity was found to be between 0.06 and 0.9 with a mean of 0.6. Mass was between 0.277 and 68.861 g with a mean of 7.971 g (see “Appendix” for complete dataset).

The spiral bromalites had a mean observed volume of 2.8 ml ± 3.0, and a mean calculated volume of 2.8 ml ± 2.9. Observed volume was in the range of 0.1–25 ml, and the calculated volume had a range of 0.11 to 25.8 ml. Absolute differences between the observed and calculated volumes ranged between 0.001063 and 1.824556 ml. The absolute difference in the densities ranged between 0.000879 and 1.811996 g/ml (see “Appendix”). The percentage differences between the observed and calculated volumes and their respective densities ranged from 0.04 to 56 %. 95 % of the statistical sample had a percent difference of <30.

Linear regressions between the volumes and physical characteristics have R 2 values and slopes that are very similar when compared with the observed and calculated volumes (Fig. 6). For example, Fig. 6a and b show the regressions for length, R 2 values 0.7498 and 0.7544, slopes of 0.2434 and 0.2422.

When comparing the two volume histograms, they show an almost identical result (Fig. 5a, b). 40 % of all bromalites (120) occur between zero and 1.5 ml (see “Appendix”). Length shows a bell curve with the greatest concentration between 20 and 35 mm (Fig. 5c). This suggests that only one species of fish produced the spiral bromalites studied.

Eccentricity and testing William’s prediction

Like the length histogram, the eccentricity histogram also shows a bell curve with 50 % between 0.6 and 0.9 (Fig. 5d). 2.7 % fall between 0.9 and 1.0, which is approaching extreme flatness. Only 0.3 % of the bromolites fall between 0 and 0.1, the most unaltered end of the scale.

The 300 specimen used in the statistical analysis showed an average length to width ratio of 2.2:1. Williams (1972) predicted that a comparison with uncrushed spiral bromalites from Texas could reveal the length to width ratio is closer to 2.5:1. It is interesting to note that if only the spiral bromalites with eccentricity values from 0 to 0.3 are used, we find 24 out of 300 (8 %) in the statistical collection meet this criterion (see “Appendix”). The resulting length to width ratio of these 24 specimens is 2.5:1. In these cases William’s prediction was correct. In contrast, 50 out of 300 (17 %) have an eccentricity ranging from 0.8 to 1.0, with a length to width ratio of 1.94:1, these of course being the most crushed (see “Appendix”).

Discussion and conclusions

Published data sets (linear measurements with accompanying volume) from other spiral bromalites could not be found for comparison in the literature. However, Chin et al. (1998) reported the length (44 cm), width (16 cm), and thickness (13 cm) of a probable Tyrannosaurus rex coprolite with an accompanying volume of 2.4 L. This volume was obtained by first determining the density of a representative piece of the coprolite using water displacement and then extrapolating the volume of the entire mass by correlating the density with the total weight of the specimen (Karen Chin: personal communication 2005). The volume of the probable T. rex coprolite was calculated using the new volume formula (Fig. 1) given the three dimensions reported by Chin et al. (1998). The resulting calculated volume was 2.39 L, without multiplying by the constant (1.7088). Another example involves a similar supposed T. rex coprolite published by Chin et al. (2003). They reported the dimensions of length (64 cm), width (17 cm), and thickness (8 to 16 cm), with a conservative estimated volume to be 6 L. With the variation in thickness an estimated volume of 3.89 to 7.78 L is found using the new formula, this time the constant (1.7088) was used. The T. rex comparison is an interesting coincidence as this formula was developed with the use of presumed freshwater shark bromalites.

The bromalite volume formula needs to be further tested on other spiral bromalite collections not only from the Lower Permian but also from other geologic ages in general to compare the values and to check accuracy and consistency of the calculations and the constant. A comparison of morphometric data from spiral amphipolar bromalites (Fig. 2b) needs to be done as well . From the data we can only interpret a single species produced the heteropolar bromalites indicated by the bell curve in the length histogram (Fig. 5c). It is obvious by the presence of the amphipolar bromalites, however, that at least a second species coexisted here with the species producing the spiral heteropolar bromalites. This warrants a closer look at the microvertebrate fauna and differences in morphology of the shark teeth from the site Johnson (1992, 1996, 1999).

Problems with this formula include accuracy of the physical measurements, which would be skewed due to any extra matrix adhered on the specimen. Also, the formula assumes that all specimens terminate in a point, but many bromalites are incomplete or have blunt tips, due to damage, erosion, or lack of preservation. This would allow some room for error and perhaps explain the high percent difference in some specimens (see “Appendix”).

Data from this study and the formula developed here will help to understand not only the spiral bromalites from ACBB III and V, but also bromalites from different localities, geological ages, and different origins. A standard precedent for classifying these fossils based on external as well as internal morphometric data is crucial to understanding their origin and producers.


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I would like to thank the owner of the Circle A Ranch, George Allan, for giving me access to his land and permission to collect, and also, Shane Bagley and Dave Wallace for their help in locating the bonebed. Steven Tudor, Mike Pettibon, Pam Buzas-Stephens, and “Geo” Jack Kelley are thanked for helping with collecting specimens. Thanks goes to Jack Loftin of Archer County Texas for his assistant, lending specimens, and providing background on the area. I want to thank Pat Mitchell (Midwestern State University) for help deriving the new volume formula, and Joel Schmitter (Midwestern State University) for lending his expertise in statistics. I also would like to thank Karen Chin of the University of Colorado Boulder for her expertise in coprolites, for sending article reprints, and her willingness to communicate with me. I would also like to thank Gary Johnson of the Southern Methodist University for his expertise in Paleozoic sharks, willingness to share specimens, and for sending reprints of his articles. I thank Fred Stangl (Midwestern State University) for allowing me to use his lab and equipment, help with the NCSS program, and for his editorial critiques. I want to recognize and thank Michael Shipley (Midwestern State University) for the use of his lab and supplies and for his guidance. I would also like to acknowledge and thank Adrian Hunt (New Mexico Museum of Natural History), Conrad Labandeira (Smithsonian Institute) and Tucker Hentz (Bureau of Economic Geology of Texas) for allowing the reproduction and use of their figures, modified for this study. Finally I would like to thank Martin Sander, from the University of Bonn, for his advice, editing and for picking up where others have left off.

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Correspondence to Christen D. Shelton.



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Shelton, C.D. A new method to determine volume of bromalites: morphometrics of Lower Permian (Archer City Formation) heteropolar bromalites. Swiss J Palaeontol 132, 221–238 (2013). https://doi.org/10.1007/s13358-013-0057-z

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  • Orthacanthus
  • Spiral coprolite
  • Texas
  • Amphipolar