Published in: Journal of Astrobiology 10: 11-20
STATISTICAL ANALYSIS OF ‘TUBE-LIKE’ STRUCTURES ON MARS
PHOTOGRAPHED BY CURIOSITY AND OPPORTUNITY AND COMPARISON WITH
Richard A. Armstrong
Vision Sciences, Aston University, Birmingham, B4 7ET, UK.
Statistical comparisons were made between various ‘tube-like’ structures photographed on Mars
by Curiosity and Opportunity rovers in Gale and Endurance craters respectively and the worm
‘cases’ of terrestrial tube worms. Various statistical analyses, including principal components
analysis (PCA) based on various metrics, suggested considerable similarities between the
Martian tube-like structures and their terrestrial counterparts. Although, statistical comparisons
cannot ‘prove’ that these tube-like structures on Mars represent tube worms, they provide a more
objective basis for morphological comparison, thus supporting the conclusions of Joseph et al.
(2021a). Given the significance and implications of such data, further observations are urgently
needed to increase sample sizes available for statistical study.
Key words: Martian tube-like structures, Tube worm cases, Fossil tube worms, Principal
components analysis (PCA)
Previous studies suggest that on Mars there were lakes of water in Gale and Endurance craters in
the past which could have provided a suitable habitat for eukaryotes (Grotzinger et al. 2014,
Hynek et al. 2015). Moreover, there is evidence that in Endurance crater, ‘salty-brine’ conditions
(Squyres et al. 2006) heated by hydrothermal vents may have existed, which could have provided
an environment for a variety of organisms such as tube worms (Monastersky 2012). Hence, there
is considerable interest in a recent article in the Journal of Astrobiology (Josephs et al. 2021a)
which reports the presence of ‘tube-like’ structures on Mars which may represent tube worms or
the outer cases of tube worms. The tube worm-like structures in Endurance crater are visually
and subjectively similar in morphology to terrestrial tube worm that inhabit hydrothermal vents
(Joseph et al. 2020a. This interpretation is supported by the presence of holes in the surface
which could be the remnants of collapsed hydrothermal vents, the observation of numerous
tubular structures adjacent to or within a few centimetres of these holes, and the observation that
the mineralogy of Endurance crater and its outcrops are similar to those of terrestrial
hydrothermal vents and chimneys (see Joseph et al. 2021a). Previous studies have also described
structures resembling fossil tube worms in Gale crater photographed by the Curiosity rover
(Baucon et al. 2020), features which have been subjected to preliminary statistical analysis
(Josephs et al. 2020). The similarity of the tube-worm like structures in Endurance crater to
possible terrestrial analogues is based on subjective observation. This present study includes
additional specimens, a re-analysis of Gale crater tubular specimens (Joseph et al. 2020), and a
statistical comparative analysis of the new tubular specimens photographed in Endurance crater
(Joseph et al. 2021a). These analyses were performed to test the hypothesis that the perceived
similarities between the Martian tube-like structures and terrestrial tube worms have a
statistically significant objective basis. Statistical approaches to comparing Martian features with
putative terrestrial analogues have been published previously (Joseph et al. 2020, 2021b,
Armstrong 2021, Rizzo et al. 2021).
The images analysed in this study are listed in Table 1. In the Gale crater study, three types of
feature were compared: (1) eight examples of tube-like structures from Mars which may
represent the fossils of worm cases; an example of which is shown in Fig 1, (2) two images of
terrestrial trace fossils of tube worms, and (3) an image of a pseudofossil resembling fossil tube
worms. In the Endurance crater study, three types of feature were compared: (1) five Martian
tube-like structures which are shown in Fig 2, (2) an image of a group of terrestrial tube worm
cases (Fig 3) , and (3) four images of terrestrial fossil tube worm cases (Turonian, Cyprus).
Table 1. Details of images analysed. All figure numbers refer to images in Joseph et al. 2020 or
Josephs et al. 2021a
Study Origin Images
Gale crater Mars (Curiosity) Sols 1905, 1923; Josephs et al. 2020, Fig 7
Terrestrial trace fossils Josephs et al 2020, Fig 6
Pseudofossil Hänzschel 1975, Joseph et al. 2020, Fig 5
Endurance crater Mars (Opportunity) Sols 177,199; 299; Joseph et al. 2021a, Figs
Terrestrial tube worm cases Stainken (2020)
Terrestrial fossil worm cases Georgieva et al. 2019, Joseph et al. 2021a,
Quantitative analysis was carried out using ‘Image J' software developed by the National
Institute of Health (NIH), Bethesda, USA (Syed et al. 2000; Girish and Vijayalakshmi 2004).
Each image was opened using the software and magnified to clearly reveal the features of
interest. Images were manipulated using brightness, contrast, sharpening, and if necessary edge
detection, to optimize the appearance of the features.
Fig 1. Example of ‘tube-like’ structures on Mars (A,B) resembling fossil tube worm cases
photographed in Gale crater (Curiosity Sol 1905; NASA/JPL-Caltech)
It is difficult to establish an absolute scale measure for all images to enable accurate comparisons
of metrics. As a consequence, all metrics were based either on degree of variation such as the
coefficient of variation (CV); a measure of variation independent of the mean, or the ratios of
different measurements, e.g., total length to width, which do not depend on establishing an
accurate absolute scale. In the Gale crater study, both the Martian and terrestrial specimens
consist of filaments each comprising a number of often distinct segments connected together and
exhibiting multiple changes in direction (Fig 1). The following data were obtained from each of
these ‘filaments’: (1) total number of segments, (2) the number of directional changes along the
filament per segment, (3) the length of each segment in arbitrary units, and (4) the width of each
segment measured from 3 – 8 randomly located positions along its length, (5) the shortest
distance between the two ends of the filament, and (6) the angle between each pair of adjacent
segments. In the Endurance crater study, the following data were obtained from each tube case:
(1) variation in the width of the case measured from 5 – 13 randomly located positions along its
length, (2) the shortest distance between the two visible ends of the case, and (3) the width of the
‘opening’ at the end of the case.
Fig 2. Example of ‘tube-like’ structures on Mars (A,B) resembling fossil tube worm cases
photographed in Endurance crater (Opportunity Sols 177,199; Joseph et al. 2021a; NASA/JPL-
In the Gale crater study, a number of metrics were calculated from the data to compare the
Martian (Fig 2) with the terrestrial specimens (Fig 3) and the pseudofossil: (1) the number of
directional changes per segment, (2) degree of variation in segment length along the filament
expressed as the CV (CVL), (3) variation in width of the segments along each filament expressed
as the CV (CVW), (4) ratio of mean lengths of segments per filament to mean width (L/W), (5)
the degree of ‘tortuosity’ (T) of the filament, i.e. the ratio of the total length of all the segments
to the shortest distance between the two ends of the filament, and (6) the degree of ‘bending’ (B)
of the filament per segment, i.e., the total of the angles between adjacent pairs of segments
divided by the total number of segments (Hoffman et al. 2008). In the Endurance crater study,
the following metrics were calculated: (1) the degree of variation in case width along its length
expressed as the CV (CVW), (2) the ratio of the width of the ‘opening’ to the mean width of the
case (Op/W), and (3) the degree of ‘tortuosity’ (T) of the specimen (Hoffman et al. 2008). In
both studies, the metrics were either ratios or sources of variation and hence, not likely to be
normally distributed. Consequently, either the non-parametric Mann-Whitney or Kruskal-Wallis
tests were used to compare among the various groups.
Fig 3. Examples of terrestrial tube worm trace fossils (A) (Josephs et al 2020, Fig 6) and tube
worm cases (B) (Stainken 2020) for comparison with the tube-like structures on Mars
The data were also analysed using principal components analysis (PCA) (Statistica Software,
Statsoft Inc., Tulsa, OK, USA) (Armstrong and Hilton 2011, Rizzo et al. 2021). The analyses
were carried out using all individual filaments or tubes as variables and the various metrics as
defining features. In a PCA scatter plot of the different structures, the distance between them
reflects their relative similarity or dissimilarity based on the defining metrics. To correlate the
location of a filament or tube on a PC axis with a specific metric, correlations (Pearson’s ‘r’)
were calculated between the values of each metric from each variable and the factor loadings of
the structure relative to the PC1 and PC2. For example, a high correlation between a specific
metric and PC1 would identify that feature as particularly important in determining the
separation of filaments or tubes along PC1.
As summarized in Table 2, in the Gale crater study, there were no statistical differences between
Martian ‘tube-like’ structures and terrestrial trace fossils in number of directional changes along
the filament per segment (P = 0.89), variation in segment length (P = 0.19), variation in segment
width (P = 0.51), tortuosity (P = 0.60), and degree of bending (P = 0.19). The exception is the
L/W ratio of the segments which is significantly different (P = 0.04), the terrestrial specimens
having a higher ratio than the Martian segments. The Martian specimens also had less variation
in segment width and a smaller L/W ratio compared with the pseudofossil.
A PCA of the various specimens from the Gale crater study plotted in relation to PC1 and PC2 is
shown in Fig 4. Most of the variation (94% of total variance) was associated with PC1 and only
5% of the total variance was associated with PC2. Tour of the Mars filaments and the terrestrial
fossils exhibit a close similarity and form a cluster to the left of the plot. The remaining Mars
filaments either form a cluster nearby or at a considerable distance to the right. The latter
filament has relatively few segments compared to the others and therefore, less statistical
variation among widths and segment lengths and fewer directional changes. All Martian and
terrestrial fossil filaments were not similar to the pseudofossil which is located towards the upper
centre of the plot. Degree of ‘bending’ and L/W ratio were the metrics most closely related to
variation along PC1.
Table 2. Quantitative analysis using various metrics (D/S = Number of directional changes per
segment, CVL = Coefficient of variation of segment lengths, CVW = Coefficient of variation of
segment widths, L/W = Length/width ratio, T = Tortuosity, B = Bending) of Martian ‘tube-like’
structures (M1-M8) in Gale crater and comparison with terrestrial trace fossils (T1-T2) of tube
worms/priapulids and a pseudofossil (PS)
Specimen D/S CVL CVW L/W T B
M1 0.75 51 23 3.4 2.28 101.9
M2 0.67 12 14 4 1.14 80
M3 0.6 45 22 3 1.88 102.3
M4 0.75 22 44 2.79 2.5 60.7
M5 0.6 27.8 17 2.41 1.22 50
M6 0.4 52 15 2.54 1.44 32.5
M7 0.89 19 12 3.4 1.48 52.8
M8 0.88 13 31 2.85 1.88 63.7
T1 0.88 34 22 4.8 1.8 75.6
T2 0.43 8 24 4.1 2.06 123.2
PS 0.57 44 39 1.99 1.5 51.4
Mann-Whitney non-parametric U-test to compare between Martian and terrestrial specimens:
D/S U = 7.50, P = 0.89; CVL U = 3.0, P = 0.19; CVW U = 5.5 P = 0.51; L/W U = 2.08, P = 0.04;
Tortuosity U = 6.0, P = 0.60, Bending H =3.0, P = 0.19
Fig 4. Gale crater study: PCA of Martian tube-like structures, terrestrial tube worm fossils, and a
terrestrial pseudo-fossil resembling tube worms: A plot of PC1 against PC2. PC1 accounts for
most of the variation in the data (90%)
As summarized in Table 3, there were no significant differences among the three groups in each
of the three metrics, viz, CVW (P = 0.17), Op/W ratio (P = 0.57), and tortuosity (P = 0.68).
Hence, the Martian specimens morphologically resemble both the terrestrial and the fossil tube
A PCA of the various specimens from the Endurance crater study plotted in relation to PC1 and
PC2 is shown in Fig 5. Variation along PC2 (0.1% of total variance) was negligible compared
with that along PC1 (99% of total variance). With one exception, all specimens formed a closely
related cluster located towards the lower left of the plot. The exception was a single terrestrial
fossil worm case located some distance to the right of the main cluster which had less variation
in case width in combination with a low Op/W ratio than the other specimens. Op/W was the
metric most closely related to variation along PC1.
Table 3. Quantitative analysis using various metrics (CVW = Coefficient of variation of segment
widths, Op/W = ratio of ‘opening’ to width, T = Tortuosity, of putative Martian ‘tube-like’
structures (M1 –M5), terrestrial worm tubes (T1-T3, and fossil worm tube cases (F1-F4) in
Specimen CVW OP/W T
M1 11 1.19 1.06
M2 12.5 1.6 1.41
M3 32 1.3 1.0
M4 11 0.69 1.0
M5 16 0.71 1.0
T1 9 1.25 1.01
T2 8 0.91 1.1
T3 13 0.65 1.05
F1 7.4 0.96 1.05
F2 16 1.14 1.03
F3 4 0.67 1.06
F4 8 1.09 1.01
Kuskal-Wallis non-parametric test to compare among multiple groups: CVW H = 3.56 P = 0.17;
Op/W H = 1.14, P = 0.57; Tortuosity H = 0.76, P = 0.68
The major limitation of this type of statistical study is inevitably the small sample sizes,.
Considerable time, effort, and observational skills are necessary to detect and interpret these rare
Martian structures (Josephs et al. 2021a). In addition, tube-like structures on Mars do not show
the entire length of the specimen, are orientated differently to the camera, and exhibit few
characters on which to base metrics making it difficult to quantify and compare with terrestrial
specimens. Of the two most ‘complete’ Endurance crater specimens examined in detail, in
specimen A (Fig 2 left), only the upper contorted portion of the ‘tube’ is apparent with an
anterior depression which could constitute an anterior ‘opening’. More of specimen B is present
(Fig 2 right) with a more convincing ‘opening’ but not all the specimen is visible and is obscured
by an adjacent partially eroded ‘spheroid’. The remaining specimens analysed (Joseph et al.
2021a, Fig 11,15) also suffer from these limitations to varying extents. However, this article
includes all specimens known to date from which suitable metrics can be extracted.
-1.0005 -1 -0.9995 -0.999 -0.9985 -0.998 -0.9975 -0.997 -0.9965 -0.996 -0.9955 -0.995
Terrestrial fossil tubes
Fig 5. Endurance crater study: Principal components analysis (PCA) of Martian ‘tube-like’
structures, terrestrial worm tubes, and fossil worm tube cases: A plot of PC1 against PC2. PC1
accounts for most of the variation in the data (99%) and is correlated with CV width
Small sample sizes result in low statistical ‘power’ such that small but ‘real’ differences between
Martian and terrestrial specimens may not be detected; a statistical Type 2 error. The results of a
PCA in particular are strongly affected by the specific images selected for analysis and the
metrics used to define them (Costello and Osborne 2005). In mitigation, however, both the Gale
and Endurance crater data sets have a ‘simple structure’ in which the variables show strong
loadings onto a single component (PC1), which makes smaller samples more valid. Nevertheless,
the results should be regarded as a preliminary analysis of these features until further more
complete specimens and additional metrics can be added to the data set.
Despite these caveats, the data suggest there are considerable similarities in the quantitative
metrics between the Martian tube-like structures in Gale and Endurance craters and various
terrestrial specimens. These include similarities in width variation (CV) along the specimens
(both studies), which is relatively small, the ratio of the number of directional changes along the
filament (Gale crater only), and the degree of tortuosity (both studies). All of these variables are
more characteristic of biotic than abiotic structures (Schopt et al. 2007, Williams et al. 2015). If
confirmed by more extensive analyses, these data in combination with the evidence of ‘salty-
brine’ like habitats have considerable implications for the presence of ancient life on Mars and
its subsequent evolution, issues extensively discussed in Josephs et al. (2021a).
Statistical analysis of data based on images reported in Joseph et al. (2020a) suggest considerable
morphological similarities between Martian ‘tube-like’ structures and various terrestrial
analogues such as tube worm cases and fossils. Although, such statistical comparisons can never
‘prove’ that these ‘tube-like’ structures on Mars represent tube-worms, they do provide a more
objective basis for morphological comparison and within their limitations, are consistent with the
conclusions of Josephs et al. 2021a.
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