Quantification of morphological variability expressed by a “log sem” statistic: Examples from extant and extinct hominoid species (craniodental anatomy)

Abstract

In this review of a morphometric technique, conspecific pairwise comparisons are made between craniodental measurements of adult hominoid specimens (representing extant and extinct species), in least squares linear regression analyses which are associated with equations of the form y = mx + c , where m is the slope and c is the intercept. The log of the standard error of the m -coefficient (“log sem”) is a reflection of the degree of scatter around a regression line, related to variability in shape. The m -coefficient is a reflection of size. Regressions are undertaken when measurements of any specimen P are on the x-axis, and those of another (conspecific) specimen Q on the y-axis; and vice-versa. Respectively, mean log sem values of -1.61 ± 0.13 and − 1.62 ± 0.12 have been observed in the context of crania and dentition of extant (Holocene) Homo, Pan (chimpanzee) and Gorilla conspecifics. Values of circa − 1.61 also appear to be the case in conspecific comparisons of extinct Plio-Pleistocene hominins, notably Early Homo (Early Pleistocene), Paranthropus (also Early Pleistocene) and Pliocene Australopithecus. A mean log sem value of -1.61 ± 0.1 is confirmed as a reflection of a typical degree of morphological variability within hominoid species if not also in other taxa.

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Quantication of morphological variability
expressed by a “log sem” statistic: Examples from
extant and extinct hominoid species (craniodental
anatomy)
Francis Thackeray (  mrsples@global.co.za )
University of the Witwatersrand https://orcid.org/0000-0001-6884-382X
Method Article
Keywords: Morphometrics, hominoid, Holocene, Pleistocene, Pliocene, species denition
Posted Date: September 6th, 2022
DOI: https://doi.org/10.21203/rs.3.rs-2019746/v1
License:   This work is licensed under a Creative Commons Attribution 4.0 International License. 
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Abstract
In this review of a morphometric technique, conspecic pairwise comparisons are made between
craniodental measurements of adult hominoid specimens (representing extant and extinct species), in
least squares linear regression analyses which are associated with equations of the form
y = mx + c
,
where
m
is the slope and
c
is the intercept. The log of the standard error of the
m
-coecient (“log sem”) is
a reection of the degree of scatter around a regression line, related to variability in shape. The
m
-
coecient is a reection of size. Regressions are undertaken when measurements of any specimen P are
on the x-axis, and those of another (conspecic) specimen Q on the y-axis; and vice-versa. Respectively,
mean log sem values of -1.61 ± 0.13 and − 1.62 ± 0.12 have been observed in the context of crania and
dentition of extant (Holocene)
Homo, Pan
(chimpanzee) and
Gorilla
conspecics. Values of
circa
− 1.61
also appear to be the case in conspecic comparisons of extinct Plio-Pleistocene hominins, notably Early
Homo
(Early Pleistocene),
Paranthropus
(also Early Pleistocene) and Pliocene
Australopithecus.
A mean
log sem value of -1.61 ± 0.1 is conrmed as a reection of a typical degree of morphological variability
within hominoid species if not also in other taxa.
Introduction
One of the major challenges in biology, and especially in palaeobiology, concerns quantication of the
degree of morphological variability within a species. This issue is closely related to the question of what
constitutes a species and how it can be dened in such a way that the denition applies to both modern
and fossil fauna. The intention of this review is to conrm that a “log sem” morphometric method
(outlined here, with clarications) reects a way in which the degree of morphological variability within a
species may be quantied for a diversity of taxa, including Holocene, Pleistocene and Pliocene
hominoids.
The approach has been previously used in pairwise comparisons of cranial or dental dimensions in
extant hominoids (
Homo sapiens
,
Pan troglodyes
(common chimpanzee),
Pan paniscus
(bonobo) and
Gorilla gorilla
) (Thackeray and Dykes, 2016). It has also been used by Thackeray and Dykes (2016) to
analyse craniodental measurements of East African and South African Plio-Pleistocene hominins
(
Australopithecus, Paranthropus
and early
Homo
) as an extension of initial exploratory studies of
anatomical measurements of extant vertebrates (Thackeray, 2007; Thackeray et al, 1997)). New
examples of the application of the method are presented here in which the dentition of specimens
attributed to
P. robustus
is compared, and in which cranial measurements of specimens attributed to
A.
africanus, H. habilis
and
H. erectus
are analysed in conspecic comparisons. As a demonstration of
method, the results of previous and current research reect what appears to be a fundamental degree of
morphological variability within hominin species. This relates to Darwin’s (1859) appeal, in the last
chapter of
The Origin of Species
, to “weigh more carefully and to value higher the actual amount” of
variation in species.
Method

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Pairwise comparisons are made between craniodental measurements of adult hominoids in least
squares linear regression analyses which are associated with equations of the form
y = mx + c
, where
m
is
the slope and
c
is the intercept (Thackeray 2007, 2022; Thackeray & Dykes, 2016; Thackeray et al, 1997;
Thackeray & Odes, 2013). The log of the standard error of the
m
-coecient (“log sem”) is a reection of
the degree of scatter around a regression line, related to shape. The
m
-coecient is a reection of size,
sensitive to sexual dimorphism (Thackeray et al, 2000) and age (Thackeray and Kashe-Katiya, 2002). For
any two specimens P and Q, two regression analyses are undertaken, one with measurements of P on the
x-axis and Q on the y-axis. A second analysis is undertaken with P on the y-axis and with Q on the x-axis.
A mean log sem value is obtained from the two regressions. “Delta log sem” expresses the difference
between log sem values (Thackeray & Dykes, 2016). Clarications are given in Appendix 1.
Results
A mean log sem value of
circa
− 1.61 for conspecics is expressed by the following results based on data
published by Gordon and Wood (2013):
• -1.61 (Crania: female-female comparisons of
Pan paniscus
) (Gordon and Wood, 2013)
• -1.62 (Crania: male-male comparisons of
Pan paniscus
) (Gordon and Wood, 2013)
• -1.61 (Crania: female-male comparisons of
Pan paniscus
) (Gordon and Wood, 2013)
• -1.62 (Crania: female-female comparisons of
Pan troglodyes
) (Gordon and Wood, 2013)
• -1.60 (Crania: male-male comparisons of
Pan troglodytes
) (Gordon and Wood, 2013)
• -1.60 (Crania: female-male comparisons of
Pan troglodytes
) (Gordon and Wood, 2013)
• -1.61 (Crania:
H. sapiens, P. troglodytes, Gorilla gorilla) (
Thackeray and Dykes, 2016
)
These mean log sem values, with central tendency around − 1.61, are remarkably consistent. The
standard deviations associated with each set of data for
Pan-Pan
comparisons are consistently
circa
0.1
(Gordon and Wood, 2013). Thackeray and Dykes (2016) showed that the mean log sem value of -1.61
from a study restricted to crania of three extant hominoid conspecics is associated with a standard
deviation of 0.13 (n = 8,072 regressions). The mean delta log sem value is small (0.03).
The following mean log sem value has been obtained from analyses of measurements of lower rst
molars (extant conspecics):
• -1.62 (Molars:
H. sapiens, P. troglogdytes, P. paniscus, Gorilla gorilla
(Dykes, 2014)
The mean delta log sem value is small (0.05). The standard deviation associated with the mean log sem
value of -1.62 is 0.12 (n = 1520 regressions) for molars. The result is essentially identical to that which
was obtained for crania (-1.61 ± 0.13, n = 8072 regressions).

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The following mean log sem value has been obtained from pairwise comparisons between rare Early
Pleistocene crania attributed to
H. erectus
, as an example of a particular case (based on Thackeray and
Odes, 2013) using data published by Wood (1991). KNM-ER 3733 and KNM-ER 3883 are skulls from the
Turkana Basin (Kenya).
Mean log sem = -1.56 (KNM-ER 3733 and KNM-ER 3883,
H. erectus
).
This value of -1.56 (for two specimens of the same species) falls within one standard deviation from a
mean log sem value of -1.61 ± 0.1 calculated for conspecics (Thackeray and Dykes, 2016). The delta log
sem value is small (< 0.01).
The following mean log sem value has been obtained from pairwise comparison between Early
Pleistocene crania attributed to
H. habilis
, as another example of a particular case (based on Thackeray
and Odes, 2013), using data published by Wood (1991). OH 24 is a skull from Olduvai Gorge (Tanzania)
and KNM-ER 1813 is from the Turkana Basin (Kenya).
Mean log sem = -1.69 (OH 24 and KNM-ER 1813,
H. habilis
)
This value of -1.69 (for two specimens of the same species) falls within one standard deviation from a
mean log sem value of -1.61 ± 0.1 calculated for conspecics (Thackeray and Dykes, 2016). The delta log
sem value is small (0.02).
The following mean log sem value has been obtained from pairwise comparison between Pliocene skulls
that have been attributed to
Australopithecus africanus
, as a particular example for hominins based on
data published by Wood (1991) and analysed by Thackeray and Odes (2013). Sts 5 (“Mrs Ples”, an
almost complete skull) and Sts 71 (a partial skull) are both from Sterkfontein (South Africa).
Mean log sem = -1.67 (Sts 5 and Sts 71).
This mean log sem value of -1.67 (for two specimens of the same species) falls within one standard
deviation from a mean log sem value of -1.61 ± 0.1 calculated for conspecics (Thackeray and Dykes,
2016). The delta log sem value is small (0.04).
The mean of the mean log sem values for pairwise comparisons of these six Plio-Pleistocene hominin
crania (representing
H. erectus, H. habilis
and
A. africanus
) is -1.64 ± 0.06 (mean delta log sem = 0.02),
which is not signicantly different from the mean log sem value of -1.61 ± 0.13 (mean delta log sem =
0.03) obtained from crania of extant hominoid conspecics (n = 8,072 regressions).
The following mean log sem values have been obtained from pairwise comparisons between rst lower
molars (M1) attributed to
Paranthropus robustus
(early Pleistocene), based on data obtained by Dykes
(2014). TM 1517 is the holotype from Kromdraai (South Africa). Other specimens are from Swartkrans
(South Africa).

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Mean log sem = -1.59 (TM 1517 and SK 6 L)
Mean log sem = -1.64 (TM 1517 and SK 6 R)
Mean log sem = -1.56 (TM 1517 and SK 23 L)
Mean log sem = -1.51 (TM 1517 and SK 23 R)
Mean log sem = -1.70 (TM 1517 and SK 63 L)
Mean log sem = -1.63 (TM 1517 and SK 63 R)
Mean log sem = -1.66 (TM 1517 and SKW5 R)
The mean of the mean log sem values equals − 1.61 ± 0.06 (mean delta log sem = 0.03) which is
essentially identical to the mean log sem of -1.62 ± 0.12 (n = 1520 regressions) obtained for conspecic
pairs in the case of dentition in extant (Holocene) hominoids, notably
H. sapiens, P. troglodytes, P.
paniscus
, and
Gorilla gorilla (
Thackeray and Dykes, 2016).
The following mean log sem value has been obtained for rst lower molar analyses undertaken on Plio-
Pleistocene conspecic hominins, based on data obtained by Dykes (2014) and published by Thackeray
and Dykes (2016):
• -1.61 (Molars:
A. africanus
,
A. afarensis
,
H. habilis
,
H. erectus
,
P. robustus, P. boisei
).
The mean delta log sem value is 0.05. The standard deviation associated with the mean log sem value of
-1.61 is 0.10 (n = 176 pairwise regressions). This is essentially identical to the result obtained by Dykes
(2014) for extant hominoid dentition (-1.62 ± 0.12, n = 1520 regressions), as published by Thackeray and
Dykes (2016).
Discussion
The method reviewed here facilitates quantication of the degree of morphological variability within a
species. It has the potential to be used in the development of a probabilistic morphometric denition of
species (Thackeray, 2007; Thackeray and Dykes, 2016, Thackeray and Schrein, 2017), applicable in
palaeoanthropological contexts by using anatomical landmarks for purposes of pairwise comparisons of
measurements in regression equations (see Appendix 1 for clarications).
The method has potential value in other contexts, not just in palaeoanthropology. The study by
Thackeray et al (1997) was pioneering in the sense that it described the approach. This led on to the
calculation of a mean log sem value of -1.61, designated T, based on cranial measurements of terrestrial
vertebrates (a diversity of mammals, reptiles and birds, taken together) (Thackeray, 2007).
Conclusion

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This study reviews examples in which a morphometric method has been applied to hominoids,
summarizing results of earlier and current analyses obtained from extant species and extinct (Plio-
Pleistocene) hominins. Dentition of
P. robustus
is a new example which serves to conrm that a mean log
sem value of -1.61 ± 0.1 appears to reect a typical degree of morphological variability in extinct as well
as in extant hominoid species (Table1). At least for hominoids there is the potential to develop a
probabilistic morphometric denition of a species of the kind postulated by Thackeray and Dykes (2016),
based on T = -1.61 ± 0.1. The probabilistic approach is related to “sigma taxonomy” (Thackeray and
Schrein, 2017; Thackeray, 2018) which is dened as “The classication of taxa in terms of probabilities
of conspecicity, without assuming distinct boundaries between species” (Thackeray, 2018).
Declarations
Acknowledgements
The approach presented in this paper was developed with nancial support awarded to JFT from the
National Research Foundation in South Africa. I am most grateful toCaitlin Schrein
(Independent Researcher, Washington DC) and to the late Sue Dykes (palaeoanthropologist formerly at
the Evolutionary Studies Institute, University of the Witwatersrand in Johannesburg) for their enthusiastic
support and encouragement.
Statements and Declarations.The author has no competing interests.
Data availability:
Wood BA (1991) Koobi Fora Research Project, Volume 4. Hominid cranial remains.

Oxford: Clarendon
Press.
Gordon AD, Wood BA (2013) Evaluating the use of pairwise dissimilarity metrics in paleoanthropology.
Journal of Human Evolution 65, 465–477. Supplementary Files.
Thackeray JF, Odes E (2013) Morphometric analysis of early Pleistocene African hominin crania in the
context of a statistical (probabilistic) denition of a species. Antiquity, 87 (335).
http://antiquity.ac.uk/projgall/thackeray335/
Thackeray, J.F., Dykes, S. (2016) Morphometric analyses of hominoid crania, probabilities of
conspecicity and an approximation of a biological species constant. HOMO: Journal of Comparative
Human Biology, 67 (1), 1–10. http://doi:10.1016/j. jchb.2015.09.003
References
1. De Manuel M, Kuhlwilm M, Frandsen P et al. (2016) Chimpanzee genomic diversity reveals ancient
admixture with bonobos. Science 354 (6311): 477–481. doi: 10.1126/science.aag2602. Epub 2016

Page 7/10
Oct 27. PMID: 27789843; PMCID: PMC5546212. https://doi.org/10.1126/science. aag2602
2. Dykes SJ (2014). A morphometric analysis of hominin teeth attributed to different species of
Australopithecus, Paranthropus
and
Homo
. Dissertation, University of the Witwatersrand,
Johannesburg.
3. Gordon AD, Wood BA (2013) Evaluating the use of pairwise dissimilarity metrics in
paleoanthropology. Journal of Human Evolution 65, 465–477
4. Thackeray JF (2007) Approximation of a biological species constant? South African Journal of
Science, 103, 489. https://journals.co.za/doi/pdf/10.10520/EJC96631
5. Thackeray JF (2018) Alpha and sigma taxonomy of
Pan
(chimpanzees) and Plio-Pleistocene
hominin species. South African Journal of Science 114 (11/12), 1–2.
https://sajs.co.za/article/view/5823
. Thackeray JF (2022) Morphometric (‘log sem’) analysis of anatomical measurements of Galápagos
nches (
Geospiza
), chimpanzees (
Pan
) and Plio-Pleistocene hominins (
Paranthropus,
Australopithecus
and early
Homo
). South African Journal of Science, 118, 1–3.
https://doi.org/10.17159/sajs.2022/11913
7. Thackeray JF, Bellamy CL, Bellars D et al (1997) Probabilities of conspecicity: Application of a
morphometric technique to modern taxa and fossil specimens attributed to
Australopithecus
and
Homo
. South African Journal of Science, 93, 195–196.
. Thackeray JF, Mdaka S, Navsa N et al (2000) Morphometric analyses of conspecic males and
females: an exploratory study of extant primate and extinct hominid taxa. South African Journal of
Science 96:534–536.
9. Thackeray JF, Kashe-Katiya X (2002) Morphometric analysis of juvenile and adult baboon crania.
Annals of the Transvaal Museum 39:76–78.
10. Thackeray JF, Odes E (2013) Morphometric analysis of early Pleistocene African hominin crania in
the context of a statistical (probabilistic) denition of a species. Antiquity, 87 (335).
http://antiquity.ac.uk/projgall/thackeray335/
11. Thackeray, J.F., Dykes, S. (2016) Morphometric analyses of hominoid crania, probabilities of
conspecicity and an approximation of a biological species constant. HOMO: Journal of
Comparative Human Biology, 67 (1), 1–10. http://doi:10.1016/j. jchb.2015.09.003
12. Thackeray JF, Schrein C (2017) A probabilistic denition of a species, fuzzy boundaries and ‘sigma
taxonomy’. South African Journal of Science, 113 (5/6),1–2.
https://doi.org/10.17159/sajs.2017/a0206
13. Wood BA (1991) Koobi Fora Research Project, Volume4. Hominid cranial remains. Oxford: Clarendon
Press.
Table 1

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Table 1. Summary of results obtained from morphometric analyses of crania and dentition of extant
(Holocene) hominoids including humans (
Homo sapiens
), common chimpanzees (
Pan troglodytes
),
bonobos (
P. paniscus
) and gorillas (
G. gorilla
), in addition to Plio-Pleistocene hominins (
Homo habilis, H.
erectus, Paranthropus robustus, P. boisei, Australopithecus africanus
and
A. afarensis
). The mean of the
mean log sem values in this Table is -1.618 ± 0.1 for both modern and fossil sets of data (9,788
regressions).
Appendix 1 (Clarications)
  In their analyses of cranial measurements of
Pan troglodytes
(the common chimpanzee),
G.
gorilla
and
H. sapiens
(using more than 20 measurable dimensions as published by Gordon and Wood,
2013), Thackeray and Dykes (2016) obtained the following results from pairwise comparisons:
A. Mean of mean log sem values = -1.612 ± 0.129 (n = 8,072 pairwise regressions) reects what is
considered to be a typical degree of
intraspecic variation
within extant hominoids.
B. Mean of mean log sem values = -1.063 ± 0.126 (n = 26,780 regressions), reecting the degree of
variability from
interspecic comparisons.
These results clearly show (from very large numbers of regressions), that there is indeed a signicant
difference between the mean log sem values calculated for intraspecic and interspecic comparisons.
Mean delta log sem values are small (0.03) for comparisons between specimens that belong to the same
species, contrasting with higher delta log sem values for interspecic comparisons.

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The results above are relevant to a comparison between two idealised skulls sketched by Gordon and
Wood (2013), comprising a “monkey-like” skull (M) and an idealised “australopith-like” cranium (A). They
selected only a few dimensions (k = 4) based on landmarks in their example. Clearly the two crania are
different in shape, but they suggested that according to log sem, “the shape of these two crania would be
identical”. However, it is possible to calculate a log sem value for pairwise comparisons of at least 28
measurable dimensions (k = 28), based on landmarks for the idealised crania. Measurements have been
obtained for homologous pairs as if A and M were actual skulls. When measurements of M (x-axis) are
plotted against those of A (y-axis), there is a high degree of scatter around the regression line, reecting
differences in shape, and a log sem value of -1.165 is obtained. When measurements of A (x-axis) are
plotted against those of M (y-axis), a log sem value of -1.216 is obtained (k = 28). Differences in shape
are again associated with a high degree of scatter around the regression line. The mean log sem value is
-1.190 (delta log sem = 0.051), signicantly different from T = -1.61 ± 0.1 for conspecics. It would not
be correct to suggest (in the context of the log sem approach) that the two obviously different-shaped
crania ("monkey" M and "australopithecine" A) could be mistakenly thought to be identical in morphology,
when the number of available measurements is increased (k = 28 in this case). Gordon and Wood (2013)
had used only a few measurements (k

= 4) and as such were being highly selective, giving an incorrect
impression that log sem was not sensitive to shape differences.The log sem statistic is sensitive to
variability in shape when one increases the number of measurements from available landmarks. Ideally
there should be at least 20 measurements per specimen for reasons given by Thackeray and Dykes
(2016). Contrary to the view expressed by Gordon and Wood (2013), the idealised monkey (M) is
distinguishable from an idealised australopithecine A. They are most certainly not “identical”.
When comparing two crania representing different species, for example the common chimpanzee (
Pan
troglodytes
) and bonobo (
P. paniscus
), it is necessary to examine pairs of log sem values obtained from
two regressions (one with P on the x axis and Q on y axis, and vice versa), in relation to delta log sem.
About 50% of log sem values in a set of pairwise comparisons would be relatively low, in some cases <
-1.61. As noted by Thackeray and Dykes (2016), “in all cases where there is a very low log sem value
(around −1.61 or even less), the corresponding “paired” log sem value (with specimens compared on the
opposing axes) is always very high”. Under the latter conditions, delta log sem values would tend to be
relatively high (> 0.03). The associated mean log sem values would also be relatively high (> -1.61).
Together the log sem and delta values would reect differences in shape. The fact that the lower of a pair
of log sem values may be < -1.61 does
not
necessarily imply a high probability of conspecicity, because
it is only one of a pair. It is necessary to calculate mean log sem values from pairs of regressions, and to
examine them in relation to delta log sem. These factors must be taken into account in relation to two
statements by Gordon and Wood (2013). Firstly, they stated that “Many comparisons between one
bonobo cranium and one common chimpanzee cranium resulted in dissimilarity values [log sem] well
within the range of conspecic comparisons”; and secondly that “Approximately half or more of
comparisons between one bonobo cranium and one chimpanzee cranium…have dissimilarity values [log
sem] lower than a threshold”. These statements do not take into account delta log sem values which are

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based on two regression analyses, one in which specimen P is on the x-axis, and the other in which it is
on the y-axis.
The question arises as to which variables are being measured. In response, one can note that the degree
of intraspecic variability reected by a mean log sem value of
circa
   -1.61 has been obtained not only
from cranial variables (Thackeray, 2007; Thackeray and Dykes, 2016), but also from measurements from
teeth (Dykes, 2014; Thackeray and Dykes, 2016), as well as from postcrania (Thackeray, unpublished).
The degree of morphological variability expressed by -1.61 ± 0.1 appears to be typical within many (not
necessarily all) species, irrespective of which particular variables are being measured (as in the case of
crania, dentition and postcrania).
Viability of the log sem statistic has been demonstrated by Thackeray (2022) in the context of vertebrates
(including common chimpanzees, bonobos and extinct hominins). In particular, two species of
Pan
can
be generally distinguished with a small degree of overlap which can be explained in part by evidence for
hybridization (de Manuel et al, 2016), reecting the lack of a clear boundary between the two species.
Hybridisation is a phenomenon that is more common than previously thought (Thackeray and Schrein,
2017), hence the need for a probabilistic denition of a species.