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South African Journal of Science

On-line version ISSN 1996-7489
Print version ISSN 0038-2353

S. Afr. j. sci. vol.114 n.11-12 Pretoria Nov./Dec. 2018 



Alpha and sigma taxonomy of Pan (chimpanzees) and Plio-Pleistocene hominin species



Francis J. Thackeray

Evolutionary Studies Institute, University of the Witwatersrand, Johannesburg, South Africa




Keywords: biological species constant; species variation; conspecificity; morphometrics; taxonomy



A fundamental question in biology, and more specifically in palaeontology, is 'how much variation is there within a biological species?' To answer that question, it is necessary to define a species, notably in a way that can be applied in palaeontological contexts. Recognising that boundaries between taxa may not always be clear, an appeal has been made for a probabilistic definition of a species1-3, based on pairwise comparisons of specimens and morphometric analyses using least squares linear regression analysis associated with a general equation of the form y=mc+c, where x and y are linear dimensions of a skeletal element such as a cranium4. The degree of scatter around the regression equation (associated with morphology) is quantifiable using the log of the standard error of the m co-efficient (log sem). Here it is shown how this morphometric approach can be applied to cranial specimens attributed to two extant species of Pan, and to extinct Plio-Pleistocene hominins in a temporal sequence, indicating the lack of clear boundaries between species, thereby challenging the prevailing concept of alpha taxonomy5 which assumes discrete entities. An appeal is made for an alternative concept, namely sigma taxonomy.3


Applications and a probabilistic definition of a species

The approach has been applied to measurements obtained from more than 70 taxa1, and more recently to measurements of crania of Pan troglodytes, the common chimpanzee, and also to those of P. paniscus, the bonobo2,6. The results were remarkable in the sense that, in the case of both species analysed separately (using alpha taxonomy), a mean log sem value of -1.6 was obtained for conspecific pairs. The data confirmed a hypothesis proposed by Thackeray1 that -1.61 for mean log sem values constitutes an approximation of a biological species constant (T), relating to a central tendency for the degree of variation within a species. An associated standard deviation for this proposed biological constant was given as 0.1 when using more than 2000 regression analyses for pairwise comparisons of specimens of the same species.2

A mean log sem value of -1.61±0.1 based on log sem statistics was considered to be a probabilistic definition of a species2, relating to the degree of variability typically expressed within a single (extant) species.


Application to Plio-Pleistocene crania

The approach has been applied to cranial measurements of Plio-Pleistocene hominins.4 Here, attention is restricted to five well-preserved and almost complete crania which have been attributed either to the genus Australopithecus or to the younger genus Homo. The five specimens and associated data are given in Table 1, in chronological order, from 1.6 million years ago (mya) to 2.5 mya.

A matrix of log sem values, based on pairwise comparisons of cranial measurements of these specimens4 is given in Figure 1.

The mean log sem value for the data set is -1.59±0.12 (n=20 pairwise comparisons). This result for a temporal sequence is remarkable in the sense that it expresses almost exactly the degree of variability that is found spatially in two modern species of chimpanzees (-1.61±0.1), examined more specifically below.

Four sets of independent data of mean log sem values, published by Gordon and Wood6 and discussed by Thackeray and Dykes2, are given in Table 2 for conspecific chimpanzees (male and female individuals are considered separately), to demonstrate consistency in the mean value of log sem for conspecific comparisons.




On the basis of log sem statistics, it is evident that the spectrum of variability through evolutionary time (from 2.5 to 1.6 mya) in five Plio-Pleistocene hominins (mean log sem = -1.59±0.12) is comparable to the spectrum of variability in geographical space (-1.61±0.1) at the present time in Pan paniscus to the south of the Congo River. It is also comparable to the spectrum of variability in geographical space (-1.61±0.1) in Pan troglodytes to the north of that river.

Notably, the degree of variability (mean log sem = -1.61±0.1) in each of the two species of Pan developed within a period of (at least) one million years since the time of their divergence. However, when P. troglodyes and P. paniscus were compared with each other, log sem values did not show a clearly distinct separation.2,6 This finding is consistent with genetic evidence for hybridisation between P. troglodytes and P. paniscus within the last million years.7


Hypotheses and a definition

Using the results presented here for two species of chimpanzees which diverged about 1 million years ago, and also for five Plio-Pleistocene hominins in a sequence within about one million years, the following hypotheses are presented:

H1: There is no clear boundary between P. troglodytes and P. paniscus.

H2: There is no clear boundary between certain species attributed to Australopithecus and Homo.

H3: Certain hominin species attributed to Australopithecus and to Homo were capable of interbreeding within a period of a million years (a spectrum of time between 1.6 and 2.5 million years ago).

These observations and hypotheses serve to underscore the importance of developing a probabilistic definition of a species that relates to sigma taxonomy, where sigma is the Greek letter for S (Σ) standing for the concept of a spectrum3,8,9, as opposed to alpha taxonomy which assumes clear boundaries between species5. A formal definition for sigma taxonomy is: 'The classification of taxa in terms of probabilities of conspecificity, without assuming distinct boundaries between species'.



This work is supported by the National Research Foundation of South Africa and the DST/NRF Centre of Excellence for the Palaeosciences.



1.Thackeray JF. Approximation of a biological species constant? S Afr J Sci. 2007;103:489.         [ Links ]

2.Thackeray JF, Dykes S. Morphometric analyses of hominoid crania, probabilities of conspecificity and an approximation of a biological species constant. Homo. 2016;67(1):1-10.        [ Links ]

3.Thackeray JF, Schrein CM. A probabilistic definition of a species, fuzzy boundaries and 'sigma taxonomy'. S Afr J Sci. 2017;113(5/6), Art. #a0206, 2 pages.        [ Links ]

4.Thackeray JF, Odes E. Morphometric analysis of early Pleistocene African hominin crania in the context of a statistical (probabilistic) definition of a species. Antiquity. 2013;87(335):1-3. Available from:        [ Links ]

5.Mayr E, Linsley EG, Usinger RL. Methods and principles of systematic zoology. New York: McGraw-Hill; 1953.         [ Links ]

6.Gordon AD, Wood BA. Evaluating the use of pairwise dissimilarity metrics in paleoanthropology. J Hum Evol. 2013;65:465-477.        [ Links ]

7.De Manuel M, Kuhlwilm M, Frandsen P, Sousa VC, Desai T, Prado-Martinez J, et al. Chimpanzee genomic diversity reveals ancient admixture with bonobos. Science. 2016;354(6311):477-481.        [ Links ]

8.Thackeray JF. Sigma taxonomy in relation to palaeoanthropology and the lack of clear boundaries between species. Proc Eur Soc Stud Hum Evol. 2015;4:220.         [ Links ]

9.Thackeray JF. Homo habilis and Australopithecus africanus, in the context of a chronospecies and climatic change. In: Runge J, editor. Changing climates, ecosystems and environments within arid southern Africa and adjoining regions: Palaeoecology of Africa 33. Leiden: CRC Press/Balkema; 2015. p. 53-58.         [ Links ]



Francis Thackeray

Published: 27 November 2018

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