Invariance of diversity parameters of the lower jaw of the common shrew (<i>Sorex araneus</i>) based on standard measurements, Procrustes coordinates and centroid size

Puzachenko, A.Yu.; Voyta, L.L.

Russian Journal of Theriology. Main page

Invariance of diversity parameters of the lower jaw of the common shrew (Sorex araneus) based on standard measurements, Procrustes coordinates and centroid size
Puzachenko A.Yu., Voyta L.L.
P. 92-100
Information parameters of morphometric diversity (entropy, self-organisation index) of the lower jaw (hemimandible) of the common shrew (Sorex araneus Linnaeus, 1758) were estimated and compared based on (i) standard measurements or (ii) Procrustes coordinates and centroid size. In each case, two multivariate descriptive models were developed using Euclidean distances or Kendall’s t_b rank correlations. In the first case, size diversity was evaluated; in the second case, diversity of shape was evaluated. For each model, entropy and self-organisation index, which were independent of sample size, were determined. It was shown that the value of the self-organisation index for models describing size diversity was independent — or invariant — of the type of source data. (invariance) of the type of initial data. In contrast, the models based on Kendall’s t_b rank correlation were not equivalent. The self-organisation index for landmark Procrustes coordinates was significantly higher than the index calculated based on standard lower jaw measurements.

DOI: 10.15298/rusjtheriol.24.2.02

Литература

Ashby W.R. 1956. An introduction to cybernetics. London: Chapman & Hall. 306 p.

Ashby W.R. 1958. Requisite variety and its implications for the control of complex systems // Cybernetica. Vol.1. No.2. P.83–99.

Ashby W.R. 1962. Principles of the self-organizing system // Foerster H. von G. & Zopf W., Jr. (eds.). Principles of Self-Organization: Transactions of the University of Illinois Symposium. London: Pergamon Press. P.255–278

Bookstein F.L. 1991. Morphometric tools for landmark data: geometry and biology. Cambridge: Cambridge University Press. 435 p.

Conant R.C. & Ashby R.W. 1970. Every good regulator of a system must be a model of that system // International Journal of Systems Science. Vol.1. No.2. P.89–97.

Foerster H. von. 1960. On self-organizing systems and their environments // Yovits M.C. & Cameron S. (eds.). Self-Organizing Systems. London: Pergamon Press. P.31–50.

Foote M. 1997. The evolution of morphological diversity // Annual Review of Ecology and Systematics. Vol.28. P.129–152.

Haken H. 2006. Information and Self-Organization. A Macroscopic Approach to Complex Systems. Berlin, Heidelberg: Springer-Verlag. 258 p.

Hammer Ø. & Harper D.A.T. 2005. Paleontological Data Analysis. Malden: Wiley. 351 p.

Kendall M.G. 1975. Rank Correlation Methods. London: Charles Griffin and Co., Ltd. 202 p.

Klingenberg C.P. 2011.MorphoJ: An integrated software package for geometric morphometrics // Molecular Ecology Resources. Vol.2. No.11. P.353–357.

Klingenberg C.P. 2016. Size, shape, and form: concepts of allometry in geometric morphometrics // Development Genes and Evolution. Vol.226. No.3. P.113–137.

O’Keefe F.R., Meachen J.A. & Polly P.D. 2022. On information rank deficiency in phenotypic covariance matrices // Systematic Biology. Vol.71. No.4. P.810–822.

Puzachenko A.Yu. 2013. [Invariants and dynamics of morphological diversity (a case study of mammalian skull)]. Doctoral (Biol.) Thesis. Moscow: IPEE RAN. 494 p. [in Russian].

Puzachenko A.Yu. 2016. [The quantitative patterns of morphological disparity of mammalian skull] // Archives of Zoological Museum of Lomonosov Moscow State University. Vol.54. P.229–268 [in Russian].

Puzachenko A.Yu. 2020. [Shannon-Hartley law and the limit of internal ordering of biological systems] // Principles of Ecology. Vol.3. P.28–44 [in Russian].

Puzachenko A.Yu. 2023. Basic limitations of self-organization by the example of high and low-integrated very complex systems (mammalian skeleton elements and mammalian fossil assemblages): from empirical evidence to theory // Biology Bulletin. Vol.50. Suppl.1. P.34–47.

Puzachenko A.Yu. & Kupriyanova I.F. 2023. Morphological diversity of the skull and lower jaw of three shrew species (Eulipotyphla, Sorex) during depressions and abundance peaks // Biology Bulletin. Vol.50. Suppl.2. P.52–68.

Rohlf F. J. & Slice D. 1990. Extensions of the Procrustes method for the optimal superimposition of landmarks // Systematic Zoology. Vol.1. No.39. P.40–59.

Shannon C.E. 1949. Communication in the presence of noise // Proceedings of the Institute of Radio Engineers. Vol.37. No.1. P.10–21.

Shchipanov N.A. & Pavlova S.V. 2017. Density-dependent processes determine the distribution of chromosomal races of the common shrew Sorex araneus (Lipotyphla, Mammalia) // Mammal Research. Vol.62. P.267–282.

Shchipanov N.A., Voyta L.L., Bobretsov A.V. & Kuprianoba I.F. 2014. Intra-species structuring in the common shrew Sorex araneus (Lipotyphla: Soricidae) in European Russia: morphometric variability could give evidence of limitation of interpopulation migration // Russian Journal of Theriology. Vol.13. P.119–140.

Simpson G.G. 1944. Tempo and Mode in Evolution. New York: Columbia University Press. 217 p.

Stirling A. 1998. On the economics and analysis of diversity // Science Policy Research Unit (SPRU), Electronic Working Papers Series. No.28. P.1–156.

Stirling A. 2007. A general framework for analysing diversity in science, technology and society // Journal of the Royal Society Interface. Vol.4. No.15. P.707–719.

Sturges H. 1926.The choice of a class-interval // Journal of the American Statistical Association. Vol.21. P.65–66.

Vasil’ev A.G., Vasil’eva I.A., Shkurikhin A.O. 2018. [Geometric Morphometrics: from Theory to Practice]. Moscow: KMK Scientific Press. 471 p. [in Russian]

Vernadsky V.I. 1978. [Living Substance]. Moscow: Nauka. 358 p. [in Russian].

Zelditch M.L., Swiderski D.L., Sheets H.D. & Fink W.L. 2004. Geometric Morphometrics for Biologists: a Primer. London: Elsevier Academic Press. 437 p.

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