Puzachenko A.Yu., Voyta L.L. 2025. Invariance of diversity parameters of the lower jaw of the common shrew (Sorex araneus) based on standard measurements, Procrustes coordinates and centroid size // Russian J. Theriol. Vol.24. No.2. P.92–100 [in English].
Andrey Yu. Puzachenko [puzak@igras.ru], Institute of Geography, Russian Academy of Sciences, Moscow 119017, Russia; Leonid L. Voyta [leonid.voyta@zin.ru], Zoological Institute, Russian Academy of Sciences, Universitetskaya nab. 1, Saint Petersburg 199034, Russia.
doi: 10.15298/rusjtheriol.24.2.02
ABSTRACT. 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 tb 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 tb 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.
KEY WORDS: common shrew, morphological diversity, entropy, self-organisation index, geometric morphometrics.