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Under consideration is a numerical approach to analysis of morphospace volume and occupation based on calculation of Euclidian distances among specimens. The approach, unlike the one of M. Foot (1996), presumes consideration of inter-group distances as one of the morphospace subspaces and definition of the entire morphospace as a totality of both within and between group differences. The subspaces overlap, as a part of morphospace occupation, is defined as a ratio of the volumes of all subspaces to the entire morphospace volume. In calculation of the morphospace specific (relative) volume, the dimension of respective distance matrix is defined as including number of subgroups recognized. The following indices (number of characters being equal and they are preliminary standartized) are suggested to evaluate specific volumes of entire morphospace MD, its k-th subspace PDk, inter-group dissimilarity subspace ID, and subspaces overlap OD: MD = 2sigma(d)/[N(N - K)], PDk = 2sigma(k)d/[n(k)(n(k) - 1)], ID = 2(MD - sigmaPD(k))/[N(N - K) - sigma(k)(n(k) - 1)], OD = K(-1)(ID + sigma(k)PD(k) - MD)/MD, where d is Euclidian distance between any pair of specimens in the entire group, N is number of specimens in that group, K is number of its subgroups, n(k) is number of specimens in k-th subgroup. It is shown that estimates of portions of sex and age differences in the overall disparity obtained by the above distance based method are similar to those derived by the variances component analysis. Bootstrap is shown to provide biased estimates of confidence intervals for the above indices, which is caused by the mathematical properties of the method and not by intrinsic properties of the morphospace. Applications of the approach under consideration are illustrated by analysis of sex and age variaiton of craniometrical traits of the pine marten and the polar fox.

Interrelations between some forms of group variation (FGVs) (age, sex, geographic, inter-species, differences among breeds) of 12 to 15 measurable skull traits are studied in 6 mammal species (pine marten, polar fox, Przewalskii horse, and 3 jird species) by means of dispersion analysis (model III, MANOVA). The above FGVs are considered as factors in the MANOVA, and skull traits are considered as dependent variables. To obtaine commeasurables estimates for the FGVs, each of them is assessed numerically as a portion of its dispersion in the entire morphological disparity defined for each character (or a set of characters) by MANOVA. The data obtained indicate a wide diversity of interrelations between FGVs. It is shown that statistical analysis of significance of joint effects of FGVs does not substitute the analysis of numerical interrelations of their dispersion portions. It is concluded that it is unproductive to study such interrelations as simple "statistical regularities" like the Kluge-Kerfoot phenomenon, so the character sets are not to be considered as statistical ensembles. A kind of content-wise null-model for FGVs of measurable traits is formulated according to which there is a "background" age variation while other FGVs are its derivatives. Respectively, other factors structuring the morphological disparity under investigation being absent, a positive correlation between FGVs is to be anticipated (strong succession). With the significant deviations of the postulated correlation being observed, other factors regulating respective FGVs that cannot be reduced to the age variation are to be supposed (weak succession). Possible interpretations of interrelations between age variation and some other FGVs in carnivores are considered. Craniological variation in the Przewalskii horse is just slightly effected by maintenance conditions under its domestication, a significant influence of other factors is to be supposed. Negative correlation between geographic and inter-species differences in the jirds (genus Meriones) could be interpreted as an evidence for the speciation described by the punctuated equilibrium model.