title: [Toward exploration of morphological disparity of measurable traits of mammalian skull. 3. Distance-based analysis of the morphospace volume and occupation].
abstract: 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.
authors.forename: I Ia
authors.initials: IIa
authors.lastname: Pavlinov
authors.forename: O G
authors.initials: OG
authors.lastname: Nanova