Kaszab Zoltán (szerk.): A Magyar Természettudományi Múzeum évkönyve 76. (Budapest 1984)

Demeter, A. ; Lázár, P.: Morphometric analysis of field mice Apodemus: character selection for routine identification (Mammalia)

With this procedure part of the original variance of the data matrix was removed, and by standardizing to age-class IV animals of lowland localities, only interspecific (and of course sexual) differences remained. DELANY & HEALY (1964) used this method to remove age-related variation from the original data in their study of variation in A. sylvaticus. One-way analysis of variance was carried out to indicate any significant differences between the three species by using a procedure called a posteriori contrast test (KIM & KOHOLT 1975b). This procedure consists of comparing the means of groups pairwise. uniting those which are not significantly different, in homogenous subsets. There are several methods suitable for the reduction of dimensionality for parsimony of description, visualization and interpretation. One of these, a straightforward linear reduction technique is principal component analysis (GNANADESIKAN 1977), in which a set of new orthogonal linear coordinates, the principal components are imposed upon the original array of n points in the p-dimensional space (where n is the number of observations and p is the number of variables). This is done in such a way that the variance of the points with respect to these axes decrease in order of magnitude. Another technique is factor analysis, with which we attempt to explain variation in a jp-dimensional space by identifying a q«p vector of "common factors" and a p-dimensional vector of "unique factors". Many of the computational steps are similar in these two methods, and a thorough discussion of these, and a comparison of the two analyses are given in GNANADESIKAN (1977). One method for classifying unknown individuals, if the properties of the groups are known, is discriminant analysis. The computations are carried out using a within-groups and a betweengroups covariance matrix. The discriminant functions are such linear combinations of the original variables which exhibit the largest ratio of variance between the groups in relation to that within the groups. This ratio, the so-called F-ratio is found by eigenanalysis; having found the coefficients, a second linear combination of the original variables with the next largest F-ratio is sought for, and so on for #-1 times, where g is the number of groups. For details, see GNANADESIKAN (1977) and MARDIA et al. (1979). Canonical analysis is a technique for determining the relationship between two sets of variables by finding linear combinations of each set of variables in such a way that the new variables, called canonical variâtes, have the largest possible correlation. Similarly to principal component analysis, the coordinate geometry of the sample space (nXp) is rotated but it is the covariance between the two sets of variables that is of interest. The canonical variâtes are such that the ones within a group are uncorrelated with one another, but the corresponding pairs of the two sets are maximally correlated (GITTINS 1979). — In another analysis the characters were ranked by using the dispersion criterion proposed by ORLÓCI (1973), ordering the variables by partitioning the sum of squares to provide Fig. 4. Relative frequency distribution diagrams of two selected characters for each of the three species. The vertical lines join species which were found to be non-significantly different in the oneway ANOVA. Top = A. microps, middle — A

. sylvaticus, bottom = A.flavicoliis