Morphometric investigations in cyprinid biology

Abstract

Following the publication of Multivariate Morphametries (Blackith and R,ey-ment, 1971), the field of morphometrics has witnessed a renaissance in both theory and practice. Bookstein (1977, 1982) attributed the theoretical foundation of morphometrics to D'Arcy Thompson's On Growth and Form (1942). which sought to express biological form in terms of physical laws. There followed a long period of quiescence, when little or no advancement to the conceptual framework was made. Meanwhile, the foundations of multi-variate statistics were being laid by T. W. Anderson. R. A. Fisher, H. Hotelling, C. R. Rao. and others. Several obstacles prevented application of multivariate statistics to bio log-ical problems. The absence of rapid computational techniques was partly overcome by the pocket calculator and was abolished by mainframe statistical packages. The availability and moderate cost of several packages for the microcomputer places multivariate statistical techniques within reach of many users. The second obstacle was somewhat more intractable: the choice of appropriate statistical methods for a given biological problem, and the attendant difficulty of interpreting the results. The problems posed by this second obstacle were the focus ofBlackith and Reyment's book. They remark that practical experience is the only way a biologist may learn to choose and interpret his multivariate analyses (1971: v). Case studies were presented and analysed to illustrate the statistical background required and the often subtle, intuitive nature of biological interpretation involved in, for example, factor analysis. Since 1977 there has been areturn to the conceptual foundation of D' Arcy Thompson and a closer examination of the theoretical principles behind morphometric techniques (e.g. Bookstein, 1977, 1978. 1982; Bookstein et al. , 1985). While morphometrics can be broadly defined as a body oftechniques for describing body form (Reist. 1986), a somewhat more narrowly defined I. J. Winfield et al. (eds.), Cyprinid Fishes © Ian J. Winfield and Joseph S. Nelson 1991 56 Morphometric investigations in cyprinid biology usage iscurrentlypopular. Bookstein (1982: 451) views morphometrics as the empirical fusion of geometry and biology. Bookstein et al. (1985: 256) define morphometrics as 'the statistical analysis of biological homology treated as geometrical deformation'. The 'new morphometrics' of the Michigan Mor-phometrics Study Group (Bookstein et al., 1985) is not simply about quantita-tive description of the phenotype, but also about phenotypic change with respect to a homology function in a multivariate setting. Bookstein (1982: 451) remarked that the morphometric literature was oriented entirely with respect to application rather than methodology. The balance of treatment has now swung heavily in the favour of method. Biologists, especially non-systematists, may easily be confused by the prolifer-ation of terms, techniques, and theoretical arguments favouring one method over another. The publication of Morphometrics in Evolutionary Biology (Bookstein et al., 1985) marked a milestone in the synthesis of theory and