THE KARYOTYPES OF DIPLOID CESPITOSE ZINNIAS: A METHOD AND ANALYSIS

The karyotypes of the three diploid (n = 10) species of the subg. Diplothrix (Zinnia-Compositae) were compared to determine whether there were any demonstrable differences which could then be sought in their polyploid derivatives. Because many of the chromosomes in a set were too similar to distinguish confidently between them, a method of analysis was developed which measures the similarity of whole sets of chromosomes rather than individual ones. The method consists of measuring the distances between graph-plotted vertices representing arm lengths of chromosomes of real or paper hybrids and then comparing these distances by means of U tests with those simiIarly derived for the "parents." This procedure obviates the need of attempting to identify morphologues (morphologically similar chromosomes) in a somatic diploid root-tip cell and to equate corresponding pairs of chromosomes from different cells of a single plant or from different species or hybrids. No demonstrable differences in the karyotypes of diploid cespitose zinnias were found. Analysis of previously published data by this method indicated that there has been a general non-objectivity and non-operationalism in the determination of homologous chromosomes, and a general but unwarranted assumption that morphologues are in reality genologues (genetically corresponding chromosomes). IN MANY systematic studies karyotypic evidence has been used to establish or substantiate evolutionary relationship based upon evidence from other approaches (see Stebbins, 1950, and Swanson, 1957, for general references; Battaglia, 1957a, b; Bhattacharuya, 1959; Sharma and Datta, 1959; Tanaka, 1960; Heimburger, 1961, 1962; Kawano and Iltis, 1963; Khan, 1963; Smith and Levin, 1967). Such studies may be especially interesting in those taxa having an aneuploid series, but they are also obviously of importance in diplo-polyploid complexes in which more than one possible ancestry must be considered in the evolution of a given polyploid species (for a recent example see De Jong, 1965). Often, however, karyotypic data and comparisons based on them are largely subjective and nonoperational in the sense that the logical steps which yielded the evidence and led to the interpretations are not indicated and therefore are not repeatable. The comments of Sokal and Camin (1965) in their discussion of operationalism in taxonomy are pertinent to this point. There have been only a few attempts to treat karyotypic data statistically. Heimburger's (1962) problem was similar to that examined here in that she used a statistical approach to study 1 Received for publication 19 October 1967. Supported by National Science Foundation Grant GB-3842. The author thanks Mr. William Bilkovich and Mr. James A. Tharp for their assistance in this project. He is particularly grateful to Dr. Morris W. Katz of Wayne State University for assistance with the statistical treatment of the data derived in this study. karyotypes of different absolute lengths and to show these differences were maintained in hybrids derived from them. Lighty and Plaisted (1960) and Maguire (1962) were concerned with sources of variation in sizes of chromosomes. In general there are three methods with which to obtain comparisons of karyotypes of different taxa. One is to study the chromosome pairing in hybrids during meiosis. This method may be quantified by comparing the frequency of chiasmata in the hybrids with that in the parental species. A modification of this system which involves a study of the maximal modal configurations found during diakinesis in aneuploid hybrids has been found to provide valuable evidence for interspecific relationships in Chaenactis (Khyos, 1965) and Haplopappus (Smith, 1965). This method is obviously limited to those organisms which can be hybridized. A second technique is to compare chromomere or band patterns along the lengths of the chromosomes as may be done with pachytene chromosomes of Zea and salivary gland chromosomes of Drosophila and other Diptera, but this is not presently feasible for most other organisms. Both of these methods can be made objective and can be quantified. The third, ordinarily not quantified, involves a comparison of chromosomes based on arm lengths and arm ratios. A modification recently proposed by Martin and Hayman (1965) consists in part of measuring the DNA content of the cells with a microdensitometer (Patau and Srinivasachar, 1960). Chromosomal pairing, the first method men-