Abstract: Proposed in this paper is a quantitative method which can be effectively used for measuring karyotype asymmetry of chromosome complements. As well known, karyotype symmetry of a complement is determined by arm ratios and relative lengths. We define the karyotype as a theoretical symmetrical karyotype in which all chromosome ann ratios are 1 and all chromosomes are equal in length. An observed complement can be assumed to have a corresponding theoretical symmetrical karyotype, and different complements with the same ploidy and the same basic number share a common theoretical symmetrical karyotype. There- fore, to measure the karyotype asymmetry of an observed complement only requires deter- mining the differences in both arm ratios and relative lengths between the observed karyotype and its corresponding theoretical symmetrical karyotype. Based on this idea, and employing absolute value distance to measure the difference in symmetry two formulas for measuring asymmetry respectively in arm ratio and relative length are developed as follows: Here r is arm ratio (long / short); Lis relative length (long+short); k is ploidy; x is basic chromosome number; m is the number of homologous chromosomes by which both mean r and mean Late caculated, and L is the total length of a complement. D, and Dt are called arm ratio asymmetry coefficient and length asymmetry coefficient respectively. If the complements concerned have the same basic number, their karyotype asymmetry can be compared by their Dc and D~ values; the greater the D, and Dt val- ues are, the more asymmetrical the karyotype is. When Dc = 0 and Dt = 0, the karyotype is theoretical symmetrical one. In other cases, where basic numbers compared are differ- ent, we can use Dc and Ut instead of De and Dt: In investigations on karyotype divergence between populations and chromosome evolution in a group, a plot of two dimensions, De and Dt, is easily used tn show rela- tionships between any two chromosome complements in respect of karyotype asymmetry. Before making a plot, both D, and Dt values are standardized becaues De values are usually different from Dt in order of magnitude. In this paper, normalization is employed, with the mean being zero and square deviation being I of the standardized data set. Three examples, where karyotype data (arm ratios and relative lengths)were pub- hshed earlier, are analysed in order to test the validity and sensitivity of the present method. The results are quite satisfactory. Example 1: Karyotype divergence among populations of Streptolirion volubile ssp. volubile(Commclinaceae). Dc and Dt values of five populations, one from Beijing, one from Tibet, two from Yunnan, China, and one from Japan, are calculated. Two-dimen- sion plot (Fig.l) shows that the Japanese population is less asymmetrical than the four Chinese populations. Among the Chinese populations, the two from Yunnan are quite similar to each other in karyotype asymmetry, while they are somewhat different from Beijing and Tibet populations. These results clearly demonstrate that the karyotype di vergence among different populations has taken place though they cannot be distin- guished by Levan's karyotype formula and Stebbins' 12-type system. Therefore, the present method is valid and sensitive, and is specially useful fin those cases, where karyotype differences between chromosome complements are too small to be recognized by other methods. Example 2: Homology between Triticum and Aegilops. The karyotype divergence trend within Triticum is distinct in Dt direction (Fig.2), with tetraploid species distrib- uted in the 3rd quadrant and hexaploid in the 2nd quadrant. For Aegilops, karyotype di- vergence trend in Dt is not as obvious as that in Dc direction. It is interesting to note that the investigated chromosome complements of Aegilops with C genome are usually separated from those of Triticum, while those without C genome but with S or D genome are located within or near Triticum distribution area (Fig.2). This result might indicate that C genome of Aegilops has not been introduced into Triticum, but S and D genomes are closely related to Triticum genome constitution. Example 3: Karyotype evolution in the Taxodiaceae. Karyotype asymmetrization in the Taxodiaceae has taken place in both Dc and Dt directions. ( Fig.3 ) Cryptomeria fortunei is characterized by the most symmetrical karyotype among the taxa studied. The karyotypes of Taxodium and Metasequoia are more asymmetrical than that of Cryptomeria. In contrast, Cunninghamia and Taiwania have the most asymmetrical karyotypes in the family. This trend of karyotype asymmetry divergence coincides with the generally recognized phylogenetic pattern of the family. The conclusion is thatkaryotype of the Taxodiaceae has evolved from symmetrical to asymmetrical type.

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