A Quantitative Method Measuring Karyotype Asymmetry and Its Application to Evolutionary Study
核型不对称性的一种定量测定法及其在进化研究中的应用

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