Progeny test of tetraploid Betula platyphylla and preliminary selection of hybrid parents
Estimating genetic parameters of parental lines through progeny testing and choosing good hybrid parents are important for genetically improving seed orchard trees. In this study, 24 tetraploid progeny seedlings were used as experimental materials, which came from test cross design: six tetraploid Betula platyphylla lines (Q33, Q13, Q103, Q19, Q83 and Q14) as female parents and four individual B. platyphylla diploid lines (F3, F4, F9 and F11) as male parents were crossed. Variance analysis of height, diameter, height-to-diameter ratio, and internodal distance showed that the differences between hybrid combinations reached highly significant levels. Using multi-objective decisionmaking, we performed a comprehensive assessment of the various hybrid combinations. Using a selection rate of 20 % of the standard, five hybrids were selected; their genetic gains in average height, diameter, height-to-diameter ratio, and internodal distance were 20.95, 6.07, 13.07 and 8.96 %, respectively. We also analyzed the combining ability and genetic parameter effect values of parents and hybrid combinations. The combined analysis revealed that Q13, Q103, Q33 and Q83 were superior females; F3, F4, and F9 were superior males; and F3 × Q13, F4 × Q83 and F9 × Q33 were superior hybrid combinations. The heights and diameters of these progenies were 22.49 and 11.48 % greater than average, respectively.
Selection and grade definition of high-essential-oil superior individuals of Melaleuca altennifolia
There were 41 superior individuals selected out primarily through observation by eyes.Based on international criteria of tea-oil,there were 14 superior individuals screened out,with biomass of branches and leaves,content of tea-tree oil,content of terpinen-4-ol and 1,8-cineloe as the indexes.By method of polygonal decision,14 superior individuals were defined into 3 grades,5 individuals were grade Ⅰ,3 individuals were grade Ⅱ,6 individuals were grade Ⅲ.The biomass of branches and leaves of 8 superior individuals were 230.86-147.32 g per individual,which were 2.87-1.83 times of the average values,content of tea-oil reached 1.51%-1.15%,which was 1.70-1.29 times of the average values,and the gain by selection was very significant.
NUMBER OF TRIANGULATIONS OF A MÖBIUS STRIP
Consider a Möbius strip with n chosen points on its edge. A triangulation is a maximal collection of arcs among these points and cuts the strip into triangles. In this paper, we proved the number of all triangulations that one can obtain from a Möbius strip with n chosen points on its edge is given by 4n−1 + (2n−2 n−1 ) , then we made the connection with the number of clusters in the quasi-cluster algebra arising from the Möbius strip.