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.
Genetic Diversity and Mating System Analysis of Pinus massoniana in a Second-Generation Clonal Seed Orchard
A total 61 clone parents and 320 open-pollination progenies from 8 clone individuals were identified by 12 polymorphic SSR loci.The result showed that the level of genetic diversity in progeny population was the same as in maternal population,progeny population had all alleles detected in maternal population,and there were not obvious surplus phenomenon of homozygotes in progeny population(F=0.046).The south crown had more strobili than the north crown,however the genetic diversity of the north crown strobili was not substantially reduced.The progeny of neutral trees had the same level of genetic diversity as in the progeny of partial female trees,with the fixation index tended to be zero,which was accorded with Hardy-Weinberg equilibrium.The multilocus outcrossing rate in the seed orchard was 1.097,and there was no significant inbreeding between parents(tm-ts=-0.031).The multilocus outcrossing rate and singlelocus outcrossing rate in the south crown were higher than that in the north crown.The multilocus outcrossing rate of partial female trees was the same as in neutral trees,and the neutral tree had no obvious declining outcrossing rate with reduced proportion of female and male strobilus compared with partial female tree,with the fixation index tended to be zero.The progeny of the second generation clonal seed orchard still had rich genetic diversity,gene exchange among clones was relatively sufficient,and biparental inbreeding was not significant.
The parallel waveform relaxation stochastic Runge–Kutta method for stochastic differential equations
For large-scale non-autonomous Stratonovich stochastic differential equations, we study a very general parallel waveform relaxation process which is on the basis of stochastic Runge–Kutta (SRK) method of mean-square order 1.0 in this literature. The convergence of the whole parallel numerical iterative scheme can be guaranteed and the scheme provides better properties in terms of decreasing the load of the computation and operating speed. At the same time, the related limit method is also introduced as the continuous approximation derived from the iterative scheme. In the approximation interval, it is worth noting that the mean-square order of the parallel numerical iterative scheme can be kept consistent with the previous SRK method at any arbitrary time point, not just at discrete points. Some numerical simulations are presented to elaborate the computing efficiency of the parallel numerical iterative scheme.