This paper discusses the use of projections for the sums of squares in the analyses of variance for two-way nested design data. The model for this data is assumed to only have random effects. Two different sizes of experimental units are required for a given experimental situation, since nesting is assumed to occur both in the treatment structure and in the design structure. So, variance components are coming from the sources of random effects of treatment factors and error terms in different sizes of experimental units. The model for this type of experimental situation is a random effects model with more than one error terms and therefore estimation of variance components are concerned. A projection method is used for the calculation of sums of squares due to random components. Squared distances of projections instead of using the usual reductions in sums of squares that show how to use projections to estimate the variance components associated with the random components in the assumed model. Expectations of quadratic forms are obtained by the Hartley's synthesis as a means of calculation.

Mankyua chejuense is the only member of the monotypic genus Mankyua (Ophioglossaceae) and is endemic to Jejudo Island, Korea. To determine the precise phylogenetic position of M. chejuense, two cpDNA regions of 42 accessions representing major members of lycophytes are obtained from GenBank and analyzed using three phylogenetic analyses (maximum parsimony, maximum likelihood, and Bayesian inference). In addition, the divergence time is estimated based on a relaxed molecular clock using four fossil calibration points. The phylogenetic position of Mankyua still appears to be uncertain, representing either the earliest diverged lineage within Ophioglossaceae or a sister to the clade containing Ophioglossum and Helminthostachys. The most recent common ancestor of Ophioglossaceae and its sister lineage, Psilotum, was estimated to be 256 Ma, while the earliest divergence of Mankyua was estimated to be 195 Ma in the early Jurassic.

Orbicule(소구상체)의 분포를 확인하기 위하여 꿀풀과에 속하는 6속 11분류군과 마편초과 3속 4분류군의 약벽을 주사전자현미경(scanning electron microscope)을 이용하여 관찰하였으며, 문헌조사를 통해 현화식물 내 소구상체의 분포가 갖는 계통분류학적 유용성 및 융단조직 유형과의 관련성에 대해 검토하였다. 그 결과 꿀풀과 분류군들에서는 모두 소구상체가 관찰되지 않았고, 마편초과 분류군들에서는 평균 1 μm 이하, 구형의 소구상체들이 조밀하게 분포하는 것을 살펴볼 수 있었다. 이와 같은 과 수준에서 일관성 있는 소구상체의 분포 특징은 현화식물 전체 orbicules에 대해 조사된 150과 중 123과와 일치하는 것으로 소구상체의 분포 유형 자체가 분류학적 예견적 가치를 지니는 것으로 나타났다. 또한, 융단조직 유형이 확인된 분류군들 중 분비형 융단조직을 갖는 분류군의 약 84%에서 소구상체가 나타나고, 아메바형 융단조직을 갖는 분류군의 약 80%은 소구상체가 나타나지 않는 것으로 조사되어 소구상체의 발달이 융단조직 유형과 밀접한 관련이 있는 것으로 조사되었다. 하지만, 현재까지 수행된 소구상체 연구는 현화식물 전체 416과들 중 150과에 제한되어 있고, 이들 분류군들 중 융단조직 유형은 92과에서만 알려져 있어 소구상체의 기능 및 융단조직 유형과의 유연관계를 규명하기 위해서는 보다 광범위한 분류군을 대상으로 한 연구가 필요한 것으로 나타났다.

The distribution of orbicules was investigated for eleven taxa of six genera in Lamiaceae and four taxa of three genera in Verbenaceae using scanning electron microscopy. A literature survey to evaluate the phylogenetic potential of the orbicules and their possible correlations with tapetum types was also conducted. The orbicules are consistently absent in all investigated taxa of Lamiaceae, while small orbicules of an average size of less than 1 μm are densely distributed in Verbenaceae. In fact, orbicules appear consistently in 123 of 150 angiosperm families when investigated in at least one species. Thus, the distribution patterns of orbicules could be a useful diagnostic character in angiosperms. In addition, orbicules occur in 84% taxa of the secretory tapetum type, while they are commonly absent in the amoeboid tapetum type (ca. 80%). The presence of orbicules may be correlated with the secretory tapetum type. However, the study of orbicules is restricted in 150 families and the tapetum type within these families can be applied for 92 families out of a total of 416 angiosperm families. Thus, further investigation of orbicules is necessary in extended taxa to address the questions pertaining to orbicules.