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It is pointed out that cytological, palynological, and morphological investigations support the division of the collective genus Polygonum into natural units. The 13 sections of the collective genus are grouped into six natural genera, two of which include five and four sections, respectively, while the remaining four genera are monosectional. The present paper is a report on combined cytological and taxonomical studies of the genus Polygonum s.str. in eastern North America, including 25 taxa of the section Polygonum (= Avicularia) and one species of the section Duravia. The basic number of chromosomes of Polygonum s.str. is x = 10; all the chromosomes have an almost median centromere and thus cannot be morphologically distinguished from each other. The chromosome numbers within the group range from the diploid number 2n = 20 to the octoploid number 2n = 80. Nine species (12 taxa) are diploid; seven species (eight taxa) are tetraploid; four species (five taxa) are hexaploid, and one species is octoploid. Hybrids between several of these taxa revealed that while most species with even the same chromosome number are so different cytogenetically that their offspring are almost completely sterile, others show such close relationship that they cannot be regarded as more distinct than are intraspecific races. In spite of the use here of a system very different from those accepted in recent North American manuals, no new names or combinations are needed, since all the taxa here studied have been described in acceptable categories by previous botanists. It has been suggested that the great variability of at least one of the collective species included in recent North American manuals might be due to the occurrence of apomixis. This suggestion could not be verified, although a low degree of facultative apomixis is possible. The variation which occurs in the same locality is shown to be caused mainly by the fact that the false populations are composed of several morphologically and biologically distinct taxa at the species level, and the constancy of intraspecific races, even when they are growing together as a result of the activities of man, seems to be the result of a high degree of autogamy.

The small section Capillares of the genus Carex has been studied from the cytological and taxonomical points of view. It comprises nine distinct species, one of which (C. Boecheriana) is raised to specific status in this paper. Three species include two distinct subspecies each; two varieties and three formae are accepted for two species respectively. The chromosome numbers of the taxa involved are 2n = 18, 36, 38, 40, 54, 56, and 58. It is pointed out that the chromosomes of Carex have a polycentric or diffuse kinetochore and that this explains the aneuploid variations in number known to be typical of the genus. Karyotypic analysis of the chromosome complements of the section Capillares revealed that in the basic diploid set of 2n = 18 chromosomes four units are long, 10 are medium and about half the length of the long ones, while four are small and about half the length of the medium ones. This frequency of size classes is also met with in the plants with 2n = 36 and 54 chromosomes. Those taxa with 2n = 38, 40, 56, and 58 chromosomes show, however, such a deviation in the frequency of the size classes that it seems logical that these numbers have been produced by a secondary fragmentation of the chromosomes. On the basis of karyotypic analysis of this section and other groups of the genus it is concluded that the primary basic number for the genus Carex in particular and the family Cyperaceae in general must have been x = 5, all other numbers having been derived mainly by fragmentation of chromosomes with a polycentric or diffuse kinetochore. This phenomenon of partial agmatoploidy is widespread in Cyperaceae, whereas complete agmatoploidy is typical of the closely related Juncaceae.

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