Research Articles 
Corresponding author: Lorenzo Peruzzi ( lorenzo.peruzzi@unipi.it ) Academic editor: Marcelo Guerra
© 2014 Lorenzo Peruzzi, Fahim Altınordu.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0) which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Peruzzi L, Altınordu F (2014) A proposal for a multivariate quantitative approach to infer karyological relationships among taxa. Comparative Cytogenetics 8(4): 337349. doi: 10.3897/CompCytogen.v8i4.8564

Until now, basic karyological parameters have been used in different ways by researchers to infer karyological relationships among organisms. In the present study, we propose a standardized approach to this aim, integrating six different, not redundant, parameters in a multivariate PCoA analysis. These parameters are chromosome number, basic chromosome number, total haploid chromosome length, M_{CA} (Mean Centromeric Asymmetry), CV_{CL} (Coefficient of Variation of Chromosome Length) and CV_{CI} (Coefficient of Variation of Centromeric Index). The method is exemplified with the application to several plant taxa, and its significance and limits are discussed in the light of current phylogenetic knowledge of these groups.
Comparative cytogenetics, cytotaxonomy, karyotype asymmetry, karyotype variation, PCoA
Chromosomes, especially those of plants, have been efficient material for almost every kind of cytogenetic research (
The karyotype of a species is generally subject to little variation and it is generally assumed that two similar species can be different for a number of chromosome rearrangements correlated with phylogenetic distance among them (
Hence, the aims of our study were (1) to propose a standardized use of basic karyological characters as a valid, of general use, complement to other source of systematic data to understand the relationships among taxonomic groups as families, tribes, genera, sections and species, and (2) to demonstrate the using of this new quantitative method in cytotaxonomy in selected groups, for which data were available in literature.
The data about Smilacaceae, Liliaceae and its tribes and genera were derived by
To determine the karyological relationships among taxa, we used chromosome number (2n), basic chromosome number (x), and other basic karyomorphological characters such as genome size, grossly estimated as total haploid length of the chromosome set, THL (
Other karyological characters might have been used, such as number of 45S and 5S sites or “best practice” genome size estimations, but this kind of data is not yet widespread (
Since our main objective was to highlight correctly karyological relationships among objects (e.g. single accessions) and not to form groups, we avoided multivariate classification techniques such as cluster analysis etc. and focused on a general ordination method as PCoA (Principal Coordinate Analysis). In cases where specific a priori grouping hypotheses (based on independent sources of systematic data) needed to be tested, this approach was complemented by subjecting the same data matrix to DA (Discriminant Analysis). To perform PCoA, a similarity matrix was created using
We analyzed 434 accessions for Liliaceae and 35 accessions for Smilacaceae by PCoA (cumulative variance explained by the first two axes: 54.21%). Only a modest overlap among the two families was evident (Fig.
Within Liliaceae, 103 accessions for Tulipeae tribe, 252 accessions for Lilieae tribe, 14 accessions for Medeoelae tribe, 13 accessions for Streptopeae tribe, 27 accessions for Tricyrtideae tribe and 25 accessions for Calochorteae tribe were analyzed by PCoA (cumulative variance explained by the first two axes: 53.96%). Also in this case, the accessions belonging to the same tribe clearly tend to cluster together (Fig.
Within Liliaceae tribe Tulipeae, Erythronium Linnaeus, 1753 (3), Tulipa Linnaeus, 1753 (42), Amana Honda, 1935 (2), Gagea (56) accessions were analyzed by PCoA (cumulative variance explained by the first two axes: 48.3%). The isolated position of Gagea respect with other genera was particularly evident (Fig.
We analyzed 24 accessions belonging to three sections (Annui, Cyananthus, and Stenolobi) representing 15 species of the genus Cyananthus (Campanulaceae) by PCoA (cumulative variance explained by the first two axes: 65.52%). We can see a certain overlap among all sections, with Stenolobi seemingly more isolated and Cyananthus forming a homogeneous group within of Annui (Fig.
PCoA for Cyananthus accessions based on 6 quantitative karyological parameters (Axis 1 vs. Axis 2).
We analyzed 36 accessions belonging to nine species of Crocus ser. Verni (Iridaceae): C. etruscus Parlatore, 1858 (1), C. heuffelianus Herbert, 1847 (9), C. ilvensis Peruzzi et Carta, 2011 (4), C. kosaninii Pulević, 1976 (1), C. neapolitanus (Ker Gawler) LoiseleurDeslongchamps, 1817 (6), C. neglectus Peruzzi et Carta, 2014 (5), C. siculus Tineo, 1832 (3), C. tommasinianus Herbert, 1847) (3) and C. vernus (Linnaeus) Hill, 1765 (4) (cumulative variance explained by the first two axes: 58%). We can see the accessions belonging to same species close each other (Fig.
Our method allows to describe basic karyological relationships among taxa in a correct way, avoiding redundant data or the use of statistically not well founded parameters. Concerning the examples presented, there is always a certain degree of agreement among the information resulting from karyological multivariate analysis and the available phylogenetic information (used to form the groups highlighted in the PCoA and tested by means of DA). Liliaceae and Smilacaceae are sister families (
For various reasons, researchers used until very recently outdated, wrong or redundant parameters in order to establish relationships among taxa. We propose here a standardized method, taking into account six quantitative parameters: 2n (somatic chromosome number), x (basic chromosome number), THL (total length of haploid chromosome set), CV_{CI} (Coefficient of Variation of Centromeric Index, measuring the heterogeneity in the centromere position), M_{CA} and CV_{CL} (Mean Centromeric Asymmetry and Coefficient of Variation of Chromosome Length, both measuring the karyotype asymmetry). We used a multivariate ordination approach (PCoA), eventually complemented by DA, if specific grouping hypotheses need to be tested. We think this method is best suited to establish karyological relationships, relationships, compared with classification approaches (i.e. clustering, used for instance by