Caryologia. International Journal of Cytology, Cytosystematics and Cytogenetics 77(4): 43-60, 2024 Firenze University Press https://riviste.fupress.net/index.php/caryologia ISSN 0008-7114 (print) | ISSN 2165-5391 (online) | DOI: 10.36253/caryologia-3034 Caryologia International Journal of Cytology, Cytosystematics and Cytogenetics Citation: Araújo, L. F., Dornelas, C. S. M., Felix, L. P. & Nollet, F. (2024). What defines a bimodal karyotype? Bimo- dality revisited. Caryologia 77(4): 43-60. doi: 10.36253/caryologia-3034 Received: October 15, 2024 Accepted: April 18, 2025 Published: July 15, 2025 © 2024 Author(s). This is an open access, peer-reviewed article pub- lished by Firenze University Press (https://www.fupress.com) and distrib- uted, except where otherwise noted, under the terms of the CC BY 4.0 License for content and CC0 1.0 Uni- versal for metadata. Data Availability Statement: All rel- evant data are within the paper and its Supporting Information files. Competing Interests: The Author(s) declare(s) no conflict of interest. What defines a bimodal karyotype? Bimodality revisited Leylson Ferreira Araújo1, Charlys Seixas Maia Dornelas2, Leonardo P. Felix2, Felipe Nollet1,* 1 Laboratório de Citogenética e Evolução Vegetal, Departamento de Botânica, Universi- dade Federal de Pernambuco, Recife, PE, Brasil 2 Departamento de Biociências, Laboratório de Citogenética Vegetal, Centro de Ciências Agrárias, Universidade Federal da Paraíba, Campus II, Areia, PB, Brasil *Corresponding author. Email: nolletmedeiros@yahoo.com.br Abstract. Bimodal karyotypes, initially defined by Avdulov, are characterized by one large and one small set of chromosomes, reflecting a particular type of karyotype asymmetry. Despite later discussions by Stebbins, the absence of a quantitative crite- rion has led to subjective classifications. This study revisits the concept of bimodal- ity through a literature review and proposes an objective criterion based on the ratio between the smallest chromosome of the larger set and the largest of the smaller set. Chromosome morphology and asymmetry were analyzed in 32 species previously clas- sified as bimodal. Statistical tests were applied to detect size discontinuities and assess bimodality. We propose two forms of bimodality, interchromosomal and intrachromo- somal, considering differences in size and morphology. Our results show that Dros- ophila melanogaster and Scaphura nigra exhibit trimodal karyotypes. A ratio of ≥1.5:1 between chromosomal subsets provides a clear and objective criterion for defining bimodality, aligning with the original concepts of Avdulov and Stebbins. Keywords: Avdulov, bimodal karyotype, chromosome asymmetry, chromosome varia- tion, cytogenetics, Stebbins. INTRODUCTION Delaunay (1923) is credited with possibly coining the term “karyotype,” which refers to the complete set of chromosomes found in the nucleus of a somatic cell. Each functional metaphase chromosome is equipped with tel- omeres and replication origins, as well as a primary constriction known as the centromere, which plays a crucial role in cell division by anchoring to a molecular structure called the kinetochore (Bodor et al. 2014). The cen- tromere divides the chromosome into two parts, typically a short arm and a long arm. Its position determines the classification of each chromosome based on the ratio of their arms, which can be categorized as metacentric, submetacentric, acrocentric, or telocentric (Guerra 1986). However, varia- tions of this classification can be found in the literature (Levan et al. 1964). https://riviste.fupress.net/index.php/caryologia https://doi.org/10.36253/caryologia-3034 https://doi.org/10.36253/caryologia-3034 https://www.fupress.com https://creativecommons.org/licenses/by/4.0/legalcode https://creativecommons.org/publicdomain/zero/1.0/legalcode mailto:nolletmedeiros@yahoo.com.br 44 Leylson Ferreira Araújo et al. The exception is holokinetic chromosomes, which lack a primary constriction because they have kinetochores distributed along the entire length of the chromosomes (Wrensch et al. 1994), as in some genera of the families Cyperaceae and Juncaceae (Greilhuber 1995; Balslev 1996; Guerra et al. 2019). The karyotype represents the first phenotypic expres- sion of the genotype (Guerra 2008), exhibiting remark- able diversity that reflects evolutionary processes (Carta et al. 2018). Karyotype evolution involves multiple levels of variation, resulting from changes in both chromosome number and structure (Mayrose and Lysak 2021). These changes often exhibit phylogenetic correlations, as evi- denced by the multitude of traits commonly observed in comparative analyses (Oliveira et al. 2015; Moraes et al. 2017; Chase et al. 2023). Karyotypes exhibit variations in terms of chromosome number, size, and centromere positioning, as well as the presence and positioning of secondary constrictions. These differences encompass aspects of chromosome morphology and molecular com- position (Weiss-Schneeweiss and Schneeweiss 2013). In eukaryotes, the smallest chromosome number is 2n = 2. This has been documented in the helminth Paras- caris univalens (Nielsen et al. 2014) and the ant Myrmecia pilosula (Crosland and Crozier 1986). In plants, the small- est chromosome number is 2n = 4, as seen in Haplopap- pus gracilis A.Gray and Brachyscome dichromosomatica C.R. Carter (Asteraceae) (Tanaka 1967; Leach et al. 2004), along with certain Poaceae, Cyperaceae, and Asparagace- ae species (Bennett et al. 1986; Vanzella et al. 2003; Vio- letta et al. 2005). On the opposite end of the spectrum, Sedum suaveolens Kimnach. (Crassulaceae), with 2n = ca. 640 between the angiosperms, and the monilophyte Ophi- oglossum reticulatum L. have the highest chromosome count recorded with 2n = 1,260 (Guerra 1988a). A symmetrical karyotype is characterized by the predominance of metacentric and submetacentric chro- mosomes of relatively uniform sizes, a trait observed in different groups (Bertollo et al. 1983; Castro et al. 2016). Asymmetrical karyotypes exhibit an increasing number of acrocentric chromosomes, along with greater vari- ation in chromosome size, making the karyotype more heterogeneous (Levitsky 1931; Stebbins 1971; Paszko 2006), exemplified by Welwitschia mirabilis Hook. with 2n = 42 acrocentric chromosomes (Khoshoo and Ahuja 1962) and several species of Oxalis L. (De Azkue and Martinez 1983), insects as Frankliniella and Selenothrips (Brito et al. 2010) and mammals (Yang et al. 1997). Typically, variations in chromosome size and mor- phology are evaluated using inter- and intrachromosom- al asymmetry indices, respectively (Paszko 2006; Chi- arini and Barboza 2008; Souza et al. 2010; Pierozzi 2011; Alves et al. 2011; Assis et al. 2013; Medeiros-Neto et al. 2017). Chromosome size and morphology varies con- siderably and, according to Stebbins (1971), asymmetric karyotypes originated from symmetrical ones. There must be definite limits to the number, size, and mor- phology of chromosomes within a karyotype; exceeding these limits could impair processes like mitosis and mei- osis. However, these limits exhibit remarkable flexibility. Occasionally, this asymmetry becomes extreme, showcasing pronounced differences in chromosome size and shape, thus allowing for the formation of two distinct subsets of chromosomes within the karyotype. Concerning interchromosomal asymmetry specifically in terms of chromosome size, these subsets emerge: one comprising larger chromosomes and the other small- er ones. Avdulov (1931) coined the term “bimodal” to describe karyotypes that consist of two sharply discon- tinuous chromosomal subsets: one with large chromo- somes and the other with small chromosomes. Although asymmetry and bimodality are related concepts, they are distinct. A bimodal karyotype always exhibits some level of asymmetry; however, an asymmetrical karyotype is not necessarily bimodal. Bimodality is evident in certain cases, such as Eleutherine bulbosa Urb. and species within the family Asparagaceae, where classifying the karyotype as bimod- al is straightforward (Goldblatt and Snow 1991). How- ever, in other plant groups like certain orchids, karyo- types are classified as bimodal, such as Vanilla planifolia Andrews (Piet et al. 2022), where a gradual variation in chromosome size is observed. In this case, the variation in chromosome size differs significantly from tradition- ally recognized bimodal karyotypes (Avdulov 1931; Wat- kins 1936; Stebbins 1971). It is evident that the concept of bimodality is primarily related to interchromosomal variation. On the other hand, could karyotypes charac- terized by a predominance of metacentric and acrocen- tric chromosomes, without submetacentric ones, be con- sidered as a form of intrachromosomal bimodality? All These questions arise due to the absence of a clear criterion defining a bimodal karyotype. For instance, in some representatives of Drosophila mela- nogaster Meigen, one chromosome pair is notably small- er than the others, leading to a distinct discontinuous variation in size among the chromosomes. Although this karyotype exhibits clear discontinuity, it is not classified as bimodal in the literature, illustrating instances where bimodal karyotypes are overlooked. Conversely, there are cases where karyotypes exhibit continuous varia- tions in chromosome size but are classified as bimodal. Some karyotypes feature three sets of chromosomes in terms of size, a trait observed in many grasshopper spe- 45What defines a bimodal karyotype? Bimodality revisited cies, which are referred to as bimodal (Mesa et al. 2010). Additionally, there are karyotypes composed of meta- centric and acrocentric only, as in Chaetanthera renifolia (J.Rémy ) Cabrera (Asteraceae) with 2n = 44, being two metacentric and 42 acrocentric chromosomes only (Bae- za et al. 2010), opening the possibility of being consid- ered bimodal with respect to chromosome morphology. The objective of this work is to reassess the concept of bimodal karyotypes. We conducted a thorough review of the literature to examine the usage of the term and to identify any deviations from Avdulov’s original concept. Additionally, we delved into the primary theories con- cerning the evolutionary origins of bimodal karyotypes, supported by clear evidence in the literature. Further- more, we undertook a comparative statistical analysis of bimodal karyotypes. This was done with the aim of establishing a clear criterion for defining bimodality, consistent with the framework established by Avdulov (1931) and later expanded upon by Stebbins (1971). MATERIALS AND METHODS Data collection A literature review was conducted by searching for articles containing the keywords “Bimodal Karyotype or Bimodality”. In each article, the concept of bimodal karyotype was highlighted when available, along with the species whose karyotypes were classified as bimodal. All concepts, including the criteria used for the applica- tion of the term, were compared and discussed with the definition of bimodal karyotype as originally established by Avdulov (1931) and Stebbins (1971). Images of the karyotypes of some species recorded in the papers as presenting bimodal karyotypes were selected for analysis, provided they included a microm- eter scale for comparison and clear chromosome mor- phology. For each karyotype, the size of all chromo- somes was measured using the software Imagetool® version 3.0 (available at http://compdent.uthscsa.edu/ dig/itdesc.html), calibrated with the scale available in the selected images. Additionally, the morphology of all chromosomes per karyotype was established based on Guerra (1986). Among the asymmetry indices, the A1 and A2 by Romero-Zarco (1986) were utilized in our analyses as they are considered the most accurate in assessing dis- similarity among chromosomes in a karyotype (Paszko 2006). The classification of karyotypic asymmetry by Stebbins (1971) was also employed for karyotype com- parisons (Paszko 2006). Ideal karyotypes according to Stebbins (1971), representing the theoretically possible extremes of symmetry and asymmetry, were constructed using Photoshop CS3 (Figure 1). Real karyotypes close to the ideal schematic karyotypes were also presented to demonstrate the analyses (Figure 2). Inter- and intrachromosomal asymmetry, as well as the discontinuity in size between chromosome groups of the analyzed species, were compared with three species classified by Stebbins (1971) as presenting bimodal kar- yotypes: Aloe zebrina Baker and Consolida regalis Gray (now Delphinium consolida L.) and Muscari comosum (L.) Mill. (Figure 3). Based on this information, clear quantitive and qualitative criteria were established to better define the bimodality of a karyotype. Statistical analyses The chromosome size data were collected and organ- ized into a vector containing measurements in microm- eters. These measurements were subsequently converted into a data frame to facilitate subsequent analyses in the R 4.4.1 statistical environment. To compare the efficien- Figure 1. Idiograms of the theoretically possible ideal karyotypes with n = 6. The first represents the extreme of symmetry, composed of exactly identical metacentric chromosomes (M), classified by Stebbins as 1A, and Romero-Zarco (1986) indices A1 = 0 and A2 = 0. The second represents the extreme of asymmetry, composed of acrocentric chromosomes (A), classified by Stebbins as 4C, and Romero-Zarco (1986) indices A1 = 1 and A2 = 1. The chromo- somes are aligned at the centromere position. A scale in µm is dis- played on the left. http://compdent.uthscsa.edu/dig/itdesc.html http://compdent.uthscsa.edu/dig/itdesc.html 46 Leylson Ferreira Araújo et al. cy of different statistical methods in detecting disconti- nuities and bimodality in chromosome size within each karyotype, Hartigan’s Dip Test, Silverman’s Test and pro- portionality analysis were also utilized. All analyses were conducted using the statistical software R 4.4.1. Criteria such as sensitivity in detecting bimodality, robustness to different distribution patterns of chromosome sizes, and interpretability of the results were considered to compare the efficiency of each method. The results were analyzed based on the consistency and interpretation of evidence provided by Stebbins (1971) and Avdulov (1931). Histograms and density plots To verify the continuous or discontinuous variation in chromosome sizes, histograms and density plots were used. The histogram allowed the observation of the fre- Figure 2. Karyograms of a real symmetric karyotype (Opuntia cochenillifera (L.) Mill with 2n = 22) and an asymmetric Trimodal karyo- type (Scaphura nigra Stål with 2n = 26). The first karyogram represents symmetry, composed of very similar metacentric chromosomes (M), classified by Stebbins as 1A, with Romero-Zarco (1986) indices of A1 = 0.08 and A2 = 0.09. The second karyogram (schematic draw- ing based in Mesa et al. 2010) represents almost extreme asymmetry, composed of submeta and acrocentric chromosomes, classified by Stebbins as 4C, with Romero-Zarco (1986) indices of A1 = 0.70 and A2 = 1. The number of peaks in the density plot indicates continuous or discontinuous variation, respectively. The k-means clustering displays the number of chromosome subsets in different colors based on discontinuity. The proportion between subsets is shown for Scaphura nigra. A scale in µm is displayed on the left. 47What defines a bimodal karyotype? Bimodality revisited quency of different size measurements, while the density plot provided a continuous visualization of the data dis- tribution. The density plot was used to provide a contin- uous estimate of the distribution of chromosome sizes, helping to identify the presence of chromosomes subsets (Thrun et al. 2020). K-means clustering analysis The K-means clustering analysis is a statistical tech- nique used to partition a dataset into k clusters, where each observation belongs to the cluster with the nearest mean (Jain 2010). This technique can reveal distinct pat- terns in the variation of chromosome sizes, indicating whether the distribution is continuous and unimodal or discontinuous and bimodal (Wu 2012). When the vari- ation in chromosome size is continuous and unimodal, the data tend to distribute smoothly and gradually, forming a straight line. Statistically, this means that the data density shows a single main peak. A greater num- ber of clusters with distant centroids indicate the pres- ence of multiple modes (or chromosome subsets). Thus, the variation within clusters is smaller, but the variation between clusters is larger. The Hartigan’s Dip Test Hartigan’s Dip Test was applied to assess the unimo- dality of chromosome sizes. This statistical test evalu- ates whether the data distribution can be considered unimodal or if there is evidence of bimodality (Harti- gan and Hartigan 1985). Hartigans’ Dip Test is effective at detecting multimodality in a data distribution, and it does not assume a specific distribution of the data (such as normality), making it flexible for several distribu- tion shapes. However, it requires a sufficient number of observations to accurately detect multimodality. With small samples, it may not be able to distinguish between closely spaced modes. The choice of significance level can affect the interpretation of results, leading to some subjectivity in determining multimodality. The Silverman Test Silverman’s Test complemented Hartigan’s Dip Test by offering an alternative approach to detecting bimodal- ity in chromosome sizes using kernel density estimates to assess data distribution shape (Silverman 2017). The Sil- verman Test is specifically designed to test the hypothesis of bimodality versus unimodality, being highly sensitive to detect two distinct peaks in a distribution. This test may be more effective in detecting bimodality in small- er samples compared to Hartigan’s Dip Test. However, although it is more flexible than many parametric tests, it still assumes that the underlying shape of the distribution is smooth, which may not be suitable for all distributions. Regression analysis Regression was conducted to examine the relation- ship of the ratio between the smallest chromosome of the Figure 3. Idiograms of the species Aloe zebrina with n = 7 (clas- sified by Stebbins as 4C), Consolida regalis with n = 8 (classified by Stebbins as 3C) and Muscari comosum with n = 9 (classified by Stebbins as 2C). Chromosomes are aligned by the base and in descending order. The gray box highlights the smallest chromosome of the larger subset next to the largest chromosome of the smaller subset. The ratio between these highlighted chromosomes is given alongside. A scale in µm is displayed on the left. 48 Leylson Ferreira Araújo et al. larger subset and the largest chromosome of the smaller subset in putative bimodal karyotypes and the p-values from the Silverman Test. No specific transformations were necessary as the variables were ready for analysis. For the Welch’s t-test, the data were divided into two groups based on the chromosome ratio: one group with ratios < 1.50:1 and another with ratios ≥ 1.50:1. A simple linear regression model was chosen to assess the relation- ship between the chromosome ratio (independent vari- able) and the p-values from the Silverman Test (depend- ent variable). The analysis was performed using R soft- ware. The regression results were visualized in a scatter plot with the following characteristics: The x-axis repre- sents the chromosome ratio, and the y-axis represents the p-values from the Silverman Test. Blue points represent species with p-values ≤ 0.05, while black points represent species with p-values > 0.05. The vertical blue line rep- resents the 1.50:1 ratio, and the horizontal red line indi- cates the significance level (p = 0.05). RESULTS Kariomorphometry data and karyotype asymmetry In this study, we analyzed 32 species identified as having bimodal karyotypes in scientific articles. The species, along with their respective diploid chromosome numbers, the size of the largest and smallest chromo- some in the complement, intra- (A1) and interchro- mosomal asymmetry (A2) according to Romero-Zarco (1986), asymmetry classification of Stebbins (1971), the size of the smallest chromosome of subset 1 and the largest chromosome of subset 2 (SCh1-LCh2), and when it occurred, the smallest chromosome of subset 2 and the largest chromosome of subset 3 (SCh2-LCh3), as well as the ratio between subsets are summarized in Table 1. The chromosome numbers of the analyzed species ranged from 2n = 8 in Drosophila melanogaster and H. chillensis (Kunth) Britton to 2n = 90 in Agave fourcroydes Lem. (Table 1). The smallest chromosome among the analyzed species was recorded for Puya mirabilis (Mez) L.B.Sm. with 0.53 µm, while the largest was recorded for Scaphura nigra Stål (Orthoptera) with 25.90 µm (Table 1), which also exhibited the greatest discrepancy between the largest and smallest chromosome in the complement (27.30 times). The smallest difference was observed in Oxalis linarantha Lourteig, which varied only 2.14 times (Table 1). Most species (13 taxa) showed a variation between 3 to 3.99 times. According to Romero-Zarco’s asymmetry index (1986), Aloe zebrina exhibited the most intrachromosomal asymmetric karyotype with A1 = 0.77, while Bixa orellana L. showed the most symmetric karyotype with A1 = 0.09 (Table 1). Scaphura nigra displayed the most interchro- mosomal asymmetric karyotype with A2 = 1.0, whereas Calydorea crocoides Ravenna was the most symmetric with A2 = 0.24 (Table 1). Fifteen species demonstrated moderately asymmetric karyotypes ranging from A1 = 0.40 to 0.60, while eight species displayed slightly asym- metric karyotypes with A1 ≤ 0.39. Only six species exhib- ited highly asymmetric karyotypes with A1 ≥ 0.61 (Table 1). Regarding A2, thirteen species had moderately asym- metric karyotypes ranging from A2 = 0.40 to 0.60, while eleven species showed slightly asymmetric karyotypes with A2 ≤ 0.39. Eight species displayed highly asymmetric karyotypes with A2 ≥ 0.61 (Table 1). According to Steb- bins’ (1971) classification of asymmetry categories, Bixa orellana exhibited the most symmetric karyotype classi- fied as 1B, while Aloe zebrina and Scaphura nigra♂ were classified as 4C, highly asymmetric (Table 1). Histograms, density plots and K-means clustering analysis The analyses of the histograms reveal a variety of patterns in chromosome size distributions among the studied species, with clear examples of unimodality, bimodality, and more complex distributions. K-means cluster graphs complement these observations by iden- tifying distinct subgroups within the chromosome dis- tributions. Out of the 32 species analyzed, 24 exhibited two distinct peaks in the density histograms, suggesting a bimodal distribution. The K-means cluster graphs of these species show two distinct clusters (Figures 4-5). On the other hand, species such as Calydorea cro- coides, Cephalanthera rubra (L.) Rich. (Figure 4), Gastrodia gracilis Blume, Herbertia darwinii Roitman & J.A.Castillo, Hyacinthella dalmatica (Avé-Lall.) Trinajstic, and Puya mirabilis (Figure 5) display a single peak in their density histograms, indicating a unimodal distribution of chromo- some sizes. The K-means cluster graphs of these species present a single cluster of points. The species Drosophila melanogaster (Figure 4) and Scaphura nigra (Figure 5), showed three peaks in their density histograms, indicat- ing a trimodal distribution. The K-means cluster graphs of these species reflect this complexity with three clusters. Hartigans’ Dip Test The Hartigans’ Dip Test revealed that seven out of the 30 species analyzed (23.33%) have a bimodal distribu- tion of chromosome sizes (Table 2). The species consid- ered bimodal by the Hartigans’ Dip Test, with p-values ≤ 0.05, were: Agave angustifolia Haw., A. parviflora Torr., http://L.B.Sm 49What defines a bimodal karyotype? Bimodality revisited Aloe tenuior Haw., A. vera, A. zebrina Baker and Milium montianum (now Milium vernale M.Bieb.). The other 23 species (76.67%) were considered unimodal, with p-values greater than 0.05, indicating the absence of bimodality. Silverman Test The Silverman Test indicated that 20 out of the 30 species (66.67%) have a bimodal distribution of chromo- some sizes (Table 2). The species considered bimodal by the Silverman Test, with p-values ≤ 0.05, were: Agave angustifolia Hw., A. cupreata Trel. & A.Berger, A. four- croydes, A. parviflora, A. tequilana F.A.C.Weber, Aloe ten- uior, A. vera, A. zebrina, Cephalanthera longifolia, Con- solida regalis, Cuscuta nitida E.Meyer., Epidendrum ful- gens Brongner, H. chillensis, Muscari comosum, Luzuria- ga radicans Ruiz & Pav., Milium montianum, Sellocharis paradoxa Taub., Sprekelia formosissima (L.) Herb., and Table 1. Species mentioned in scientific articles as having bimodal karyotypes, chromosome number (2n), size of the largest and smallest chromosome in the complement (in micrometers - µm), the intra- (A1) and interchromosomal (A2) asymmetry index (Romero-Zarco, 1986) and Stebbins’ Classification (1971), size of the smallest chromosome in Subset 1 and largest chromosome in Subset 2 (SCh1-LCh2), and when present, the smallest chromosome in Subset 2 and largest chromosome in Subset 3 (SCh2-LCh3), the ratio between the largest and smallest chromosomes of the subsets. Species* 2n Size (µm) Asymmetry Index Classification of Stebbins SCh1-LCh2 SCh2-LCh3 RatioLargest/ smallest A1 A2 Agave angustifólia 60 6.48-2.16 0.39 0.62 2C 6.18-4.10 1.50:1 A. cupreata 60 5.87-1.26 0.28 0.65 2C 4.85-2.75 1.76:1 A. fourcroydes 90 16.74-2.39 0.31 0.59 2C 12.02-6.83 1.75:1 A. parviflora 60 11.51-1.21 0.22 0.55 2C 9.09-5.10 1.78:1 A. tequilana 60 6.35-0.92 0.36 0.69 2C 5.32-3.30 1.61:1 Aloe tenuior 14 9.17-2.99 0.57 0.42 3B 7.87-4.33 1.81:1 A. vera 14 16.95-3.25 0.58 0.43 3B 13.23-4.85 2.72:1 A. zebrina 14 15.58-4.04 0.77 0.49 4C 14.16-4.90 2.88:1 Bixa orellana 14 3.64-1.47 0.09 0.36 1B 3.53-2.34 1.50:1 Calydorea crocoides 14 8.55-3.34 0.39 0.24 2B 7.12-5.58 1.27:1 C. undulata 14 8.55-3.34 0.35 0.36 2B 7.26-4.50 1.61:1 Cephalanthera longifolia 32 9.54-1.88 0.46 0.53 2B 8.55-4.53 1.88:1 C. rubra 44 12.14-2.40 0.38 0.48 2C 10.71-8.72 1.22:1 Consolida regalis 16 13.76-2.14 0.49 0.51 3C 11.91-4.10 2.90:1 Cuscuta nitida 28 6.25-0.97 0.14 0.80 2C 5.18-1.65 3.13:1 Drosophila melanogaster ♂ 8 6.79-0.69 0.42 0.55 3C 6.57-4.12 4.10-0.70 1.59:1/5.85:1 Eleutherine bulbosa 12 6.19-1.49 0.18 0.67 2C 6.08-3.17 1.91:1 Epidendrum fulgens 24 3.15-1.20 0.35 0.25 2B 3.10-1.90 1.63:1 Gastrodia gracilis 22 3.10-1.00 0.28 0.26 2B 3.00-2.36 1.27:1 Herbertia darwinii 14 4.17-1.86 0.41 0.30 2B 3.55-2.44 1.45:1 Hyacinthella dalmatica 20 4.69-1.45 0.42 0.33 2B 4.54-3.16 1.43:1 H. chillensis 8 7.23-1.98 0.56 0.50 3B 5.28-2.62 2.00:1 Leopoldia comosa 18 7.48-1.21 0.30 0.72 2C 5.49-2.68 2.04:1 Luzuriaga radicans 20 11.43-3.35 0.56 0.46 3B 10.82-6.54 1.65:1 Milium montianum 22 6.00-1.81 0.34 0.55 2C 5.40-2.40 2.25:1 Oxalis linarantha 14 1.87-0.87 0.33 0.29 2B 1.84-1.19 1.54:1 Puya mirabilis 50 1.52-0.53 - 0.25 C Scaphura nigra♂ 26 25.90-1.34 0.70 1.00 4C 25.90-15.68 15.28-7.40 1.65:1/2.06:1 Sellocharis paradoxa 20 5.70-2.20 0.70 0.27 3B 5.05-2.96 1.70:1 Sprekelia formosissima 60 11.76-2.89 0.44 0.30 3C 11.66-7.72 1.51:1 Tigridia pavonia 28 7.85-1.90 0.31 0.72 2B 7.22-4.06 1.77:1 * Species classified by Stebbins (1971) as representing four different levels of karyotypic bimodality are highlighted in bold. 50 Leylson Ferreira Araújo et al. Figure 4. Density histograms and K-means clustering analysis of chromosome size variation. Karyotypes with continuous chromosome size variation exhibit a single peak. Bimodal karyotypes display two peaks, while trimodal karyotypes show three peaks. K-means clusters indi- cate the chromosomal subsets. Unimodal and trimodal karyotypes are highlighted with thicker blue lines. 51What defines a bimodal karyotype? Bimodality revisited Figure 5. Density histograms and K-means clustering analysis of chromosome size variation. Karyotypes with continuous chromosome size variation exhibit a single peak. Bimodal karyotypes display two peaks, while trimodal karyotypes show three peaks. K-means clusters indi- cate the chromosomal subsets. Unimodal and trimodal karyotypes are highlighted with thicker blue lines. 52 Leylson Ferreira Araújo et al. Tigridia pavonia (L.f.) DC. The remaining 10 species (33.33%) were considered unimodal by the Silverman Test, with p-values greater than 0.05. Table 2. Results of Hartigans’ Dip Test and Silverman Test for bimodality assessment in different species, with their respective diploid chro- mosome numbers (2n), Hartigan’s Dip Test statistic (D), and associated p-values, indicating the probability of unimodality or bimodality. P-values less than 0.05 suggest bimodality. Species 2n Hartigans’ dip test Silverman test Agave angustifolia 60 D = 0.072829 p-value = 0.01416 Bimodal p-value = 0.002002002 Bimodal A. cupreata 60 D = 0.056188 p-value = 0.1607 Unimodal p-value = 0.00 Bimodal A. fourcroydes 90 D = 0.042581 p-value = 0.2724 Unimodal p-value = 0.00 Bimodal A. parviflora 60 D = 0.065686 p-value = 0.04409 Bimodal p-value = 0.00 Bimodal A. tequilana 60 D = 0.055344 p-value = 0.1758 Unimodal p-value = 0.00 Bimodal Aloe tenuior 14 D = 0.15544 p-value = 0.001726 Bimodal p-value = 0.02002002 Bimodal A. vera 14 D = 0.17993 p-value = 0.00004786 Bimodal p-value = 0.01101101 Bimodal A. zebrina 14 D = 0.19608 p-value = 0.0000007587 Bimodal p-value = 0.01601602 Bimodal Bixa orellana 14 D = 0.071429 p-value = 0.8058 Unimodal p-value = 0.1011011 Unimodal Calydorea crocoides 14 D = 0.067901 p-value = 0.8718 Unimodal p-value = 0.1711712 Unimodal C. undulata 14 D = 0.097354 p-value = 0.2761 Unimodal p-value = 0.08008008 Unimodal Cephalanthera longifolia 32 D = 0.075225 p-value = 0.153 Unimodal p-value = 0.008008008 Bimodal C. rubra 44 D = 0.043544 p-value = 0.7966 Unimodal p-value = 0.1941942 Unimodal Consolida regalis 16 D = 0.10106 p-value = 0.1592 Unimodal p-value = 0.05505506 Bimodal Cuscuta nitida 28 D = 0.052203 p-value = 0.8241 Unimodal p-value = 0.01201201 Bimodal Drosophila melanogaster♂ 8 D = 0.12463 p-value = 0.2185 Unimodal p-value = 0.3153153 Unimodal Species 2n Hartigans’ dip test Silverman test Eleutherine bulbosa 12 D = 0.083333 p-value = 0.6877 Unimodal p-value = 0.08708709 Unimodal Epidendrum fulgens 24 D = 0.049242 p-value = 0.9431 Unimodal p-value = 0.009009009 Bimodal Gastrodia gracilis 22 D = 0.067753 p-value = 0.5714 Unimodal p-value = 0.1551552 Unimodal Herbertia darwinii 14 D = 0.084586 p-value = 0.528 Unimodal p-value = 0.1131131 Unimodal Hyacinthella dalmatica 20 D = 0.056534 p-value = 0.903 Unimodal p-value = 0.08408408 Unimodal H. Chillensis 8 D = 0.14425 p-value = 0.09007 Unimodal p-value = 0.05405405 Bimodal Luzuriaga radicans 20 D = 0.064706 p-value = 0.7327 Unimodal p-value = 0.05105105 Bimodal Milium montianum 22 D = 0.15152 p-value = 0.00004228 Bimodal p-value = 0.02002002 Bimodal Muscari comosum 18 D = 0.065046 p-value = 0.7877 Unimodal p-value = 0.02502503 Bimodal Oxalis linarantha 14 D = 0.071429 p-value = 0.8058 Unimodal p-value = 0.06906907 Unimodal Puya mirabilis 50 D = 0.038571 p-value = 0.8748 Unimodal p-value = 0.1921922 Unimodal Scaphura nigra♂ 26 D = 0.046423 p-value = 0.9567 Unimodal p-value = 0.3153153 Unimodal Sellocharis paradoxa 20 D = 0.058333 p-value = 0.8703 Unimodal p-value = 0.02502503 Bimodal Sprekelia formosissima 60 D = 0.042304 p-value = 0.6078 Unimodal p-value = 0.03803804 Bimodal Tigridia pavonia 28 D = 0.059555 p-value = 0.6144 Unimodal p-value = 0.007007007 Bimodal 53What defines a bimodal karyotype? Bimodality revisited Comparison between Hartigans’ Dip Test and Silverman Test Comparing the two tests, we observed that the Sil- verman Test was more sensitive in detecting bimodality. This difference in sensitivity suggests that the Silverman Test is less stringent in identifying bimodal distributions. On the other hand, the species that were considered bimodal by both tests are: Agave angustifolia, A. parviflo- ra, Aloe tenuior, A. vera, A. zebrina, Hypochaeris brasilien- sis, and Milium montianum. The species considered uni- modal by both tests were: Bixa orellana, Calydorea cro- coides, C. undulata, Cephalanthera rubra, Eleutherine bul- bosa, Gastrodia gracilis, Herbertia darwinii, Hyacinthella dalmatica, Oxalis linarantha, and Puya mirabilis. The results indicate that the Silverman Test is more effective in detecting bimodality compared to the Harti- gans’ Dip Test, identifying a higher proportion of species with a bimodal distribution of chromosome sizes. This sensitivity can be particularly useful in studies aiming to identify bimodality in chromosomal data sets, although the Hartigans’ Dip Test may be preferred in contexts where specificity and the reduction of false positives are crucial. Regression Analysis A regression analysis was conducted to examine the relationship between the ratio of chromosome sub- sets (according to the diagrams illustrated in the Figure 3, see Table 1) and the p-values of the Silverman test (Table 2). The results of the linear regression as follows: Intercept: 0.02004 (Standard Error: 0.03729, t = 0.538, p = 0.595) and Proportion Coefficient: 0.02619 (Stand- ard Error: 0.01752, t = 1.495, p = 0.145). The residuals showed the following distribution: Minimum: -0.09001, 1st Quartile: -0.05987, Median: -0.03335, 3rd Quartile: 0.03038, and Maximum: 0.24132. The residual standard error was 0.0842 with 30 degrees of freedom. The multi- ple R-squared was 0.06936, indicating that approximate- ly 6.94% of the variability in the Silverman test p-values can be explained by the ratio of chromosome subsets. The adjusted R-squared was 0.03834. The F-statistic val- ue was 2.236 with a p-value of 0.1453, suggesting that the relationship between the 1.50:1 ratio and the p-values is not statistically significant. To compare the means of the Silverman test p-val- ues between the ratios less than and greater than 1.50:1, a Welch’s t-test was performed. The results were as fol- lows: Mean of p-values for ratios less than 1.50:1 = 0.1516517. Mean of p-values for ratios greater than 1.50:1 = 0.05259105. Welch’s t-test indicated the following results: t-statistic: 4.0689, Degrees of Freedom: 14.321, p-value: 0.001101, with a 95% Confidence Interval for the Difference in Means (0.04695375, 0.15116747). These results indicate a significant difference in the means of the p-values between the ratio groups, with a p-value less than 0.05. According to the scatter plot (Figure 6???), most ratios less than 1.50:1 have higher p-values, indicating a greater tendency to be considered unimodal, while ratios greater than 1.50:1 tend to have lower p-values, indicat- ing a greater tendency to be considered bimodal. Species highlighted such as Scaphura nigra and Drosophila mela- nogaster have significantly higher p-values because they have trimodal karyotypes (not bimodal), while the spe- cies Bixa orellana, Eleutherine bulbosa, Calydorea undu- lata, and Oxalis linarantha are closer to the significance line, making them more difficult to classify statistically. The regression analysis results indicate that the chromosome ratio does not have a statistically signifi- cant relationship with the Silverman test p-values. How- ever, Welch’s t-test suggests that there is a significant Figure 6. Scatter plot with regression lines shows the relationship between the chromosome ratio and the Silverman test p-values. The vertical blue line represents the 1.50:1 ratio, and the horizon- tal red line indicates the significance level (p = 0.05). Blue points represent species with p-values ≤ 0.05, while black points represent species with p-values > 0.05. 54 Leylson Ferreira Araújo et al. difference in the mean p-values between ratios less than and greater than 1.50:1. These results suggest that ratios greater than 1.50:1 are associated with lower p-values, indicating a higher tendency to consider bimodality in karyotypes from this ratio. The graph corroborates these results (Figure 6), showing a clear distinction between the p-values for ratios less than and greater than 1.50:1. DISCUSSION Applying the original concept and its variations in the lit- erature The concept of bimodal karyotype was coined by Avdulov (1931) and extensively discussed by Stebbins (1971). It describes karyotypes with two distinct classes of chromosomes: one composed of large chromosomes and the other of small chromosomes, with a distinctly significant difference between the classes, representing a special type of karyotype asymmetry. Therefore, the concept of karyotypic bimodality involves several explic- it criteria: 1. The formation of two subsets (or classes) of chromosomes; 2. It is a concept exclusively related to chromosome size, disregarding chromosome number and morphology (centromere position); 3. The difference between the two subsets is distinctly significant, not merely discontinuous; 4. The concept is not related to the largest and smallest chromosome in the complement, which can have a significant difference but still show continuous variation between extremes. The discrepancy specifically refers to the difference between the classes of large and small chromosomes, i.e., the smallest chromo- some in the larger subset and the largest chromosome in the smaller subset. However, the challenge lies in estab- lishing how significant this difference between subsets must be, making the concept’s application somewhat impractical and often subjective. The literature presents various applications and/or variations of the original concept (see, for example, Báez et al. 2019; Ibiapino et al. 2022), which perfectly meet the criteria originally established and discussed (Avdulov 1931; Stebbins 1971). However, some publications pre- sent fundamentally different concepts, which can explain the divergence in interpreting the criteria related to bimodality when applying the term to a given karyotype under analysis. In most cases, the misapplication of the concept is related to the occurrence of large and small chro- mosomes in the same karyotype, classifying them as bimodal. The ambiguity here is that while every bimod- al karyotype indeed has large and small chromosomes, not every karyotype with large and small chromosomes can be considered bimodal. For instance, in Calydorea crocoides (largest chromosome = 8.55 µm, smallest = 3.34 µm), Cephalanthera rubra (largest chromosome = 12.14 µm, smallest = 2.40 µm), Gastrodia gracilis (larg- est chromosome = 3.10 µm, smallest = 1.00 µm), Herber- tia darwinii (largest chromosome = 4.17 µm, smallest = 1.86 µm), Hyacinthella dalmatica (largest chromosome = 4.69 µm, smallest = 1.45 µm) and Puya mirabilis (larg- est chromosome = 1.52 µm, smallest = 0.53 µm), the size variation between the two extremes is continuous (Fig- ures 4-5). Thus, it is not possible to determine the larger and smaller chromosome subsets due to the absence of a marked discontinuity between them. Another common inconsistency is considering a karyotype bimodal when discontinuities occur multiple times throughout the complement. If more than one dis- continuous and significant interval exists between chro- mosome sizes, there will be more than two subsets in the complement, deviating from the concept of bimodal karyotype. This is the case with the cytotype analyzed of Drosophila melanogaster (Figure 4) and Scaphura nigra (Figure 5), which have three distinct subsets of chromo- somes and are therefore trimodal (see Table 1). Another problem in applying the concept is related to the inclusion of criteria that were not established by Avdulov (1931) or Stebbins (1971), nor tested statisti- cally, such as the inclusion of relative chromosome size. Relative chromosome size is a measure that expresses the size of a chromosome in relation to the total size of the chromosome set of a karyotype. Including relative size as a criterion for establishing bimodality is problem- atic because karyotypes with high chromosome numbers will reduce the levels of discontinuity, depending on the total chromosome size, the extremes might be overval- ued, disregarding whether the variation between them is continuous or discontinuous (Table 3). Intrachromosomal Bimodality: a special case The original idea of characterizing a bimodal karyo- type is clearly interchromosomal, meaning it is related to the strong discontinuity in chromosome size within a complement. For example, some Oxalis species, such as O. linarantha, exhibit clear bimodality in chromosome size (Vaio et al. 2016). On the other hand, O. eriocarpa DC. has chromosomes with continuously varying sizes and karyotypes formed exclusively by metacentric and acro- centric chromosomes (Vaio et al. 2013). Regarding mor- phology, metacentric and acrocentric chromosomes are considered evolutionary extremes, based on the hypoth- esis that asymmetric karyotypes originate from symmetric ones (Stebbins 1971; Medeiros-Neto et al. 2017). 55What defines a bimodal karyotype? Bimodality revisited Table 3. Relative size of each metaphase chromosome of the species analyzed. Species Relative sizes Agave angustifolia 0.05 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.03 0.03 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 A. cupreata 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 A. fourcroydes 0.03 0.03 0.03 0.03 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.00 0.00 0.00 0.00 0.00 0.00 A. parviflora 0.07 0.07 0.08 0.08 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 A. tequilana 0.05 0.05 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.00 Aloe tenuior 0.10 0.10 0.10 0.10 0.10 0.09 0.09 0.09 0.05 0.04 0.04 0.04 0.03 0.03 A. vera 0.12 0.10 0.10 0.10 0.09 0.09 0.09 0.09 0.04 0.04 0.04 0.04 0.04 0.03 A. zebrina 0.24 0.22 0.22 0.22 0.22 0.21 0.20 0.20 0.07 0.07 0.07 0.07 0.07 0.06 Bixa orellana 0.12 0.12 0.08 0.08 0.07 0.07 0.07 0.07 0.06 0.06 0.06 0.06 0.05 0.05 Calydorea crocoides 0.12 0.10 0.08 0.08 0.07 0.07 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 C. undulata 0.12 0.11 0.11 0.10 0.06 0.06 0.06 0.06 0.06 0.05 0.05 0.05 0.05 0.05 Cephalanthera longifolia 0.07 0.07 0.07 0.06 0.06 0.06 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 C. rubra 0.05 0.05 0.05 0.04 0.04 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 Consolida regalis 0.12 0.12 0.11 0.11 0.05 0.05 0.04 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.02 0.02 Cuscuta nitida 0.12 0.11 0.11 0.07 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 Drosophila melanogaster♂ 0.19 0.18 0.18 0.18 0.11 0.11 0.02 0.02 Eleutherine bulbosa 0.21 0.20 0.08 0.08 0.06 0.06 0.06 0.05 0.05 0.05 0.05 0.05 Epidendrum fulgens 0.07 0.07 0.05 0.05 0.05 0.05 0.05 0.05 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.03 0.03 0.03 0.03 0.03 0.03 0.03 Gastrodia gracilis 0.08 0.07 0.06 0.05 0.05 0.05 0.05 0.05 0.04 0.05 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.03 0.03 0.03 0.03 Herbertia darwinii 0.11 0.11 0.10 0.09 0.07 0.07 0.06 0.06 0.06 0.06 0.06 0.05 0.05 0.05 Hyacinthella dalmatica 0.10 0.09 0.06 0.06 0.05 0.05 0.05 0.05 0.05 0.05 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 H. Chillensis 0.21 0.21 0.16 0.15 0.08 0.08 0.07 0.06 Luzuriaga radicans 0.11 0.11 0.07 0.07 0.05 0.05 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.03 Milium montianum 0.09 0.09 0.08 0.08 0.07 0.07 0.07 0.07 0.04 0.04 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.02 0.02 0.02 0.02 Muscari comosum 0.16 0.15 0.09 0.07 0.05 0.05 0.05 0.05 0.04 0.04 0.04 0.03 0.03 0.03 0.03 0.03 0.03 0.03 Oxalis linarantha 0.12 0.12 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.06 0.06 0.06 0.06 0.04 Puya mirabilis 0.04 0.04 0.03 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01 Scaphura nigra♂ 0.22 0.13 0.12 0.06 0.04 0.04 0.03 0.03 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01 0.01 0.01 Sellocharis paradoxa 0.09 0.08 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.04 0.04 0.04 0.04 0.04 0.04 0.04 Sprekelia formosissima 0.04 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01 0.01 0.02 0.02 0.02 0.01 0.01 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 Tigridia pavonia 0.07 0.07 0.08 0.08 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 56 Leylson Ferreira Araújo et al. Chromosome changes, especially centric fusions/ fissions, are the main causes of the direct transition between meta- and acrocentric chromosomes. Chro- mosome fusions occur when two chromosomes unite, forming a single metacentric chromosome. In contrast, chromosome fissions involve the breakage of a chromo- some, resulting in two smaller acrocentric chromosomes (Guerra 2008). This transition related to centric fission/ fusion events frequently occurs without changes in the fundamental number (without changes in the number of chromosome arms between related species with different chromosome numbers), as seen in the genera Nothoscor- dum (Souza et al. 2012) and Ipheion (Souza et al. 2010). These structural changes are important in speciation, as they can affect chromosome segregation during meiosis and generate reproductive barriers between populations. Submetacentric chromosomes are considered inter- mediate in the evolution of chromosome morphology (Stebbins 1971). In this context, karyotypes composed solely of metacentric and acrocentric chromosomes, with a complete absence of submetacentric chromosomes, exhibit intrachromosomal asymmetry. We propose here to classify these karyotypes as a form of intrachromo- somal bimodality. This is exemplified in Oxalis erio- carpa, which displays a bimodal karyotype in terms of chromosome morphology. Additionally, some species of Oxalis exhibit two levels of bimodality: one interchromo- somal and the other intrachromosomal (Vaio et al. 2013). Evolutionary hypotheses for the origin of bimodal karyotypes The debate on the origin of bimodal karyotypes began in the 1930s with Avdulov and was later expand- ed upon by Stebbins (1971). Since then, several causes have been identified for the origin of bimodal karyo- types. Structural chromosomal alterations, especially unequal translocations, fusions, and fissions, can result in the formation of chromosomal subsets of contrast- ing sizes within a complement. Generally, asymmetric karyotypes are the result of chromosomal rearrange- ments, which can occur separately involving a single chromosome, as seen in Nothoscordum Kunth (Souza et al. 2012), or simultaneously involving different chromo- somes, as observed in Arabidopsis thaliana (L.) Heynh. (Lysak et al. 2007). Numerous examples in the literature demonstrate how rearrangements lead to distinct dis- continuities in chromosome size, such as in the genus Ornithogalum L. (Liliaceae), where some species exhibit bimodal karyotypes due to fusions and fissions (Stedje 1989; Vosa 1997). Chromosome fusions are also involved in the origin of bimodal karyotypes in some reptile groups, like the genus Sceloporus Wiegmann (Lisachov et al. 2020). In the allotetraploid Tragopogon × miscellus Ownbey (Asteraceae), intergenomic translocations result in chromosomes of variable sizes, with individuals dis- playing different karyotypes exhibiting various levels of interchromosomal asymmetry, some of which are clearly bimodal (Chester et al. 2012). Another factor clearly demonstrated in the differ- entiation between chromosomal subsets is the amplifi- cation of certain repetitive DNA sequences. Two well- studied examples in the literature include Cuscuta sub- genus Pachystigma (Convolvulaceae), which has 2n = 28-30 chromosomes with one set of large chromosomes and another set of small chromosomes. The large chro- mosomes contain a wide variety of abundant repetitive sequences, such as 5S and 35S ribosomal DNAs, a satel- lite DNA superfamily SF1, and LTR retrotransposons, which are absent in the smaller chromosome subset (Ibi- apino et al. 2022). The second example is Eleutherine bul- bosa Urb., with 2n = 12 and a pair of large chromosomes four times larger than the other chromosomes in the complement. The larger pair is heteromorphic, with one chromosome having a pericentric inversion and a proxi- mal duplication within the inversion (Guerra 1988b). Dif- ferential accumulation of the most abundant genome ret- roelements, occurs only in the larger pair, explaining the cause of bimodality in E. bulbosa (Báez et al. 2019). Another possibility for the origin of bimodality is hybridization, as suggested for certain classic bimodal karyotypes like Agave L. (McKain et al. 2012), and the tetraploid Emilia fosbergii Nicolson (Guerra and Nogue- ira 1990; Moraes and Guerra 2010), allopolyploids with parents having significantly different chromosome sizes (McKain et al. 2012). In such cases involving hybridi- zation, minimal or no chromosomal rearrangements between subgenomes are necessary to maintain the dif- ference between the inherited chromosomal subsets. Although this is not a common scenario, as allopoly- ploids generally exhibit rapid rearrangements between subgenomes, it has been demonstrated in Milium mon- tianum (Poaceae - Bennett et al. 1992) and E. fosber- gii (Moraes and Guerra 2010). It is possible that many other bimodal karyotypes have a hybrid origin, related or not to polyploidy, whose analyses may be hampered by ancient events obscured over time. While we are now well-informed about the possible causes of bimodality, understanding why evolution often maintains bimodal- ity in entire clades remains challenging. Method for identifying bimodal karyotypes The interchromosomal asymmetry index (Romero- Zarco 1986) and Stebbins’ categories (1971) showed diver- 57What defines a bimodal karyotype? Bimodality revisited gent results for the same species, a direct consequence of the different factors each test considers regarding varia- tion. While the A2 index is based on the standard devia- tion of the entire chromosomal complement, Stebbins’ cat- egories consider only the ratio between the smallest and largest chromosome in the complement (Medeiros-Neto et al. 2017). Thus, although both indicate interchromosomal asymmetry, the indices provide information about differ- ent levels within chromosomal variation, often resulting in divergent responses for the same species. However, none of the tested interchromosomal asymmetry indices showed a consistent pattern to indi- cate a karyotype as bimodal. This is clearly observed in Puya mirabilis, whose karyotype is bimodal, but it is classified as symmetric by the Romero-Zarco index (A2 = 0.25) and asymmetric by Stebbins’ categorization (see Table 1). Stebbins’ categorization also classified species with bimodal karyotypes as moderately asymmetric, such as Tigridia pavonia in 2B, with A2 = 0.72 (Table 1), thus being inadequate for assessing bimodality. Statistical tests also yielded divergent results in iden- tifying bimodal karyotypes. While Hartigans’ Dip Test identified 23.33% of species as bimodal, the Silverman Test identified 66.67% (Table 2). Due to this high diver- gence, the proposal to define bimodal karyotypes based on the ratio between the smallest chromosome of the larger subset and the largest chromosome of the smaller subset may be more objective and practical than relying solely on statistical tests. This method can provide an intuitive and direct indicator of bimodality, helping to avoid ambiguities. Stebbins’ (1971) observations about bimodal karyo- types are useful because they convey a consistent idea about the operational concept of bimodality. Although he did not formally propose a limit between large and small chromosomal subsets, Stebbins compared bimodal karyotypes of various species with other related karyo- types, defined only as asymmetric, in his discussion on “the origin of bimodal karyotypes.” According to Steb- bins (1971), the karyotypes of species belonging to the genera Aloe, Yucca, and Gasteria, as well as Consolida regalis and Muscari comosum are bimodal (see Figure 3). In this study, we represented the bimodal karyo- types of these species in idiograms and analyzed them comparatively. We observed that all karyotypes consid- ered bimodal by Stebbins (1971) exhibit a ratio ≥ 1.5:1 between the smallest chromosome of the larger subset and the largest chromosome of the smaller subset. We evaluated two approaches: the first consid- ers karyotypes as bimodal based on a ratio ≥ 2:1. We found that this criterion can be more stringent, identi- fying karyotypes with a clearer distinction between the two subsets, which reduces the risk of false positives but may fail to identify some bimodal karyotypes with less pronounced differences. On the other hand, the ratio ≥ 1.5:1 is more inclusive, identifying a larger proportion of karyotypes as bimodal, aligning with the greater sensi- tivity observed in the Silverman Test. This criterion can include karyotypes with less extreme differences that are still distinctly bimodal. Based on the results of statistical analysis, the ratio of ≥ 1.5:1 seems to be the best approach for defining bimodal karyotypes. Regression analysis and Welch’s t-test suggest that the 1.5:1 ratio is associated with lower p-values, indicating a greater tendency to detect bimo- dality (Figure 6, Table 1). 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