Predicted time course of proportions of individual ploidy levels starting with proportions found at locality. a plants are monocarpic with no clonal growth (Simple Model); b plants are perennial and clonal, clonal growth of all ploidy levels is identical (Clonal Model, g = 0.1); c plants are perennial and clonal, clonal growth of triploids is 1.2 times that of tetraploids and of diploids 0.8 times that of tetraploids (Clonal Model, g = 0.1, c 2 = 0.8, c 3 = 1.2). Note different scaling of the x axis. Hybridization data in all models are parameterized by the experiment

Predicted time course of proportions of individual ploidy levels starting with proportions found at locality. a plants are monocarpic with no clonal growth (Simple Model); b plants are perennial and clonal, clonal growth of all ploidy levels is identical (Clonal Model, g = 0.1); c plants are perennial and clonal, clonal growth of triploids is 1.2 times that of tetraploids and of diploids 0.8 times that of tetraploids (Clonal Model, g = 0.1, c 2 = 0.8, c 3 = 1.2). Note different scaling of the x axis. Hybridization data in all models are parameterized by the experiment

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Background: Processes driving ploidal diversity at the population level are virtually unknown. Their identification should use a combination of large-scale screening of ploidy levels in the field, pairwise crossing experiments and mathematical modelling linking these two types of data. We applied this approach to determine the drivers of frequenci...

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... levels as those found in the field at the Havraníky locality will converge rather fast to the second stable state, i.e. diploids, trip- loids and pentaploids will cease to be dominant over two generations and eventually disappear as the system reaches the stable state with only tetraploids and hexa- ploids present (over ca. 10 generations; see Fig. ...
Context 2
... and overlapping genera- tions (g < 1; Clonal Model) yields a much larger variety of behaviours. If plants are long-lived and/or clonal but indi- vidual ploidy levels do not differ in this regard (c k = 1 for all k), the system has the same stable state structure as the Simple Model; the only difference being the much slower dynamics of the system (Fig. 4b). For example, a system initialized with the same proportion of ploidies as those found in the field would retain triploid dominance over other ploidies for over 4 years if g = 0.4, over 14 years if g = 0.1, and over 144 years if g = 0.01. The relationship is asymptotic; for obvious reasons, triploids will remain dominant in the ...
Context 3
... contrast, differences between individual ploidies in their longevity and/or capacity for clonal growth do alter the equilibrium structure of the system (Fig. 4c). The in- tensity of this effect depends on the overall role of these processes relative to generative reproduction (i.e. the par- ameter g). If the role of longevity and/or clonal growth is weak (i.e. g is high, Fig. 5, right part of the plots), the final proportions of ploidies are largely determined by sexual process and show the ...
Context 4
... to prevail indefinitely. Their proportion is determined by the parameter c k , i.e. relative capacity for clonal growth (and/or survival) of individual ploidy levels (Fig. 5). Apparently, there are parameter combinations that predict a large and stable proportion of triploids matching those found in the field system (e.g. g < 0.1 and c > 1.5; see Fig. 4). Triploids in these systems are accompanied by tetraploids and pentaploids (which are constantly generated by these ...

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... Alterations in reproductive strategies following WGM may counteract the disadvantages of a minority cytotype, e.g. by tolerating higher rates of autogamy [16] or by triggering/promoting asexual reproduction [17]. Asexuality can be achieved through the production of apomictically formed seeds, where meiosis and syngamy are bypassed [18] or through vegetative propagation [19][20][21]. Many apomicts are autopolyploids, particularly among grasses [22,23], and WGM is the primary cause of apomixis among these species, while hybridization seems to play a significant role in known allopolyploid apomicts [24,25]. ...
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... Importantly, these patterns are scale-dependent; the coexistence of cytotypes is likely over larger spatial scales, while at shorter distances ploidy-uniform clusters prevailed (Trávníček et al. 2011a;Šingliarová et al. 2019). Non-random cytotype distribution over small spatial scales can be linked to strong cytotype exclusion, clonal reproduction (Chrtek et al. 2017;Duchoslav et al. 2020), different microhabitat preferences (Fowler and Levin 1984;Sonnleitner et al. 2010) or non-adaptive processes, like a founder event with subsequent seed dispersal limitation (Baack 2005;Mráz et al. 2012b). ...
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... In evolutionary studies, it can be applied to address questions concerning the frequency of apomixis in natural populations [160][161][162] or to search for inter-ploidy hybrids in polyploid complexes. [163][164][165] Although there are a few exceptions, 166 ...
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... A perennial life-history strategy and asexual reproduction through clonal propagation both have the potential to reduce MCE (Gustafsson 1948;Stebbins 1950;Rodríguez 1996;Chrtek et al. 2017). Here, perennials refer to organisms that live for multiple years and reproduce over multiple seasons (iteroparous or polycarpic), in contrast to annuals that live for a single season, reproduce once, and die (semelparous or monocarpic; Friedman 2020). ...
... Many models incorporate this through niche shifts reducing competition between cytotypes (e.g., Rodríguez 1996), or by polyploid fitness advantages over diploids (e.g., Baack 2005). Relatively few explicitly examine other phenotypic differences between cytotypes (but see Rausch and Morgan 2005;Chrtek et al. 2017;Griswold 2021), although in practice WGD can result in sweeping changes to gene expression (Levin 2002;Soltis et al. 2016a), physiology (Maherali et al. 2009;Anneberg and Segraves 2020), or morphology (Husband et al. 2016). WGD is expected to produce bigger cells with long cell cycles, which should slow development and delay maturity (Stebbins 1950;Beaulieu et al. 2008;Blomme et al. 2014). ...
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... In recent decades, several mechanisms facilitating successful polyploid establishment and/or cytotype coexistence have been proposed (reviewed by Kolář et al., 2017). For example, the minority status of one of the coexisting cytotypes may be overcome by its recurrent origin (Ramsey, 2007), efficient vegetative spread (Chrtek et al., 2017), autogamy (Petit et al., 1997), non-random mating (Husband et al., 2008) or a substantial competitive advantage (Felber, 1991). Prominent among these mechanisms is the (fine-scale) spatial segregation of cytotypes, which can increase the rate of compatible, within-ploidy mating (Baack, 2005;Kolář et al., 2017). ...
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... The model presented by Levin (1975) predicted that polyploid establishment is very unlikely for organisms that primarily outcross, while self-fertilization and clonal reproduction mitigate the mating disadvantage experienced by polyploids as the minority cytotype due to reproductive interference from diploids (minority cytotype exclusion, or MCE). This pattern recurs in other establishment models with variable parameters representing reproductive assurance, either through selfing (Rodriguez, 1996;Baack, 2005;Rausch and Morgan, 2005;Oswald and Nuismer, 2011;Fowler and Levin, 2016) or clonality (Chrtek et al., 2017), and the prevalence of at least some form of reproductive assurance across plant lineages with frequent recent and ancient polyploidy suggests that it is a critical driver of polyploid success (Spoelhof et al., 2019). ...
... The theoretical impacts of reproductive assurance and population size on polyploid establishment have been examined in previously published deterministic and stochastic models (Rodriguez, 1996;Baack, 2005;Rausch and Morgan, 2005;Oswald and Nuismer, 2011;Fowler and Levin, 2016;Chrtek et al., 2017), and the results presented here are qualitatively similar to the results of those studies. However, these factors have not been studied extensively within a spatial context (aside from Baack, 2005). ...
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Polyploidy contributes massively to the taxonomic and genomic diversity of angiosperms, but certain aspects of polyploid evolution are still enigmatic. The establishment of a new polyploid lineage following whole-genome duplication (WGD) is a critical step for all polyploid species, but this process is difficult to identify and observe in nature. Mathematical models offer an opportunity to study this process by varying parameters related to the populations, habitats, and organisms involved in the polyploid establishment process. While several models of polyploid establishment have been published previously, very few incorporate spatial factors, including spatial relationships between organisms, habitat shape, or population density. This study presents a stochastic, spatial model of polyploid establishment that shows how factors such as habitat shape and dispersal type can influence the fixation and persistence of nascent polyploids and modulate the effects of other factors. This model predicts that narrow, constrained habitats such as roadsides and coastlines may enhance polyploid establishment, particularly in combination with frequent clonal reproduction, limited dispersal, and high population density. The similarity between this scenario and the growth of many invasive or colonizing species along disturbed, narrow habitats such as roadsides may offer a partial explanation of the prevalence of polyploidy among invasive species.
... Many factors have been used to model polyploid formation and establishment, including population size (Rausch & Morgan, 2005;Fowler & Levin, 2016), unreduced gamete production (Felber, 1991;Husband & Sabara, 2004;Rausch & Morgan, 2005;Oswald & Nuismer, 2011;Suda & Herben, 2013;Fowler & Levin, 2016), niche differentiation between cytotypes (Fowler & Levin, 1984Rodriguez, 1996;Oswald & Nuismer, 2011), assortative mating among cytotypes (Husband & Sabara, 2004;Oswald & Nuismer, 2011), clonality (Chrtek et al., 2018), self-fertilization or outcrossing rate (Rodriguez, 1996;Baack, 2005;Rausch & Morgan, 2005;Oswald & Nuismer, 2011;Fowler & Levin, 2016), and the relative fertility or fitness of each cytotype (Fowler & Levin, 1984;Felber, 1991;Husband & Sabara, 2004;Baack, 2005;Rausch & Morgan, 2005;Suda & Herben, 2013). Unfortunately, nearly all of the theoretical research on polyploid establishment is based on plant (typically angiosperm) populations, and it is not clear how many assumptions or conclusions of these studies would be applicable to animal (or other eukaryotic) systems. ...
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A broad difference in the frequencies of plant and animal polyploidy (whole‐genome duplication, WGD) has been recognized since the early 20th century (e.g., Gates, 1924; Dobzhansky, 1937; Stebbins, 1950), and is generally supported by numerous studies of plant and animal karyotypes, genome sizes, and phylogenies (Otto & Whitton, 2000; Gregory & Mable, 2005).
... The latter hypothesis, however, appears unlikely, as no clones were detected by the AFLP analysis. Longevity along with the ability to reproduce vegetatively and by selfing and, consequently, the lack of a need for regular sexual reproduction probably enabled V. uliginosum s. lat. to escape minority cytotype exclusion (see also Chrtek et al. 2017). In other polyploid complexes spatial segregation is identified as an important driver of successful cytotype co-occurrence, for example in Chamerion angustifolium (Sabara et al. 2013), Gymnadenia conopsea (Trávníček et al. 2011b), Knautia arvensis (Kolář et al. 2009), Pilosella echioides (Trávníček et al. 2011a) and Senecio carniolicus s. lat. ...
... As the amount of nuclear DNA is characteristic of a particular species, this character has been considered increasingly useful in the fields of systematics, ecology, and plant evolution (García et al. 2004;Kron et al. 2007;Loureiro et al. 2010;Greilhuber and Leitch 2013;Suda et al. 2015;Vallejo-Marín and Hiscock 2016;Rey et al. 2017). The advent of more robust and high-throughput techniques such as flow cytometry (FCM) has allowed not only the study of genome size at the population level with the screening of a large number of individuals, but also a more accurate evaluation and interpretation of genome size differences (either absolute or relative) among the analyzed individuals Chrtek et al. 2017;Castro et al. 2018;Oberprieler et al. 2018). Cases of homoploid hybridization may particularly benefit from a population-level survey of genome size when differences are sufficient to be detected by current methods (Loureiro et al. 2010). ...
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Premise of research. Interspecific hybridization was hypothesized to explain the remarkable floral phenotype variation found in overlapping areas of distribution for several Anacyclus species. We aimed to investigate genome size in natural populations of three diploid Anacyclus species with special emphasis in their contact areas to explore patterns of variation as additional evidence supporting current hybridization in these areas. Methodology. Flow cytometry was used to estimate the genome size of 564 individuals of the species complex of A. clavatus, A. homogamos, and A. valentinus from 30 sites. Additionally, genome size variation of 173 first-generation synthetic hybrids between these three species was also studied and compared with the estimates obtained in sympatric sites. Pivotal results. Differences in genome size between A. clavatus and A. valentinus were significant in non-overlapping areas of species distribution, whereas in overlapping areas, the variation increased, preventing a clear differentiation between species. In sympatric sites of A. clavatus and A. valentinus, individuals with intermediate genome sizes between them were also observed and were significantly similar to those obtained from the first-generation experimental hybrids between these species. Genome sizes of A. clavatus and A. homogamos did not differ enough to allow discrimination between these species. Conclusions. The patterns of genome size variation observed in sympatric populations of A. clavatus and A. valentinus support the occurrence of current gene flow between these species and the existence of contact areas in overlapping distribution areas where phenotypic and genomic variation increases.