Tool for Abstract Regular Tree Model Checking

Formálna verifikácia sa zaoberá dokazovaním korektnosti systému podľa daných špecifikácií.Jej potrebu znásobuje stále väčšia rozšírenosť počítačov a neustály rast zložitosti aj rozsiahlosti vyvíjaných systémov. Cieľom tejto práce je implementácia nástroja formálnejverifikácie abstraktný regulárny stromový model checking (ARTMC) nad knižnicou VATA. Pre dosiahnutie tohto cieľa bolo potrebné rozšíriť knižnicu VATA o konečné stromové prevodníky,abstrakcie stromových automatov a integrovať ich spolu s nástrojom ARTMC doknižnice VATA.Formal verification deals with proving the correctness of the system according to the given specifications. Its need is driven by an increasing number of computers and a increase in the complexity of the systems being developed. The aim of this work is to implement the formal verification tool abstract regular tree model checking (ARTMC) over the VATA library. To achieve this goal, it was necessary to extend the VATA library on the finite tree transducers, abstractions of tree automata and integrate them together with the ARTMC into the VATA library.

Interspecific hybridization in the genus Hieracium s. str.: evidence for bidirectional gene flow and spontaneous allopolyploidization

Although reticulation has indisputably played an important role in the evolutionary history of the genus Hieracium s. str. (Asteraceae), convincingly documented cases of recent interspecific hybridization are very rare. Here we report combined evidence on recent hybridization between two diploid species, Hieracium alpinum and H. transsilvanicum. The hybrid origin of the plants from the Romanian Eastern Carpathians was supported by additive patterns of nuclear ribosomal DNA polymorphism (ITS), an intermediate position of hybrid plants in principal coordinate analysis based on amplified fragment length polymorphism phenotypes (AFLP), and additivity at one allozyme locus. Flow cytometric analyses and chromosome counting showed that two hybrids were diploid (2n~2x~18) while one was surprisingly tetraploid (2n=4x=36). To our knowledge, this is the first record of spontaneous polyploidization following interspecific crossing in the genus. Allozyme data, especially the presence of unbalanced heterozygosity at one locus, suggest the origin of this tetraploid via a triploid bridge with subsequent backcrossing to H. alpinum. According to PCR-RFLP analyses of the trnT-trnL intergenic spacer, all H. ×krasani hybrids examined had the H. alpinum haplotype while H. transsilvanicum served as a pollen donor. The hybrids occurred at the locality with abundant H. alpinum plants where paternal H. transsilvanicum was missing. Previously reported instances of interspecific hybridization between the same parental taxa showed an opposite direction of crossing and relative abundance of parental taxa. This suggests that the direction of hybridization might be influenced by the frequency of parental taxa at the localit

Ploidy level and genome size variation in the homosporous ferns Botrychium

Recent cytological and molecular studies have investigated genome size variation and evolution in the homosporous ferns, but representatives of the Ophioglossaceae were largely overlooked, despite their evolutionary singularity. Flow cytometry analysis was performed on 41 individuals of eight species of the genera Botrychium (B.), Botrypus, and Sceptridium to estimate their ploidy level variation. In a subset of individuals, we also estimated the absolute genome size and corresponding C values. Additionally, a classical chromosome count was made on the recently described species B. alaskense. Ploidy level and new genome size records were determined for Botrychium alaskense, B. boreale, B. lanceolatum, B. “neolunaria” ined., B. pinnatum, Botrypus virginianus and Sceptridium multifidum. In addition, we confirmed the genome size of B. matricariifolium, B. minganense and B. lunaria. Two of the three major sub-clades of Botrychium differ slightly in their averaged homoploid genome size (subclade Lanceolatum, 24.72 ± 0.40 pg; subclade Lunaria, 27.51 ± 0.47 pg). Flow cytometry and chromosome counting confirmed that B. alaskense is a tetraploid. A new hexaploid cytotype, putatively formed through an autopolyploidization from the sympatric tetraploid cytotype, was detected in a single individual of B. boreale. This is only the second report of hexaploidy in the genus Botrychium and our data highlight the potential to find other ploidy levels within other Botrychium species. Interestingly, no difference within the monoploid genome sizes was detected between ploidy levels, thus supporting the hypothesis of genome size stability after polyploidization and rejecting the scenario of genome downsizing

Geographical parthenogenesis, genome size variation and pollen production in the arctic-alpine species Hieracium alpinum

Hieracium alpinum L. (Asteraceae) is an arctic-alpine species distributed throughout Europe with both diploid and triploid cytotypes. We determined the ploidy levels of plants from 23 populations from Austria, Bosnia and Herzegovina, Finland, Italy, Norway, Romania, Slovakia, Switzerland and Ukraine. Data showed a non-overlapping pattern of cytotype distribution: sexually reproducing diploids (2n=2x=18) occur solely in the Eastern and Southern Carpathians, while apomictic triploids (2n=3x=27) cover the rest of the range. Such clear-cut allopatry is rather rare in vascular plants with geographical parthenogenesis. Comparison of absolute genome size indicates genome downsizing (by on average 3.7%) of haploid DNA amount in triploids relative to diploids. Genome size further correlated with longitude and latitude in the Alps, with decreasing absolute DNA content from west to east, and from south to north. While previously published data indicated complete male sterility of triploid plants, we found that plants from the Alps and Bosnia and Herzegovina commonly produced some pollen, whereas populations from the Western Carpathians and Scandinavia seemed to be almost completely pollen sterile. Scenarios about the evolution of geographical parthenogenesis in H. alpinum are discusse

Biological invasion of oxeye daisy (Leucanthemum vulgare) in North America: Pre-adaptation, post-introduction evolution, or both?

Species may become invasive after introduction to a new range because phenotypic traits pre-adapt them to spread and become dominant. In addition, adaptation to novel selection pressures in the introduced range may further increase their potential to become invasive. The diploid Leucanthemum vulgare and the tetraploid L. ircutianum are native to Eurasia and have been introduced to North America, but only L. vulgare has become invasive. To investigate whether phenotypic differences between the two species in Eurasia could explain the higher abundance of L. vulgare in North America and whether rapid evolution in the introduced range may have contributed to its invasion success, we grew 20 L. vulgare and 21 L. ircutianum populations from Eurasia and 21 L. vulgare populations from North America under standardized conditions and recorded performance and functional traits. In addition, we recorded morphological traits to investigate whether the two closely related species can be clearly distinguished by morphological means and to what extent morphological traits have changed in L. vulgare post-introduction. We found pronounced phenotypic differences between L. vulgare and L. ircutianum from the native range as well as between L. vulgare from the native and introduced ranges. The two species differed significantly in morphology but only moderately in functional or performance traits that could have explained the higher invasion success of L. vulgare in North America. In contrast, leaf morphology was similar between L. vulgare from the native and introduced range, but plants from North America flowered later, were larger and had more and larger flower heads than those from Eurasia. In summary, we found litte evidence that specific traits of L. vulgare may have pre-adapted this species to become more invasive than L. ircutianum, but our results indicate that rapid evolution in the introduced range likely contributed to the invasion success of L. vulgare

Anthropogenic disturbance as a driver of microspatial and microhabitat segregation of cytotypes of Centaurea stoebe and cytotype interactions in secondary contact zones

Background and Aims In a mixed-ploidy population, strong frequency-dependent mating will lead to the elimination of the less common cytotype, unless prezygotic barriers enhance assortative mating. However, such barriers favouring cytotype coexistence have only rarely been explored. Here, an assessment is made of the mechanisms involved in formation of mixed-ploidy populations and coexistence of diploid plants and their closely related allotetraploid derivates from the Centaurea stoebe complex (Asteraceae). Methods An investigation was made of microspatial and microhabitat distribution, life-history and fitness traits, flowering phenology, genetic relatedness of cytotypes and intercytotype gene flow (cpDNA and microsatellites) in six mixed-ploidy populations in Central Europe. Key Results Diploids and tetraploids were genetically differentiated, thus corroborating the secondary origin of contact zones. The cytotypes were spatially segregated at all sites studied, with tetraploids colonizing preferentially drier and open microhabitats created by human-induced disturbances. Conversely, they were rare in more natural microsites and microsites with denser vegetation despite their superior persistence ability (polycarpic life cycle). The seed set of tetraploid plants was strongly influenced by their frequency in mixed-ploidy populations. Triploid hybrids originated from bidirectional hybridizations were extremely rare and almost completely sterile, indicating a strong postzygotic barrier between cytotypes. Conclusions The findings suggest that tetraploids are later immigrants into already established diploid populations and that anthropogenic activities creating open niches favouring propagule introductions were the major factor shaping the non-random distribution and habitat segregation of cytotypes at fine spatial scale. Establishment and spread of tetraploids was further facilitated by their superior persistence through the perennial life cycle. The results highlight the importance of non-adaptive spatio-temporal processes in explaining microhabitat and microspatial segregation of cytotype

The population genetics of the fundamental cytotype-shift in invasive Centaurea stoebe s.l.: genetic diversity, genetic differentiation and small-scale genetic structure differ between cytotypes but not between ranges

Polyploids are overrepresented in invasive species. Yet, the role of genetic diversity and drift in colonization success of polyploids remains unclear. Here, we investigate genetic diversity, genetic differentiation and small-scale genetic structure in our model system, the three geo-cytotypes of Centaurea stoebe: monocarpic diploids and polycarpic (allo)tetraploids coexist in the native range (Eurasia), but only tetraploids are reported from the invasive range (North America). For each geo-cytotype, we investigated 18–20 populations varying in size and habitat type (natural vs. ruderal). Population genetic analyses were conducted at eight microsatellite loci. Compared to diploids, tetraploids revealed higher genetic diversity and lower genetic differentiation, whereas both were comparable in tetraploids between both ranges. Within spatial distances of a few meters, diploid individuals were more strongly related to one another than tetraploids. In addition, expected heterozygosity in diploids increased with population size and was higher in natural than in ruderal habitats. However, neither relationship was found for tetraploids. The higher genetic diversity of tetraploid C. stoebe may have enhanced its colonization abilities, if genetic diversity is correlated with fitness and adaptive capabilities. Furthermore, the inheritance of a duplicated chromosome set as well as longevity and frequent gene flow reduces drift in tetraploids. This counteracts genetic depletion during initial introductions and in subsequent phases of small or fluctuating population sizes in ruderal habitats. Our findings advocate the importance of studying colonization genetic processes to gain a more mechanistic understanding of the role of polyploidy in invasion dynamic

Sympatric diploid and tetraploid cytotypes of Centaurea stoebe s.l. do not differ in arbuscular mycorrhizal communities and mycorrhizal growth response

Genome duplication is associated with multiple changes at different levels, including interactions with pollinators and herbivores. Yet little is known whether polyploidy may also shape belowground interactions.Methods: To elucidate potential ploidy‐specific interactions with arbuscular mycorrhizal fungi (AMF), we compared mycorrhizal colonization and assembly of AMF communities in roots of diploid and tetraploid Centaurea stoebe s.l. (Asteraceae) co‐occurring in a Central European population. In a follow‐up greenhouse experiment, we tested inter‐cytotype differences in mycorrhizal growth response by combining ploidy, substrate, and inoculation with native AMF in a full‐factorial design.Key Results: All sampled plants were highly colonized by AMF, with the Glomeraceae predominating. AMF‐community composition revealed by 454‐pyrosequencing reflected the spatial distribution of the hosts, but not their ploidy level or soil characteristics. In the greenhouse experiment, the tetraploids produced more shoot biomass than the diploids did when grown in a more fertile substrate, while no inter‐cytotype differences were found in a less fertile substrate. AMF inoculation significantly reduced plant growth and improved P uptake, but its effects did not differ between the cytotypes.Conclusions: The results do not support our hypotheses that the cytotype structure in a mixed‐ploidy population of C. stoebe is mirrored in AMF‐community composition and that ploidy‐specific fungal communities contribute to cytotype co‐existence. Causes and implications of the observed negative growth response to AMF are discussed