Impact of Genomic and Transcriptomic Resources on Apiaceae Crop Breeding Strategies

The Apiaceae taxon is one of the most important families of flowering plants and includes thousands of species used for food, flavoring, fragrance, medical and industrial purposes. This study had the specific intent of reviewing the main genomics and transcriptomic data available for this family and their use for the constitution of new varieties. This was achieved starting from the description of the main reproductive systems and barriers, with particular reference to cytoplasmic (CMS) and nuclear (NMS) male sterility. We found that CMS and NMS systems have been discovered and successfully exploited for the development of varieties only in Foeniculum vulgare, Daucus carota, Apium graveolens and Pastinaca sativa; whereas, strategies to limit self-pollination have been poorly considered. Since the constitution of new varieties benefits from the synergistic use of marker-assisted breeding in combination with conventional breeding schemes, we also analyzed and discussed the available SNP and SSR marker datasets (20 species) and genomes (8 species). Furthermore, the RNA-seq studies aimed at elucidating key pathways in stress tolerance or biosynthesis of the metabolites of interest were limited and proportional to the economic weight of each species. Finally, by aligning 53 plastid genomes from as many species as possible, we demonstrated the precision offered by the super barcoding approach to reconstruct the phylogenetic relationships of Apiaceae species. Overall, despite the impressive size of this family, we documented an evident lack of molecular data, especially because genomic and transcriptomic resources are circumscribed to a small number of species. We believe that our contribution can help future studies aimed at developing molecular tools for boosting breeding programs in crop plants of the Apiaceae family.

Links and Bifurcations in Nonsingular Morse–Smale Systems

Wada's theorem classifies the set of periodic orbits in NMS systems on S3 as links, that can be written in terms of six operations. This characterization allows us to study the topological restrictions that links require to suffer a given codimension one bifurcation. Moreover, these results are reproduced in the case of NMS systems with rotational symmetries, introducing new geometrical tools.

Bifurcations of Links of Periodic Orbits in Non-Singular Systems with Two Rotational Symmetries on S3

A topological characterization of all possible links composed of the periodic orbits of a Non Singular Morse-Smale flow on S3 has been made by M. Wada. The presence of symmetry forces the appearance of given types of links. In this paper we introduce a geometrical tool to represent these type of links when a symmetry around two axes is considered on NMS systems: mosaics. On the other hand, we use mosaics to study what kind of bifurcation can occur in this type of system maintaining the symmetry.