The comparison of two Zagreb-Fermat eccentricity indices

In this paper, we focus on comparing the first and second Zagreb-Fermat eccentricity indices of graphs. We show that $$\frac{\sum_{uv\in E\left( G \right)}{\varepsilon_3\left( u \right) \varepsilon_3\left( v \right)}}{m\left( G \right)} \leq \frac{\sum_{u\in V\left( G \right)}{\varepsilon_{3}^{2}\left( u \right)}}{n\left( G \right)}$$ holds for all acyclic and unicyclic graphs. Besides, we verify that the inequality may not be applied to graphs with at least two cycles

Rapid Intraspecific Diversification of the Alpine Species Saxifraga sinomontana (Saxifragaceae) in the Qinghai-Tibetan Plateau and Himalayas

An increasing number of phylogeographic studies have been conducted for plant species in the Qinghai-Tibetan Plateau (QTP) and its flanking mountains. However, these studies have mainly focused on the determination of glacial refugia and routes of inter-/post-glacial expansions. Rapid intraspecific diversification of plants in this region have not been thoroughly discussed. Herein, we investigate the effects of the Quaternary climate changes on population genetic structure and diversifications of a herbaceous alpine species, Saxifraga sinomontana, which may have an evolutionary time scale <5 million years in the QTP and Himalayan regions. Using a total of 350 individuals from 29 populations, we studied the evolutionary history of S. sinomontana by analyzing cpDNA trnL-trnF, rpl16 and nrDNA ITS sequences. A total of 89 haplotypes and 158 genotypes were detected for cpDNA and ITS sequences, respectively. Only a few haplotypes/genotypes were widespread, while an extremely large number of haplotypes/genotypes were restricted to single populations, which were scattered throughout the current geographical range of S. sinomontana. This suggests the existence of microrefugia of this species during the Quaternary glaciations. In addition, the relationships of the haplotypes/genotypes were almost completely not resolved by phylogenetic reconstruction. Combining characteristics in terms of high haplotype richness, large proportion of private haplotypes, and shallow haplotype divergence, we speculate that recent intraspecific diversification has occurred in S. sinomontana. Molecular clock analysis estimated that the onset diversification within S. sinomontana to be 1.09 Ma (95% HPD = 0.80–1.45), coinciding with the extensive Quaternary glaciations on the QTP which started ca. 1.17 Ma. The Quaternary climatic oscillations may have triggered rapid intraspecific diversification in this QTP-Himalayan species. However, large niche breadth, as well as introgression/hybridization between the studied species and its closely related sympatric saxifrages, may also played a role to some extent on the current genetic structure of S. sinomontana, which need to be further studied

Population Genetic Differentiation and Taxonomy of Three Closely Related Species of Saxifraga (Saxifragaceae) from Southern Tibet and the Hengduan Mountains

The effects of rapid, recent uplift of the Hengduan Mountains on evolution and diversification of young floristic lineages still remain unclear. Here, we investigate diversification of three closely related Saxifraga species with a distribution restricted to the Hengduan Mountains (HM) and southern Tibet, and comment on their taxonomy based on molecular evidence. Three chloroplast DNA fragments (rbcL, trnL-F, trnS-G) and the nuclear ribosomal DNA internal transcribed spacer (ITS) were employed to study genetic structure across 104 individuals from 12 populations of Saxifraga umbellulata, S. pasumensis, and S. banmaensis. Chloroplast DNA (cpDNA) phylogenies revealed two well supported clades, corresponding to S. umbellulata and S. pasumensis plus S. banmaensis. Topology of the ITS phylogeny was largely congruent with that generated from cpDNA haplotypes, but with minor conflicts which might be caused by incomplete lineage sorting. Analyses of molecular variance of both cpDNA and ITS datasets revealed that most variation was held between S. pasumensis s.l. (with S. banmaensis) and S. umbellulata (92.31% for cpDNA; 69.78% for ITS), suggesting a high degree of genetic divergence between them. Molecular clock analysis based on ITS dataset suggested that the divergence between S. pasumensis s.l. and S. umbellulata can be dated to 8.50 Ma, probably a result of vicariant allopatric diversification associated with the uplift events of the HM. Vicariance associated with HM uplifts may also have been responsible for infraspecific differentiation in S. pasumensis. In contrast, infraspecific differentiation in S. umbellulata was most likely triggered by Quaternary glaciations. The much lower levels of gene diversity within populations of S. pasumensis compared with S. umbellulata could have resulted from both range contractions and human collection on account of its putative medicinal properties. Combining evidence from morphology, geographical distributions and molecular phylogenetic data, we recommend that S. banmaensis should be treated as a synonym of S. pasumensis which in turn, and based on the same sources of evidence, should be treated as a separate species rather than as a variety of S. umbellulata

Population genetic differentiation and taxonomy of three closely related species of saxifraga (Saxifragaceae) from southern tibet and the Hengduan mountains

The effects of rapid, recent uplift of the Hengduan Mountains on evolution and diversification of young floristic lineages still remain unclear. Here, we investigate diversification of three closely related Saxifraga species with a distribution restricted to the Hengduan Mountains (HM) and southern Tibet, and comment on their taxonomy based on molecular evidence. Three chloroplast DNA fragments (rbcL, trnL-F, trnS-G) and the nuclear ribosomal DNA internal transcribed spacer (ITS) were employed to study genetic structure across 104 individuals from 12 populations of Saxifraga umbellulata, S. pasumensis, and S. banmaensis. Chloroplast DNA (cpDNA) phylogenies revealed two well supported clades, corresponding to S. umbellulata and S. pasumensis plus S. banmaensis. Topology of the ITS phylogeny was largely congruent with that generated from cpDNA haplotypes, but with minor conflicts which might be caused by incomplete lineage sorting. Analyses of molecular variance of both cpDNA and ITS datasets revealed that most variation was held between S. pasumensis s.l. (with S. banmaensis) and S. umbellulata (92.31% for cpDNA; 69.78% for ITS), suggesting a high degree of genetic divergence between them. Molecular clock analysis based on ITS dataset suggested that the divergence between S. pasumensis s.l. and S. umbellulata can be dated to 8.50 Ma, probably a result of vicariant allopatric diversification associated with the uplift events of the HM. Vicariance associated with HMuplifts may also have been responsible for infraspecific differentiation in S. pasumensis. In contrast, infraspecific differentiation in S. umbellulata was most likely triggered by Quaternary glaciations. The much lower levels of gene diversity within populations of S. pasumensis compared with S. umbellulata could have resulted from both range contractions and human collection on account of its putative medicinal properties. Combining evidence from morphology, geographical distributions and molecular phylogenetic data, we recommend that S. banmaensis should be treated as a synonymof S. pasumensis which in turn, and based on the same sources of evidence, should be treated as a separate species rather than as a variety of S. umbellulata