Let D be a digraph.The competition graph of D is the graph having the same vertex set with D and having an edge joining two different vertices if and only if they have at least one common out-neighbor in D.The phylogeny graph of D is the competition graph of the digraph constructed from D by adding loops at all vertices.The competition/phylogeny number of a graph is the least number of vertices to be added to make the graph a competition/phylogeny graph of an acyclic digraph.In this paper,we show that for any integer k there is a connected graph such that its phylogeny number minus its competition number is greater than k.We get similar results for hypergraphs.
Among mammalian phylogenies,those characterized by rapid radiations are particularly problematic.The New World monkeys(NWMs,Platyrrhini)comprise 3 families and 7 subfamilies,which radiated within a relatively short time period.Accordingly,their phylogenetic relationships are still largely disputed.In the present study,56 nuclear non-coding loci,including 33 introns(INs)and 23 intergenic regions(IGs),from 20 NWM individuals representing 18 species were used to investigate phylogenetic relationships among families and subfamilies.Of the 56 loci,43 have not been used in previous NWM phylogenetics.We applied concatenation and coalescence tree-inference methods,and a recently proposed question-specific approach to address NWM phylogeny.Our results indicate incongruence between concatenation and coalescence methods for the IN and IG datasets.However,a consensus was reached with a single tree topology from all analyses of combined INs and IGs as well as all analyses of question-specific loci using both concatenation and coalescence methods,albeit with varying degrees of statistical support.In detail,our results indicated the sister-group relationships between the families Atelidae and Pitheciidae,and between the subfamilies Aotinae and Callithrichinae among Cebidae.Our study provides insights into the disputed phylogenetic relationships among NWM families and subfamilies from the perspective of multiple non-coding loci and various tree-inference approaches.However,the present phylogenetic framework needs further evaluation by adding more independent sequence data and a deeper taxonomic sampling.Overall,our work has important implications for phylogenetic studies dealing with rapid radiations.
The ITS-Is of 24 accessions belong to 10 species of subgenus Glycine, and 2 species of subgenus Soja of genus Glycine were amplified, cloned and sequenced. According to the homology of the sequences, the phy-logeny of the 24 accessions were reconstructed. The reconstructed dendrogram showed that there were some divergent genomic types found in the previously classified species, such as G . tomentella, G. canescens and G. tabacina, and they might be some cryptic species by morphologic analysis.
