A digraph D is k-ordered if for every sequence S：v 1,v 2,…,v k of k distinct vertices,there exists a cycle C such that C encounters the vertices of S in the specified order.In particular,we say that D is k-ordered h...A digraph D is k-ordered if for every sequence S：v 1,v 2,…,v k of k distinct vertices,there exists a cycle C such that C encounters the vertices of S in the specified order.In particular,we say that D is k-ordered hamiltonian if for every sequence S：v 1,v 2,…,v k of k distinct vertices,there exists a hamiltonian cycle C such that the vertices of S are encountered on C in the specified order.In this paper,sufficient conditions for digraphs to be ordered and ordered hamiltonian have been given.展开更多
Sexual selection is expected to promote speciation by fostering the evolution of sexual traits that minimize reproductive interactions among existing or incipient species. In species that compete for access to, or att...Sexual selection is expected to promote speciation by fostering the evolution of sexual traits that minimize reproductive interactions among existing or incipient species. In species that compete for access to, or attention of, females, sexual selec- tion fosters more elaborate traits in males compared to females. If these traits also minimize reproductive interactions with het- erospecifics, then species with enhanced risk of interactions between species might display greater numbers of these sexually di- morphic characters. We tested this prediction in eight families of North American birds. In particular, we evaluated whether the number of sexually dimorphic traits was positively associated with species richness at a given site or with degree of sympatry with congeners. We found no strong evidence of enhanced sexual dimorphism with increasing confamilial species richness at a given site. We also found no overall relationship between the number of sexually dimorphic traits and overlap with congeners across these eight families. However, we found patterns consistent with our prediction within Anatidae （ducks, geese and swans） and, to a lesser degree, Parulidae （New World warblers）. Our results suggest that sexually selected plumage traits in these groups potentially play a role in reproductive isolation [Current Zoology 58 （3）： 453--462, 2012].展开更多
基金Foundation item： Supported by the National Natural Science Foundation of China（61070229） Supported by the Natural Science Foundation of Shanxi Province（2008011010）
文摘A digraph D is k-ordered if for every sequence S：v 1,v 2,…,v k of k distinct vertices,there exists a cycle C such that C encounters the vertices of S in the specified order.In particular,we say that D is k-ordered hamiltonian if for every sequence S：v 1,v 2,…,v k of k distinct vertices,there exists a hamiltonian cycle C such that the vertices of S are encountered on C in the specified order.In this paper,sufficient conditions for digraphs to be ordered and ordered hamiltonian have been given.
文摘Sexual selection is expected to promote speciation by fostering the evolution of sexual traits that minimize reproductive interactions among existing or incipient species. In species that compete for access to, or attention of, females, sexual selec- tion fosters more elaborate traits in males compared to females. If these traits also minimize reproductive interactions with het- erospecifics, then species with enhanced risk of interactions between species might display greater numbers of these sexually di- morphic characters. We tested this prediction in eight families of North American birds. In particular, we evaluated whether the number of sexually dimorphic traits was positively associated with species richness at a given site or with degree of sympatry with congeners. We found no strong evidence of enhanced sexual dimorphism with increasing confamilial species richness at a given site. We also found no overall relationship between the number of sexually dimorphic traits and overlap with congeners across these eight families. However, we found patterns consistent with our prediction within Anatidae （ducks, geese and swans） and, to a lesser degree, Parulidae （New World warblers）. Our results suggest that sexually selected plumage traits in these groups potentially play a role in reproductive isolation [Current Zoology 58 （3）： 453--462, 2012].
