HFD groups in the Solovay model

Hajnal and Juhasz proved that under CH there is a hereditarily separable, hereditarily normal topological group without non-trivial convergent sequences that is countably compact and not Lindelof. The example constructed is a topological subgroup H subset of 2(omega 1) that is an HFD with the following property (P) the projection of H onto every partial product 2(I) for I is an element of vertical bar omega(1)vertical bar(omega) is onto. Any such group has the necessary properties. We prove that if kappa is a cardinal of uncountable cofinality, then in the model obtained by forcing over a model of CH with the measure algebra on 2(kappa), there is an HFD topological group in 2(omega 1) which has property (P). Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.

Abelian torsion groups with a countably compact group topology

Comfort and Remus [W.W. Comfort, D. Remus, Abelian torsion groups with a pseudo-compact group topology, Forum Math. 6 (3) (1994) 323-337] characterized algebraically the Abelian torsion groups that admit a pseudocompact group topology using the Ulm-Kaplansky invariants. We show, under a condition weaker than the Generalized Continuum Hypothesis, that an Abelian torsion group (of any cardinality) admits a pseudocompact group topology if and only if it admits a countably compact group topology. Dikranjan and Tkachenko [D. Dikranjan. M. Tkachenko, Algebraic structure of small countably compact Abelian groups, Forum Math. 15 (6) (2003) 811-837], and Dikranjan and Shakhmatov [D. Dikranjan. D. Shakhmatov, Forcing hereditarily separable compact-like group topologies on Abelian groups, Topology Appl. 151 (1-3) (2005) 2-54] showed this equivalence for groups of cardinality not greater than 2(c). We also show, from the existence of a selective ultrafilter, that there are countably compact groups without non-trivial convergent sequences of cardinality kappa(omega), for any infinite cardinal kappa. In particular, it is consistent that for every cardinal kappa there are countably compact groups without non-trivial convergent sequences whose weight lambda has countable cofinality and lambda > kappa. (C) 2009 Elsevier B.V. All rights reserved.

Experimentação-com-Geogebra: revisitando alguns conceitos da análise real

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Almost p-compact groups

We show that if p is a selective ultrafilter, then for each cardinal alpha <= omega(1), there exists a topological group G such that G(beta) is almost p-compact (in particular, countably compact), for beta < alpha, but G(alpha) is not countably compact. If in addition, we assume Martin's Axiom, then the result above holds for every alpha < c. (C) 2012 Elsevier By. All rights reserved.

Topologias maximais com respeito a algumas famílias de subconjuntos

Seja (X; t) um espaço topológico e seja F a família de todos os subconjuntos de X que satisfazem uma propriedade topológica dada P (invariante por homeomorfismos). Se acrescentarmos abertos novos à topologia e se F\' é a família de todos os subconjuntos do novo espaço que satisfazem a propriedade P, podemos ter que F ≠ F\'. Se isto sempre acontece, dizemos que o espaço (X; t) é maximal com respeito à família F. Neste trabalho estudaremos os espaços topológicos maximais com respeito a algumas famílias de subconjuntos: discretos, compactos, densos, conexos e das sequências convergentes.

Convergent evolution of marine mammals is associated with distinct substitutions in common genes

Phenotypic convergence is thought to be driven by parallel substitutions coupled with natural selection at the sequence level. Multiple independent evolutionary transitions of mammals to an aquatic environment offer an opportunity to test this thesis. Here, whole genome alignment of coding sequences identified widespread parallel amino acid substitutions in marine mammals; however, the majority of these changes were not unique to these animals. Conversely, we report that candidate aquatic adaptation genes, identified by signatures of likelihood convergence and/or elevated ratio of nonsynonymous to synonymous nucleotide substitution rate, are characterized by very few parallel substitutions and exhibit distinct sequence changes in each group. Moreover, no significant positive correlation was found between likelihood convergence and positive selection in all three marine lineages. These results suggest that convergence in protein coding genes associated with aquatic lifestyle is mainly characterized by independent substitutions and relaxed negative selection.

Source and target enzyme signature in serine protease inhibitor active site sequences

Amino acid sequences of proteinaceous proteinase inhibitors have been extensively analysed for deriving information regarding the molecular evolution and functional relationship of these proteins. These sequences have been grouped into several well defined families. It was found that the phylogeny constructed with the sequences corresponding to the exposed loop responsible for inhibition has several branches that resemble those obtained from comparisons using the entire sequence. The major branches of the unrooted tree corresponded to the families to which the inhibitors belonged. Further branching is related to the enzyme specificity of the inhibitor. Examination of the active site loop sequences of trypsin inhibitors revealed that there are strong preferences for specific amino acids at different positions of the loop. These preferences are inhibitor class specific. Inhibitors active against more than one enzyme occur within a class and confirm to class specific sequence in their loops. Hence, only a few positions in the loop seem to determine the specificity. The ability to inhibit the same enzyme by inhibitors that belong to different classes appears to be a result of convergent evolution

Molecular systematics of pikas (genus Ochotona) inferred from mitochondrial DNA sequences

The phylogenetic relationships among worldwide species of genus Ochotona were investigated by sequencing mitochondrial cytochrome b and ND4 genes. Parsimony and neighbor-joining analyses of the sequence data yielded congruent results that strongly indicated three major clusters: the shrub-steppe group, the northern group, and the mountain group. The subgeneric classification of Ochotona species needs to be revised because each of the two subgenera in the present classification contains species from the mountain group. To solve this taxonomic problem so that each taxon is monophyletic, i.e., represents a natural clade, Ochotona could be divided into three subgenera, one for the shrub-steppe species, a second for the northern species, and a third for the mountain species. The inferred tree suggests that the differentiation of this genus in the Palearctic Region was closely related to the gradual uplifting of the Tibet (Qinghai-Xizang) Plateau, as hypothesized previously, and that vicariance might have played a major role in the differentiation of this genus on the Plateau, On the other hand, the North American species, O. princeps, is most likely a dispersal event, which might have happened during the Pliocene through the opening of the Bering Strait. The phylogenetic relationships within the shrub-steppe group are worth noting in that instead of a monophyletic shrub-dwelling group, shrub dwellers and steppe dwellers are intermingled with each other. Moreover, the sequence divergence within the sister tars of one steppe? dweller and one shrub dweller is very low. These findings support the hypothesis that pikes have entered the steppe environment several times and that morphological similarities within steppe dwellers were due to convergent evolution. (C) 2000 Academic Press.

Parallel and Convergent Evolution of the Dim-Light Vision Gene RH1 in Bats (Order: Chiroptera)

Rhodopsin, encoded by the gene Rhodopsin (RH1), is extremely sensitive to light, and is responsible for dim-light vision. Bats are nocturnal mammals that inhabit poor light environments. Megabats (Old-World fruit bats) generally have well-developed eyes, while microbats (insectivorous bats) have developed echolocation and in general their eyes were degraded, however, dramatic differences in the eyes, and their reliance on vision, exist in this group. In this study, we examined the rod opsin gene (RH1), and compared its evolution to that of two cone opsin genes (SWS1 and M/LWS). While phylogenetic reconstruction with the cone opsin genes SWS1 and M/LWS generated a species tree in accord with expectations, the RH1 gene tree united Pteropodidae (Old-World fruit bats) and Yangochiroptera, with very high bootstrap values, suggesting the possibility of convergent evolution. The hypothesis of convergent evolution was further supported when nonsynonymous sites or amino acid sequences were used to construct phylogenies. Reconstructed RH1 sequences at internal nodes of the bat species phylogeny showed that: (1) Old-World fruit bats share an amino acid change (S270G) with the tomb bat; (2) Miniopterus share two amino acid changes (V104I, M183L) with Rhinolophoidea; (3) the amino acid replacement I123V occurred independently on four branches, and the replacements L99M, L266V and I286V occurred each on two branches. The multiple parallel amino acid replacements that occurred in the evolution of bat RH1 suggest the possibility of multiple convergences of their ecological specialization (i.e., various photic environments) during adaptation for the nocturnal lifestyle, and suggest that further attention is needed on the study of the ecology and behavior of bats.

Reconsideration of Phylogenetic Relationships of the Subclass Peritrichia (Ciliophora, Oligohymenophorea) Based on Small Subunit Ribosomal RNA Gene Sequences, with the Establishment of a New Subclass Mobilia Kahl, 1933

Based on its characteristic oral apparatus, the ciliate subclass Peritrichia has long been recognized as a monophyletic assemblage composed of the orders Mobilida and Sessilida. Following the application of molecular methods, the monophyly of Peritrichia has recently been questioned. We investigated the phylogenetic relationships of the peritrichous ciliates based on four further complete small subunit ribosomal RNA sequences of mobilids, namely Urceolaria urechi, Trichodina meretricis, Trichodina sinonovaculae, and Trichodina ruditapicis. In all phylogenetic trees, the mobilids never clustered with the sessilids, but instead formed a monophyletic assemblage related to the peniculines. By contrast, the sessilids formed a sister clade with the hymenostomes at a terminal position within the Oligohymenophorea. We therefore formally separate the mobilids from the sessilids (Peritrichia sensu stricto) and establish a new subclass, Mobilia Kahl, 1933, which contains the order Mobilida Kahl, 1933. We argue that the oral apparatus in the mobilians and sessilid peritrichs is a homoplasy, probably due to convergent evolution driven by their similar life-styles and feeding strategies. Morphologically, the mobilians are distinguished from all other oligohymenophoreans by the presence of the adhesive disc, this character being a synapomorphy for the Mobilia.

Molecular phylogeny, recent radiation and evolution of gross morphology of the rhubarb genus Rheum (Polygonaceae) inferred from chloroplast DNA trnL-F sequences

Background and Aims Rheum, a highly diversified genus with about 60 species, is mainly confined to the mountainous and desert regions of the Qinghai-Tibetan plateau and adjacent areas. This genus represents a good example of the extensive diversification of the temperate genera in the Qinghai-Tibetan plateau, in which the forces to drive diversification remain unknown. To date, the infrageneric classification of Rheum has been mainly based on morphological characters. However, it may have been subject to convergent evolution under habitat pressure, and the systematic position of some sections are unclear, especially Sect. Globulosa, which has globular inflorescences, and Sect. Nobilia, which has semi-translucent bracts. Recent palynological research has found substantial contradictions between exine patterns and the current classification of Rheum. Two specific objectives of this research were (1) to evaluate possible relationships of some ambiguous sections with a unique morphology, and (2) to examine possible occurrence of the radiative speciation with low genetic divergence across the total genus and the correlation between the extensive diversification time of Rheum and past geographical events, especially the recent large-scale uplifts of the Qinghai-Tibetan Plateau.Methods The chloroplast DNA trnL-F region of 29 individuals representing 26 species of Rheum, belonging to seven out of eight sections, was sequenced and compared. The phylogenetic relationships were further constructed based on the sequences obtained.Key Results Despite the highly diversified morphology, the genetic variation in this DNA fragment is relatively low. The molecular phylogeny is highly inconsistent with gross morphology, pollen exine patterns and traditional classifications, except for identifying all samples of Sect. Palmata, three species of Sect. Spiciformia and a few species of Sect. Rheum as corresponding monophyletic groups. The monotypic Sect. Globulosa showed a tentative position within the clade comprising five species of Sect. Rheum. All of the analyses revealed the paraphyly of R. nobile and R. alexandrae, the only two species of Sect. Nobilia circumscribed by the possession of large bracts. The crude calibration of lineages based on trnL-F sequence differentiation implied an extensive diversification of Rheum within approx. 7 million years.Conclusions Based on these results, it is suggested that the rich geological and ecological diversity caused by the recent large-scale uplifts of the Qinghai-Tibetan Plateau since the late Tertiary, coupled with the oscillating climate of the Quaternary stage, might have promoted rapid speciation in small and isolated populations, as well as allowing the fixation of unique or rare morphological characters in Rheum. Such a rapid radiation, combined with introgressive hybridization and reticulate evolution, may have caused the transfer of cpDNA haplotypes between morphologically dissimilar species, and might account for the inconsistency between morphological classification and molecular phylogeny reported here.

Phylogenetic analyses of Saussurea sect. Pseudoeriocoryne (Asteraceae : Cardueae) based on chloroplast DNA trnL-F sequences

The genus Saussurea is distributed mainly in the temperate and subarctic regions of Eurasia and consists of about 300 species classified into six subgenera and 20 sections. Sect. Pseudoeriocoryne in the subgenus Eriocoryne comprises four species, and is delimited mainly by acaulescence and an inflorescence with congested capitula surrounded by a rosette of leaves. All of these species are endemic to the and Qinghai-Tibet Plateau. Sequences from the chloroplast DNA trnL-F region were obtained for the four species in this section and 26 other species from four subgenera of Saussurea to resolve phylogenetic relationships among these species and to determine whether the shared characters that define sect. Pseudoeriocoryne are synapomorphic or were acquired by convergent evolution. The resulting phylogenies indicated that Saussurea sect. Pseudoeriocoryne as traditionally defined does not constitute a monophyletic group and that each of its species belongs to separate clades. Furthermore, none of these species showed a close relationship with the other species of subgenus Eriocoryne. Our results further indicated that none of the investigated subgenera are monophyletic, and that species from different subgenera clustered together. All these conclusions are provisional and their confirmation would require stronger phylogenetic support. Two possible explanations are suggested for low sequence divergence, poor resolution of internal clades and clustering of species with the rather distinct morphology of Saussurea detected in the present study. The first is rapid radiation and diversification triggered by fast habitat fragmentation due to the recent lifting of the Qinghai-Tibet Plateau and the Quaternary climate oscillations. This could have led to rapid morphological divergence while sequences diverged very little, and also caused the convergent acquisition of similar characteristics in unrelated lineages due to similar selection pressures. The second possible explanation is that both introgressive hybridization and reticulate evolution might have caused the transferring of cpDNA sequences between morphologically dissimilar species, thus leading to homogenization of sequences between lineages. (C) 2004 Elsevier Ltd. All rights reserved.

Molecular systematics of pikas (genus Ochotona) inferred from mitochondrial DNA sequences

The phylogenetic relationships among worldwide species of genus Ochotona were investigated by sequencing mitochondrial cytochrome b and ND4 genes. Parsimony and neighbor-joining analyses of the sequence data yielded congruent results that strongly indicated three major clusters: the shrub-steppe group, the northern group, and the mountain group. The subgeneric classification of Ochotona species needs to be revised because each of the two subgenera in the present classification contains species from the mountain group. To solve this taxonomic problem so that each taxon is monophyletic, i.e., represents a natural clade, Ochotona could be divided into three subgenera, one for the shrub-steppe species, a second for the northern species, and a third for the mountain species. The inferred tree suggests that the differentiation of this genus in the Palearctic Region was closely related to the gradual uplifting of the Tibet (Qinghai-Xizang) Plateau, as hypothesized previously, and that vicariance might have played a major role in the differentiation of this genus on the Plateau, On the other hand, the North American species, O. princeps, is most likely a dispersal event, which might have happened during the Pliocene through the opening of the Bering Strait. The phylogenetic relationships within the shrub-steppe group are worth noting in that instead of a monophyletic shrub-dwelling group, shrub dwellers and steppe dwellers are intermingled with each other. Moreover, the sequence divergence within the sister tars of one steppe? dweller and one shrub dweller is very low. These findings support the hypothesis that pikes have entered the steppe environment several times and that morphological similarities within steppe dwellers were due to convergent evolution. (C) 2000 Academic Press.

Phylogenetic relationships of the globally distributed freshwater prawn genus Macrobrachium (Crustacea: Decapoda: Palaemonidae): biogeography, taxonomy, and the convergent evolution of abbreviated larval development

There has hitherto been little research into evolutionary and taxonomic relationships amongst species of the freshwater prawn genus Macrobrachium Bate across its global distribution. Previous work by the authors demonstrated that the endemic Australian species did not evolve from a single ancestral lineage. To examine whether other regional Macrobrachium faunas also reflect this pattern of multiple origins, the phylogeny of 30 Macrobrachium species from Asia, Central/South America and Australia was inferred from mitochondrial 16S rRNA sequences. Phylogenetic relationships demonstrate that, despite some evidence for regional diversification, Australia, Asia and South America clearly contain Macrobrachium species that do not share a common ancestry, suggesting that large-scale dispersal has been a major feature of the evolutionary history of the genus. The evolution of abbreviated larval development (ALD), associated with the transition from an estuarine into a purely freshwater lifecycle, was also mapped onto the phylogeny and was shown to be a relatively homoplasious trait and not taxonomically informative. Other taxonomic issues, as well as the evolutionary origins of Macrobrachium, are also discussed.

Convergent evolution of aposematic coloration in Neotropical poison frogs: a molecular phylogenetic perspective

Poison frogs of the family Dendrobatidae contain cryptic as well as brightly colored, presumably aposematic species. The prevailing phylogenetic hypothesis assumes that the aposematic taxa form a monophyletic group while the cryptic species (Colostethus sensu lato) are basal and paraphyletic. Analysis of 86 dendrobatid sequences of a fragment of the 16S rRNA gene resulted in a much more complex scenario, with several clades that contained aposematic as well as cryptic taxa. Monophyly of the aposematic taxa was significantly rejected by SH-tests in an analysis with additional 12S and 16S rDNA fragments and reduced taxon sampling. The brightly colored Allobates femoralis and A. zaparo (Silverstone) comb. nov. (previously Epipedobates) belong in a clade with cryptic species of Colostethus. Additionally, Colostethus pratti was grouped with Epipedobates, and Colostethus bocagei with Cryptophyllobates. In several cases, the aposematic species have general distributions similar to those of their non-aposematic sister groups, indicating multiple instances of regional radiations in which some taxa independently acquired bright color. From a classificatory point of view, it is relevant that the type species of Minyobates, M. steyermarki, resulted as the sister group of the genus Dendrobates, and that species of Mannophryne and Nephelobates formed monophyletic clades, corroborating the validity of these genera. Leptodactylids of the genera Hylodes and Crossodactylus were not unambiguously identified as the sister group of the Dendrobatidae; these were monophyletic in all analyses and probably originated early in the radiation of Neotropical hyloid frogs.