A Poincar\'e-Birkhoff theorem for tight Reeb flows on S3S^3

We consider Reeb flows on the tight $3$-sphere admitting a pair of closed orbits forming a Hopf link. If the rotation numbers associated to the transverse linearized dynamics at these orbits fail to satisfy a certain resonance condition then there exist infinitely many periodic trajectories distinguished by their linking numbers with the components of the link. This result admits a natural comparison to the Poincar\'e-Birkhoff theorem on area-preserving annulus homeomorphisms. An analogous theorem holds on $SO(3)$ and applies to geodesic flows of Finsler metrics on $S^2$.Comment: 67 pages. To appear in Inventiones Mathematica

Biased-corrected richness estimates for the Amazonian tree flora

Amazonian forests are extraordinarily diverse, but the estimated species richness is very much debated. Here, we apply an ensemble of parametric estimators and a novel technique that includes conspecific spatial aggregation to an extended database of forest plots with up-to-date taxonomy. We show that the species abundance distribution of Amazonia is best approximated by a logseries with aggregated individuals, where aggregation increases with rarity. By averaging several methods to estimate total richness, we confirm that over 15,000 tree species are expected to occur in Amazonia. We also show that using ten times the number of plots would result in an increase to just ~50% of those 15,000 estimated species. To get a more complete sample of all tree species, rigorous field campaigns may be needed but the number of trees in Amazonia will remain an estimate for years to come

Amazon tree dominance across forest strata

The forests of Amazonia are among the most biodiverse plant communities on Earth. Given the immediate threats posed by climate and land-use change, an improved understanding of how this extraordinary biodiversity is spatially organized is urgently required to develop effective conservation strategies. Most Amazonian tree species are extremely rare but a few are common across the region. Indeed, just 227 ‘hyperdominant’ species account for >50% of all individuals >10 cm diameter at 1.3 m in height. Yet, the degree to which the phenomenon of hyperdominance is sensitive to tree size, the extent to which the composition of dominant species changes with size class and how evolutionary history constrains tree hyperdominance, all remain unknown. Here, we use a large floristic dataset to show that, while hyperdominance is a universal phenomenon across forest strata, different species dominate the forest understory, midstory and canopy. We further find that, although species belonging to a range of phylogenetically dispersed lineages have become hyperdominant in small size classes, hyperdominants in large size classes are restricted to a few lineages. Our results demonstrate that it is essential to consider all forest strata to understand regional patterns of dominance and composition in Amazonia. More generally, through the lens of 654 hyperdominant species, we outline a tractable pathway for understanding the functioning of half of Amazonian forests across vertical strata and geographical locations

Geographic patterns of tree dispersal modes in Amazonia and their ecological correlates

This is the final version. Available on open access from Wiley via the DOI in this recordData availability statement: The percentages of dispersal modes per plot are included as Supporting Information (Table S7, based on 5433 species and morphospecies within 1877 tree-inventory plots across terra-firme, seasonally flooded, and permanently flooded forests in Amazonia). The dispersal modes assigned to these 5433 species and morphospecies are also included as Supporting Information (Table S8).Aim: To investigate the geographic patterns and ecological correlates in the geographic distribution of the most common tree dispersal modes in Amazonia (endozoochory, synzoochory, anemochory and hydrochory). We examined if the proportional abundance of these dispersal modes could be explained by the availability of dispersal agents (disperser-availability hypothesis) and/or the availability of resources for constructing zoochorous fruits (resource-availability hypothesis). Time period: Tree-inventory plots established between 1934 and 2019. Major taxa studied: Trees with a diameter at breast height (DBH) ≥ 9.55 cm. Location: Amazonia, here defined as the lowland rain forests of the Amazon River basin and the Guiana Shield. Methods: We assigned dispersal modes to a total of 5433 species and morphospecies within 1877 tree-inventory plots across terra-firme, seasonally flooded, and permanently flooded forests. We investigated geographic patterns in the proportional abundance of dispersal modes. We performed an abundance-weighted mean pairwise distance (MPD) test and fit generalized linear models (GLMs) to explain the geographic distribution of dispersal modes. Results: Anemochory was significantly, positively associated with mean annual wind speed, and hydrochory was significantly higher in flooded forests. Dispersal modes did not consistently show significant associations with the availability of resources for constructing zoochorous fruits. A lower dissimilarity in dispersal modes, resulting from a higher dominance of endozoochory, occurred in terra-firme forests (excluding podzols) compared to flooded forests. Main conclusions: The disperser-availability hypothesis was well supported for abiotic dispersal modes (anemochory and hydrochory). The availability of resources for constructing zoochorous fruits seems an unlikely explanation for the distribution of dispersal modes in Amazonia. The association between frugivores and the proportional abundance of zoochory requires further research, as tree recruitment not only depends on dispersal vectors but also on conditions that favour or limit seedling recruitment across forest types.Colombian institution Departamento Administrativo de Ciencia, Tecnología e Innovación COLCIENCIASFaculty of Sciences, Universidad de los Ande

Sleep apnea and REM sleep behavior disorder in patients with Chiari malformations Apnéia do sono e distúrbio do comportamento da fase do sono com REM em pacientes com malformações de Chiari

BACKGROUND: Chiari malformations (CM) may result in the appearance of REM sleep behavior disorder (RBD) and sleep apnea syndrome (SAS) that can be considered markers of brain stem dysfunction. PURPOSE: To evaluate the frequency of RBD and SAS in patients with CM type I and II. METHOD: Were evaluated 103 patients with CM by means of full night polysomnography. Were scoring different sleep stages, frequency of abnormal movements (through video monitoring) and abnormal respiratory events. RESULTS: Of the 103 patients, 36 showed CM type I and 67 CM type II. Episodes of RBD were observed in 23 patients. Abnormal apnea-hypopnea index (AHI) was observed in 65 patients. CONCLUSION: The high rate of RBD suggests that this parassomnia and the increased frequency of central sleep apnea episodes, may be considered as a marker of progressive brain stem dysfunction.<br>INTRODUÇÃO: Malformações de Chiari (MC) podem gerar o aparecimento de distúrbio comportamental da fase do sono com REM (DCR) e síndrome da apnéia do sono (SAS), sugerindo a ocorrência de disfunção do tronco cerebral. OBJETIVO: Avaliar a freqüência de DCR e SAS em pacientes com MC I ou II. MÉTODO: Utilizou-se a polissonografia de noite inteira para a avaliação de 103 pacientes. Classificaram-se as diferentes fases do sono e analisou-se a freqüência de movimentos anormais (monitorada por vídeo) e de eventos respiratórios anormais. RESULTADOS: Dos 103 pacientes analisados, 36 eram portadores de MC I e 67 de MC II. Episódios de DCR foram observados em 23 pacientes. O índice de apnéia/hipopnéia foi considerado anormal em 65 pacientes. CONCLUSÃO: A alta freqüência de DCR e o aumento da freqüência de episódios de apnéia central do sono podem ser considerados manifestação de disfunção progressiva do tronco cerebral