Motive of the representation varietes of torus knots for low rank affine groups

We compute the motive of the variety of representations of the torus knot of type (m, n) into the affine groups AGL1(C) and AGL2(C). For this, we stratify the varieties and show that the motives lie in the subring generated by the Lefschetz motive q = [C]

Seasonal niche differentiation among closely related marine bacteria

Bacteria display dynamic abundance fluctuations over time in marine environments, where they play key biogeochemical roles. Here, we characterized the seasonal dynamics of marine bacteria in a coastal oligotrophic time series station, tested how similar the temporal niche of closely related taxa is, and what are the environmental parameters modulating their seasonal abundance patterns. We further explored how conserved the niche is at higher taxonomic levels. The community presented recurrent patterns of seasonality for 297 out of 6825 amplicon sequence variants (ASVs), which constituted almost half of the total relative abundance (47%). For certain genera, niche similarity decreased as nucleotide divergence in the 16S rRNA gene increased, a pattern compatible with the selection of similar taxa through environmental filtering. Additionally, we observed evidence of seasonal differentiation within various genera as seen by the distinct seasonal patterns of closely related taxa. At broader taxonomic levels, coherent seasonal trends did not exist at the class level, while the order and family ranks depended on the patterns that existed at the genus level. This study identifies the coexistence of closely related taxa for some bacterial groups and seasonal differentiation for others in a coastal marine environment subjected to a strong seasonality.En prensa8,95

Brauer group of moduli spaces of pairs

We show that the Brauer group of any moduli space of stable pairs with fixed determinant over a curve is zero.Comment: 12 pages. Final version, accepted in Communications in Algebr

Symplectic Geometry of a Moduli Space of Framed Higgs Bundles

21 pages, minor modificationsLet $X$ be a compact connected Riemann surface and $D$ an effective divisor on $X$. Let ${\mathcal N}_H(r,d)$ denote the moduli space of $D$-twisted stable Higgs bundles (a special class of Hitchin pairs) on $X$ of rank $r$ and degree $d$. It is known that ${\mathcal N}_H(r,d)$ has a natural holomorphic Poisson structure which is in fact symplectic if and only if $D$ is the zero divisor. We prove that ${\mathcal N}_H(r,d)$ admits a natural enhancement to a holomorphic symplectic manifold which is called here ${\mathcal M}_H(r,d)$. This ${\mathcal M}_H(r,d)$ is constructed by trivializing, over $D$, the restriction of the vector bundles underlying the $D$-twisted Higgs bundles; such objects are called here as framed Higgs bundles. We also investigate the symplectic structure on the moduli space ${\mathcal M}_H(r,d)$ of framed Higgs bundles as well as the Hitchin system associated to it

Marked changes in diversity and relative activity of picoeukaryotes with depth in the world ocean

Microbial eukaryotes are key components of the ocean plankton. Yet, our understanding of their community composition and activity in different water layers of the ocean is limited, particularly for picoeukaryotes (0.2–3 µm cell size). Here, we examined the picoeukaryotic communities inhabiting different vertical zones of the tropical and subtropical global ocean: surface, deep chlorophyll maximum, mesopelagic (including the deep scattering layer and oxygen minimum zones), and bathypelagic. Communities were analysed by high-tthroughput sequencing of the 18S rRNA gene (V4 region) as represented by DNA (community structure) and RNA (metabolism), followed by delineation of Operational Taxonomic Units (OTUs) at 99% similarity. We found a stratification of the picoeukaryotic communities along the water column, with assemblages corresponding to the sunlit and dark ocean. Specific taxonomic groups either increased (e.g., Chrysophyceae or Bicosoecida) or decreased (e.g., Dinoflagellata or MAST-3) in abundance with depth. We used the rRNA:rDNA ratio of each OTU as a proxy of metabolic activity. The highest relative activity was found in the mesopelagic layer for most taxonomic groups, and the lowest in the bathypelagic. Altogether, we characterize the change in community structure and metabolic activity of picoeukaryotes with depth in the global ocean, suggesting a hotspot of activity in the mesopelagic

Combined stress effect of pH and temperature narrows the niche width of flagellates in acid mining lakes

Strains of the green alga Chlamydomonas acidophila and two chrysomonads, Ochromonas spp., isolated from each of two similar acid mining lakes (AMLs) with extremely low pH (∼2.6) were investigated to consider a possible synergistic stress effect of low pH and unfavourable temperature. We measured flagellate growth rates over a combination of four pH (2.5, 3.5, 5.0 and 7.0) and three temperatures (10, 17.5 and 25°C) in the laboratory. Our hypothesis was that, under highly acidic conditions (pH <3), an obligate acidophil species (C. acidophila) would be less sensitive to the combined stress of pH and temperature than acidotolerant species (Ochromonas spp.). We expected that the difference of the fundamental vs. realized pH niche would be greater in the latter. Another chrysomonad, Poterioochromonas malhamensis strain DS, served as a reference for a closely related neutrophil species. Surprisingly, C. acidophila did not survive temperatures >27°C. The lowest temperature tested reduced growth rates of all three chrysomonad strains significantly. Since all chrysomonads were tolerant to high temperature, growth rate of one Ochromonas spp. strain was measured exemplarily at 35°C. Only at this high temperature was the realized pH niche significantly narrowed. We also recorded significant intraspecific differences within the C. acidophila strains from the two AML, illustrating that the niche width of a species is broader than that of individual clones

Disentangling environmental effects in microbial association networks

Background Ecological interactions among microorganisms are fundamental for ecosystem function, yet they are mostly unknown or poorly understood. High-throughput-omics can indicate microbial interactions through associations across time and space, which can be represented as association networks. Associations could result from either ecological interactions between microorganisms, or from environmental selection, where the association is environmentally driven. Therefore, before downstream analysis and interpretation, we need to distinguish the nature of the association, particularly if it is due to environmental selection or not. Results We present EnDED (environmentally driven edge detection), an implementation of four approaches as well as their combination to predict which links between microorganisms in an association network are environmentally driven. The four approaches are sign pattern, overlap, interaction information, and data processing inequality. We tested EnDED on networks from simulated data of 50 microorganisms. The networks contained on average 50 nodes and 1087 edges, of which 60 were true interactions but 1026 false associations (i.e., environmentally driven or due to chance). Applying each method individually, we detected a moderate to high number of environmentally driven edges—87% sign pattern and overlap, 67% interaction information, and 44% data processing inequality. Combining these methods in an intersection approach resulted in retaining more interactions, both true and false (32% of environmentally driven associations). After validation with the simulated datasets, we applied EnDED on a marine microbial network inferred from 10 years of monthly observations of microbial-plankton abundance. The intersection combination predicted that 8.3% of the associations were environmentally driven, while individual methods predicted 24.8% (data processing inequality), 25.7% (interaction information), and up to 84.6% (sign pattern as well as overlap). The fraction of environmentally driven edges among negative microbial associations in the real network increased rapidly with the number of environmental factors. Conclusions To reach accurate hypotheses about ecological interactions, it is important to determine, quantify, and remove environmentally driven associations in marine microbial association networks. For that, EnDED offers up to four individual methods as well as their combination. However, especially for the intersection combination, we suggest using EnDED with other strategies to reduce the number of false associations and consequently the number of potential interaction hypotheses. Video abstrac

Long-term patterns of an interconnected core marine microbiota

Background Ocean microbes constitute ~ 70% of the marine biomass, are responsible for ~ 50% of the Earth’s primary production and are crucial for global biogeochemical cycles. Marine microbiotas include core taxa that are usually key for ecosystem function. Despite their importance, core marine microbes are relatively unknown, which reflects the lack of consensus on how to identify them. So far, most core microbiotas have been defined based on species occurrence and abundance. Yet, species interactions are also important to identify core microbes, as communities include interacting species. Here, we investigate interconnected bacteria and small protists of the core pelagic microbiota populating a long-term marine-coastal observatory in the Mediterranean Sea over a decade. Results Core microbes were defined as those present in \u3e 30% of the monthly samples over 10 years, with the strongest associations. The core microbiota included 259 Operational Taxonomic Units (OTUs) including 182 bacteria, 77 protists, and 1411 strong and mostly positive (~ 95%) associations. Core bacteria tended to be associated with other bacteria, while core protists tended to be associated with bacteria. The richness and abundance of core OTUs varied annually, decreasing in stratified warmers waters and increasing in colder mixed waters. Most core OTUs had a preference for one season, mostly winter, which featured subnetworks with the highest connectivity. Groups of highly associated taxa tended to include protists and bacteria with predominance in the same season, particularly winter. A group of 13 highly-connected hub-OTUs, with potentially important ecological roles dominated in winter and spring. Similarly, 18 connector OTUs with a low degree but high centrality were mostly associated with summer or autumn and may represent transitions between seasonal communities. Conclusions We found a relatively small and dynamic interconnected core microbiota in a model temperate marine-coastal site, with potential interactions being more deterministic in winter than in other seasons. These core microbes would be essential for the functioning of this ecosystem over the year. Other non-core taxa may also carry out important functions but would be redundant and non-essential. Our work contributes to the understanding of the dynamics and potential interactions of core microbes possibly sustaining ocean ecosystem function

Long-term patterns of an interconnected core marine microbiota

Background Ocean microbes constitute ∼70% of the marine biomass, are responsible for ∼50% of the Earth’s primary production, and are crucial for global biogeochemical cycles. Marine microbiotas include core taxa that are usually key for ecosystem function. Despite their importance, core marine microbes are relatively unknown, which reflects the lack of consensus on how to identify them. So far, most core microbiotas have been defined based on species occurrence and abundance. Yet, species interactions are also important to identify core microbes, as communities include interacting species. Here, we investigate interconnected bacteria and small protists of the core pelagic microbiota populating a long-term marine-coastal observatory in the Mediterranean Sea over a decade. Results Core microbes were defined as those present in >30% of the monthly samples over 10 years, with the strongest associations. The core microbiota included 259 Operational Taxonomic Units (OTUs) including 182 bacteria, 77 protists, and 1,411 strong and mostly positive (∼95%) associations. Core bacteria tended to be associated with other bacteria, while core protists tended to be associated with bacteria. The richness and abundance of core OTUs varied annually, decreasing in stratified warmers waters and increasing in colder mixed waters. Most core OTUs had a preference for one season, mostly winter, which featured subnetworks with the highest connectivity. Groups of highly associated taxa tended to include protists and bacteria with predominance in the same season, particularly winter. A group of 13 highly-connected hub-OTUs, with potentially important ecological roles dominated in winter and spring. Similarly, 18 connector OTUs with a low degree but high centrality were mostly associated with summer or autumn and may represent transitions between seasonal communities. Conclusions We found a relatively small and dynamic interconnected core microbiota in a model temperate marine-coastal site, with potential interactions being more deterministic in winter than in other seasons. These core microbes would be essential for the functioning of this ecosystem over the year. Other non-core taxa may also carry out important functions but would be redundant and non-essential. Our work contributes to the understanding of the dynamics and potential interactions of core microbes possibly sustaining ocean ecosystem function.Preprin