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We consider the reflection–transmission problem in a waveguide with obstacle. At certain frequencies, for some incident waves, intensity is perfectly transmitted and the reflected field decays exponentially at infinity. In this work, we show that such reflectionless modes can be characterized as eigenfunctions of an original non-self-adjoint spectral problem. To select ingoing waves on one side of the obstacle and outgoing waves on the other side, we use complex scalings (or perfectly matched layers) with imaginary parts of different signs. We prove that the real eigenvalues of the obtained spectrum correspond either to trapped modes (or bound states in the continuum) or to reflectionless modes. Interestingly, complex eigenvalues also contain useful information on weak reflection cases. When the geometry has certain symmetries, the new spectral problem enters the class of PT-symmetric problems.

The identification of geographic areas where the densities of animals are highest across their annual cycles is a crucial step in conservation planning. In marine environments, however, it can be particularly difficult to map the distribution of species, and the methods used are usually biased towards adults, neglecting the distribution of other life‐history stages even though they can represent a substantial proportion of the total population. Here we develop a methodological framework for estimating population‐level density distributions of seabirds, integrating tracking data across the main life‐history stages (adult breeders and non‐breeders, juveniles and immatures). We incorporate demographic information (adult and juvenile/immature survival, breeding frequency and success, age at first breeding) and phenological data (average timing of breeding and migration) to weight distribution maps according to the proportion of the population represented by each life‐history stage. We demonstrate the utility of this framework by applying it to 22 species of albatrosses and petrels that are of conservation concern due to interactions with fisheries. Because juveniles, immatures and non‐breeding adults account for 47%–81% of all individuals of the populations analysed, ignoring the distributions of birds in these stages leads to biased estimates of overlap with threats, and may misdirect management and conservation efforts. Population‐level distribution maps using only adult distributions underestimated exposure to longline fishing effort by 18%–42%, compared with overlap scores based on data from all life‐history stages. Synthesis and applications. Our framework synthesizes and improves on previous approaches to estimate seabird densities at sea, is applicable for data‐poor situations, and provides a standard and repeatable method that can be easily updated as new tracking and demographic data become available. We provide scripts in the R language and a Shiny app to facilitate future applications of our approach. We recommend that where sufficient tracking data are available, this framework be used to assess overlap of seabirds with at‐sea threats such as overharvesting, fisheries bycatch, shipping, offshore industry and pollutants. Based on such an analysis, conservation interventions could be directed towards areas where they have the greatest impact on populations.

The globally distributed diazotroph Trichodesmium contributes importantly to nitrogen inputs in the oligotrophic oceans. Sites of dissolved organic matter (DOM) accumulation could promote the mixotrophic nutrition of Trichodesmium when inorganic nutrients are scarce. Nano-scale secondary ion mass spectrometry (nanoSIMS) analyses of individual trichomes sampled in the South Pacific Ocean, showed significant 13 C-enrichments after incubation with either 13 C-labeled carbohydrates or amino acids. These results suggest that DOM could be directly taken up by Trichodesmium or primarily consumed by heterotrophic epibiont bacteria that ultimately transfer reduced DOM compounds to their host trichomes. Although the addition of carbohydrates or amino acids did not significantly affect bulk N 2 fixation rates, N 2 fixation was enhanced by amino acids in individual colonies of Trichodesmium. We discuss the ecological advantages of DOM use by Trichodesmium as an alternative to autotrophic nutrition in oligotrophic open ocean waters.

The rapidly changing climate in the Arctic is expected to have a major impact on the foraging ecology of seabirds, owing to changes in the distribution and abundance of their prey but also that of competitors (e.g. southerly species expanding their range into the Arctic). Species can respond to interspecific competition by segregating along different niche axes. Here, we studied spatial, temporal and habitat segregation between two closely related seabird species: common guillemot Uria aalge (a temperate species) and Brünnich’s guillemot Uria lomvia (a true Arctic species), at two sympatric sites in Iceland that differ in their total population sizes and the availability of marine habitats. We deployed GPS and temperature-depth recorders to describe foraging locations and behaviour of incubating and chick-rearing adults. We found similar evidence of spatial segregation at the two sites (i.e. independent of population sizes), although segregation in environmental space was only evident at the site with a strong habitat gradient. Unexpectedly, temporal (and, to a limited extent, vertical) segregation appeared only at the least populated site. Overall, our results show complex relationships between the levels of inferred competition and that of segregation.

In the Western Tropical South Pacific, patches of high chlorophyll concentrations linked to the occurrence of N 2 -fixing organisms are found in the vicinity of volcanic islands. The survival of these organisms relies on a high bioavailable iron supply whose origin and fluxes remain unknown. Here, we measured high dissolved iron (DFe) concentrations (up to 66 nM) in the euphotic layer, extending zonally over 10 degrees longitude (174 E−175 W) at ∼20°S latitude. DFe atmospheric fluxes were at the lower end of reported values of the remote ocean and could not explain the high DFe concentrations measured in the water column in the vicinity of Tonga. We argue that the high DFe concentrations may be sustained by a submarine source, also characterized by freshwater input and recorded as salinity anomalies by Argo float in situ measurements and atlas data. The observed negative salinity anomalies are reproduced by simulations from a general ocean circulation model. Submarine iron sources reaching the euphotic layer may impact nitrogen fixation across the whole region.

The photosynthetic cyanobacterium Trichodesmium is widely distributed in the surface low latitude ocean where it contributes significantly to N 2 fixation and primary productivity. Previous studies found nifH genes and intact Trichodesmium colonies in the sunlight-deprived meso- and bathypelagic layers of the ocean (200–4000 m depth). Yet, the ability of Trichodesmium to fix N 2 in the dark ocean has not been explored. We performed 15 N 2 incubations in sediment traps at 170, 270 and 1000 m at two locations in the South Pacific. Sinking Trichodesmium colonies fixed N 2 at similar rates than previously observed in the surface ocean (36–214 fmol N cell −1 d −1 ). This activity accounted for 40 ± 28% of the bulk N 2 fixation rates measured in the traps, indicating that other diazotrophs were also active in the mesopelagic zone. Accordingly, cDNA nifH amplicon sequencing revealed that while Trichodesmium accounted for most of the expressed nifH genes in the traps, other diazotrophs such as Chlorobium and Deltaproteobacteria were also active. Laboratory experiments simulating mesopelagic conditions confirmed that increasing hydrostatic pressure and decreasing temperature reduced but did not completely inhibit N 2 fixation in Trichodesmium . Finally, using a cell metabolism model we predict that Trichodesmium uses photosynthesis-derived stored carbon to sustain N 2 fixation while sinking into the mesopelagic. We conclude that sinking Trichodesmium provides ammonium, dissolved organic matter and biomass to mesopelagic prokaryotes.

The abundance and distribution of cyanobacterial diazotrophs were quantified in two regions (Melanesian archipelago, MA; and subtropical gyre, SG) of the western tropical South Pacific using nifH quantitative polymerase chain reaction (qPCR) assays. UCYN-A1 and A2 host populations were quantified using 18S rRNA qPCR assays including one newly developed assay. All phylotypes were detected in the upper photic zone (0–50 m), with higher abundances in the MA region. Trichodesmium and UCYN-B dominated and ranged from 2.18 × 102 to 9.41 × 106 and 1.10 × 102 to 2.78 × 106 nifH copies L−1, respectively. Het-1 (symbiont of Rhizosolenia diatoms) was the next most abundant (1.40 × 101–1.74 × 105 nifH copies L−1) and co-occurred with het-2 and het-3. UCYN-A1 and A2 were the least abundant diazotrophs and were below detection (bd) in 63 and 79, respectively, of 120 samples. In addition, in up to 39 % of samples in which UCYN-A1 and A2 were detected, their respective hosts were bd. Pairwise comparisons of the nifH abundances and various environmental parameters supported two groups: a deep-dwelling group (45 m) comprised of UCYN-A1 and A2 and a surface group (0–15 m) comprised of Trichodesmium, het-1 and het-2. Temperature and photosynthetically active radiation were positively correlated with the surface group, while UCYN-A1 and A2 were positively correlated with depth, salinity, and oxygen. Similarly, in a meta-analysis of 11 external datasets, all diazotrophs, except UCYN-A were correlated with temperature. Combined, our results indicate that conditions favoring the UCYN-A symbiosis differ from those of diatom diazotroph associations and free-living cyanobacterial diazotrophs.

Oceanic N 2 fixation by diazotrophic microorganisms is the primary external source of new nitrogen to the surface ocean sustaining net production of organic matter. Studying long-term trends in biomass within N 2 fixation hotspots is crucial for understanding and predicting the response of N 2 fixation to global climate change. Here we developed a bio-optical model based on the spectral phytoplankton absorption coefficient derived from satellite ocean color observations to estimate a proxy for particulate organic nitrogen in the western tropical South Pacific. We demonstrate the existence of a seasonal new biomass production annually over the past 20 years, likely driven by recurrent N 2 fixation. Importantly, our results also reveal a gradual decline in biomass within this N 2 fixation hotspot over the last two decades. This decline indicates that seasonal nitrogen inputs via N 2 fixation are decreasing. This trend inevitably could lead to a decline in the efficiency of the biological carbon pump, with potential implications for global biogeochemical cycles and climate regulation. Using satellite ocean-color data, this study reveals a 20-year decline in plankton biomass in a major nitrogen-fixation hotspot, suggesting reduced nitrogen inputs and potential implications for global biogeochemical cycles and climate regulation.

Dinitrogen (N2) fixation was investigated together with organic matter composition in the mesopelagic zone of the Bismarck (Transect 1) and Solomon (Transect 2) Seas (Southwest Pacific). Transparent exopolymer particles (TEP) and the presence of compounds sharing molecular formulae with saturated fatty acids and sugars, as well as dissolved organic matter (DOM) compounds containing nitrogen (N) and phosphorus (P) were higher on Transect 1 than on Transect 2, while oxygen concentrations showed an opposite pattern. N2 fixation rates (up to ~1 nmol N L-1 d-1) were higher in Transect 1 than in Transect 2, and correlated positively with TEP, suggesting a dependence of diazotroph activity on organic matter. The scores of the multivariate ordination of DOM molecular formulae and their relative abundance correlated negatively with bacterial abundances and positively with N2 fixation rates, suggesting an active bacterial exploitation of DOM and its use to sustain diazotrophic activity. Sequences of the nifH gene clustered with Alpha-, Beta-, Gamma- and Deltaproteobacteria, and included representatives from Clusters I, III and IV. A third of the clone library included sequences close to the potentially anaerobic Cluster III, suggesting that N2 fixation was partially supported by presumably particle-attached diazotrophs. Quantitative polymerase chain reaction (qPCR) primer-probe sets were designed for three phylotypes and showed low abundances, with a phylotype within Cluster III at up to 103 nifH gene copies L-1. These results provide new insights into the ecology of non-cyanobacterial diazotrophs and suggest that organic matter sustains their activity in the mesopelagic ocean.

Nitrogen is essential for life but is often a major limiting nutrient for growth in the ocean. Biological dinitrogen fixation is a major source of new nitrogen to surface waters and promotes marine productivity. Yet the fate of diazotroph-derived nitrogen (DDN) in marine ecosystems has been poorly studied, and its transfer to auto- and heterotrophic plankton has not been measured. Here, we use high-resolution nanometer scale secondary ion mass spectrometry (nanoSIMS) coupled with 15N₂ isotopic labelling and flow cytometry cell sorting to examine the DDN transfer to specific groups of natural phytoplankton and bacteria during three diazotroph blooms dominated by the cyanobacterium Trichodesmium spp. in the South West Pacific. During these experiments, 13%±2% to 48%±5% of the fixed 15N₂ was released into the dissolved pool and 6%±1% to 8%±2% of this DDN was transferred to non-diazotrophic plankton after 48 h. The primary beneficiaries of this DDN were diatoms (45%±4% to 61%±38%) and bacteria (22%±27% to 38%±12%), followed by pico-phytoplankton (3%±1% to 21%±14%). The DDN was quickly converted to non-diazotrophic plankton biomass, in particular that of diatoms, which increased in abundance by a factor of 1.4–15 over the course of the three experiments. The single-cell approach we used enabled quantification of the actual transfer of DDN to specific groups of autotrophic and heterotrophic plankton in the surface ocean, revealing a previously unseen level of complexity in the pathways that occur between N₂ fixation and the eventual export of DDN from the photic zone.