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    Author Correction: MiDAS 4: A global catalogue of full-length 16S rRNA gene sequences and taxonomy for studies of bacterial communities in wastewater treatment plants

    Center for Microbial Communities, Department of Chemistry and Bioscience, Aalborg University, Aalborg, DenmarkMorten Kam Dahl Dueholm, Marta Nierychlo, Kasper Skytte Andersen, Vibeke Rudkjøbing, Simon Knutsson, Per H. Nielsen, Mads Albertsen & Per Halkjær NielsenEnvironmental Science Department, The Institute for Scientific and Technological Research of San Luis Potosi (IPICYT), San Luis Potosí, MexicoSonia ArriagaDepartment of Process, Energy and Environmental Technology, University College of Southeast Norway, Porsgrunn, NorwayRune BakkeCenter for Microbial Ecology and Technology, Ghent University, Ghent, BelgiumNico BoonInstitute for Water and Wastewater Technology, Durban University of Technology, Durban, South AfricaFaizal Bux & Sheena KumariVeolia Water Technologies AB, AnoxKaldnes, Lund, SwedenMagnus ChristenssonDepartment Of Chemical Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur, MalaysiaAdeline Seak May ChuaEnvironmental Engineering, Newcastle University, Newcastle, EnglandThomas P. CurtisThe Cytryn Lab, Microbial Agroecology, Volcani Center, Agricultural Research Organization, Rishon Lezion, IsraelEddie CytrynINGEBI-CONICET, University of Buenos Aires, Buenos Aires, ArgentinaLeonardo ErijmanDepartment of Biochemistry and Microbial Genetics, Biological Research Institute “Clemente Estable”, Montevideo, UruguayClaudia EtchebehereNIREAS-International Water Research Center, University of Cyprus, Nicosia, CyprusDespo Fatta-KassinosEnvironmental Engineering, McGill University, Montreal, QC, CanadaDominic FrigonSchool of Microbiology, Universidad de Antioquia, Medellín, ColombiaMaria Carolina Garcia-ChavesSchool of Civil and Environmental Engineering, Cornell University, Ithaca, NY, USAApril Z. GuWater Chemistry and Water Technology and DVGW Research Laboratories, Karlsruhe Institute of Technology (KIT), Karlsruhe, GermanyHarald HornDavid Jenkins & Associates, Inc, Kensington, CA, USADavid JenkinsInstitute for Water Quality and Resource Management, TU Wien, Vienna, AustriaNorbert KreuzingerWater Innovation and Research Centre, University of Bath, Bath, EnglandAna LanhamSingapore Centre of Environmental Life Sciences Engineering (SCELSE) Nanyang Technological University, Singapore, SingaporeYingyu LawWater Desalination and Reuse Center, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi ArabiaTorOve LeiknesProcess Engineering in Urban Water Management, ETH Zürich, Zürich, SwitzerlandEberhard MorgenrothDepartment of Biology, Warsaw University of Technology, Warsaw, PolandAdam MuszyńskiEnvironmental Microbial Genetics Lab, La Trobe University, Melbourne, VIC, AustraliaSteve PetrovskiTechnologies and Evaluation Area, Catalan Institute for Water Research, ICRA, Girona, SpainMaite PijuanVA Tech Wabag Ltd, Chennai, IndiaSuraj Babu PillaiBiochemical Engineering Group, Universidade Nova de Lisboa, Lisboa, PortugalMaria A. M. ReisState Key Laboratory of Environmental Aquatic Chemistry, Research Center for Eco-Environmental Sciences, Chinese Academy of Sciences, Beijing, ChinaQi RongWater Research Institute IRSA – National Research Council (CNR), Rome, ItalySimona RossettiLa Trobe University, Melbourne, VIC, AustraliaRobert SeviourDepartment of Civil and Environmental Engineering, University of Massachusetts Amherst, Amherst, MA, USANick TookerKemira Oyj, Espoo R&D Center, Espo, FinlandPirjo VainioEnvironmental Biotechnology, TU Delft, Delft, The NetherlandsMark van LoosdrechtVA Tech Wabag, Philippines Inc., Makati City, PhilippinesR. VikramanDepartment of Water Technology and Environmental Engineering, University of Chemistry and Technology, Prague, Czech RepublicJiří WannerEnvironmental Life Science Engineering, TU Delft, Delft, The NetherlandsDavid WeissbrodtSchool of Environment, Tsinghua University, Beijing, ChinaXianghua WenEnvironmental Biotechnology Lab, Department of Civil Engineering, The University of Hong Kong, Hong Kong, Hong KongTong Zhang More

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    Reply to: No new evidence for an Atlantic eels spawning area outside the Sargasso Sea

    The Sargasso Sea has long been considered as the spawning area for Atlantic eels, despite the absence of direct observations after more than a hundred years of the survey. We proposed a new insight on the location of Atlantic eels spawning areas eastward of the Sargasso Sea at the intersection between the Mid-Atlantic Ridge and the oceanic fronts1. Our hypothesis is based on a body of corroborating cues from literature. We suggested that European silver eels converge towards the Azores whatever their departure point from Europe and Northern Africa, then they follow the Mid-Atlantic Ridge south westerly until they reach oceanographic fronts where temperature and depths are favourable for reproduction. These orientation behaviours are potentially based on magnetic fields and odours that might be generated by the Mid-Atlantic Ridge volcanic activity and detected by eels during their diel vertical movements. The first favourable meeting point is then located at the crossing between the Mid-Atlantic Ridge and the oceanic thermic isotherms located around 45° W and 26° N. Our hypothesis is supported by (i) microchemical differences between the core of otoliths extracted from leptocephali collected in the Sargasso Sea and from glass eels collected across Europe suggesting that glass eels hatch in different chemical environments than leptocephali (ii) an asymmetric genetic introgression between American and European eels2 suggesting that the overlapping spawning areas favour transport of hybrids towards northern Europe rather than to America and to southern Europe. This supports the possible existence of several distinct spawning areas, where currents favour transport either westward (American eel), north eastward (hybrids and European eels) or eastward (European eels). To test this hypothesis, we developed a transport model and compared the dispersion dynamics of virtual leptocephali released from the Sargasso Sea and from above the Mid-Atlantic Ridge. The transport models showed that virtual eels released from the Mid-Atlantic Ridge reached Europe and America following similar patterns than those released from the Sargasso Sea thus supporting the Mid-Atlantic Ridge spawning hypothesis.Hanel et al.3 have raised several concerns, one of which being that “microchemical evidence was the only was the major argument supporting the Mid-Atlantic Ridge hypothesis”. This was their start point of a critical rebuttal of our findings to question our hypothesis. Instead, we consider that our regrettable error does not fundamentally contradict the possibility that eels do indeed successfully spawn outside the so-called Sargasso Sea.(Comment 1) The importance of seamounts as orientation and navigation cues towards a spawning area was hypothesized, no clear mechanism is proposed for how the migrating eels can detect the ridge.(Response 1) Our Hypothesis does not state that eels find a kind of shallow seamount where they spawn. Instead, we propose that orientation of silver eels during their spawning migration could be based on a combination of behavioural mechanisms including geomagnetism, odours, temperature and salinity gradients4,5,6,7,8. These environmental cues and related gradients are strongly controlled or influenced by the topography of the oceanic floor. The Mid-Atlantic Ridge and the Mariana areas have similarities with ridges and seamount chains oriented perpendicularly to temperature and salinity fronts surrounded by deep abyssal plains. Our Mid-Atlantic Ridge hypothesis proposed that Atlantic eels could use similar signposts as Japanese eel, which hatch near the Mariana Ridge9. Indeed, as for the Japanese eels, the orientation mechanism that lead Atlantic eels from the growth areas to the ridge are not understood, but the empirical observations from Righton et al.10 suggest that eels converge towards the Azores whatever their release point across Europe and that their diel vertical migration takes them down to 500–1000 m every day. The reasons for this behaviour are not elucidated, but since they cost energy, they are likely compensated by advantages such as orientation together with predator avoidance and sexual maturation11,12,13. Following our hypothesis, eels search for orientation cues during DVM. The geomagnetic fields are suggested to provide detectable information for silver eels on their oceanic spawning migration14. However, whether magnetic characteristics of the Mid-Atlantic ridge may provide detectable orientation cues still needs to be documented. Similarly, the existence of detectable odours that might be generated by the tectonic activity and hydrodynamics of the Mid-Atlantic ridge and serve as orientation cues for eels is still unknown. Hydrodynamic mesoscale turbulence and vertical flows have been shown to be generated along the Mid-Atlantic Ridge15, which we propose eels might be able to detect. There are no well supported spawning areas of freshwater eels other than A. japonica and one north Pacific population of A. marmorata. The spawning areas of the other species remain unknown. In the south west Indian Ocean, spawning areas of 3 species (A. mossambica, A. marmorata and A. bicolor) were proposed on the east of the Mascarene Ridge with a similar topography (although shallower) than along the Mid-Atlantic Ridge and the Mid-Pacific ridge and seamounts16,17. Inaccurate spawning areas were also proposed for the South Pacific A. diffenbachii between Fiji, New Caledonia and New Zealand; in the vicinity of a number of oceanic ridges and trenches18 that may also serve as landmarks. Because all eel species studied on their spawning migration show similar diel vertical migration behaviours, it is likely that common orientation mechanisms could lead to detection of oceanographic variability related to the topography of the sea floor and related geomagnetism, local hydrodynamic turbulence and odour caused by vertical currents. This kind of oceanic landscape (chains of seamounts) occurs on narrow areas which strongly increase the meeting probability of spawners searching for partners and favourable spawning places.(Comment 2) Drift simulation with departures from the Mid-Atlantic Ridge and from the Sargasso Sea showed similar results. This is not surprising since the modelling of larval drift seems essentially just to reflect the slow westward drift prevailing both in the Sargasso Sea and Mid-Atlantic Ridge areas. The assumption of using the intersection of the Mid-Atlantic Ridge by the two thermal fronts as presumed spawning places seems to have little basis. There is no indication neither of one nor two temperature fronts at depths where leptocephali are found along a 45  W latitudinal section in the middle of the Mid-Atlantic Ridge area.(Response 2) We agree with the comments that the similar distributions between the departure from the Sargasso Sea and the Mid-Atlantic Ridge are expected, as they mainly reflect the ocean circulation. This is also what we wanted to address, if different departures could lead to similar distributions, either Sargasso Sea or Mid-Atlantic Ridge could be candidates for the spawning area. We also agree that many eel larvae were collected at the two fronts in the Sargasso Sea, but not near the Mid-Atlantic Ridge. However, if the departure from the Sargasso Sea and the Mid-Atlantic Ridge led to similar distributions after 720 days, they were not the result of westward current, but the cause of a relatively quiet ocean in the Sargasso Sea and its surrounding area (i.e. Fig. 1). Without prevailing current, small larvae were mainly transported by ocean dispersion, and would later be transported by the major currents that lie in the north (Azores Current), south (North Equatorial Current), and west (Gulf Stream) of the Sargasso Sea. So, we compared departures at 100 km from west and east of the Mid-Atlantic Ridge. Subtle differences occurred (figure below). V-larvae departing from the east of the ridge dispersed relatively less northward compared to larvae released 100 km at the west of the ridge (this figure and original paper). Secondly v-larvae released at the south east of the study area (red dots on the figure, right panel) disperse relatively less towards the Caribbean Sea than when released at the west (red dots of the figure, left panel). This suggests that the dispersion of European eel larvae is optimum in an area comprised between the Mid-Atlantic Ridge and the Sargasso Sea (our previous simulation in the original paper), and declines eastward of the Mid-Atlantic Ridge (present simulation below).Figure 1Distribution of v-larvae released departure at the west (left) and east (right) of Mid-Atlantic Ridge. The tracking method is the same as described in the paper, v-larvae were release within 100 km west and east of the ridge.Full size imageHanel et al. also indicate that the convergence front weakens from West, in the Sargasso Sea, to East above the ridge. We consider that this constitutes an additional argument that the Mid-Atlantic Ridge is indeed at the edge of the convergence zone at the first area of the Atlantic Ocean where currents and temperatures are favourable for reproduction of eels.(Comment 3) Elevated manganese (Mn) concentrations in the otolith cores of glass eels as a hint for successful spawning only in areas with volcanic activity based on observations of Martin et al.18. However, the results from Martin et al.19 were entirely misread, resulting in a mis-interpretation of the data.(Response 3) Based on Martin et al.19, we stated that higher concentrations of Mn were found in glass eels’ otoliths collected across European estuaries than in otoliths of leptocephali larvae sampled in the Sargasso Sea. We suggested that this was the indication that glass eels were born in areas where volcanic activity produces high loads of Mn and other metals. This formed one of the arguments supporting our hypothesis that Atlantic eels could spawn in the proximity to the Mid-Atlantic Ridge. Thanks to Reinhold Hanel and colleagues, we realized that Martin et al.19 in fact showed that concentrations of Mn were higher in the center of otoliths of leptocephali larvae than in those of glass eels collected along the European coasts. Consequently, this argument is no longer valid. Nonetheless, otolith microchemical fingerprints significantly differ between young leptocephali sampled in the Sargasso Sea in 2008 and glass eels collected in Europe, hence suggesting that they have distinct spawning areas19. These authors indicated that the incorporation of elements from the environment to the otoliths needed to be better understood, namely as stated by Hanel et al., because of physiological and environmental control such as temperature and salinity. In addition, they outline that the dynamics of elements from the sea floor to the subsurface is not well understood and could be slow. We totally share these conclusions that are well known facts, and that simply confirm that environmental characteristics (trace element concentrations, salinity and temperature) are responsible for the elemental signature of the central part of otoliths. Hanel et al. also state that the composition of otoliths are also controlled by elemental maternal transfer from the egg to the otoliths. We are aware of this fact that has been shown is other fish species. However, the laser ablations were performed after the first feed check where maternal influence is reduced and is overruled by environment18. This supports the idea that glass eels collected in Europe do not originate from the same environments as leptocephali captured in the Sargasso Sea.(Comment 4) Insufficient sampling efforts and a limited area coverage of recent surveys as a possible reason for “false negative” observations along the Mid-Atlantic Ridge. This statement does not recognize the investigations by Johannes Schmidt as well as earlier and later surveys in the Mid-Atlantic Ridge area. The ICES “Eggs and Larvae database” records a total of 48 A anguilla leptocephali caught within the area 15–29 N and 43–48 W, at 10 stations between 1913 and 1970.Thanks for pointing out that larvae have been caught near the Mid-Atlantic Ridge, in which larvae were not newly hatched because of their relatively large size (23–45 mm). Ocean currents were weak and could flow either eastward or westward in this region, indicating that the spawning could occur from west to east of the ridge, without considering swimming. Note that ocean currents could change directions, so that it was also possible to spawn near the ridge after been transported eastward and westward.The observed distribution of small larvae  More

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    Routes of soil microbiome dispersal

    Dispersal is assumed to contribute to microbiome composition and function; however, it is difficult to measure. Walters et al. now set out a 6-month experiment looking at different dispersal routes of environmental microorganisms to the surface soil layer. They set up different ‘traps’, either glass slides or freshly cut grass, to determine the number, identity and function of incoming microorganisms. The traps ‘recorded’ dispersal through air, from plants and their litter, or from below through the decomposing litter and bulk soil. This was achieved by placing the traps either on a pedestal, closing them off at the bottom or leaving them open, respectively. The authors found that the overall dispersal rate was low, with little influence of the route, with only 0.5% incoming bacterial cells per day compared with the number of resident cells. However, the dispersal routes did influence microbiome composition, at least if from above and close to the surface. Finally, without dispersal, the initial decomposition of the cut grass was slower.
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    Impact of squid predation on juvenile fish survival

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    Cumulative cultural evolution and mechanisms for cultural selection in wild bird songs

    Study population and song recordingsAll animal procedures were carefully reviewed by the Williams College IACUC (WH-D), the Bowdoin College Research and Oversight Committee (2009–18), and the University of Guelph Animal Care Committee (08R601), and were carried out as specified by the Canadian Wildlife Service (banding permit 10789D).We studied Savannah sparrows (Passerculus sandwichensis) at the Bowdoin Scientific Station on Kent Island, New Brunswick, Canada (44.5818°N, 66.7547°W). Since 1988, individuals nesting within a 10 ha study area in the middle of the island (30–70 pairs each year; part of a larger population of 350–500 males breeding on Kent Island and two adjacent islands) have been colour-banded to facilitate visual identification, and complete demographic information is available for birds on the study site (though not for the entire population) for the years 1989–2004 and 2009–2013. Because of strong natal and breeding philopatry51, birds hatched on the study site itself represent 40–80% of adult breeders in that area, and because of the systematic banding program, ages are known. Each year adds a new generation to the population, with yearlings making up approximately half of the adult breeding males. The birds banded and recorded on the study site are estimated to make up 10–20% of the Savannah sparrow population on Kent Island and two nearby islands.Details of the recording methods used in this study (covering the years 1980, 1982, 1988-9, 1993-8, and 2003–13) can be found elsewhere36,49. Using digitally generated sound spectrograms (using SoundEdit Pro and Audacity), birds were scored as having either a) high note cluster=a final introductory segment interval including at least two different note types, or b) a click train=one or more introductory segment intervals including at least two clicks and no other note types, or c) both features36 (see Supplementary Fig. 1 for a full description of note types). Although a small proportion of birds (mean = 8.3%) did not include either feature in their songs (such birds either had no feature in the introductory segment intervals or one non-click note type in the final interval), we did not include this option in the model and omitted these birds from summaries of the data. We did not include data after the breeding year 2013 because of we began an experimental field tutoring study in the summer of 201364.ModellingWe used a dynamic, discrete time model which allowed us to focus our analysis to specific time points within the year that are related to song learning (the beginning and end of the breeding season). These were: (1) the return of older birds between breeding seasons, (2) the recruitment of young birds singing newly crystallized songs in the spring, and (3) reproduction, resulting in the addition of juveniles during the summer breeding season.Because survival data were not available for every year during the time span we studied, we captured the variation in survival rates observed in the field57 by using a binomial distribution centered on the average historical survival rate for each age class (addressing the possibility that cultural drift resulting from random differences in survival rates was responsible for the shift in song features). The model incorporates stochasticity to capture the variation in population dynamics and return rates by assigning parameter values for survival and return rates from empirically generated probability distributions.We did not include spatial distribution of song variants in the model; although spatial patterns can be important for the dynamics of language loss58, territories with birds singing click trains and high note clusters were intermixed and no spatial structure was apparent (Fig. 3).The model assumes that males choose which features to incorporate into the introductory sections of their songs during song development. Individuals fall into one of six mutually exclusive classes of male Savannah sparrows. The classes are defined by (1) the bird’s developmental stage in the song learning process: juvenile (J, the first year, when the song is plastic) or adult (A, after the first spring, when the song is crystallized), and (2) the variant or variants sung as part of the bird’s introduction (high note clusters, click trains, or both). Denoting note high note clusters with X and click trains with C, the adult classes are therefore AX, AC, and AXC, and the juvenile classes are JX, JC, and JXC. The sum of the individuals in these classes is the total male population.We used two times during each year – late spring and late summer – to correspond to stages in song development (Fig. 5). At a given time t, when breeding is underway in the late spring, the male population consists entirely of adults singing crystallized song, and therefore each juvenile class is empty. At the end of the summer, the population of males has been augmented by juveniles, which are initially assigned to the same variant class as their fathers. To capture these dynamics, we define an intermediate time step, denoted ti. Time t + 1 then corresponds to the following breeding season (late spring), when juvenile males hatched the previous year have completed song development, crystallized their songs, and joined the adult class.Fig. 5: Model of song development.We used two age classes (J = juvenile and A = adult) and three classes of introductions (C = click trains, X = high note clusters, and  XC = both). In the late spring of a given year (time = t), only adult males are present. In late summer, those adults have bred and both they and juvenile males are present; at this intermediate time (ti) each male is initially allocated the same introduction type as his father (solid lines). Then, as song development progresses and juvenile males can be influenced by other tutors, they may retain their initial introduction type or switch to either of the other two types (dashed lines) before they crystallize their songs late in the following spring (time = t+1), and join the breeding cohort, which also includes adult males from the previous year who returned to breed again.Full size imageIn the late summer the male population increases with the addition of juveniles hatched that year, some of which will return to join the singing population the following year; survivors will return to breed within a few hundred meters of where they hatched51. To fit the observed historical decline in the Kent Island population57, the total number of returning juveniles, r (including both those hatched on site and those immigrating from nearby populations at time), follows a Poisson distribution where m = 33.6 – .182x and x is the number of years since 1980 (this function results in a decline of 5 males per decade; the initial number on the study site used in the model, 70, was extrapolated from historical data). The size of each returning juvenile class at time ti then takes the form:$${{{{{{rm{JY}}}}}}}_{{{{{{{rm{t}}}}}}}^{{{{{{rm{i}}}}}}}} sim {{{{{rm{Poisson}}}}}}left(mright)frac{{{{{{rm{A}}}}}}{{{{{{rm{Y}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}}}{{{{{{rm{A}}}}}}{{{{{{rm{X}}}}}}}_{{{{{{rm{t}}}}}}}+{{{{{rm{A}}}}}}{{{{{{rm{C}}}}}}}_{{{{{{rm{t}}}}}}}+{{{{{rm{AX}}}}}}{{{{{{rm{C}}}}}}}_{{{{{{rm{t}}}}}}}}$$
    (1)
    for each Y ∈ {X, C, XC}.After the following winter, the proportion of surviving adults at time t + 1 follows a binomial distribution where the mean survival rate s = 0.48 is derived from historical data. Therefore, each adult class takes the form:$${{{{{rm{A}}}}}}{{{{{{rm{Y}}}}}}}_{{{{{{rm{t}}}}}}+1} sim {{{{{rm{Binomial}}}}}}left({{{{{rm{AY}}}}}},{{{{{rm{s}}}}}}right)* {{{{{rm{A}}}}}}{{{{{{rm{Y}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}}$$
    (2)
    At the beginning of the next breeding season, juveniles complete song learning64, choosing which variant to crystallize as part of the song, and enter an adult song class; thus all of the juvenile classes disappear at t + 1. Which adult class juveniles join depends on separate learning functions for each of the two variants, ϕX for the high note cluster and ϕC for the click train. The ϕ function takes values between 0 and 1 and gives the probability of crystallizing a song form during the transition from natal year to breeding, depending upon the frequency-dependent bias and selection parameters (see below). These functions define the proportion of features that appear in the next generation as compared to that of the previous generation. Therefore we have:$${{{{{rm{A}}}}}}{{{{{{rm{X}}}}}}}_{{{{{{rm{t}}}}}}+1}={left({{{upphi }}}_{{{{{{rm{X}}}}}}}right)}^{2}{{{{{rm{J}}}}}}{{{{{{rm{X}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}}+{left(1-{{{upphi }}}_{{{{{{rm{C}}}}}}}right)}^{2}{{{{{rm{J}}}}}}{{{{{{rm{C}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}}+{{{upphi }}}_{{{{{{rm{X}}}}}}}left(1-{{{upphi }}}_{{{{{{rm{C}}}}}}}right){{{{{rm{JX}}}}}}{{{{{{rm{C}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}}+{{{{{rm{A}}}}}}{{{{{{rm{X}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}}$$
    (3)
    $${{{{{rm{A}}}}}}{{{{{{rm{C}}}}}}}_{{{{{{rm{t}}}}}}+1}={left(1-{{{upphi }}}_{{{{{{rm{X}}}}}}}right)}^{2}{{{{{rm{J}}}}}}{{{{{{rm{X}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}}+{left({{{upphi }}}_{{{{{{rm{C}}}}}}}right)}^{2}{{{{{rm{J}}}}}}{{{{{{rm{C}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}}+left(1-{{{upphi }}}_{{{{{{rm{X}}}}}}}right){{{upphi }}}_{{{{{{rm{C}}}}}}}{{{{{rm{JX}}}}}}{{{{{{rm{C}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}}+{{{{{rm{A}}}}}}{{{{{{rm{C}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}}$$
    (4)
    $${{{{{rm{A}}}}}}{{{{{{rm{XC}}}}}}}_{{{{{{rm{t}}}}}}+1}=2{{{upphi }}}_{{{{{{rm{X}}}}}}}left(1-{{{upphi }}}_{{{{{{rm{X}}}}}}}right){{{{{rm{J}}}}}}{{{{{{rm{X}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}}+2{{{upphi }}}_{{{{{{rm{C}}}}}}}left(1-{{{upphi }}}_{{{{{{rm{C}}}}}}}right){{{{{rm{J}}}}}}{{{{{{rm{C}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}}+({{{upphi }}}_{{{{{{rm{X}}}}}}}{{{upphi }}}_{{{{{{rm{C}}}}}}}left(1-{{{upphi }}}_{{{{{{rm{X}}}}}}}right)left(1-{{{upphi }}}_{{{{{{rm{C}}}}}}}right){{{{{rm{JX}}}}}}{{{{{{rm{C}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}})+{{{{{rm{A}}}}}}{{{{{{rm{XC}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}}$$
    (5)
    The sum of probabilities defining all of song crystallization outcomes for the songs of fathers with song type X is:$${left({{{upphi }}}_{{{{{{rm{X}}}}}}}right)}^{2}+{left(1-{{{upphi }}}_{{{{{{rm{X}}}}}}}right)}^{2}+2{{{upphi }}}_{{{{{{rm{X}}}}}}}left(1-{{{upphi }}}_{{{{{{rm{X}}}}}}}right)=1$$
    (6)
    Learning curvesTo define how young males’ song learning is influenced by the songs they hear, we used learning curves based on type III Holling response curves59 which provide a means to numerically capture functional responses. In our model, the type III curve models the response of juvenile to the song form of adults in the population based on two variables: (1) frequency-dependent bias that favors one form based on its prevalence within the adult population, and (2) selection that favors a particular form of the song.The learning curves, ϕx for the high note cluster and ϕc for the click train, are modified forms of the type III Holling response curve):$${{{upphi }}}_{{{{{{rm{x}}}}}}}=frac{{x}^{{{{{{rm{beta }}}}}}}/{{{{{rm{sigma }}}}}}}{{(1-x)}^{{{{{{rm{beta }}}}}}}+({x}^{{{{{{rm{beta }}}}}}}/{{{{{rm{sigma }}}}}})}$$
    (7)
    and$${{{upphi }}}_{{{{{{rm{c}}}}}}}=frac{{{{{{rm{sigma }}}}}},{c}^{{{{{{rm{beta }}}}}}}}{{(1-c)}^{{{{{{rm{beta }}}}}}}+{{{{{rm{sigma }}}}}}{{c}}^{{{{{{rm{beta }}}}}}}}$$
    (8)
    where x is the proportion of the high note cluster within the population, c is the proportion of the click train within the population, β is frequency-dependent bias (favoring learning the novel or retaining the common variant), and σ is selection on the novel variant (a preference for learning the variant that is not dependent on frequency of the variant and includes factors such as prestige bias, success bias, status, and content bias). Note that the two learning curves do not have identical equations, because selection is not frequency-dependent. In these equations, β  > 1 corresponds to conformist selection, and when β  1 correspond to selection for a novel variant and values of σ  More

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    Transatlantic spread of highly pathogenic avian influenza H5N1 by wild birds from Europe to North America in 2021

    Epidemiological description of exhibition farm outbreakThe index farm where highly pathogenic avian influenza (HPAI) H5N1 virus in captive birds occurred was an exhibition farm in St. John’s, Province of Newfoundland and Labrador, Canada. The farm housed 409 birds of different species, namely chickens, guineafowl, peafowl, emus, domestic ducks, domestic geese, and domestic turkeys. On 9th December 2021, the farm owner first noticed mortality. On 13th December, the farm owner reported the increased mortality to a local veterinarian. Autopsies on four chickens showed swollen heads and cutaneous haemorrhages. Oropharyngeal and cloacal swabs from these chickens tested positive for H5 avian influenza virus at the Atlantic Veterinary College, University of Prince Edward Island, and the Canadian Food Inspection Agency (CFIA) was notified. On 16th December, by which time 306 birds (mostly chickens, turkeys and guineafowl) had died, staff of the CFIA collected tissue samples from dead chickens, as well as oropharyngeal and cloacal swabs and sera from different species of captive birds still present (Table 1), after which all remaining captive birds were culled. All oropharyngeal and cloacal swabs tested positive for HPAI virus of the subtype H5N1 by real-time RT-PCR, and all sera tested positive for influenza nucleoprotein antibodies by ELISA. On 20th December, the CFIA confirmed the diagnosis of HPAI of the subtype H5N1.Table 1 List of samples for virological and serological analysis collected by CFIA on 17 December 2021 from different species of captive birds still present at the farm.Full size tableWild birds were frequently observed co-mingling with the captive population. Captive birds except emus were allowed to move freely in and out of the open pens in which they were housed. At an on-site pond, domestic ducks were reported to mingle with free-living mallards (scientific names of wild birds in Table 2), and a snowy egret had been observed around 2nd to 6th December. Other wild birds reported on the farm were common starlings, feral pigeons, and unspecified gulls.Table 2 Common and scientific species names of the birds mentioned in the text.Full size tableRetrospectively, HPAI H5N1 virus also was identified in tissues of a great black-backed gull found at a nearby pond in St. John’s. The gull had been found ill on 26th November 2021 and taken to a local wildlife rehabilitation centre, where it died the following day.Phylogenetic analysisPhylogenetic analyses were performed to compare the genome sequences of the Newfoundland viruses from the exhibition farm birds and a great black-backed gull found nearby to other influenza viruses in the database. Based on BLAST analysis all eight gene segments of the virus had a Eurasian origin, and the virus was identified as a clade 2.3.4.4b H5N1 virus. Based on maximum likelihood and time-resolved trees inferred by use of whole genome sequences, the Newfoundland viruses had a shared common ancestor with European viruses circulating in early 2021 (Figs. 1, 2). The dates for the most recent common ancestor (MRCA) of all gene segments ranged from December 2019 to April 2021 (Table 3). There was no evidence that the Newfoundland viruses were genetically closely related to other current or recent viruses circulating in Europe. In contrast to currently circulating European viruses, the sequences of the Newfoundland viruses had no evidence of reassortment with other avian influenza viruses after ancestral emergence (Fig. 3). The virus from the great black-backed gull was highly similar to those from the exhibition farm, except for a small number of nucleotide differences in the neuraminidase (N) gene segment.Figure 1Maximum likelihood phylogenetic tree of the H5 HA gene. Relationships among the European 2021 H5 2.3.4.4b HPAI strains (magenta) and the Newfoundland wild bird and outbreak strains (red) are shown. The tree is rooted by the outgroup and nodes placed in descending order. Clades are collapsed for clarity.Full size imageFigure 2Maximum likelihood phylogenetic tree of the H5 gene segments. Relationships among the European 2021 H5 2.3.4.4b HPAI strains (magenta) and the Newfoundland wild bird and outbreak strains (red) are shown. The tree is rooted by the outgroup and nodes placed in descending order; order: HA, NA, PA, PB1, PB2, NP, MP, NS.Full size imageTable 3 Dates for the most recent common ancestor (MRCA) of all gene segments.Full size tableFigure 3Phylogenetic incongruence analyses. Maximum likelihood trees for the H and N gene segments and internal gene segments from equivalent strains were connected across the trees. Tips and connecting lines are coloured according to the legend.Full size imageAnalysis of avian migration and potential routes for HPAI H5 virus to be carried across the Atlantic with migrating birdsThere are several pathways for HPAI H5N1 virus to be carried across the Atlantic with migrating birds, based on the multitude of migration routes of wild birds and their overlapping ranges at breeding, stop-over, and wintering sites. Ring-recovery data confirm the regular movements of wild birds from Europe to Iceland and other North Atlantic islands, and from there to North America, and also provide evidence for direct movements of for example seabirds and gulls (Supplementary Table 1). Ringed individuals with a European origin have been found on Newfoundland for 10 of the 24 species in Supplementary Table 1: barnacle goose (1 ringed individual), Eurasian wigeon (5), Eurasian teal (1), great skua (13), European herring gull (1), black-headed gull (1), black-legged kittiwake (102), purple sandpiper (1), Brunnich’s guillemot (15), and Atlantic puffin (50). Given that the most likely ancestor of the virus detected in Newfoundland was circulating in Northwest Europe between the beginning of the 2020/2021 outbreak in Europe in October 2020 and April 2021 (see above), likely routes include spring migration of bird species moving to Icelandic, Greenlandic or Canadian High Arctic breeding grounds, or migration directly across the Atlantic Ocean (Fig. 4).Figure 4Maps of transatlantic migration. Putative virus transmission pathways between Europe and Newfoundland via migratory waterfowl/shorebirds (a) and pelagic seabirds (b). Many Icelandic waterfowl and shorebirds (a) winter in Northwest Europe and return to Iceland to breed in spring (1), including whooper swans, greylag geese, pink-footed geese, Eurasian wigeons, Eurasian teals, northern pintails, common ringed plovers and purple sandpipers. Some bird populations use Iceland as a stopover site, and continue to breeding grounds in East Greenland (2; barnacle geese and pink-footed geese), the East Canadian Arctic (3; light-bellied brent geese, red knots, ruddy turnstones) and West Greenland (4; greater white-fronted geese). Migratory birds from Europe share these breeding areas with species that winter in North America, including Canada geese and snow geese from East Greenland and the East Canadian Arctic (5), and some Iceland-breeding species of duck, including small numbers of Eurasian wigeons, Eurasian teals, and tufted ducks (6). Several seabird species (b), such as gulls, skuas, fulmars and auks, have large breeding ranges in the Arctic. After the breeding season many species become fully pelagic and can roam large parts of the northern Atlantic. The mid-Atlantic ridge outside Newfoundland is an important non-breeding area for seabirds, and is frequented by auks from Iceland (7), Svalbard (8) and Norway (9), including large numbers of Atlantic puffins and Brünnich guillemots, and by black-legged kittiwakes and northern fulmars originating from Iceland, Norway and the United Kingdom (7–8, 10). There these birds are joined by seabirds from Canadian and Greenlandic waters (11). Direct migratory links to Newfoundland occurs through greater and lesser-black backed gulls as well as black-headed gulls from Iceland and Greenland (12, 13), and gulls also link the pelagic and the coastal zone around Newfoundland (14). Thickness of the lines highlights the relative approximate population sizes. Dashed lines show where small numbers of individuals, or vagrants, provide a potential pathway. For more details on species and population numbers see Table 2. This figure was prepared using the software R (version 4.0.5, https://www.r-project.org/) and the following packages: -ggplot2 (version 3.3.5, https://cran.r-project.org/web/packages/ggplot2/index.html), -sf (version 1.0.5, https://cran.r-project.org/web/packages/sf/index.html).Full size imageThe first possible route via Iceland seems to be the strongest link between Newfoundland and Europe14,15,16,17, because it is a meeting point of breeding bird populations which winter in Europe as well as along the East coast of North America. Numerous species, totaling almost two million individual birds, migrate annually from northwestern Europe to breeding grounds in Iceland and beyond. Several populations breed on Iceland, including swans (whooper swan) (Supplementary Table 1), geese (greylag goose, pink-footed goose), ducks (Eurasian wigeon, Eurasian teal, Northern pintail), gulls (great- and lesser black-backed gull, black-headed gull, black-legged kittiwake) and shorebirds (common ringed plover, purple sandpiper, Supplementary Table 1). In addition, several species (e.g. barnacle geese and pink-footed geese) migrating to breeding grounds further away (Greenland and/or Canadian High Arctic) make spring and autumn stopovers in Iceland18,19. This creates potential for the virus to have been spread northwards to Iceland (or further northward) in spring, where it could have circulated among breeding birds, or transmitted during autumn migration by species returning from the Arctic. Several Iceland-breeding species of ducks (Eurasian wigeon, Eurasian teal, tufted duck), gulls (lesser black-backed gull, black-legged kittiwake, black-headed gull) and alcids (Brunnich’s guillemot, Atlantic puffin) winter along the Atlantic coast of North America in variable numbers (Supplementary Table 1). If the virus was transmitted to one of these populations during their stay on Iceland, it could have been spread to Newfoundland during the subsequent autumn migration. Importantly, Iceland-breeding Eurasian wigeons or Eurasian teals could be responsible for both the journey to Iceland from European wintering grounds, as well as the journey from Iceland to Newfoundland, where these species are frequently encountered as vagrants (Supplementary Table 1)20,21.The second possible route is via species that migrate from northwestern Europe to the Canadian High Arctic and/or Northwest Greenland. These include shorebirds (e.g. ruddy turnstone, red knot) and some geese (light-bellied brent goose and greater white-fronted goose). If the virus circulated in these breeding populations and then moved to other coastal marine bird populations bordering Baffin Bay, which include huge numbers of colonial seabirds and marine waterfowl22,23, the virus could have followed a coastal or even pelagic route south with the large autumn migration of Arctic marine birds (various sea ducks, auks and larids)24,25 to emerge in Newfoundland. Alternatively, shorebirds and waterfowl may have played a role: several European-wintering populations have overlapping breeding grounds with populations wintering along the east coast of North America. Regarding geese, greater white-fronted geese share breeding grounds in western Greenland with Canada geese26,27, which migrate south along the Canadian Atlantic coast. Also, brent geese have overlapping breeding grounds with snow geese18. In addition, individual barnacle geese and pink-footed geese breeding in Greenland could also have travelled south to Newfoundland carrying the virus, as these birds are regular vagrants to the North American Atlantic coast28. While geese occur only in small numbers on Newfoundland, two barnacle geese and four pink-footed geese, probably originating from Greenland breeding grounds, were observed in the autumn of 2021. St. John’s is the first major population center on a coastal route south from Baffin Bay/Davis Strait and along the Labrador Shelf, so emergence in eastern Newfoundland is consistent with this route.Three wild bird species involved in the Iceland and/or Greenland/High Canadian Arctic routes deserve particular attention. Eurasian wigeon have been prominently involved in outbreaks in Eurasia, and are considered prime candidates for carrying HPAI virus over long distances29. Also, during the first stages of an outbreak they are one of the first species to be detected HPAI virus positive, often without clinical signs. Barnacle geese and greylag geese, which congregate in Iceland, were in the top three most abundant species detected H5-positive in Europe in late winter and early spring 20215. Given that both greylag and barnacle geese have populations breeding on Iceland/Greenland and wintering in Europe (particularly the UK), these two species are high on the list of probable vectors that transported the virus to Iceland/Greenland and finally to Newfoundland. The high involvement of infected geese in the HPAI dynamics, which was not seen before October 2020, together with the unusually high levels of HPAI H5 virus presence in wild birds in Northwest Europe in spring 2021, might also explain why HPAI H5 virus spread to Newfoundland this winter (2021/2022), and not in the previous winters (2020/2021, 2016/2017, 2014/2015, 2005/2006). It is, however, striking that no cases of HPAI H5 virus have been recorded on Iceland in 2021.A third possible, pelagic, route is directly across the Atlantic Ocean. Such a route could have started with coastal and pelagic seabirds in Northwest Europe, where the virus may have remained undetected for much of the summer of 2021. A subsequent migration of seabirds to Newfoundland waters in the autumn of 2021 could have brought the virus to North America. The large populations of black-legged kittiwakes and northern fulmars that breed in the U.K. have long been known to frequent Newfoundland waters30, and these movements have been corroborated by recent telemetry studies31. Further, recent telemetry information reveals that millions of pelagic seabirds breeding all across the Atlantic congregate over the Mid-Atlantic Ridge in the central North Atlantic at all times of year32, making a pelagic transmission route a possibility. From the pelagic wintering grounds off Newfoundland, a species that uses both pelagic and coastal habitats, possibly a gull, may have brought the virus to shore in St. John’s. Trans-Atlantic transmission via seabirds has been suggested for LPAI viruses, including detection of mosaic Eurasian-North American viruses in gulls and alcids12,33,34,35.For the time period and geographical frame considered, HPAI-H5-positive species included ducks (Eurasian wigeon, mallard, common eider), geese (barnacle, greylag, brent, pink-footed and greater white-fronted goose), swans (whooper), gulls (black-headed, herring, lesser black-backed, great black-backed), and shorebirds (red knot, ruddy turnstone) (Supplementary Table 2). Of these 15 species, ringed individuals with a European origin have been recorded on Newfoundland for barnacle goose (1 ringed individual), Eurasian wigeon (5), great skua (13), and black-headed gull (1) (Supplementary Table 1). Ringed individuals with a European origin have been found on Newfoundland for 5 species which were found to be HPAI-H5-positive between October 2020 and April 2021, such as Barnacle Goose (1), Eurasian Wigeon (5), Great Skua (13), Black-headed Gull (1). These species might be considered to be possible carriers of HPAI H5 virus from Europe in late winter 2020/2021 or early spring 2021 partly or all the way to Newfoundland. However, given the incompleteness of sampling and the possibility of wild birds carrying HPAI virus subclinically, the involvement of other wild bird species in transatlantic virus transport cannot be ruled out.Having reached the Avalon Peninsula of Newfoundland via one of above routes, the virus may have spread further within the abundant local populations of ducks and gulls wintering in the city of St. John’s. The peridomestic populations of some of these species may be candidates for incursion of the virus into the farm in St John’s. More

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    A 26-year time series of mortality and growth of the Pacific oyster C. gigas recorded along French coasts

    Experimental designData collection took place in different sites disseminated along the mainland French coastline in sectors dedicated to Pacific oyster farming. Over the years, the number of sites monitored varied from 43 sites until 2009, to 13 between 2009 and 2013, and finally to 8 sites since 2015. Here, we focus on 13 sites (Fig. 1 & Table 1) that were almost continuously monitored since 1993. All these sites stand in tidal areas except Marseillan, located in the Mediterranean Thau lagoon, for which tidal variations are only tenuous and Men-er-Roué which is in subtidal deep-water oyster culture area in the Bay of Quiberon. Sentinel oysters were reared in plastic meshed bags fixed on iron tables, mimicking the oyster farmers practices. In Marseillan, half-grown oysters were cemented onto vertical ropes (from 1993 to 2007 and from 2015 to 2018), reared in Australian baskets (from 2008 to 2011), or put in bags fixed on iron tables (2012, 2013, 2014). As for spat oysters, they were reared in pearl-nets between 2008 and 2011 or put in bags since 2012.Fig. 1Site locations (coordinates in WGS84) along the French coastline. The site numbers refer to Table 1.Full size imageTable 1 Site identification and coordinates in WGS84.Full size tableDuring the 1993–2013 period, at the beginning of each annual campaign, one batch of diploid spat (three in 2012 and 2013) and one batch of diploid half-grown oysters were bought from an oyster farmer (i.e., wild-caught individuals) and then deployed simultaneously on all sites of the monitoring network. Here, the term “batch” designates a group of oysters born from the same reproductive event (spatfall or hatchery cohort), having experienced strictly the same zootechnical route. One batch could eventually be reared in several different bags (up to 3) deployed in the same site. Different batches were never mixed in the same bag.During the 2009–2013 period, up to three additional batches of triploid spat were bought in commercial hatcheries and included in the survey strategy (for a maximum of 6 batches of spat per site in 2012 and 2013). In 2009, the batches that were bought had already been exposed to a first wave of mortality before being followed by the network. Thus, the data collected this year should be interpreted with caution. Since 2014, the origin of spat and half-grown oysters has changed notably to better control the initial health status of oysters (no contact with the natural environment before deployment in all sites). The hatchery facility of Ifremer-Argenton now produces the sentinel diploid spat used in the monitoring network (one batch for all sites per campaign), whereas, the half-grown oysters was composed of spat reared on the same location the previous year but not monitored.Data collectionAfter the deployment of the different batches at the beginning of the campaign (seeding dates from February to April depending on the year), growth and mortality were longitudinally monitored yearly. Until 1999, annual campaigns usually ended in the winter of the year the monitoring began (i.e. in December), whereas, during the period 2000–2018, all sites frequently extended the campaign to end in the winter (February to March) of the following year.Observations were collected on each site quarterly until 2008 but then monthly to bimonthly depending on the season. At each sampling date, local operators carefully emptied each bag in separate baskets, counted the dead individuals (those with open or empty shells) and alive ones, and removed the dead individuals. Then local operators weighed all alive individuals in each basket (mass taken at the bag level, protocol mainly used between 1993 and 1998 and since 2004) and/or collected 30 individuals to individually weigh them in the laboratory (mass taken at the individual level, protocol used between 1995 and 2010 for spat and since 1996 for half-grown oysters).Data cleaningDuring the 2009–2013 period, several batches of spat were monitored per site and campaign. Some had a similar background to the batches monitored before 2009 (i.e., wild-caught spat from natural spatfall collected in the bay of Arcachon). To ensure the continuity of the time-series, we thus decided to remove all mass and mortality data of spat that did not originate from natural spatfall in the Bay of Arcachon, as well as triploid spat bought in hatcheries (see Table 2 for the origin and number of batches kept per site and campaign). To ensure that the life-cycle indicators are as comparable as possible between campaign and site (i.e. estimated in a common restricted time window), we removed data collected after December 31 of the year the monitoring began, as well as the site × campaign combinations when monitoring ended before October because the growth or mortality could still be in the exponential phase during this end-of-follow-up periods26. As the protocol of mass data collection changed over the years, we could not only use the mass data taken at the bag level or that at the individual level without greatly breaking the continuity of the time-series. We thus kept data taken at the individual level until 2008 and those taken at the bag level since 2009. We then checked for nonsense or missing data (e.g., the mass of a bag was equal to 0 or missing although they were still alive oysters in the bag), duplicated values and removed data for bags not part of the protocols or incorrectly identified. Finally, we removed site × campaign combinations for which we had fewer than four mass or mortality data because more data is necessary to study the temporal pattern of growth and mortality.Table 2 Origins of the different oyster batches retained after data cleaning.Full size tableData processing and analysisAt this point, the available data were, therefore, the number of living individuals per bag, the number of dead individuals since the last visit, the individual mass (g) of oysters (until 2008) and the total mass (g) of the living individuals per bag (since 2009).For mass data collected until 2008, we calculated the mean of the individual mass per date × site × age class combination by averaging the mass of the individuals. In other cases (mass data collected since 2009), we calculated the mean mass of individuals for each bag × date × site × age class combination by dividing the total mass of living oysters by the number of living individuals and then averaged data by date × site × age class combination. Our mass data, hereafter called mean mass data, is thus composed of the mean of the individual mass until 2008 and the mean mass of individuals since 2009.For mortality data, we could not calculate a cumulative mortality per bag × date × site × age class combination as (1-frac{number;of;alive;oysters;at;sampling;date}{number;of;oysters;at;previous;sampling;date}) because the total number of oysters (dead and alive) on a specific date often differed from the number of alive oysters at the previous date (e.g., because oysters were lost from the bags, or were sampled for complementary analyses such as pathogen detection). We thus took into account changes in oyster numbers between visits and calculated cumulative mortality using the following formula: CMt = 1 − ((1 − CMt-1) × (1 − IMt)). CMt = Cumulative mortality at time t; CMt-1 = Cumulative mortality at time t-1; IMt = Mortality rate at time t. IMt was obtained by dividing the number of dead oysters by the sum of alive and dead oysters at time t. When several bags were followed, we then averaged the cumulative mortality per date × site × age class combinations.We modeled the evolution of the mean mass and cumulative mortality data as a function of time to cope with changes in data frequency acquisition during annual monitoring campaigns. According to previous studies, annual mortality and growth curves in C. gigas follow a sigmoid curve11,26. Therefore, we fitted a logistic model, Eq. (1), and a Gompertz model, Eq. (2), which correspond to the most commonly used sigmoid models for growth and other data27, to describe Yt = mean mass (in grams) and cumulative mortality at time t.$${Y}_{t}=frac{a}{left(1+{e}^{left(-btimes left(t-cright)right)}right)}$$
    (1)
    $${Y}_{t}=atimes {e}^{left(-eleft(-btimes left(t-cright)right)right)}$$
    (2)
    These equations estimate three parameters: the upper asymptote (a), the slope at inflection (b), and the time of inflection (c).As the mean mass of half-grown individuals at the beginning of the campaign was higher than 0, we also fitted a four-parameter version of the logistic model, Eq. (3), and Gompertz model, Eq. (4), which is commonplace in the growth-curve analysis of bacterial counts27, and estimated (d) which represents the lowest asymptote of the curve. This parameter also moves the model curve vertically without changing its shape. The upper asymptote thus becomes equal to d + a.$${Y}_{t}=d+frac{a}{left(1+{e}^{left(-btimes left(t-cright)right)}right)}$$
    (3)
    $${Y}_{t}=d+atimes {e}^{left(-eleft(-btimes left(t-cright)right)right)}$$
    (4)
    Model fitting was carried out using non-linear least squares regressions (R package nls.multstrat28). This method allows running 5000 iterations of the fitting process with start parameters drawn from a uniform distribution and retaining the fit with the lowest score of Akaike Information Criterion (AIC). The sigmoid curve (i.e. logistic or Gompertz) with the lowest mean AIC of all models was selected as the best curve describing the data (see technical validation section). More

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    Shell thickness of Nucella lapillus in the North Sea increased over the last 130 years despite ocean acidification

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