Ecology

Filtering threshold for handling spurious sequencesWe first used bacterial communities of known composition (simplified communities) to assess the occurrence of spurious taxa and to determine at which relative abundances they begin to appear. To propose a cutoff that is potentially applicable to different 16S rRNA gene amplicon studies, we included reference data obtained with different variable regions and sequencing pipelines and originating from both in vitro an in vivo communities varying in number and type of species (max. 58) (Tables 1 and 2). To determine a filtering threshold that allowed exclusion of most spurious taxa, we recorded the relative abundance of the first spurious OTU occurring in each of the reference community datasets (Fig. 2a). Median values of approx. 0.12% relative abundance were observed (Fig. 2b). Besides one outlier in the mock communities (0.44% relative abundance), all values were below 0.25% relative abundance.Fig. 2: Determination of filtering thresholds using artificial communities of known composition in vitro (mock; n = 9 different types; 21 replicates in total) and in mice (gnotobiotes; n = 4 different communities; 28 mice in total).a Example of the occurrence of all molecular species detected without filtering in the gut of a gnotobiotic mouse [49]. The arrow indicates the position of the first spurious molecular species, all following taxa being considered as having a high risk of being spurious (light gray bars in the enlarged inset). b Distribution of the relative abundances of first occurring spurious molecular species (as shown in panel a) across all mock communities and samples from gnotobiotes. The orange dashes on the y-axis indicate the consensus threshold of 0.25% relative abundance, above which no spurious taxa occurred with the exception of one outlier in a mock community at a relative abundance of 0.44%. c Comparison of various standard filtering cutoffs (see explanations in the text) in terms of spurious taxa (i.e., those molecular species not matching sequences of the known species contained in the artificial communities). d Corresponding percentages of positive hits retained by the different filtering strategies, with positive hits being defined as the reference sequences found in the respective amplicon datasets. e Percentage of spurious taxa and positive hits in the same reference communities using the DADA2 pipeline for analysis based on amplicon sequence variants (ASVs) [6]. f Effect of filtering thresholds at increments of 0.05% relative abundance on the detection of spurious taxa and positive hits in all mock and gnotobiotic datasets for OTUs (upper panel) and ASVs (lower panel). Lines correspond to mean values; ribbons represent standard deviations.Full size imageWithout any filtering, sequence clustering generated an average of 508 ± 355 OTUs (min. 52; max. 1081) per mock community (10–58 target species in theory) and 105 ± 50 OTUs (min, 55; max. 215) per gnotobiotic community (4–12 target species in theory). Up to 87% of these OTUs were spurious (i.e., they did not match the expected classification of species contained in the corresponding artificial community) (Fig. 2c). On average, the proportion of spurious OTUs in both the mock communities and samples from gnotobiotic mice was slightly lower after removing singletons, although this did not reach statistical significance (50.8 vs. 64.3%, p = 0.227; 57.5% vs. 65.7%; p = 0.70, pairwise comparison by t-test, including Benjamini–Hochberg correction following ANOVA). Interestingly, the proportion of spurious molecular species was higher in gnotobiotic mice independent of filtering (p  0.50) (Fig. 2d). Note that the diversity of reference communities in the gnotobiotic mice was relatively low (4–12 members; Table 2), resulting in a marked drop in the percentage of positive hit (8–25%) when even just one true member is excluded after filtering because of its low relative abundance (which is an expectable event considering a classical, exponentially decreasing distribution of species occurrence in gut environments).We next employed the widely used ASV analysis approach to confirm the aforementioned results. Processing of the same simplified communities generated a total number of 42 ± 25 ASVs (min. 16; max. 98) for mock communities (10–58 target species) and 14 ± 8 ASVs (min. 4; max. 25) for gnotobiotes (4–12 target species). Altogether, a marked decrease in spurious taxa was observed compared with OTU clustering, with an average of 8.6 ± 11.8 and 4.4 ± 6.4% spurious sequences for mock and gnotobiotic communities, respectively (comparison of purple box plots in Fig. 2e, top panels, and Fig. 2c). Of note, the DADA2 pipeline used for the ASV approach does not infer sequence variants that are only supported by a single read (singletons) due to a lack of confidence in their existence relative to sequencing errors. Consequently, data corresponding to “no filtering” with the OTU-based approach were not generated. On average, the first spurious ASV occurred at a relative abundance of 0.10 ± 0.32%. By applying the cutoff of 0.25% relative abundance, spurious sequences were completely removed (except for three outlying samples), albeit with a slight drop in positive hits for both mock and gnotobiotic communities (Fig. 2e).To obtain a more comprehensive view on how filtering thresholds affect the detection of spurious taxa, all datasets (mock and gnotobiotic mice) were processed using a range of relative abundance filtering thresholds (from 0 to 0.5% at increments of 0.05%) after either OTU- or ASV-based processing of raw sequence reads (Fig. 2f). These data indicate that filtering thresholds between 0.1 and 0.3% are appropriate to reduce the occurrence of spurious taxa to 600 of the 678 spurious OTUs occurred in fewer than five of the ten sequencing runs tested, with approximately 450 of them occurring in only one run (Fig. 3c). This observation indicates that the majority of spurious taxa are sporadic cross-contaminations rather than generalist artifacts across sequencing runs, suggesting that fully independent technical replicates would improve data quality. Although most of the spurious taxa were characterized by relative abundances between 0.25 and 2% in the IMNGS-amplicon datasets tested, they represented very dominant populations in a few samples (Fig. 3d).Fig. 3: Origin and occurrence of spurious taxa.a Taxonomic profile and ecological distribution. Inner ring: SILVA-based classification of all non-redundant spurious molecular species at the phylum and family level. Outer colored ring: sample type characterized by the highest prevalence for the given taxon. Outer bars: corresponding highest prevalence values. Only samples with relative abundances >0.25% for any given OTU were counted as positive for prevalence calculation. The total numbers of samples considered were: human, 46,153; soil, 29,864; freshwater, 13,977; mouse, 10,409; marine, 8478. b Distribution of the spurious taxa across sample types. The exclusivity of each OTU for any given sample type was assessed using a Z-test: those assumed to be non-specific for any given sample type appear in red (p 0.25% in at least one replicate were kept). Richness was calculated using ampvis2 [29]. Applying the 0.25% cutoff decreased the number of observed ASVs from 408 ± 71 to 139 ± 5 and, more importantly, the IQR from 101 to 7 (Fig. 6b). Unweighted UniFrac distances within and between runs as calculated using ampvis2 were also compared before and after filtering. Sequences were aligned using MAFFT [30] and phylogeny was inferred using FastTree. Whilst the community makeup in the soil sample varied substantially between sequencing runs without additional filtering, the 0.25% cutoff reduced this variation to the level observed within runs without filtering (Fig. 6c). Replicates within a run were very similar after applying the 0.25% cutoff. Altogether, these data serve as an independent confirmation that stringent filtering delivers more stable values obtained for the exact same sample sequenced in replicates across several sequencing runs. More

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Data sourcesNo single comprehensive dataset of planktonic foraminiferal distributional records currently exists. Instead, these data are available from a wide range of sources in many different structures. Some of these sources are compilations of existing data (e.g., Neptune14,15,16, ForCenS21), and others derive from individual sampling sites (e.g. ocean drilling expeditions). Triton combines these disparate sources (Fig. 1) to produce a single spatio-temporal dataset of Cenozoic planktonic foraminifera with updated and consistent taxonomy, age models, and paleo-coordinates.Neptune is currently the most comprehensive database of fossil plankton data, with records exclusively from the DSDP, ODP and IODP representing planktonic foraminifera, calcareous nannofossils, diatoms, radiolaria and dinoflagellates14,15,16. A subset of these sites is included in Neptune, representing those with the most continuous sampling through time. The raw data from Neptune form the core of our dataset. All foraminiferal occurrences for the Cenozoic (i.e. last 66 Ma) were downloaded using the GTS 2012 timescale. In the download options, all questionable identifications and invalid taxa were removed, as were records that had been identified as reworked.In addition to Neptune, three other compilation datasets were included in Triton: ForCenS21, which consists of global core-top samples; the Eocene data from Fenton, et al.8 created based on literature searches for planktonic foraminiferal data in the Eocene; and the land-based records from Lloyd, et al.22 that were created from literature searches. The marine records in Lloyd, et al.22 were not included, as they were obtained from Neptune.Following preliminary compilation of existing datasets, we identified all legacy DSDP, ODP and IODP cores missing from Triton. The online DESCLogik (http://web.iodp.tamu.edu/DESCReport/) and Pangaea17 databases were then mined for .csv files containing planktonic foraminiferal species count data for the missing cores, supplemented with data from AWI_Paleo (URI: http://www.awi.de/en/science/geosciences/marine-geology.html), GIK/IFG (URI: http://www.ifg.uni-kiel.de/), MARUM (URI: https://www.marum.de/index.html), and QUEEN (URI: http://ipt.vliz.be/eurobis/resource?r=pangaea_2747). All additional cores were assessed individually by inspecting the scientific drilling proceedings to determine whether sites were suitable to contribute to our dataset. The primary assessment criterion was identification of continuous sedimentary sections, wherein two or more confidently assigned consecutive chronostratigraphic tie points existed to allow for construction of age models.In addition to these longer cores, many sediment sampling projects have produced planktonic foraminiferal distribution data from shorter cores that tend to correspond in age to the last few million years. The website PANGAEA17 (www.pangaea.de) has been used as a repository for most of these occurrence data. This website was searched using the terms “plank* AND foram”, with resulting datasets downloaded using the R package ‘pangaear’23. These datasets were filtered to exclude records collected using multinets, sediment traps or box cores, as these methods produce samples not easily correlated to sediment cores. Column names allowed for further filtering to exclude records with no species-level data, records that had only isotopic data (rather than abundance data), or records with no age controls.Data processingThe data sources underpinning Triton serve their records in different formats. Therefore, processing was necessary to convert records into a unified framework, with one species per row for each sample and associated metadata (see below for details). Some metadata could be used without modification when available (e.g. water depth, data source), whereas other data needed processing to ensure consistency (e.g. abundance, paleo-coordinates, age). Without this processing, samples from different sources were not directly comparable. Where data were not available, they were set to NA. Those records with missing data in crucial columns (species name, abundance, age, and paleo-coordinates) were removed from the final dataset. All data processing was performed using R v. 3.6.124.Taxonomic consistency is essential to enable comparison of datasets created at different times. The species and synonymy lists used in Triton are based on the Paleogene Atlases20,25,26, with additional information from mikrotax27 (http://www.mikrotax.org/pforams/). These sources were supplemented, when necessary with more up to date literature including Poole and Wade28 and Lam and Leckie29. (A full list of the taxonomic sources can be found in the PFdata.xlsx file18.) A synonymy list was generated to convert species names to the senior synonym. At the same time, typographic errors were corrected. For example, Globototalia flexuosa should be Globorotalia flexuosa. Exclusively Mesozoic taxa were omitted, as were all instances when species names were unclear or imprecise (i.e. not at the species level). Junior synonyms were merged with their senior synonyms and their abundances summed, although the original names and abundances are also retained in the processed dataset. For presence/absence samples, these numerical merged abundances were set to one (i.e. present). The full species list and list of synonyms can be found in the accompanying data.Abundance data for planktonic foraminifera are provided in different formats: presence/absence, binned abundance, relative abundance, species counts, and number of specimens per gram. These metrics were converted into numeric relative abundance to make comparisons easier, although both the original abundance value and its numeric version are retained, as is a record of the abundance type. Presence/absence data were converted to a binary format (one for present; zero for absent). Species counts were converted to relative percent abundances based on the total number of specimens in the sample (this was calculated where it was not already recorded). When full counts were not performed, binned abundances were frequently used. These binned abundances were converted into numeric abundances based on the sequence. So, for example, the categorical labels of N, P, R, F, C, A, D (indicating none, present, rare, few, common, abundant, dominant) were converted to a numerical sequence of 0 to 6. As the meaning of letters can depend on the context (e.g. ‘A’ could be absent or abundant), conversion was done in a semi-automated fashion on a sample-by-sample basis. A value of 0.01 was assigned to records where an inconsistent abundance was recorded (e.g. samples with mostly numeric counts but a few species were designated ‘P’, indicating presence). Samples with zero abundance were retained in the full dataset to provide an indication of sampling.The age of samples were recorded in multiple ways. For some samples, age models provide precise numerical estimates of the age (e.g., those in Neptune). Other samples are dated relative to stratigraphic events such as biostratigraphic zones (including benthic and planktonic foraminifera, diatoms, radiolarians and nannofossils) or magnetic reversals. In this case, ages sometimes needed to be converted to reflect revised age estimates. The start and end dates of biostratigraphic zones are defined in relation to events in marker species, e.g. their speciation, extinction or acme events. All such marker events were updated to their most recent estimates and tuned to the GTS 2020 timescale19. The process of updating included correction of synonymies. Additional care was taken to ensure the correct interpretation of abbreviations (e.g. determining whether LO meant lowest occurrence or last occurrence) based on the entire list of events for a study. Where up-to-date ages were not available or events were ambiguous, they were removed from the age models.The marker events defining a zone can depend on the zonal scheme used. For example, Berggren30 defined the base of the planktonic foraminifera zone M8 as the first occurrence of Fohsella fohsi. Wade et al.31 used this same event to define the base of M9. Therefore, the zonal scheme was recorded when collecting age models, to accurately convert ages to the GTS 2020 time scale. Some marker events have different ages depending on the ocean basin or latitude, and these differences are not necessarily well studied31,32. Where these differences in marker events have been recorded, the coordinates of a site were used to determine whether sites were in the Atlantic or Indo-Pacific Ocean, and whether they were tropical or temperate (with the division at 23.5° latitude). However, this is an area where more research is needed to improve the accuracy of higher-latitude dating32. Magnetostratigraphic ages were also tuned to the GTS 2020 timescale.We constructed new age models for samples not already assigned a numeric age. Where the depths of biostratigraphic events were already recorded, these were converted directly to GTS 2020. Where samples were not given any ages, often the case for the cores collected in the early days of ocean drilling, ages were reconstructed from the shipboard and post-cruise biostratigraphic data available in DESCLogik, Pangaea, and drilling publications. For holes where no tie point data were retrievable, biostratigraphic count data were extracted directly from drilling publications, and biostratigraphic events were assigned via GTS 2020. The first and last occurrences in raw shipboard biostratigraphic data often do not represent true datums, and careful assessment of the shipboard, and post-cruise literature was a prerequisite to confidently assigning chronostratigraphic datums. Tie point depths were assigned as the midpoint depth between the core sample before and after an event. For example, for an extinction event, the recorded depth was the midway point between the last recorded occurrence of a species and the first sample from which the species is absent. All sites were assessed individually to determine the age of the seafloor. Where IODP reports or sample-based publications strictly stated that the sediment surface (i.e. 0.00 meters below seafloor (mbsf)) was deemed to be “Holocene”, “Recent” or “Modern” in age, an additional 0 Ma tie point was assigned appropriately. All samples present outside the maximum/minimum age tie points for that site were removed, as they could not be confidently assigned an age. During assessment, individual drilling reports were investigated for geological structures. Where features such as unconformities, reverse faults, stratigraphic inversions, décollements, and major slips and slumps were identified, separate age models were generated for individual intact stratal intervals to account for potential externally emplaced or repeated strata (see “Age models” and “Triton working” in the figshare data repository18). Similarly, age gaps of greater than 10% of the age range of the core were classified as hiatuses, leading to separate age models (see Fig. 4). Cores of denser sediments that have been sampled using rotary drilling will often have only ~50–60% recovery in a core (9.5 m)33. As it is not possible to determine where the recovered core material came from within this length, all intact core pieces are grouped together as a continuous section from the section top, regardless of where the pieces were sourced (e.g. 4.5 m of recovered material will be recorded as 0–4.5 m of cored interval even if some came from 9–9.5 m). Consequently, age estimates within cores where recovery was low, typically the samples collected longer ago, will necessarily be less certain.Fig. 4Different age model estimates applied to core material from IODP Site U1499A in the South China Sea. Mag – mean age based only on the magnetostratigraphic marker events. Zones – mean age based on all the marker events. Int Mag – interpolation of the points between the magnetostratigraphic marker events. Interp – interpolation between the full set of marker events. Model – the model of age as a function of depth. Note the hiatus between 50 and 100 m. For the shallower section of the dataset, with only three data points, a simple linear model was used. For the deeper section, a GAM smooth was fitted. For this site, the model predictions were chosen as the best fit.Full size imageUsing the updated marker event ages, we created age-depth plots and modelled the best fit to the data. There are different ways of creating these models, and multiple methods were applied to each core. The one that provided the best fit to the original data was chosen (the different age models are available in “Age models” in the figshare data repository18). These choices were confirmed manually (see Fig. 4). The simplest age model used interpolation of the marker events to create ‘zones’ and assign estimated ages assuming a continuous sedimentation rate between the start and end of each of these zones. Where the events do not provide a continuous sequence (e.g. gaps in the zonal markers), age estimates were assigned as the mean of that zone with error estimates of the width of the zone. Where magnetostratigraphic events were present they were given preference. This method leads to different estimates of sedimentation rate for each zone. The more complex age model estimates a smoother sedimentation rate. When there were fewer than 5 marker events, a linear model of age as a function of depth was fitted for the entire core. For larger datasets, generalised additive models (GAMs) for the same variables were used, to allow for variation in sedimentation rates through time. GAMs were run using the mgcv R library, with a gamma value of 1.134. The type of age model used in the analysis was recorded. Where appropriate, the number of points and the r2 of the model are recorded to give an indication of the accuracy of the age model.The latitude and longitude coordinates of samples were recorded in decimal degrees. For all samples except modern ones, plate tectonic reconstructions were necessary to determine the coordinates at which the sample was originally deposited. Reconstructions were performed using the Matthews, et al.35 plate motion model, which is an updated version of the Seton, et al.36 model used by Neptune. Comparisons of age models35,36,37,38,39 suggest this model is most appropriate for the deep sea environment where most of the samples occur, and is able to assign coordinates to significantly more sites than the Scotese39 GPlates model. This test was performed with a subset of the data (10633 unique sites); the Matthews, et al.35 model provided paleocoordinates for 95% of the data, whilst the GPlates model only provided coordinates for 17% of the data. The calculation of paleocoordinates was automated using an adaptation of https://github.com/macroecology/mapast.When sediment samples are derived from multiple sources, duplication will inevitably occur. All such duplicated records, identified based on the combination of species, abundance, sample depth, and coordinate values, were removed. Additionally, working on an individual record level, species that occurred significantly outside their known ranges were flagged (following updated age models) on the assumption these records were misidentifications, contamination or re-working. Records were classified as falling significantly outside their known range if they were more than 5 Ma outside the species’ range in the Palaeogene (66-23 Ma) and more than 2 Ma in the Neogene (23-0 Ma). These values were chosen based on the tradeoff between removing reworked specimens and allowing for some errors in the age estimates. Age estimates for older samples tend to be less precise. Ages were obtained from Lamyman et al. (in prep) and are available in “PFdata” in the figshare data repository18. In total, 10,990 suspect records were flagged (~2% of all records). More

Based on the present-day distribution of photosynthetic bacteria31, we assume a competitive advantage for anoxygenic photosynthetic bacteria in early environments where electron donors such as Fe2+, H2S, or H2 were present. We also assume the contemporaneous existence of environments where cyanobacterial populations could thrive, providing a seedbed for migration. Non-marine waters provide an example of the latter, supported by the branching of non-marine taxa from basal nodes in cyanobacterial phylogenies44,45 and also by the presence of stromatolites in Archean lacustrine successions46, despite the likelihood that many Archean lakes and rivers had low levels of potential electron donors such as Fe2+ and H2S47.Following Jones et al.40 and Ozaki et al.42, we use Fe (iron) and P (phosphorus) to represent the environment, which is similar to the H2 and P employed in other studies48,49. The logic of this choice is that in Archean oceans, Fe2+ is thought to have been the principal electron donor for anoxygenic photosynthesis50,51, whereas P governed total rates of photosynthesis. (Kasting14 argued that H2 was key to photosynthesis on the early Earth, a view supported by low iron concentrations in some early Archean stromatolites52.). In any event, under the conditions of low P availability thought to have characterized early oceans25,40,49,53,54,55, anoxygenic photosynthesis would have depleted limiting nutrients before alternative electron donors were exhausted. In consequence, rates of photosynthetic oxygen production would be low. As iron availability declined and/or P availability increased, the biosphere would inevitably reach a point where P would remain after Fe2+ had been depleted, expanding the range of environments where cyanobacteria are favored by natural selection42.Our model keeps track of the abundances of anoxygenic photosynthetic bacteria (APB), x1, cyanobacteria, x2, and three crucial chemicals: iron(II) (Fe2+), y1, phosphate (PO43−), y2, and dioxygen (O2), z. Both types of bacteria require phosphate for reproduction. APB needs iron(II) (or some other suitable reductant) as an electron donor in photosynthesis. The following five equations describe the reproduction and death of APB and of cyanobacteria as well as the dynamics of iron(II), phosphate, and dioxygen:$${rm{APB}}: {dot{x}}_{1} ={x}_{1}{y}_{1}{y}_{2}-{x}_{1}+{u}_{1}\ {rm{Cyano}}: {dot{x}}_{2} =c{x}_{2}{y}_{2}-{x}_{2}+{u}_{2}\ {{rm{Fe}}}^{2+}: {dot{y}}_{1} ={f}_{1}-{y}_{1}-{x}_{1}{y}_{1}{y}_{2}-{y}_{1}z\ {{rm{PO}}_{4}}^{3-}: {dot{y}}_{2} ={f}_{2}-{y}_{2}-{x}_{1}{y}_{1}{y}_{2}-{x}_{2}{y}_{2}\ {{rm{O}}}_{2}: dot{z} =a{x}_{2}{y}_{2}-bz-{y}_{1}z$$
(1)
Here, we have omitted to write symbols for those rate constants that, for understanding the GOE, can be set to one without loss of generality (Supplementary Note 1). Each remaining rate constant is a free parameter. Equations (1) thus satisfy redox balance by construction. We are left with a system that has five main parameters: c specifies the rate of reproduction of cyanobacteria; f1 and f2 denote the rates of supply of iron(II) and phosphate, respectively; a denotes biogenic production of oxygen; b denotes geochemical consumption of oxygen. Note that iron(II) and phosphate are also removed by geochemical processes at a rate proportional to their abundance. In addition, iron(II) is used up during anoxygenic photosynthesis, and iron(II) reacts with oxygen and is thereby removed from the system. Phosphate is used up during the growth of APB and cyanobacteria. (We investigate extensions of the model that incorporate bounded bacterial growth rates and organic carbon in Supplementary Note 2 and Supplementary Note 3, respectively.)We posit iron(II) as the primary electron donor for anoxygenic photosynthesis, and for simplicity of presentation, we refer to y1 and f1 in this context. However, as noted above, y1 and f1 can similarly represent the abundances and influxes of other alternative electron donors, especially dihydrogen (H2)56,57 and hydrogen sulfide (H2S)58. Our model, its analytical solution, and the conclusions that follow hold equally well by considering any of these electron donors or all together.We also include small migration rates, u1 and u2, which allow for the possibility that APB and cyanobacteria persist in privileged sites from which they can migrate into the main arena of competition. On the Archean Earth, these parameters could have been affected by the flow of water and by surface winds. For the mathematical analysis presented in the main text, we assume that these rates are negligibly small.The GOE represents the transition from a world dominated by APB (Equilibrium E1) to one that is dominated by cyanobacteria (Equilibrium E2) (Figs. S1, S2). On a slowly changing planet, the abundances of APB and cyanobacteria and of the three chemicals are approximately in steady state. Therefore, we consider the fixed points of Eqs. (1).Pure equilibriaIn the absence of APB and cyanobacteria, the abiotic equilibrium abundances of iron(II) and of phosphate are given by f1 and f2, respectively, and there is no oxygen in the system. If f1f2  > 1, then APB can emerge. Subsequently, the system settles to Equilibrium E1, where only APB are present and there is still no oxygen. E1 is stable against invasion of cyanobacteria if$${f}_{1}-{f}_{2}, > ,frac{(c+1)(c-1)}{c}.$$
(2)
This condition can be fulfilled if the influx of iron, f1, is large enough, or if the influx of phosphate, f2, is small enough. The term on the right-hand side of the inequality is an increasing function of the reproductive rate, c, of cyanobacteria.If cf2  > 1, then the system admits another equilibrium, E2, where only cyanobacteria are present and oxygen is abundant. Equilibrium E2 is stable against invasion of APB if$$a(c{f}_{2}-1), > ,(b+c)({f}_{1}-c).$$
(3)
The left-hand side of the inequality is positive. If the right-hand side is negative (that is, if f1  ,c(a-1).$$
(4)
Condition (4) is understood as follows. If b is sufficiently large, then there is not enough atmospheric oxygen for rusting to render E2 stable against invasion of APB before E1 loses stability; the result is stable coexistence. But if b is sufficiently small, then rusting causes E2 to become stable before E1 becomes unstable. The critical value of b therefore depends on the input of atmospheric oxygen for Equilibrium E2; it is an increasing function of the reproductive rate of cyanobacteria and of their rate of production of oxygen.If a  c(a − 1). Figure 3 shows gradual oxygenation due to decreasing f1. In this case, the transition occurs via the mixed equilibrium, (hat{E}), where both types of bacteria coexist (Fig. 4). A subsequent increase in f1 can cause APB to regain dominance (Fig. S3a).Fig. 3: The GOE can be triggered by a decline in the influx of iron(II) and is gradual if b  > c(a − 1).Equilibrium E1 (APB dominate) loses stability and Equilibrium E2 (cyanobacteria dominate) gains stability when f1 drops below ({f}_{1}^{* }) and (f_1^{prime}), respectively. We set f2 = 80, c = 10, a = 10, b = 100, and u1 = u2 = 10−3. a We simulate Eqs. (8) from Supplementary Note 1 with α1 = α2 = β1 = β2 = 1, and we set f1 = 100 − 40(t/105). t* denotes the time at which Equilibrium E1 loses stability. b There is stable coexistence of both types of bacteria for (f_1^{prime} , More

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Effects of waterlogging stress on leaf morphology in mulberry seedlingsFigure 1 shows the change in the leaf morphology of mulberry seedlings under different submergence depths. The results showed that the seedlings under both SS and HS could grow well, and there were 3 slightly wilted leaves on average under FS. There were 3 wilted leaves and 2 defoliated leaves on average in the HS group after 10 days of flooding, and a few adventitious roots began to appear at the base of the stem. In the SS group, there slight wilting and falling of mulberry leaves were observed on the 15th day after submergence, and there were 5 wilting leaves and a few adventitious roots per plant. In the SS group, there were 3 defoliated leaves and 2 wilted leaves per mulberry seedling, and no adventitious roots developed. The HS group showed an average of 7 adventitious roots per plant. Additionally, there were 8 wilted leaves, 10 defoliated leaves and 4 brown spots per plant under HS.Figure 1Effect of submergence stress on leaf morphology in Morus alba: (a) The number of curled or wilted leaves per plant; (b) The number of brown spots or rotten leaves per plant; (c) The number of fallen leaves per plant; (d) The number of adventitious roots. This figure was drawn using Origin Pro 2021 v. 9.8.0.200.Full size imageEffects of waterlogging stress on initial fluorescence (Fo), and maximum fluorescence (Fm) under dark adaptation in mulberry leavesThe initial fluorescence value (Fo) and the maximum fluorescence value (Fm) of mulberry seedlings significantly decreased over time. Figure 2a shows that the Fo values of mulberry seedlings under SS, HS, and FS decreased by 31.27%, 22.51%, and 42.45%, respectively, on day 4 and were significantly different (p  More