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Cohort demographicsA total of 206 female participants were enrolled in the study and passed our quality control standards. All participants were required to be between the ages of 18–26 years old (22.5 ± 2.1) and to be born and at the time living in one of four geographically distinct regions of the world: Barbados; Santiago, Chile; Pretoria, S. Africa; and Bangkok, Thailand. The regions do, however, differ by an order of magnitude in their geographic spread as the intra-distance separating the residence neighborhood of participants ranged from 34 (Barbados) to 681 km (Pretoria, S. Africa) (Fig. S2). The Chilean and the South African datasets are further divided into two contiguous sub-regions, or neighborhoods, to allow for a micro-geographic analysis. The study population is largely dominated by individuals with self-identified Thai heritage (33%), followed by Black African (16%), Afro-Caribbean (14%) and white (14%) descent, although 19% of the Chilean population did not report ethnicity.Study participants, despite the divergent geographies, mostly have similar dietary and lifestyle habits (Table S1). Over half the study population (62%) have a normal BMI, with the mean BMI in this range (22.6 ± 5.5). The diets of the different cohorts are also similar as of the total cohort, 78% consume a starch heavy diet (≥ 4 days a week) of rice, bread and pasta, followed by 66% who frequently consume (≥ 4 days a week) vegetables and fruit and 49% who frequently consume dairy products. The study population is split by level of tobacco exposure, with 51% of the population having never smoked, and 43% being exposed to second-hand smoke through living with a smoker. Over half (56%) of the study population own one or more pets.Stool microbiomeThe OTUs identified using the UPARSE pipeline17 were used to compute the alpha diversity of the microbial communities using the Chao1 (species richness) and Shannon (species evenness) indices. The mean Shannon indices reveal that the microbiota diversity is only significant between Thailand-Chile with FDR  More

DataWe tested our models on ten publicly available datasets. In Fig. 4 we show examples of images from each of the datasets. When applicable, the training and test splits were kept the same as in the original dataset. For example, the ZooScan, Kaggle, EILAT, and RSMAS datasets lack a specific training and test set; in these cases, benchmarks come from k-fold cross-validation51,52, and we followed the exact same procedures in order to allow for a fair comparison.Figure 4Examples of images from each of the datasets.(a) RSMAS (b) EILAT (c) ZooLake (d) WHOI (e) Kaggle (f) ZooScan (g) NA-Birds (h) Stanford dogs (i) SriLankan Beetles (j) Florida Wildtrap.Full size imageRSMAS This is a small coral dataset of 766 RGB image patches with a size of (256times 256) pixels each53. The patches were cropped out of bigger images obtained by the University of Miami’s Rosenstiel School of Marine and Atmospheric Sciences. These images were captured using various cameras in various locations. The data is separated into 14 unbalanced groups and whose labels correspond to the names of the coral species in Latin. The current SOTA for the classification of this dataset is by52. They use the ensemble of best performing 11 CNN models. The best models were chosen based on sequential forward feature selection (SFFS) approach. Since an independent test is not available, they make use of 5-fold cross-validation for benchmarking the performances.EILAT This is a coral dataset of 1123 64-pixel RGB image patches53 that were created from larger images that were taken from coral reefs near Eilat in the Red sea. The image dataset is partitioned into eight classes, with an unequal distribution of data. The names of the classes correspond to the shorter version of the scientific names of the coral species. The current SOTA52 for the classification of this dataset uses the ensemble of best performing 11 CNN models similar to RSMAS dataset and 5-fold cross-validation for benchmarking the performances.ZooLake This dataset consists of 17943 images of lake plankton from 35 classes, acquired using a Dual-magnification Scripps Plankton Camera (DSPC) in Lake Greifensee (Switzerland) between 2018 and 2020 14,54. The images are colored, with a black background and an uneven class distribution. The current SOTA22 on this dataset is based on a stacking ensemble of 6 CNN models on an independent test set.WHOI This dataset 55 contains images of marine plankton acquired by Image FlowCytobot56, from Woods Hole Harbor water. The sampling was done between late fall and early spring in 2004 and 2005. It contains 6600 greyscale images of different sizes, from 22 manually categorized plankton classes with an equal number of samples for each class. The majority of the classes belonging to phytoplankton at genus level. This dataset was later extended to include 3.4M images and 103 classes. The WHOI subset that we use was previously used for benchmarking plankton classification models51,52. The current SOTA22 on this dataset is based on average ensemble of 6 CNN models on an independent test set.Kaggle-plankton The original Kaggle-plankton dataset consists of plankton images that were acquired by In-situ Ichthyoplankton Imaging System (ISIIS) technology from May to June 2014 in the Straits of Florida. The dataset was published on Kaggle (https://www.kaggle.com/c/datasciencebowl) with images originating from the Hatfield Marine Science Center at Oregon State University. A subset of the original Kaggle-plankton dataset was published by51 to benchmark the plankton classification tasks. This subset comprises of 14,374 greyscale images from 38 classes, and the distribution among classes is not uniform, but each class has at least 100 samples. The current SOTA22 uses average ensemble of 6 CNN models and benchmarks the performance using 5-fold cross-validation.ZooScan The ZooScan dataset consists of 3771 greyscale plankton images acquired using the Zooscan technology from the Bay of Villefranche-sur-mer57. This dataset was used for benchmarking the classification models in previous plankton recognition papers51,52. The dataset consists of 20 classes with a variable number of samples for each class ranging from 28 to 427. The current SOTA22 uses average ensemble of 6 CNN models and benchmarks the performance using 2-fold cross-validation.NA-Birds NA-Birds58 is a collection of 48,000 captioned pictures of North America’s 400 most often seen bird species. For each species, there are over 100 images accessible, with distinct annotations for males, females, and juveniles, totaling 555 visual categories. The current SOTA59 called TransFG modifies the pure ViT model by adding contrastive feature learning and part selection module that replaces the original input sequence to the transformer layer with tokens corresponding to informative regions such that the distance of representations between confusing subcategories can be enlarged. They make use of an independent test set for benchmarking the model performances.Stanford Dogs The Stanford Dogs dataset comprises 20,580 color images of 120 different dog breeds from all around the globe, separated into 12,000 training images and 8,580 testing images60. The current SOTA59 makes use of modified ViT model called TransFG as explained above in NA-Birds dataset. They make use of an independent test set for benchmarking the model performances.Sri Lankan Beetles The arboreal tiger beetle data61 consists of 380 images that were taken between August 2017 and September 2020 from 22 places in Sri Lanka, including all climatic zones and provinces, as well as 14 districts. Tricondyla (3 species), Derocrania (5 species), and Neocollyris (1 species) were among the nine species discovered, with six of them being endemic . The current SOTA61 makes use of CNN-based SqueezeNet architecture and was trained using pre-trained weights of ImageNet. The benchmarking of the model performances was done on an independent test set.Florida Wild Traps The wildlife camera trap62 classification dataset comprises 104,495 images with visually similar species, varied lighting conditions, skewed class distribution, and samples of endangered species, such as Florida panthers. These were collected from two locations in Southwestern Florida. These images are categorized in to 22 classes. The current SOTA62 makes use of CNN-based ResNet-50 architecture and the performance of the model was benchmarked on an independent test set.ModelsVision transformers (ViTs)31 are an adaptation to computer vision of the Transformers, which were originally developed for natural language processing30. Their distinguishing feature is that, instead of exploiting translational symmetry, as CNNs do, they have an attention mechanism which identifies the most relevant part of an image. ViTs have recently outperformed CNNs in image classification tasks where vast amounts of training data and processing resources are available30,63. However, for the vast majority of use cases and consumers, where data and/or computational resources are limiting, ViTs are essentially untrainable, even when the network architecture is defined and no architectural optimization is required. To settle this issue, Data-efficient Image Transformers (DeiTs) were proposed32. These are transformer models that are designed to be trained with much less data and with far less computing resources32. In DeiTs, the transformer architecture has been modified to allow native distillation64, in which a student neural network learns from the results of a teacher model. Here, a CNN is used as the teacher model, and the pure vision transformer is used as the student network. All the DeiT models we report on here are DeiT-Base models32. The ViTs are ViT-B16, ViT-B32, and ViT-L32 models31.ImplementationTo train our models, we used transfer learning65: we took a model that was already pre-trained on the ImageNet43 dataset, changed the last layers depending on the number of classes, and then fine-tuned the whole network with a very low learning rate. All the models were trained with two Nvidia GTX 2080Ti GPUs.DeiTs We used DeiT-Base32 architecture, using the Python package TIMM66, which includes many of the well-known deep learning architectures, along with their pre-trained weights computed from the ImageNet dataset43. We resized the input images to 224 x 224 pixels and then, to prevent the model from overfitting at the pixel level and help it generalize better, we employed typical image augmentations during training such as horizontal and vertical flips, rotations up to 180 degrees, small zoom up’s to 20%, a small Gaussian blur, and shearing up to 10%. To handle class imbalance, we used class reweighting, which reweights errors on each example by how present that class is in the dataset67. We used sklearn utilities68 to calculate the class weights which we employed during the training phase.The training phase started with a default pytorch69 initial conditions (Kaiming uniform initializer), an AdamW optimizer with cosine annealing70, with a base learning rate of (10^{-4}), and a weight decay value of 0.03, batch size of 32 and was supervised using cross-entropy loss. We trained with early stopping, interrupting training if the validation F1-score did not improve for 5 epochs. The learning rate was then dropped by a factor of 10. We iterated until the learning rate reached its final value of (10^{-6}). This procedure amounted to around 100 epochs in total, independent of the dataset. The training time varied depending on the size of the datasets. It ranged between 20min (SriLankan Beetles) to 9h (Florida Wildtrap). We used the same procedure for all the datasets: no extra time was needed for hyperparameter tuning.ViTs We implemented the ViT-B16, ViT-B32 and ViT-L32 models using the Python package vit-keras (https://github.com/faustomorales/vit-keras), which includes pre-trained weights computed from the ImageNet43 dataset and the Tensorflow library71.First, we resized input images to 128 × 128 and employed typical image augmentations during training such as horizontal and vertical flips, rotations up to 180 degrees, small zooms up to 20%, small Gaussian blur, and shearing up to 10%. To handle class imbalance, we calculated the class weights and use them during the training phase.Using transfer learning, we imported the pre-trained model and froze all of the layers to train the model. We removed the last layer, and in its place we added a dense layer with (n_c) outputs (being (n_c) the number of classes), was preceded and followed by a dropout layer. We used the Keras-tuner72 with Bayesian optimization search73 to determine the best set of hyperparameters, which included the dropout rate, learning-rate, and dense layer parameters (10 trials and 100 epochs). After that, the model with the best hyperparameters was trained with a default tensorflow71 initial condition (Glorot uniform initializer) for 150 epochs using early stopping, which involved halting the training if the validation loss did not decrease after 50 epochs and retaining the model parameters that had the lowest validation loss.CNNs CNNs included DenseNet38, MobileNet39, EfficientNet-B240, EfficientNet-B540, EfficientNet-B640, and EfficientNet-B740 architectures. We followed the training procedure described in Ref.22, and carried out the training in tensorflow.Ensemble learningWe adopted average ensembling, which takes the confidence vectors of different learners, and produces a prediction based on the average among the confidence vectors. With this procedure, all the individual models contribute equally to the final prediction, irrespective of their validation performance. Ensembling usually results in superior overall classification metrics and model robustness74,75.Given a set of n models, with prediction vectors (vec c_i~(i=1,ldots ,n)), these are typically aggregated through an arithmetic average. The components of the ensembled confidence vector (vec c_{AA}), related to each class (alpha ) are then$$begin{aligned} c_{AA,alpha } = frac{1}{n}sum _{i=1}^n c_{i,alpha },. end{aligned}$$
(2)
Another option is to use a geometric average,$$begin{aligned} c_{GA,alpha } = root n of {prod _{i=1}^n c_{i,alpha }},. end{aligned}$$
(3)
We can normalize the vector (vec c_g), but this is not relevant, since we are interested in its largest component, (displaystyle max _alpha (c_{GA,alpha })), and normalization affects all the components in the same way. As a matter of fact, also the nth root does not change the relative magnitude of the components, so instead of (vec c_{GA}) we can use a product rule: (displaystyle max _alpha (c_{GA,alpha })=max _alpha (c_{PROD,alpha })), with (displaystyle c_{PROD,alpha } = prod _{i=1}^n c_{i,alpha }).While these two kinds of averaging are equivalent in the case of two models and two classes, they are generally different in any other case33. For example, it can easily be seen that the geometric average penalizes more strongly the classes for which at least one learner has a very low confidence value, a property that was termed veto mechanism36 (note that, while in Ref.36 the term veto is used when the confidence value is exactly zero, here we use this term in a slightly looser way). More

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Isotope labelling and phylogenetic analysis of a natural marine bacterioplankton population at seaMediterranean seawater was collected during August 2017 (station N1200, 32.45° N, 34.37 °E) from 11 depths by Niskin bottles and divided into triplicate 250 ml polycarbonate bottles. Two bottles from each depth were labelled with 1 mM sodium bicarbonate-13C and 1 mM ammonium-15N chloride (Sigma-Aldrich), and all three bottles (two labelled and one control) were incubated at the original depth and station at sea for 3.5 h around mid-day. The stable isotopes were chosen to enable direct comparison of C and N uptake in single cells, and the short incubation time was chosen to minimize isotope dilution and potential recycling and transfer of 13C and 15N between community members25. After incubation, bottles were brought back on board and the incubations were stopped by fixing with 2× electron-microscopy-grade glutaraldehyde (2.5% final concentration) and stored at 4 °C until sorting analysis. Cell sorting, NanoSIMS analyses and the calculation of uptake rates were performed as described in Roth-Rosenberg et al.26.DNA collection and extraction from seawaterSamples for DNA were collected on 0.22 µm Sterivex filters (Millipore). Excess water was removed using a syringe, 1 ml lysis buffer (40 mM EDTA, 50 mM Tris pH 8.3, and 0.75 M sucrose) was added and both ends of the filter were closed with parafilm. Samples were kept at −80 °C until extraction. DNA was extracted by using a semi-automated protocol including manual chemical cell lysis before automated steps using the QIAamp DNA Mini Protocol: DNA Purification from Blood or Body Fluids (Spin Protocol, starting from step 6, at the BioRap unit, Faculty of Medicine, Technion). The manual protocol began with thawing the samples, then the storage buffer was removed using a syringe and 170 µl lysis buffer added to the filters. Thirty microlitres of Lysozyme (20 mg ml−1) were added to the filters and incubated at 37 °C for 30 min. After incubation, 20 µl proteinase K and 200 µl buffer AL (from the Qiagen kit) were added to the tube for 1 h at 56 °C (with agitation). The supernatant was transferred to a new tube, and DNA was extracted using the QIAcube automated system. All DNA samples were eluted in 100 μl DNA-free distilled water.ITS PCR amplificationPCR amplification of the ITS was carried out with specific primers for Prochlorococcus CS1_16S_1247F (5′-ACACTGACGACATGGTTCTACACGTACTACAATGCTACGG) and Cs2_ITS_Ar (5′-TACGGTAGCAGAGACTTGGTCTGGACCTCACCCTTATCAGGG)21,22. The first PCR was performed in triplicate in a total volume of 25 μl containing 0.5 ng of template, 12.5 μl of MyTaq Red Mix (Bioline) and 0.5 μl of 10 μM of each primer. The amplification conditions comprised steps at 95 °C for 5 min, 28/25 (16 S/ITS) cycles at 95 °C for 30 s, 50 °C for 30 s and 72 °C for 1 min followed by one step of 5 min at 72 °C. All PCR products were validated on a 1% agarose gel, and triplicates were pooled. Subsequently, a second PCR amplification was performed to prepare libraries. These were pooled and after a quality control sequenced (2 × 250 paired-end reads) using an Illumina MiSeq sequencer. Library preparation and pooling were performed at the DNA Services facility, Research Resources Center, University of Illinois at Chicago. MiSeq sequencing was performed at the W.M. Keck Center for Comparative and Functional Genomics at the University of Illinois at Urbana-Champaign.ITS sequence processingPaired-end reads were analysed using the Dada2 pipeline46. The quality of the sequences per sample was examined using the Dada2 ‘plotQualityProfile’ command. Quality filtering was performed using the Dada2 ‘filterAndTrim’ command with parameters for quality filtering truncLen=c(290,260), maxN=0, maxEE=c(2,2), truncQ=2, rm.phix=TRUE, trimLeft=c(20,20). Following error estimation and dereplication, the Dada2 algorithm was used to correct sequences. Merging of the forward and reverse reads was done with minimum overlap of 4 bp. Detection and removal of suspected chimaeras was done with command ‘removeBimeraDenovo’. In total, 388,417 sequences in 484 amplicon sequence variants were counted. The amplicon sequence variants were aligned in MEGA6 (ref. 47), and the first ~295 nucleotides, corresponding to the 16S gene, were trimmed. The ITS sequences were then classified using BLASTn against a custom database of ITS sequences from cultured Prochlorococcus and Synechococcus strains as well as from uncultured HL and LL clades.Individual-based modelPlanktonIndividuals.jl (v0.1.9) was used to run the individual-based simulations48. Briefly, the cells fix inorganic carbon through photosynthesis and nitrogen, phosphorus and DOC from the water column into intracellular quotas and grow until division or grazing. Cell division is modelled as a probabilistic function of cell size. Grazing is represented by a quadratic probabilistic function of cell population. Cells consume nutrient resources, which are represented as Eulerian, density-based tracers. A full documentation of state variables and model equations are available online at https://juliaocean.github.io/PlanktonIndividuals.jl/dev/. Equations related to mixotrophy are shown below as an addition to the online documentation.$$V_{{mathrm{DOC}}} = V_{{mathrm{DOC}}}^{{mathrm{max}}} cdot {{mathrm{max}}}left( {0.0,{{mathrm{min}}}left( {1.0,,frac{{q_{mathrm{C}}^{{mathrm{max}}} – q_{mathrm{C}}}}{{q_{mathrm{C}}^{{mathrm{max}}} – q_{mathrm{C}}^{{mathrm{min}}}}}} right)} right) cdot frac{{{mathrm{DOC}}}}{{{mathrm{DOC}} + K_{{mathrm{DOC}}}^{{mathrm{sat}}}}}$$
(1)
$$f_{{mathrm{PS}}} = frac{{P_{mathrm{S}}}}{{P_{mathrm{S}} + V_{{mathrm{DOC}}}}}$$
(2)
$$V_{{mathrm{DOC}}} = 0,,{mathrm{if}},f_{{mathrm{PS}}} < f_{{mathrm{PS}}}^{{mathrm{min}}}$$ (3) where VDOC is the cell-specific DOC uptake rate (mol C cell−1 s−1), (V_{{mathrm{DOC}}}^{{mathrm{max}}}) is the maximum cell-specific DOC uptake rate (mol C cell−1 s−1), (q_{mathrm{C}}^{{mathrm{max}}}) is the maximum cell carbon quota (mol C cell−1), (q_{mathrm{C}}^{{mathrm{min}}}) is the minimum cell carbon quota (mol C cell−1). The maximum and minimum functions here is used to keep qC between (q_{mathrm{C}}^{{mathrm{min}}}) and (q_{mathrm{C}}^{{mathrm{max}}}). (K_{{mathrm{DOC}}}^{{mathrm{sat}}}) is the half-saturation constant for DOC uptake (mol C m−3). fPS is the fraction of fixed C originating from photosynthesis (PS, mol C cell−1 s−1). DOC uptake stops when fPS is smaller than (f_{{mathrm{PS}}}^{{mathrm{min}}})(minimum fraction of fixed C originating form photosynthesis, 1% by default) according to laboratory studies of Prochlorococcus that showed that they cannot survive long exposure to darkness (beyond several days) even when supplied with organic carbon sources13. (1 − fPS) is also shown in Fig. 3 as the contribution of DOC uptake.We set up two separate simulations; each of them has a population of either an obligate photo-autotroph or a mixotroph that also consumes DOC. The initial conditions and parameters (Supplementary Table 3) are the same for the two simulations except the ability of mixotrophy. The simulations were run with a timestep of 1 min for 360 simulated days to achieve a steady state. We run the two simulations for multiple times in order to get the range of the stochastic processes.Evaluation of autotrophic growth ratesWe evaluated the carbon-specific, daily-averaged carbon fixation rate, ℙ as a function of light intensity (I, µE), following Platt et al.33:$${Bbb P} = frac{1}{{Delta t}}{int}_0^{Delta t} {frac{{q_{{mathrm{Chl}}}}}{{q_{mathrm{C}}}}} P_{mathrm{S}}^{{mathrm{Chl}}}left( {1 - e^{ - alpha _{{mathrm{Chl}}}I/P_{mathrm{S}}^{{mathrm{Chl}}}}} right)e^{ - beta _{{mathrm{Chl}}}I/P_{mathrm{S}}^{{mathrm{Chl}}}}Delta t$$ (4) Here, (P_{mathrm{S}}^{{mathrm{Chl}}}), αChl and βChl are empirically determined coefficients representing the chlorophyll-a-specific carbon fixation rate (mol C (mol Chl)−1 s−1), the initial slope of the photosynthesis–light relationship and photo-inhibition effects at high photon fluxes, respectively. We impose empirically determined values for (P_{mathrm{S}}^{{mathrm{Chl}}}), αChl and βChl from the published study of Moore and Chisholm24. The natural Prochlorococcus community comprises HL and LL ecotypes, which have different values of (P_{mathrm{S}}^{{mathrm{Chl}}}), αChl and βChl, and the community growth rate is expected to be between that of HL extremes and LL extremes. Therefore, we use photo-physiological parameters for an HL-adapted ecotype (MIT9215), acclimated at 70 µmol photons m−2 s−1 and an LL-adapted ecotype (MIT9211), acclimated 9 µmol photons m−2 s−1. The models with these values are shown as the different lines in Fig. 2b,d. I is the hourly PAR, estimated by scaling the observed noon value at each depth with a diurnal variation evaluated from astronomical formulae based on geographic location and time of year37,38.(frac{{q_{{mathrm{Chl}}}}}{{q_{mathrm{C}}}}) is the molar chlorophyll-a to carbon ratio, which is modelled as a function of growth rate and light intensity using the Inomura34 model (equation 17 therein) where parameters were calibrated with laboratory data from Healey49. In addition, the maximum growth rate ((mu _{{mathrm{max}}}^I)) based on macromolecular allocation is also estimated using the Inomura model (equation 30 therein). An initial guess of the growth rate and the empirically informed light intensity are used to estimate (frac{{q_{{mathrm{Chl}}}}}{{q_{mathrm{C}}}}), which is then used to evaluate the light-limited, photoautotrophic growth rate$${Bbb V}_{mathrm{C}}^{{mathrm{auto}}} = min left( {{Bbb P} - K_{mathrm{R}},mu _{{mathrm{max}}}^I} right)$$ (5) from which the (frac{{q_{{mathrm{Chl}}}}}{{q_{mathrm{C}}}}) is again updated. The light-limited growth rate is used to re-evaluate the (frac{{q_{{mathrm{Chl}}}}}{{q_{mathrm{C}}}}). Repeating this sequence until the values converge, ({Bbb V}_{mathrm{C}}^{{mathrm{auto}}}) and (frac{{q_{{mathrm{Chl}}}}}{{q_{mathrm{C}}}}) are solved iteratively.The nitrogen-specific uptake rate of fixed nitrogen (day−1) is modelled as$${Bbb V}_{{{mathrm{N}}}} = {Bbb V}_{mathrm{N}}^{{mathrm{max}}}frac{1}{{Q_{mathrm{N}}}}frac{N}{{N + K_{{{mathrm{N}}}}}}$$ (6) where values of the maximum uptake rate, ({Bbb V}_{mathrm{N}}^{{mathrm{max}}}), and half-saturation, KN, are determined from empirical allometric scalings35, along with a nitrogen cell quota QN from Bertilsson et al.39.The P-limited growth rate, or the phosphorus-specific uptake rate of phosphate (day−1), is modelled as$${Bbb V}_{mathrm{P}} = {Bbb V}_{mathrm{P}}^{{mathrm{max}}}frac{1}{{Q_{mathrm{P}}}}frac{{{mathrm{PO}_{4}}^{3 - }}}{{{mathrm{PO}_{4}}^{3 - } + K_{mathrm{P}}}}$$ (7) where values of the maximum uptake rate, ({Bbb V}_{mathrm{P}}^{{mathrm{max}}}). and half-saturation, KP, are determined from empirical allometric scalings35, along with a nitrogen cell quota QP from Bertilsson et al.39.Iron uptake is modelled as a linear function of cell surface area (SA), with rate constant ((k_{{mathrm{Fe}}}^{{mathrm{SA}}})) following Lis et al.36.$${Bbb V}_{{mathrm{Fe}}} = k_{{mathrm{Fe}}}^{{mathrm{SA}}} cdot {mathrm{SA}}frac{1}{{Q_{{mathrm{Fe}}}}}{mathrm{Fe}}$$ (8) The potential light-, nitrogen-, phosphorus- and iron-limited growth rates (({Bbb V}_{mathrm{C}},{Bbb V}_{mathrm{N}},{Bbb V}_{mathrm{P}},{Bbb V}_{{mathrm{Fe}}})) were evaluated at each depth in the water column and the minimum is the local modelled photo-autotrophic growth rate estimate, assuming no mixotrophy (Fig. 2b,d, blue lines). Parameters used in this evaluation are listed in Supplementary Table 2.An important premise of this study is that heterotrophy is providing for the shortfall in carbon under very low light conditions, but not nitrogen. It is known that Prochlorococcus can assimilate amino acids9 and therefore the stoichiometry of the heterotrophic contribution might alter the interpretations. However, it is also known that Prochlorococcus can exude amino acids40, which might cancel out the effects on the stoichiometry of Prochlorococcus.For the estimates of phototrophic growth rate from local environmental conditions (Fig. 2) we employed photo-physiological parameters from laboratory cultures of Prochlorococcus24. For the purposes of this study, we have assumed that the photosynthetic rates predicted are net primary production, which means that autotrophic respiration has been accounted for in the measurement. However, the incubations in that study were of relatively short timescale (45 min), which might suggest they are perhaps more representative of gross primary production. If this is the case, our estimates of photo-autotrophic would be even lower after accounting for autotrophic respiration, and thus would demand a higher contribution from heterotrophic carbon uptake. In this regard, our estimates might be considered a lower bound for organic carbon assimilation.Reporting summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More

The evolutionary origins of zebra stripes have been investigated—and debated—for centuries. The trait is rare, conspicuous, and intensely expressed, and thus appears to beg an adaptationist explanation. However, the utility of a complete coat of densely packed, starkly contrasting black-and-white stripes is not immediately apparent. Unlike many conspicuous visual traits, striped pelage is expressed with comparable intensity in both sexes and is thus unlikely to have arisen through sexual selection alone (although in plains zebras, Equus quagga, males have stripes closer to true black than females). Stripes are clearly not aposematic warning signals, nor do they provide camouflage in either the woodland or savannah habitats common across zebra ranges1,2. So, striping presents an ideal evolutionary puzzle: a trait so refined it seems it must be “for” something, but one that confers no clear advantage upon its bearers and imposes apparent costs (conspicuousness) that cannot be explained in Zahavian terms.Scientists have proposed and investigated several possible explanations for the evolution of zebra stripes (reviewed in3). The hypotheses suggest various ways in which stripes may provide a social function (species or individual recognition or social cohesion1,4), a temperature-regulation benefit5,6, an anti-predator effect7,8, or an anti-parasite effect9,10. There is continued debate over both the merits of individual hypotheses and the likelihood of stripes having arisen via a single driver vs. a confluence or alternation of multiple selective pressures6,11.The present study addresses the hypothesis that has thus far received the most empirical support: the anti-parasite hypothesis (also known as the ectoparasite hypothesis12). Zebras, like most ungulates, are harassed by tabanid, glossinid and Stomoxys species of biting flies, which can inflict significant blood loss, transmit disease, and weaken hosts when fly-avoidance behaviors reduce the host’s feeding rate9,13,14. Yet zebras are attacked far less than sympatric ungulates across their African range15,16, and also less than other equids9,17. Zebras also produce odors that may augment their anti-fly defenses18, but so do other sympatric ungulate species18,19, and a host of observations and experiments have demonstrated that black-and-white stripes alone are unattractive, or actively repellent to tabanid, glossinid, and Stomoxys flies17,20,21,22,23.Though the effect of stripes on flies is well-established, the source of the effect remains unexplained. Since Waage’s foundational studies in the 1970s and 1980s9,24 most hypotheses have suggested ways that stripes might interfere with the visual and navigational systems of flies, making it harder for them to locate, identify, or successfully land on striped targets. These hypothetical mechanisms can be roughly grouped by the distance (and the attendant phase of a fly’s orientation and landing behavior) at which they would likely operate:

From afar: stripes might make it harder for flies to locate and distinguish zebras from background vegetation, perhaps by breaking up their outline9 or varying the way they polarize or reflect light17,31 especially from distances at which composite eyes support only low-resolution vision and cannot resolve zebra stripes as clear bands of alternating color on a single host (estimated at  > 2.0 m22,  > 4.4 m24, and even  > 20 m25).

At close range (estimates range from 0.5 to 4.0 m26): stripes might interfere with orientation or landing behavior via any of several disruptive or ‘dazzle’-related visual effects27. For example, stripes might affect ‘optic flow’, or the fly’s perceived relative motion to its target as it approaches, by creating an illusion of false direction or speed of motion (e.g., via variants of the ‘barber pole’ or ‘wagon wheel’ effects28). Alternatively, relative motion to a striped pattern within the visual field may create the perception of self-rotation, inducing the fly’s involuntary ‘optomotor response’ and resulting in an avoidance turn in an effort to stay on a straight course29.

Finally, stripes might cause confusion in the transition between long- and short-distance orientation. If zebras appear as blurred gray from a distance and then, at closer range, suddenly resolve into a sequence of floating black and white bars, this abrupt ‘visual transformation’26 might disrupt the behavioral sequence that facilitates landing.

Within these categories, hypotheses have proliferated faster than experimental tests of many of the proposed mechanisms. The very active literature on this question has grown in somewhat haphazard fashion, as curious researchers test new possibilities without eliminating old ones6. Importantly, few experiments have controlled the distance from which flies are first able to view potential landing sites (but see23). While growing evidence supports a mechanism operating at close range22,26, failing to restrict the starting distance of the fly means that the full set of possible mechanisms outlined above all remain plausible contributors to most previous results.Additionally, while many studies have, appropriately, used artificial stimuli to isolate basic effects of color, pattern, brightness, and light polarization of (usually flat) test surfaces, possible contributions of several aspects of natural zebra pelage remain untested. Controlled experiments have used various landing substrates, including striped and solid oil tray traps, sticky plastic, smooth plastic17, cloth (Experiment 2 in22), horse blankets or sheets26, and paint on live animals30. These have all clearly demonstrated a broadly replicable visual effect: stripes, and some other juxtapositions of black and white (e.g., checkerboard patterns26), repel flies. However, insofar as specific features of zebra pelage factor into proposed mechanisms of fly repellence—the reflective properties of “smooth, shiny” coats31; the orientation of the stripes17,32; the light-polarizing effects of black and white hair vs. background vegetation25; and the complex structure of hair25—there is a need for more experiments that present natural targets to wild flies (but see22,33). Similarly, most experiments have compared landing preferences between black-and-white striped, solid black, solid white, and occasionally solid grey substrates, which have served as important controls for determining that light polarization, rather than a combination of polarization and brightness, is sufficient to induce the effect of stripe avoidance17. However, it is now time to refocus on the original question by presenting flies with more realistic choices. Since biting flies seeking a bloodmeal on the African savannah seldom encounter solid black hosts, and even more rarely solid white hosts, landing choices should be compared between zebra stripes and common coat colors of sympatric mammals, namely various shades of brown. Further, tabanid, glossinid, and Stomoxys flies all avoid landing on stripes that are the same width or narrower than the widest zebra stripes 17,23, and there is some evidence that narrower stripes are even more repellent to tabanids17. This pattern is potentially significant in the application of the anti-parasite hypothesis to an adaptive explanation for the striking variation in stripe width across zebra species and between the different areas of the body on individual zebras22, but must first be confirmed with experiments using real zebra pelage.Here, we present a simple experiment designed to address each of these gaps in the literature on the anti-fly benefits of zebra stripes. In this field experiment, the landing choices of flies were tested entirely within the range at which all estimates agree flies should be able to perceive the presented stripes ( More