Philippa Kaur

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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

Our results show that GoM BFT larval survey samples can provide the crucial mark events for eventual CKMR estimates of adult abundance. The adult parents marked by larval samples can be directly recaptured in the fishery many years later as POPs, and indirectly through their progeny in future samples of larvae, as evidenced by the two cross-cohort HSPs (XHSPs) recovered in this study, which imply that a parent survived and spawned in the GoM in consecutive years. As more cohorts are sampled in future, the growing number of XHSPs could be used to estimate average adult survival rates, in addition to helping with the estimation of adult abundance31, as is now done for southern blue tuna40.There is a modest level of sibship within our 2016 samples, and a high level (involving over half the samples) in 2017, but it turns out not to be high enough to cause serious problems for POP-based CKMR. High sibship per se does not lead to bias in CKMR by virtue of the statistical construction of the estimate, but it does increase variance, which can be summarized through a reduction in effective sample size. In a POP-based CKMR model, our effective sample size would be about 75% of nominal for the two years combined, or 66% of nominal for the targeted sampling of 2017. Since it is actually the product of adult and juvenile sample sizes which drives precision in CKMR14, one way to think about the 75% is that we will need about 33% more adult samples to achieve a given precision on abundance estimates than if we had somehow been able to collect the same number of “independent” juvenile samples (i.e. without oversampling siblings). That increase is appreciable but entirely achievable; for WBFT, it is logistically much easier to collect more feeding-ground adult samples than to collect more larvae, and at present there is no known practical way to collect large numbers of older, more dispersed, and thus more independent, juvenile western origin bluefin tuna (WBFT).This study was motivated by the concern that sibship might be a serious impediment to use of WBFT larvae for CKMR. High levels of sibship have been found in larval collections for other taxa despite a pelagic larval phase, suggesting that abiotic factors can impede random mixing of larvae after a spawning event41. Our larval samples were only a few days old (4–11) and thus had little time to disperse since fertilization; our concern beforehand was that each tow might sample the offspring of a very small number of adults (one spawning group in one night), and in 2017 that repeatedly towing the same water mass might simply be resampling the same “family”. In practice, though, the cumulative effect was limited. Samples were not dominated by progeny from just a few adults; the maximum DPG size (i.e., number of offspring from any one adult) was 5, which is under 2% of the larval sample size. There are several possible reasons for this finding. First, plankton sample tows are typically standardized to a ten-minute duration, covering on average about 0.3 nautical miles. Based on continuous plankton cameras42, each tow is likely to tow through multiple patches of zooplankton, and therefore potentially multiple patches of BFT larvae. Second, spawning aggregations of BFT may contain many adults. For example, on the spawning grounds near the Balearic Islands in the Mediterranean, purse seine fisheries target spawning fish and individual net sets routinely capture upwards of 500 mature individuals43. These numbers suggest that BFT spawner aggregations can be quite large, although the number of individuals that contribute gametes to a single spawning event may be lower. The results of this study pose intriguing scenarios for understanding BFT larval ecology and spawning behavior, which could be explored with larger sample sizes paired with data on oceanographic conditions, direct observation of spawning aggregations, and modeling to compare observed and predicted dispersal. The results of this study are based on just two years of sampling, and numerous practical and theoretical challenges remain to fully understand BFT reproduction in the GoM.Our sibship impact calculations assume use of an unmodified adult-size-based CKMR POP model, where each juvenile is compared to each adult taking into account the latter’s size (e.g.,14). That will give unbiased estimates, which we regard as essential in a CKMR model. However, for WBFT the estimates are not fully statistically efficient, in that some adults receive more statistical weight than others because they are marked more often (by having a large DPG), and thus variance might not be the lowest achievable. Modifying the model to fix that would be simple in a “cartoon” CKMR setting where all adults are identical (e.g., Fig. 1 of14), simply by first condensing each DPG to a single representative, then only using those representatives (rather than all the larvae) in POP comparisons. Each marked parent then receives the same weight, giving maximum efficiency. For the cartoon, this condensed-DPG model still gives an unbiased estimate of abundance, because each DPG has one parent of given sex, and the chance of any sampled cartoon adult of that sex being that parent is 1/N. The DPG-condensed effective sample size is simply half the number of distinct parents, which would be a little larger than the effective sample sizes for the unmodified model shown in Table 3; e.g., in 2017, 504/2 = 252 versus 209. However, no such straightforward improvement is available for an adult-size-based CKMR model such as is needed for WABFT. Using condensed DPGs directly would bias the juvenile sampling against larger more-fecund adults, whose DPGs will tend on average to be larger and thus to experience disproportionate condensation. Those adults would be marked less often by the DPG-condensed juveniles than the model assumes, violating the basic requirements for unbiased CKMR in14. A more sophisticated model might be able to combine unbiasedness with higher efficiency but, since the unmodified adult-size-based POP model that we expect to use is unbiased and only mildly inefficient (at worst 209/252 = 83% efficient, in 2017) there seems no particular need for extra complications at present. However, that may not hold true if we eventually move to a POP + XHSP model, where the impact on unmodified CKMR variance is worse (though there is still no bias, for the same reason as with POPs). Intuitively, the biggest impact that a DPG of size 5 can have in a POP model is to suddenly raise the number of POPs by 5 if its parent happens to be sampled; within a useful total of, say, 75 POPs, the influence is not that large. But if two DPGs both of size 5 in different cohorts happen to share a parent, then the total of XHSPs suddenly jumps by 25— likely a substantial proportion of total XHSPs. Supplementary Material B also includes effective sample size formulae for a simplified XHSP-only model, which demonstrate the increased impact of within-cohort sibship; for our WBFT samples, it turns out that the XHSP-effective size is slightly lower for the targeted 2017 samples (110) than for the 2016 samples (130), unlike the POP-only effective size. Dropping from a maximum theoretical effective sample size of 252 (half the number of DPGs) down to 110 would be rather inefficient and would increase the number of years of sampling required to yield a useful XHSP dataset. This motivates developing a modified POP + XHSP model that retains unbiasedness without sacrificing too much efficiency. In principle, that can be done by condensing each DPG but then conditioning its comparison probabilities on the DPG’s original size, in accordance with the framework in14. This is a topic for subsequent research, and the results will inform future sampling strategy decisions for WBFT.One potential difficulty for western BFT CKMR might occur if a substantial proportion of animals reaching maturity are the offspring of “Western” (in genetic terms) adults who persistently spawn in the western North Atlantic but outside the GoM. However, as long as the adults marked by GoM larvae are well mixed at the time of sampling with any western adults that do spawn outside of the GoM, the total POP-based population estimate of genetically-western BFT from CKMR will remain unbiased. Given evidence from tagging of widespread adult movements within the western North Atlantic2, good mixing in the sampled feeding grounds seems likely; so, even if successful non-GoM western BFT spawning really is commonplace, there should not be a problem with relying on GoM larvae for at least the POP component of CKMR14.Studies of fish early life history have long been considered to have great potential to provide novel insight into the unique population dynamics of fishes44,45,46. Sampling efforts aimed at estimating fish recruitment dynamics have spawned a diversity of larval survey programs. Examples of these long-term programs include the California Cooperative Oceanic Fisheries Investigations, International Council for the Exploration of the Sea (ICES) surveys in the North Atlantic and adjacent areas, Southeast Monitoring and Assessment Program (SEAMAP) in the GoM, Ecosystem Monitoring (EcoMon) in the Northeast U.S., and numerous others, many of which provide indices of larval abundance widely used in fisheries and ecosystem assessments. Yet, as a result of the inherent patchiness of larvae42, sampling variability, and highly variable density dependent mortality45, fisheries scientists have often struggled to determine how larval surveys relate to the adult fish populations. Inclusion of estimates of sibship among larvae collected in surveys could refine estimates of adult spawning stock biomass estimated from these surveys.The results of this study also represent products of decades of work and coordination in obtaining high-quality DNA from larval specimens. Key steps to successful genotyping of larvae include ensuring that larvae are preserved, sorted, and handled in 95% non-denatured ethanol. In addition, strict instrument cleaning protocols must be followed, and stomachs should be removed or avoided (this study used larval tails and, when possible, eyes to avoid cross contamination of prey contents, including possible congeners and other BFT individuals). Exposure to hot lamps during the sorting and dissection processes should also be minimized to ensure that DNA quality is sufficiently high for genotyping-by-sequencing. Although the tissues available for genetic analysis were limited by the needs of other experiments that required BFT tissues, otoliths, gut contents, and other information from the same larvae, we were able to successfully genotype most larvae greater than 6 mm SL and identify thousands of informative SNPs. 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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

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