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Settlement stage fishesSpecimen collectionData for settlement stage tropical larval fishes includes 1372 swimming speed measurements, collected from >75 unique taxa across 35 families of fishes, most of which are coral reef associated as adults. The data are collected from five locations, including: South Caicos Island (Turks and Caicos Islands, Caribbean – TCI), Green Island or Magnetic Island (exact location not recorded for individual samples, Great Barrier Reef, Australia GI/MI), Lizard Island (Great Barrier Reef, Australia – LI), Calabash Caye (Turneffe Islands Atoll, Belize – BLZ), and Moorea, Society Islands (MOR) (Table 1).Table 1 Sampling locations for settlement stage Ucrit data. Included are the Region, year of collection, location and associated name, as well as the total number of recorded measurements (count).Full size tableData from LI and TCI were obtained almost exclusively from specimens collected using light traps, placed 100–500 m meters off the leeward side of the Island, near either the School for Field Studies facilities (TCI) or the Lizard Island Research Station (LI). An additional eight specimens of newly hatched Acanthochromis polyacanthus, a pomacentrid species which does not have a pelagic phase, were captured with nets on the Lizard Island reefs. Data from GI/MI were obtained using a combination of light traps, beach seines, fence and dip nets.For data collected in Moorea (Mor), specimens arriving over night from the open ocean and attempting to settle on the reef were captured in nets placed on the reef crest. In Belize (BLZ) specimens were collected using a variety of techniques including crest nets, channel nets, light traps and night-light lift nets, although most individuals were collected using light traps and crest nets. Crest net locations were those reported in29. Unless stated otherwise in the “notes” field of the “ucrit_sett_dat” data table (see Online-only Table 1), all U-crit measurements on individuals captured by light traps or crest nets were made on the morning of capture, usually within 6 or 12 hours (please refer to the original publications for methodological details). In a few cases, some individuals were kept in the laboratory for up to 2 days to study changes in swimming speed associated with settlement (see24,30), and here the post-settlement status of the larvae was recorded in the field “stage” in the “fish_id_dat” data table (see Online-only Table 1). Some specimens of the pomacentrid, Abudefduf saxatilis were collected with hand nets from a fish attracting device deployed over a seagrass bed from a dock and are best considered as early post-settlement individuals, although the time since settlement is unknown. All specimens of the labrid, Clepticus parrae were collected with hand-nets from deep fore-reefs. Although they had settled to the fore-reef an unknown period of time before capture, these individuals had yet to undergo complete metamorphosis. Data from such post-settlement individuals should be used with caution, as it is known that swimming performance in some species decreases markedly upon settlement11,24.Most data were collected during the summer months (May through September for TCI and BLZ, November through February for LI), but in MOR, the data came from winter (August). In Belize, data were collected in 2003, 2004 and 2005, totalling 401 U-crit measurements. Data from TCI were collected in 2003, from 109 individuals. Data from LI represented just over half of the settlement stage swimming data (556 measurements), and were collected in 2001, 2002, 2003, 2004 and 2005. A total of 144 measurement were available from GI/MI and were collected in 1992. The 152 U-crit measurements from MOR were from 2010.Captured settlement stage larvae/pelagic juveniles were held in fresh seawater for a minimum of 1–2 hours to reduce stress prior to swimming trials, either with an aeration stone in 24 L buckets (BLZ), or in flow-through seawater aquarium facilities at the Lizard Island Research Station (LI) and the Department of Environment and Coastal Resources at South Caicos (TCI).U-crit protocolAll swimming experiments were conducted at ambient seawater temperatures, which ranged between 25 °C and 30 °C, depending on location and date.Settlement-stage individuals were swum using one of several swimming flumes, including a single-lane swimming chamber11,22, a six-lane swimming chamber12 (see Fig. 1), or a three-lane swimming chamber modified from the design of12. All swimming chambers were constructed from transparent Plexiglass (internal dimensions of swimming area: 185 mm × 50 mm × 50 mm). A removable lid, sealed with an O-ring was used to introduce fish to, and remove them from the chambers. One section of flow straighteners, 45-mm long, was placed just after the inflow in order to reduce turbulence within the chamber. Fish were retained within the swimming area by two 4.0 mm mesh metal retaining fences, which were covered with a finer mesh when required for very small larvae.Fig. 1Design of the swimming channel used for settlement stage larvae, pelagic juveniles and settled juveniles. Shown are Side view (a) & Top view (b, modified from12). This swimming channel can be operated at up to 50 cm s−1. Smaller designs with three channels, or only 1 channel that could obtain higher speeds were used for swimming faster individuals. For data collected by Leis and colleagues, higher speeds were obtained by blocking some lanes using Perspex.Full size imageFlow was generated using a 2.4 Kw swimming pool pump (although the size of the pump varied across the studies), or plumbed into a laboratory seawater system. The speed was set using a protractor mounted on a gate valve and calibrated using the procedures described under the technical validation section below. Faster speeds were also calibrated using an inline blue-white F-300 series flow meter. Flumes were plumbed using union valves so they could be dismantled and easily relocated and installed in field locations. Because the pumps used to run the flumes can heat the water temperature over time, they were plumbed with a minimum reservoir volume of 70 L, with a constant flow through of fresh seawater. A mercury thermometer located in the reservoir was used to ensure temperature remained ambient during the swimming trials. Example field deployments of the swimming channels at various locations can be seen in Fig. 2.Fig. 2Examples of the ‘fast’ swimming flume setup at various field locations. Shown are the Lizard Island Research Station (Great Barrier Reef, Australia, a), the Department of Environment and Coastal Resources aquarium facilities at South Caicos (Turks and Caicos Islands, b), and the dock at the University of Belize Institute of Marine Field Studies at Calabash Caye (Belize, c).Full size imageU-crit was measured by placing specimens in the swimming flume and incrementally increasing water speed until the individual could no longer maintain position for the full-time increment interval. The exact experimental protocols differed slightly among the studies. For fish measured at Lizard Island in November 2000–January 2001, November–December 2001 and South Caicos Island, and most fish at Calabash Caye, the experimental protocol followed7, with speed increments equivalent to approximately three total standard body lengths per second (bls−1) with a time interval of 2 min. This protocol was adopted because settlement stage larvae can vary substantially in size and subsequently their swimming capacity, as swimming speeds are strongly controlled by body size4. Aligning the speed increments with the approximate size category of fishes ensured that the overall duration of the U-crit experiment was relatively similar. For fish measured at Lizard Island during December 2003, speed increments used were 1.6 cm s−1 with a time interval of 5 min. At Lizard Island in 2005, specimens of Amblyglyphidon curacao were subjected to speed increments of 4.2 cm s−1 at intervals of 5 minutes. In Moorea in 2010, all individuals were subjected to speed increments of 6.1 cm s−1 at intervals of 2 minutes. For fish measured at Green Island and Magnetic Island speed increments used were 5 cm s−1 with a time interval of 5 min. At Calabash Caye an experiment was conducted to examine the impact of time increments on U-crit measurements, and the experimental protocol was recorded in this instance.U-crit swimming speed was calculated following17:$$U mbox{-} crit=U+left(t/ti,ast ,Uiright)$$
(1)
Where:U = penultimate speed (speed increment for which the fish swam for the entire duration of the set time interval). Ui = the velocity increment (varied by the specific study).t = the time swum in the final velocity incrementti = the set time interval for each velocity increment (varied by the specific study).While the speed increments used varied across studies in this collated dataset, previous studies have found no effect of varying the length of the time interval (ti) in terms of the resulting swimming speed between fish swum at two minute intervals and those swum at 15 minute intervals for six reef fish species10.Sample handling and morphological measurementsAfter each trial specimens were anaesthetised in chilled water or using clove oil (depending on the location and according to the relevant ethics approvals) and some were photographed while still fresh to maintain body flexibility and to avoid issues with shrinkage due to dehydration associated with preserved samples. Following photographing, the samples were preserved in either 70% ethanol, 95% ethanol, or 10% buffered formalin.From digital images the ImageTool (UTHSCSA 2002) software was used for image analysis. Measurements made from digital images (where available) are shown in Fig. 3, and included: total length (from the outer edge of the caudal fin to the tip of the upper jaw), caudal fin length (from the tip of the caudal fin to the caudal peduncle), body depth (the vertical height of the fish measured at the deepest region), body area (the area of the fish in lateral view excluding the fins but including the head and gut region), propulsive area (the area of the fish including the fins but excluding the head and gut region), muscle area (the area of the fish excluding the fins and the head and gut region), caudal fin depth, caudal peduncle depth and caudal fin area. All measurements were taken to the nearest 0.1 mm. Body width (at the widest region, usually the head) was also measured to the nearest 0.1 mm using vernier callipers. In some cases total lengths (TL) were measured pre-trial using callipers (BLZ, 2003 and 2004). Body length (BL, which is equivalent to SL for postflexion stages) was measured using an ocular micrometer on a dissecting microscope in some studies23.Fig. 3Morphological measurements of settlement stage fishes. Measurements include: total length (TL; outer edge of the caudal fin to the tip of the upper jaw), caudal fin length (CFL; tip of the caudal fin to the caudal peduncle), body depth (BD; height at the deepest region), body area (BA; area in lateral view excluding the fins), propulsive area (PA; area including the fins (naturally fully extended) but excluding the head and gut region where they are inflexible or lack overlaying muscle and cannot be used for propulsion), muscle area (MA; area excluding the fins and the head and gut region), caudal fin depth (CFD; widest section when fully extended), caudal peduncle depth (CPD; height at the narrowest point between the caudal fin and the fish’s body) and caudal fin area (CFA; area with the caudal fins naturally fully extended). Callipers were used to measure head width. Adapted from8.Full size imageLarval development dataset (Australia)Rearing protocolData gathered using a combination of the ‘fast’ and ‘slow’ swimming chambers (see below) on swimming abilities throughout development are available for six species, including two damselfish – Pomacentrus amboinensis and Pomacentrus mollucensis (Pomacentridae; Pomacentrinae); two cardinalfish – Ostorhinchus (Apogon) compressus and Sphaeramia nematoptera (Apogonidae); and two anemone fish – Amphiprion percula and Amphiprion melanopus (Pomacentridae; Amphiprioninae). Note that the pomacentrids have demersal eggs, whereas the apogonids orally brood their eggs.Australian specimens for assessing swimming speeds throughout larval development were obtained mostly from larvae reared at the James Cook University Aquarium facility, from adult broodstock collected from the northern Great Barrier Reef. Adult brood stock were kept in outside aquaria ranging in size from 1000 to 3000 L. The temperature of aquaria was kept between 27 and 29.5 °C, with larvae reared in the Autumn and Winter of 1998. Brood stock were fed a diet of chopped pilchards, prawns and Ascetes twice per day. Eggs were obtained from spawning broodstock before dark on the night of hatching and transferred to a rearing tank. Once hatched, larvae were reared and maintained in 200 L (120 × 60 × 30 cm) black painted glass aquaria that were illuminated by four “daylight” fluorescent tubes. The larvae were maintained in a 14:10 light/dark photo-period at 27.5–29 °C. Cultures of the algae Nannochloropsis sp. were used to green the water during the day. This kept light at the right intensity to prevent “bashing” behaviour (young larvae have a tendency to continually butt their heads against surfaces if the water is clear and the light intensity is too bright). Larvae were fed a diet of >52 micron sieved wild caught plankton, which was occasionally supplemented by rotifers and Artemia spp. when necessary. Larvae were fed twice per day to maintain prey densities of between 2–6 individuals per ml. Examples of ontogenetic series obtained through these rearing methods, and showing pre- and post- flexions stages are show in Fig. 4.Fig. 4Examples of larval developmental series obtained for larvae reared at the James Cook University Aquarium facility. Showin are Amphiprion melanopus (a) and Sphariamia nemaptopera (b).Full size imageU-crit protocolSwimming experiments for older [i.e., postflexion] larvae (see Fig. 4(a)ii–iv and Fig. 4(b)iv–vii) were carried out using the flumes described above for settlement stage fishes. However, these flumes were unsuitable for measurement of swimming capabilities of the delicate younger [i.e., preflexion] larvae (see Fig. 4(a)i and Fig. 4(b)ii,iii). Several characteristics had to be addressed in order to design equipment suitable for the measurement of the swimming capabilities of very young larvae. These included:

The apparatus needed to produce slow flow rates while maintaining laminar flow and minimal boundary layer effects. This is because newly hatched larvae are small enough to effectively utilise the boundary layer, which is broader for slower moving water.

The apparatus had to provide an environment suitable for very young larvae as the trauma of transferring larvae between containers can be fatal. Accordingly, stress associated with sudden changes in light intensity or water quality was minimised by “greening” the water with algae and the use of dark or clear surfaces to avoid “bashing” behaviour. In addition, the apparatus had to be set up within the immediate vicinity of the rearing tanks (or possibly in a rearing tank) to minimise the distance larvae had to be moved.

Two swimming channels were designed and used for younger larvae that were able to meet these requirements. These were designed to operate at “slow” and “medium” speeds. Both channels were able to produce laminar flow at much slower speeds. They consisted of a much wider swimming area so that most of the water flow occurred away from the sides, maximising the area of water not influenced by boundary layer effects. Both were able to be placed in a rearing aquarium of “greened” water. This prevented the larvae from exhibiting “bashing” behaviour, minimised the distance that larvae had to be transferred and meant that there was no change in water quality between the experimental apparatus and rearing tanks (Fig. 5).Fig. 5Design of swimming channels for younger larvae. Shown are side view (a) & Btop view (b). Dimensions are for the “slow” and “medium” flumes respectively.Full size imageFish were retained by a 0.3 mm mesh at the end of the swimming channel for the “slow” chamber and a 1 mm mesh for the “medium” chamber. The “slow” channel was powered by an Eheim 2,000 L per hour pump and the “medium” channel was powered by two such Eheim pumps. The speed for both channels was set using a protractor mounted on a gate valve as for the “fast” swimming chamber used for older larvae, and calibrated according to the description below under technical validation.Each clutch of eggs from each species was raised from hatching through to settlement and experiments were performed periodically throughout this larval period, with sampling days depending on the species. The first swimming trial was conducted on day 1, approximately 12 hours after hatching. Three clutches of each species were used for each swimming trial for the species Pomacentrus amboinensis, Sphaeramia nematoptera and Amphiprion melanopus to ensure that any clutch effects were considered4. While multiple broodstock were available for each species, no record was made at the time from which broodstock the replicate clutches were obtained. For other species only a single clutch was available. In some cases these data included light trap caught specimens to supplement the latest settlement stage. At each experimental age for each clutch 8–12 fish were used in the swimming trials.Larvae were subjected to incremental increases in flow rates equivalent to approximately 3 body lengths (BL) every two minutes until they could no longer maintain position, as for the experimental protocol described above for settlement stage fishes and U-crit calculated as per Eq. 1. Aligning the speed increments with the approximate size category of fishes ensured that the overall duration of the U-crit experiment was relatively similar throughout ontogeny.Sample handling and morphological measurementsFish that were swum, or siblings from the same batch at the same age, were anaesthetised in chilled water then fixed in 10% buffered formalin. After 12–48 hours, larvae were transferred to 70% alcohol and stored. Morphological measurements were carried out by capturing the image of each fish using a stereo dissecting microscope linked to a video recorder. These images were then saved as files on computer. As for settlement stage larvae, the image analysis program ImageTool was then used to measure lengths and areas for different regions of the fish.Measurements were made of total length (from the tip of the caudal fin to the tip of the upper jaw), body depth (the height of the fish measured at the deepest region), body area (the entire area of the fish excluding the fins) and total propulsive area (the area of the fish including the fins but excluding the head and gut region). The regions measured for both pre-flexion and post flexion larvae can be seen in Fig. 6.Fig. 6Measurements made on developmental series larvae. This includes post-flexion larvae which have developed a true caudal fin supported by a hypural plate and discrete soft rays) (a); and pre-flexion larvae that had no hypural plate or soft rays, but a continuous rayless fin-fold from anus to nape (b).Full size imageLarval development dataset (Taiwan and France)Data on development of swimming in larvae of ten species of pelagic-spawning tropical species of commercially important fishes reared by aquaculturists in Taiwan6,27,28 and two tropical species that brood their eggs that were reared for the aquarium trade in France are included26,28 (see Table 2). In addition, very limited, previously unpublished data on larvae of three species of pelagic spawning, commercial species reared in Taiwan are included. The emphasis in these studies was on postflexion-stage larvae, but for some species, swimming data on preflexion and flexion-stage larvae are included. The ‘standard’ six-lane swimming chamber was used for these measurements of U-crit. For larger larvae of some species, half of the lanes were closed off to achieve the faster speeds that these larvae can achieve. Despite this adjustment, some individuals were able to swim faster than the fastest speeds the swim chamber could achieve. In these cases, the speeds are reported in the database as greater than the maximum chamber speed.Table 2 Species whose U-crit swimming ontogeny were studied using reared larvae in Taiwan and France. Included are the location, family, species, the number of specimens assayed (N), the size range of the specimens, and the associated publication of the original data (where available).Full size tableIn Taiwan, larvae were obtained from commercial aquaculture farms (~22.4°N, 120.6°E) SE of Kaohsiung, southern Taiwan, in May 2004 and in May and June 2005. Rearing conditions varied with species, but most were reared in outdoor concrete or earth ponds. Exceptions were Epinephelus spp., which were reared in indoor concrete tanks, and Chanos chanos and some Eleutheronema tetradactylum, which were reared in outdoor concrete tanks under shade cloth. In most cases, the larvae were provided with a “natural” food source (phytoplankton and zooplankton that were resident in the pond). The aquaculturists did not maintain breeding stock, but obtained the pelagic eggs for rearing from elsewhere. The larvae obtained from the aquaculturists were placed in oxygenated plastic bags placed in insulated boxes and transported about 1 h by road to the National Museum of Marine Biology and Aquarium (NMMBA), Kenting, Taiwan (~22.1°N, 120.7°E). In the laboratory the larvae were acclimated in 40 l aquaria filled from the NMMBA seawater system. Each aquarium was fitted with an aerator and kept at ca. 25 °C. The larvae were fed twice daily with live, newly hatched brine shrimp (Artemia nauplii) and 50% of the total volume of water was exchanged with fresh seawater. The aquaria were cleaned daily by suctioning debris off the bottom. The species studied in Taiwan were all native to the western central Pacific, but the original brood stock may not have been obtained locally. The U-crit measurements were made in a shaded outdoor area where large tanks were located to hold adult fishes intended for either research purposes or for addition to the large public aquarium that forms part of the NMMBA campus. The extensive seawater system of NMMBA was used to supply seawater directly into the swimming chamber on a flow through basis. In some cases, this resulted in fluctuations in the calibration of the swimming chamber, which, as a result was calibrated more frequently than was normally the case. Water temperature in the chamber was recorded for each run, and all were within the range of temperatures in the nearby ocean, or in a few cases, the aquaculture ponds from which the larvae were obtained. The swimming chamber time increment interval was five minutes, with an increase in speed at each increment that varied with the flow from the seawater system and the number of lanes open in the swimming chamber, ranging from 1.6 to 5.3 cm s−1.The larvae studied at Lautan Production, a small company located in Meze, France (42.4°N, 3.6°E) in September 2010 were of two species reared for the aquarium trade. Gramma loreto is native to the western tropical Atlantic, and the brood stock came from Cuba. Pseudochromis fridmani is found only in the Red Sea, but the origin of the brood stock is otherwise unknown. Both species produce ‘egg balls’ that are laid in crevices or small caves and tended by an adult until hatching. The eggs typically hatch at night with little remaining yolk and with no fin-ray development, but with mouth open and eyes pigmented. Recently hatched larvae were removed from the spawning tank to rearing tanks with constant illumination and ‘green water’ at a temperature of 26 °C to 28 °C. Cohort date is for the morning when the larvae were removed from the spawning tank. For the first 5 days rotifers were supplied, and from 6 days after hatch (DAH), the larvae were fed with Artemia nauplii all by Lautan employees. Temperatures in the swimming chamber were similar to those in the rearing tank. Larvae of about 5 mm to settlement size (10–12 mm) were used to measure U-crit. The swimming chamber time increment interval was two minutes, with an increase in speed at each increment of 3.2 cm s−1.Larvae from Taiwan were either preserved in 75% ethanol or in some cases in Bouins Solution for future histology research. Larvae from Lautan were preserved in 75% ethanol. Measurements were made within 24–48 hours after preservation. Body length (BL) was measured on all larvae using a dissecting microscope ocular micrometer: this is Notochord Length (tip of snout to tip of notochord) for preflexion and flexion-stage larvae, and Standard Length for postflexion larvae (tip of snout to end of hypural plate). For some larvae from Taiwan additional measurements were made using Scion Image for Windows (Beta 4.02, Scion Corporation, Frederick, MD): Total Length (tip of snout to tip of posterior-most fin), Total Lateral Area (including fins) and Propulsive Area (Fig. 6), the last as defined by4 (see Fig. 6).Ethic declarationsData collated here are from a large array of studies collected across a range of institutions and locations, and to our knowledge in all cases complied with the required ethics procedures at the relevant institution at the time of data collection. Portions of this work were carried out under Australian Museum Animal Care and Ethics Approval 01/01 (JML) and James Cook Ethics Approvals A202, 402 (RF). In France, research was carried out under permits issued by CNRS to the USR 3278 CNRS/EPHE team to conduct research experiments in the field and laboratory at all locations (under the “Hygiène et Sécurité” section). In Moorea, the research was carried out under permits issued by le Délégué Régional à la recherche et à la technologie de la Polynesie française. More

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Patch formationThe individual-based simulations produce, as an immediate result, the position of all slugs at any given time t; an example is given in Fig. 2a in the case of ‘small’ field (10times 10) m. Analysing information describing the system state when it is presented in this format can be difficult. It is a particular problem when comparing it with field data where the system state is quantified by the slug trap counts (regarded as a proxy for the local slug density) at selected spatial locations, e.g. in a rectangular grid (cf. Fig. 1a). We therefore split the spatial domain into 100 bins by dividing its linear size both in x and y into 10 equal intervals and calculate the number of slugs in each bin, i.e. the population density at the location of each bin. In order to make the results more accessible for the visual perception, we then show the binned numbers as a continuous plot of the population density. As an example, Fig. 2b shows the distribution of the population density corresponding to the simulation data shown in Fig. 2a.Figure 2Example of simulation results and their visualization obtained at (t=100) for (R=1) (meters) and the total number of slugs (N=10^4) in a (10times 10) m field. The chosen threshold density is equal to the average slug density, i.e. (d=100) (slugs/m(^{-2})). Other movement parameters are given in the text, see the lines after Eqs. (1), (3) and (5). (a) Positions of all individual slugs, (b) the corresponding density distribution reconstructed from the bin counts (see details in the text) using linear interpolation.Full size imageWe readily observe that the simulated spatial distribution of slugs is apparently heterogeneous. Two questions immediately arise here as to (i) whether this heterogeneity is different from the heterogeneity of a purely statistical origin and (ii) how the density distribution evolves in time. To answer these questions, Fig. 3b,c show the simulation results after a series of increasing time periods using the same initial condition (Fig. 3a) used for Fig. 2. It is readily seen that the distribution evolves with time and the degree of heterogeneity (e.g. as described by the difference between the smallest and the largest values of the population density, inferred from the numbers on the colour bar) tends to increase over the course of time resulting in the formation of high density patches (shown by the yellow colour). Also, the size of individual patches changes, with a tendency to increase until it reaches a certain value (see the next section for details). For comparison, Fig. 3e,f show the spatial distribution obtained at the same moments of time as in Fig. 3b,c respectively, but in case of purely random density-independent movement; no high density patches emerge in that case.Figure 3The spatial distribution of (N=10^4) slugs shown at different moments of time: (a,d) (t=0), (b,e) (t=10^3), (c,f) (t=10^4). Distributions in the upper row (a–c) are obtained using the density dependent movement model (as is described in “Methods” section). Parameter values are the same as in Fig. 2. For comparison, the lower row (d–f) shows the distributions obtained in the case of density independent movement. While patches of high density (shown by yellow colour) emerge in the course of time in the case of density dependent movement, they do not emerge in the case of purely random, density independent movement.Full size imageSimulations show that the emerging high density patches are dynamic rather than stationary (even in the large-time limit, for more details, see Appendix A.2 in online Supplement Information). No stationary distribution emerges in the course of time. However, inspection of the results shown in Figs. 2b and 3b,c (as well as results obtained in other simulation runs, not shown here for the sake of brevity) reveals that the patch dynamics is rather slow, so that some of the patches roughly preserve their size and location on the timescale of (t=10^4), i.e. about 3 weeks in dimensional units, which is in a good agreement with the field data, see Section 2.Note that, since our model is inherently stochastic, the emerging spatial distribution will differ in the precise shape and position of the patches between model runs. However, the formation of a distinct patchy structure is a generic property of the system. In this sense, the patterns shown in Fig. 3b,c are typical for the system’s dynamics. Moreover, the formation of the patchy structure appears to be robust and does not depend on the initial conditions. For example, in the case where the initial condition is chosen as a dense release (i.e., all animals are initially inside a single patch), over the course of time the initial patch eventually splits into a number of smaller patches resulting, for the same parameter values as in Fig. 3, in a spatial distribution qualitatively similar to those shown in Fig. 3; see34 for all simulation details.We now recall that, while the movement parameters in Eqs. (1–5) are determined from the field data with a sufficient accuracy, the value of threshold density d where the movement type switches is only roughly estimated. Therefore, the next step is to investigate whether the formation of a patchy spatial distribution is sensitive to the threshold density. For this purpose, simulations were run with a different value of d. The results are shown in Fig. 4. We observe that the variation in d will not eliminate the heterogeneity, a distinctly patchy spatial distribution develops for all values of d used in Fig. 4. The shape and size of the patches (as is readily seen from the visual inspection of the spatial distributions) as well as the difference between the maximum and minimum values of the population density varies slightly for different d without showing a clear tendency. Patchiness appears to be robust to the value of density threshold in a broad range of d (see also Fig. 9 below), unless the average slug density is much smaller than the density threshold; in this case, slug movement is always density independent and distinct patches never form (apart from purely stochastic fluctuations of a small magnitude, cf. Fig. 3e,f).Figure 4The spatial distribution of (N=10^4) slugs at (t=10,000) simulated for different values of the threshold density: (a) (d=80), (b) (d=100) and (c) (d=120) (slugs/m(^{-2})). Other parameters are as in Fig. 2.Full size imageA similar question arises about the effect of the perception radius, which value is only roughly estimated. Figure 5 shows the results obtained for different R. We observe that a distinct patchy structure emerges for values of R over a broad range, which includes the range estimated from the field data. However, contrary to the density threshold, the degree of spatial heterogeneity clearly depends on R. The typical size of the patches tends to increase with R while the number of the patches decreases accordingly. For a sufficiently large R, a single high density patch is formed, cf. Fig. 5c. This effect of the increase in R can be explained as follows. The perception radius is, by its definition, the distance within which slugs react to each other by slowing down their movement. It is a characteristic length of the population distribution, with the meaning similar to the correlation length. Slowing down of slug movement eventually leads to their numbers building up at the scale consistent with that characteristic length. Note that the average radius of the single patch shown in Fig. 5c is about 2–3 m, and this is consistent with the used value (R=3).Figure 5The spatial distribution of (N=10^4) slugs at (t=10^4) simulated for different values of the perception radius: (a) (R=0.5), (b) (R=1) and (c) (R=3). Other parameters are as in Fig. 2.Full size imagePatchiness quantificationWe now complement the visual inspection of the patchy pattern with a more quantitative assessment. There are several measures or indices that are used in statistical ecology for this purpose35. In particular, the Morisita index36 (I_M) provides a measure of how likely two individuals randomly selected from a given spatial domain are found within the same bin (e.g., quadrat) compared to that of a random distribution. It can be shown37 that (I_M=1) if the individuals are distributed randomly (with a constant probability density) and (I_M >1) if the individuals are aggregated for reasons other than purely statistical ones. The Morisita index has been widely used to quantify the heterogeneity of the spatial distribution38,39,40. It can be calculated as follows:$$begin{aligned} I_M = frac{Q}{N(N-1)}sum _{k=1}^{Q}n_k(n_k-1), end{aligned}$$
(8)
where (n_k) is the number of individuals in the kth bin, Q is the total number of bins (quadrats) and N is the total number of individuals.Figure 6 shows the Morisita index calculated at each time step for a few cases with a different total number of slugs. Note that, since the movement of any individual slug is a stochastic process, (I_M) is a stochastic quantity. In order to make sure that any tendency in (I_M) to change is not obscured by random fluctuations (which can be of considerable amplitude), Fig. 6 shows (I_M) averaged over ten simulation runs.Figure 6The mean Morisita Index from 10 simulation runs for different number of slugs: (a) (N=2.5cdot 10^3), (b) (N=5cdot 10^3) and (c) (N=10^4). Here (R=200) and (d=10), other parameters are as in Fig. 2. The red curves show the Morisita index obtained in the corresponding cases of a purely random individual movement, i.e., without any density dependence.Full size imageIt is readily observed that, in each case shown in Fig. 6, starting from (I_M=1) at (t=0) (which corresponds to our choice of a uniform random initial distribution), the Morisita index then shows a clear tendency to increase on average (apart from the random fluctuations) until approximately (t=8000) when it stabilizes at a certain value (I_M^* >1). We therefore conclude that (i) the spatial patterns obtained in our model are self-organized, i.e. caused by interactions between the individual slugs and not by purely random, statistical effects, and (ii) in the course of time, the system reaches a dynamical equilibrium so that the Morisita index stops growing. For comparison, the red curves in Fig. 6 show the Morisita index obtained in the corresponding cases of purely random density independent movement when no high density patches are formed (cf. Fig. 3e,f).Note that the Morisita index tends to increase slightly with an increase in the average slug density (i.e., for a fixed size of the spatial domain, with an increase in the total number of slugs N). Indeed, the value (I_M^*) at which the patchiness stabilizes after a long time period rises somewhat with an increase in N, cf. Fig. 6a–c.In order to provide an overall description of the emerging heterogeneous distribution, with a focus on the density dependence of the properties of the emerging patchy pattern, we use the Taylor’s Power Law aggregation index25. It is well known41 that, for populations of many different species, the mean (m) and the variance (v) of population numbers in a sample are not independent but related by a power law:$$begin{aligned} v = alpha m^{beta }, end{aligned}$$
(9)
where (alpha) is a coefficient and exponent (beta) is called the aggregation index. In the case where a species has a uniform spatial distribution, (beta) tends towards zero; for a purely random distribution (e.g., described by Poisson distribution), (beta =1). Values (beta >1) reflect progressively greater aggregation, i.e. formation of patches in the field resulting from self-organized, density dependent dynamics of the system.By writing Eq. (9) on the logarithmic scale:$$begin{aligned} log (v)=alpha + beta log (m), end{aligned}$$
(10)
values of (alpha) and (beta) can be established by fitting (10) to relevant data; in particular, the aggregation index (beta) is defined as the slope of the regression line.Figure 7 shows the aggregation index calculated for the patchy spatial patterns obtained in simulations. Recall that, when starting with a random uniform distribution, it takes a certain time for the patchy structure to develop. Correspondingly, in each simulation, the system was allowed to evolve over a certain time (t^*) before the population was binned and the mean and the variance of the distribution were calculated. The (a) and (b) panels in Fig. 7 are obtained for (t^*=10^3) and (t^*=10^4), respectively. We readily see that in both cases (beta >1) ((beta =1.066) and (beta =1.173), respectively) confirming the self-organised, inherent nature of the spatial patterns. Note that (beta) is larger in Fig. 7b, that is for a larger (t^*), which is consistent with an earlier observation that the patchy structure becomes fully developed by (tsim 8000).Figure 7The variance of bin populations plotted against the mean bin population on a grid of 100 bins shown on a log-log scale. Each point is calculated from a single simulation and the total population is varied between simulations from (N=300) to (N=9900) in intervals of 300. The density dependent parameters are (d=1) (equal to the average slug density) and (R=2). (a) (t=1000), the regression equation (10) is (log (v)=1.066log (m)-0.1774), (r^2=0.9686), (b) (t=10,000), (log (v)=1.173log (m)-0.4551), (r^2=0.9427).Full size imageEvaluating trap countsIn the above, we have shown that our IBM model parameterized using field data on individual slug movement produces a distinctly heterogeneous, patchy spatial distribution. The degree of aggregation, both in terms of the Morisita index and Taylor’s aggregation index is higher than it would be due to purely stochastic reasons. The emerging patchy structure is self-organized in the sense that it emerges not due to the effect of external factors but due to an inherent property of the system such as the density dependent slug movement.The simulated spatial patterns exhibit properties similar to the distribution of slugs in the field, in particular showing similar values of the aggregation index, which in the field data was found18 to be in the range (1.09 More

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Epithemia isolation and cultureThe Epithemia cells were isolated from 0.5 L of seawater collected from depths of 25, 75, and 100 m in the North Pacific Subtropical Gyre (22°45′ N, 158°00′ W). Seawater was collected during the near-monthly Hawaii Ocean Time-series (HOT) expeditions to the long-term monitoring site Station ALOHA (water depth ca. 4800 m) in October 2014 (HOT cruise #266) and February–July 2019 (HOT cruises #310–313). Serial dilution (unialgal strains UHM3202, UHM3203, UHM3204) or micropipette isolation of single cells (clonal strains UHM3200, UHM3201, UHM3210, UHM3211) were used to establish the Epithemia cultures, which were grown in a seawater-based, low-nitrogen medium. Filtered (0.2 µm) and autoclaved, undiluted Station ALOHA seawater was amended with 2 μM EDTA, 50 nM ferric ammonium citrate, 7.5 μM phosphoric acid, trace metals (100 nM MnSO4, 10 nM ZnCl2, 10 nM Na2MoO4, 1 nM CoCl2, 1 nM NiCl2, 1 nM Na2SeO3), vitamins (50 μg/L inositol, 10 μg/L calcium pantothenate, 10 μg/L thiamin, 5 μg/L pyridoxine HCl, 5 μg/L nicotinic acid, 0.5 μg/L para-aminobenzoic acid, 0.1 μg/L folic acid, 0.05 μg/L biotin, 0.05 μg/L vitamin B12), and 106 μM Na2SiO3. Although not tested here, simpler formulations of diazotroph media such as PMP40 or RMP41 may also be suitable for growing Epithemia, when made with 100% seawater and adding Na2SiO3. The cultures were subsequently incubated at 24 °C on a 12:12 h light:dark cycle with 50–100 μmol quanta m−2 s−1 using cool white fluorescent bulbs. All E. pelagica and E. catenata symbioses were stable under these medium and incubation conditions. E. pelagica was successfully isolated from at least one of the three depths that were targeted during each sampling occasion.Morphological observationsEpithemia living and fixed cells were imaged by light and epifluorescence microscopy using a Nikon Eclipse 90i microscope at 40×–60× magnification. Diatom cell sizes were determined using >60 live, exponentially growing cells, imaged in either valve view (E. pelagica) or girdle view (E. catenata). Endosymbiont (spheroid body) cell sizes were averaged from DNA-stained cells for E. pelagica UHM3200 (n = 78) and E. catenata UHM3210 (n = 91), imaged by epifluorescence microscopy after preparing samples as follows: Epithemia cells were fixed in 4% glutaraldehyde for 30 min, pelleted at 1000 × g for 1 min, the supernatant was exchanged with 0.5% Triton X-100 (in autoclaved filtered seawater), samples were incubated for 10 min with gentle agitation, cells were then pelleted at 4000 × g for 1 min, supernatant was exchanged with autoclaved filtered seawater and fixed in 4% glutaraldehyde, and samples were stained with 1× final concentration of SYBR Gold nucleic acid stain (Invitrogen, cat. # S11494) for 2 h. For routine observations of endosymbionts (e.g., determining presence/absence and number per host cell), osmotic shock was used to disrupt the cell contents of diatom host cells and improve visualization of the endosymbionts. This was achieved by gently pelleting cells and exchanging the medium with either ultrapure water or 2–3 M NaCl solution, followed by immediate observation. While this is a simple technique for detecting and visualizing endosymbionts (Fig. 1c, f), it does not accurately represent the natural location of endosymbionts within the host cells, as seen when compared to fixed cell preparations for epifluorescence microscopy (Fig. 1n, o). To assess the presence of fluorescent photopigments in endosymbiont cells, live host cells were pelleted at 4000 × g for 5 min and crushed using a microcentrifuge tube pestle (SP Bel-Art, cat. # F19923-0000) to release the endosymbionts. The crushed pellet was resuspended in 75% glycerol containing live Synechococcus WH7803 cells (positive control for fluorescence), and samples were observed by epifluorescence microscopy using filter cubes appropriate for observing phycoerythrin (EX: 551/10, BS: 560, EM: 595/30) and chlorophyll (EX: 480/30, BS: 505, EM: 600LP).The loss of endosymbionts from Epithemia cultures (UHM3200 and UHM3210) was observed after propagating cells for four months in nitrogen-replete medium (K)18, where approximately 5–10% of the culture was transferred to fresh medium about every two weeks. Observations were only made at the end of the four-month period. Endosymbionts were not observed growing freely in these cultures, and the absence of endosymbionts within host cells was confirmed by the failure to observe spheroid bodies by light microscopy after osmotic shock of the diatoms, as well as a failure to amplify the endosymbiont SSU (16S rRNA) and nifH genes from cellular DNA extracts. PCR reactions were performed in parallel with DNA extracts from control cultures (grown in low-nitrogen medium), using the same template DNA amount (10 ng) and PCR conditions (see methods for Marker gene sequencing and phylogenetics).Ultrastructural observations by electron microscopy (EM) were conducted for E. pelagica UHM3200 and E. catenata UHM3210. EM preparations of diatoms typically involve the oxidative removal of organic matter to uncover the fine details of frustule ultrastructure. However, in the case of E. catenata, oxidatively cleaned cells lacked structural integrity, leading to collapsed frustules when dried and viewed by scanning EM (SEM). For this reason, both species were prepared for SEM with and without (Fig. 1a, d) the oxidative removal of organic matter, and cleaned E. catenata frustules were further analyzed by transmission EM (TEM). To remove organic matter, 100 mL of exponentially growing culture was pelleted by centrifugation at 1000 × g for 10 min and resuspended in 30% H2O2. Cells were boiled in H2O2 for 1–2 h, followed by rinsing cells six times in ultrapure water by sequential centrifugation at 1000 × g for 10 min and resuspension of cell pellets. Suspensions of the cleaned cells were dried on aluminum foil and mounted on aluminum stubs with double-sided copper tape. For some E. catenata SEM preparations, the cleaned frustules were dehydrated in an ethanol dilution series and exchanged into hexamethyldisilazane (HMDS) prior to drying on aluminum foil; this was to minimize the collapse of frustules resulting from drying. To prepare cells with organic matter intact, 25 mL of exponentially growing culture was mixed with an equal volume of fixative solution (5% glutaraldehyde, 0.2 M sodium cacodylate pH 7.2, 0.35 M sucrose, 10 mM CaCl2) and incubated overnight at 4 °C. Cells were gently filtered onto a 13 mm diameter 1.2 μm pore size polycarbonate membrane filter (Isopore, Millipore Sigma), washed with 0.1 M sodium cacodylate buffer (pH 7.4, 0.35 M sucrose), fixed with 1% osmium tetroxide in 0.1 M sodium cacodylate (pH 7.4), dehydrated in a graded ethanol series, and critical point dried. Filters were mounted on aluminum stubs with double-sided conductive carbon tape. All SEM stubs were sputter coated with Au/Pd, prior to observing on a Hitachi S-4800 field emission scanning electron microscope at the University of Hawai’i at Mānoa (UHM) Biological Electron Microscope Facility (BEMF). Cleaned E. catenata cells were prepared for TEM by drying a drop of sample on a formvar/carbon-coated grid and observing on a Hitachi HT7700 transmission electron microscope at UHM BEMF.Additional light microscopy of hydrogen-peroxide cleaned frustules was conducted for E. pelagica UHM3201 and E. catenata UHM3210. Samples were mounted in Naphrax (PhycoTech, Inc., cat. # P-Naphrax200) and observed at 100× using an Olympus BX41 Photomicroscope (Olympus America Inc., Center Valley, Pennsylvania) with differential interference contrast optics and an Olympus SC30 Digital Camera at California State University San Marcos.A key to the strains used in each micrograph is provided in Supplementary Table 2.Marker gene sequencing and phylogeneticsFor each Epithemia strain, 25–50 mL of culture was pelleted at 4000 × g for 10 min, and DNA was extracted from the pellet using the ZymoBIOMICS DNA Miniprep Kit (Zymo Research, cat. # D4300). Marker genes were amplified with the Expand High Fidelity PCR System (Roche, cat. # 4743733001), using conditions previously described for genes SSU encoding 18S rRNA (Euk328f/Euk329r)42, LSU encoding 28S rRNA (D1R/D2C)43, rbcL (rbcL66+/dp7−)44,45, psbC (psbC+/psbC−)44, and cob (Cob1f/Cob2r)21. For the endosymbionts, a partial sequence for the SSU (16S rRNA) gene was amplified using a primer set targeting unicellular cyanobacterial diazotrophs, CYA359F/Nitro821R46,47, and the nifH gene was amplified using new primers specific to the nifH of Cyanothece-like organisms, ESB-nifH-F (5′-TACGGAAAAGGCGGTATCGG-3′) and ESB-nifH-R (5′-CACCACCAAGRATACCGAAGTC-3′), with a 55 °C annealing temperature and 75 s extension time. All primers were synthesized by Integrated DNA Technologies (IDT). Amplified products were cloned and transformed into E. coli using the TOPO TA Cloning Kit for Sequencing (Invitrogen, cat. # K457501), and plated colonies were picked and grown in Circlegrow medium (MP Biomedicals, cat. # 113000132). Plasmids were extracted with the Zyppy Plasmid Miniprep kit (Zymo Research, cat. # D4019) and sequenced from the M13 vector primers using Sanger technology at GENEWIZ (South Plainfield, NJ). For the diatom SSU (18S rRNA) gene, sequencing reactions were also performed using the 502f and 1174r primers48.Phylogenetic trees (Fig. 2) were inferred using concatenated alignments for both diatom host genes (SSU encoding 18S rRNA, psbC, rbcL) and endosymbiont genes (SSU encoding 16S rRNA, nifH). For each gene, nucleotide sequences were aligned using MAFFT v7.45349 (L-INS-i method), and sites with gaps or missing data were removed. An appropriate nucleotide substitution model was selected for each gene alignment using jModelTest v2.1.1050. Bayesian majority consensus trees were inferred from the concatenated alignments using MrBayes v3.2.751 with two runs of 4–8 chains, until the average standard deviation of split frequencies dropped below 0.01. Maximum likelihood bootstrap values were generated for the Bayesian tree using RAxML v8.2.1252, implemented with 1000 iterations of rapid bootstrapping. To further analyze the phylogenetic position of the new Epithemia species in the broader context of Surirellales and Rhopalodiales diatoms, individual gene trees (SSU encoding 18S rRNA, LSU, rbcL, psbC, and cob; Supplementary Figs. 13–19) were constructed from sequences aligned using MAFFT (automatic detection method) and trimmed using trimAl v1.253 (gappyout method). rRNA gene phylogenies were also inferred using sequences aligned according to the global SILVA alignment for SSU and LSU genes using SINA54, which were either left untrimmed in the case of the LSU gene or trimmed to remove highly variable positions (SINA’s “012345” positional variability filter) and gappy positions (trimAL v1.2, gappyout method) in the case of the SSU gene. These trimming strategies were selected based on their ability to maximize the monophyly of the previously described Rhopalodiales clade and minimize the separation of known conspecific strains, such as the strains of E. pelagica described here. All gene phylogenies were inferred using the Bayesian methods described above. To investigate the level of support for constrained tree topologies placing E. catenata within or outside of the genus Epithemia and family Rhopalodiaceae, SH55 and AU56 statistical tests were performed in IQ-TREE 257 (implementing ModelFinder58) using all alignments from the individual gene trees (Supplementary Table 3).Given E. catenata’s unusual morphology, test trees were inferred with the inclusion of diatom sequences from orders Bacillariales (Nitzschia, Pseudo-nitzschia), Cymbellales (Didymosphenia), Naviculales (Amphiprora, Navicula, Pinnularia), and Thalassiophysales (Amphora, Halamphora, Thalassiophysa); however, E. catenata was consistently placed within Rhopalodiales, and these trees were not pursued further.An additional nifH phylogeny was constructed using all environmental sequences from NCBI’s non-redundant nucleotide (nt) database >300 bp and sharing >95% nucleotide sequence identity with EpSB and EcSB nifH sequences (Supplementary Fig. 23), including 51 environmental sequences from prior studies investigating marine diazotrophs34,59,60,61,62,63,64,65,66. Environmental nifH sequences were aligned to the previously generated nifH sequence alignment using MAFFT (automatic method detection and addfragments options), and the best-scoring maximum likelihood phylogeny was inferred using RAxML with 1000 iterations of rapid bootstrapping. NCBI accession numbers for all tree sequences are in the Source Data file.Analysis of Epithemia endosymbiont nifH sequences in environmental datasetsNucleotide sequences for EpSB and EcSB nifH were queried against NCBI’s non-redundant nucleotide (nt) database using webBLAST67 (megablast; https://blast.ncbi.nlm.nih.gov/) and SRA databases for nifH amplicon sequencing projects from the marine environment using the SRA Toolkit68 (dc-megablast, with database validation using vdb-validate; https://github.com/ncbi/sra-tools). Database hits with 98–100% nucleotide identity over an alignment of the entire subject sequence (BLAST alignment length = subject sequence length) were identified, and the associated sample’s latitude and longitude coordinates (where available) were mapped. Coordinates were also mapped for metagenome and metatranscriptome samples containing matches to unigene MATOU-v1_93255274 from the Marine Atlas of Tara Oceans Unigenes69, a unigene that shares 100% identity over the entire length of the EpSB UHM3202 nifH sequence and >99.4% identity with all other EpSB nifH sequences.The presence of EpSB and EcSB nifH sequences was examined in metagenomes prepared from sinking particles collected at 4000 m depth at Station ALOHA27,28. The sinking particles were collected during intervals of 12, 10, and 8 days during 2014, 2015, and 2016, respectively, using a McLane sediment trap equipped with a 21-sample bottle carousel. The presence of EpSB and EcSB nifH sequences in the metagenomes was assessed by blastn70, after first removing low quality bases from metagenomic reads using Trimmomatic v0.3971 (parameters: LEADING:20 TRAILING:20 MINLEN:100). For each sediment trap metagenome, the total number of reads matching EpSB or EcSB nifH nucleotide sequences with 100% identity were tallied and normalized to the total number of reads in the database. Only EpSB-matching reads were detected in this analysis.Quantitative PCRSpecific PCR primers were designed targeting a 102 bp region of E. pelagica’s LSU gene (Epel-LSU-F, 5′-GAAACCAGTGCAAGCCAAC-3′; Epel-LSU-R, 5′-AGGCCATTATCATCCCTTGTC-3′) and an 85 bp region EpSB’s nifH gene (EpSB-nifH-F, 5′-CACACTAAAGCACAAACTACC-3′; EpSB-nifH-R, 5′-CAAGTAGTACTTCGTCTAGCTC-3′) and were synthesized by IDT. Gene copy concentrations were quantified for Station ALOHA water samples (~2 L) collected by Niskin bottles at 5, 25, 45, 75, 100, 125, 150, and 175 m on January 16 and July 1 (except 5 m), 2014, during HOT cruises #259 and #264. Samples were filtered onto 25 mm diameter, 0.02 μm pore size aluminum oxide filters (Anotop; Whatman, cat. # WHA68092102) and stored at −80 °C until extracting DNA using the MasterPure Complete DNA and RNA Purification Kit (Epicentre, cat. # MC85200) according to Mueller et al.72. Briefly, a 3-mL syringe filled with 1 mL of tissue and cell lysis solution (MasterPure) containing 100 μg mL−1 proteinase K was attached to the outlet of the filter, and the filter inlet was sealed with a second 3-mL syringe. The lysis solution was pulled halfway through to saturate the filter membrane, and the entire assembly was incubated at 65 °C for 15 min while attached to a rotisserie in a hybridization oven rotating at ca. 16 rpm. The lysis buffer was then drawn fully into the inlet syringe, transferred to a microcentrifuge tube, and placed on ice. The remaining steps for protein precipitation and removal and nucleic acid precipitation were carried out following the manufacturer’s instructions. For each sample, DNA was resuspended in a final volume of 100 μL. Quantitative PCR (qPCR) was performed using the PowerTrack SYBR Green Master Mix system (Applied Biosystems, cat. # A46109) and run on an Eppendorf Mastercycler epgradient S realplex2 real-time PCR machine. Reactions (20 µL total volume) were prepared according to the manufacturer’s protocol, containing 500 nM of each primer. Sample reactions (four replicates) contained 2 μL of environmental DNA extract (24–76 ng DNA), while standards (three replicates) contained 2 μL of gBlocks Gene Fragments (IDT) that were prepared at 1, 2, 3, 4, 5, and 6 log gene copies/μL. The gBlocks Gene Fragments were 500 bp in length and encompassed the entire E. pelagica UHM3201 LSU sequence and positions 1–500 of the EpSB UHM3201 nifH sequence, respectively. The main cycling conditions consisted of an initial denaturation and enzyme activation step of 95 °C for 2 min, followed by 40 cycles of 95 °C for 5 s and 57 °C or 55 °C for 30 s for the LSU and nifH genes, respectively. Melting curves were analyzed to verify the specificity of the amplifications, and reactions containing Epithemia catenata DNA extract were included as negative controls. Reaction efficiencies were 104.23% and 95.15% for the LSU and nifH genes, respectively. The limit of detection for these assays was not empirically determined. gBlocks sequences, qPCR threshold cycle values, and conversion equations are provided in the Source Data file.Physiology experimentsThe daily patterns of N2 fixation were quantified for E. pelagica UHM3200 and E. catenata UHM3210 using two techniques: acetylene (C2H2) reduction to ethylene (C2H4) and argon induced dihydrogen (H2) production (AIHP). Both analyses were conducted using a gaseous flow-through system that quantified the relevant trace gas on the sample outlet line with a temporal resolution of 10 min73. To conduct the measurements, a 10-mL subsample of each Epithemia culture was placed in a 20-mL borosilicate vial and closed using gas-tight rubber stoppers and crimp seals. Separate bottles were used for H2 production and C2H2 reduction. During the experimental period, the temperature was maintained at 25 ± 0.2 °C using a benchtop incubator (Incu-Shaker; Benchmark Scientific) and light exposure was 200 μmol photons m−2 s−1 at wavelengths of 380–780 nm with a 12:12 h square light:dark cycle (Prime HD+; Aqua Illumination). To conduct the AIHP method, the sample vial containing the culture was flushed with a high purity gas mixture consisting of argon (makeup gas; 80%), oxygen (20%), and carbon dioxide (0.04%). In the absence of N2, all of the electrons that would have been used to reduce N2 to NH3 are diverted to H2 production, thereby providing a measure of Total Nitrogenase Activity (TNA). The C2H2 reduction assay also represents a measure of TNA. Our analytical set-up introduced C2H2 at a 1% addition (vol/vol) to the high purity air with a total flow rate (13 mL min−1) identical to the AIHP method. The gas emissions were analyzed using separate reductive trace gas analyzers that were optimized for the quantification of H2 and C2H4. To verify the observed daily patterns in N2 fixation, 15N2 assimilation measurements were conducted on triplicate samples of Epithemia cultures at targeted time points. Five milliliters of 15N-enriched seawater was added to the subsamples, which were subsequently crimp sealed and incubated for a 2 h period with the same light and temperature conditions as the daily gas measurements. At the end of the incubation, the contents of each vial were filtered onto a pre-combusted glass fiber filter. The concentration and isotopic composition (δ15N) of particulate nitrogen for incubated and non-incubated (i.e., natural abundance) samples was measured using an elemental analyzer/isotope ratio mass spectrometer (Carlo-Erba EA NC2500 coupled with a ThermoFinnigan Delta Plus XP). For each of the described analyses, cell-specific rates were calculated based on the average of triplicate cell concentration measurements, obtained from cell samples preserved at 4 °C with Lugol’s iodine solution and quantified within a week using a Sedgwick-Rafter counting chamber (Electron Microscopy Sciences, cat. # 68050-52). All rate measurement data is provided in the Source Data file.Reporting summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More

A workflow for the calculation of CSI is presented in Fig. 1c. For all the analyses, we used the R v. 4.0.3 software environment20 implemented in RStudio v. 1.4.1103. The scripts used for each methodological step are available at the Figshare repository21. After data download from primary sources (PaleoClim and WorldClim), specifically for the CSI-future map set we performed an initial step aimed to obtain individual bioclimatic variables for each future time period for the four SSPs (Fig. 1b). To achieve this, the median values of nine GCMs were calculated in functions compiled in raster R package22 for each individual bioclimatic variable (see a few exceptions of number of GCMs used in Table 2).Table 2 General circulation models (GCM) used to construct the future map sets.Full size tableThe standard deviation (SD) was estimated as a measure of the amount of variation or dispersion along time series, from which the resulting output maps showed the places where climate conditions remained constant or variable across the temporal periods considered (Fig. 1a,b). The SD, as a way to identify stable/unstable climatic areas, was previously used in other climatic or evolutionary studies4,14. To compute the SD output rasters, we applied the mosaic function setting “fun = sd” from raster R package, calculating the SD for each pixel in the 12 time period rasters for CSI-past and five times for CSI-future, independently for each variable. The mosaic function was also used for the range calculation, with “fun = min” and “fun = max” to obtain the minimum and maximum values of input rasters, respectively, with a further step for subtracting maximum to minimum values.Specifically, for CSI-past, as it includes several time periods with sea-level dropping below the present level (T1, T3, T5, T6, T7, T8, T9; Fig. 1a), we applied a mask of the current land surface, i.e. taking the T12 (Anthropocene) as a template. With this additional step, we were able to remove those pixels (grid cells) currently under the sea but that were once emerged. Most of these pixels, however, were only emerged during the LGM (ca. 21 ka), thus having values for bioclimatic variables for just a single time period (instead of the 12 routinely used for the variability estimation). The inclusion of these areas would result in highly climatically stable regions (low SD values; Supplementary Fig. 1), but this would be an obviously biased result. In contrast, we did not remove those areas affected by the sea-level rising periods, as only three periods contained “NoData” values (T2, T4, T10; Fig. 1a). However, to take this fact into consideration, we created a raster file in which these areas submerged during warm periods are indicated (see Supplementary Fig. 1). Finally, for both CSI-past and CSI-future, the resulting SD values were normalized to values between 0 and 1, with 0 representing completely stable areas and 1 the most unstable ones.The next step was focused on the selection of a relatively uncorrelated set of variables for each map set. We used the removeCollinearity function from virtualspecies R package23 that estimates the correlation value among pairs of variables from a given number of random sample points (10,000 in present case) according to a given method (Pearson for the present case) and a threshold of statistic selected (r  > 0.8 as a cut-off value). The function removeCollinearity returns a list of uncorrelated variables according to the settings specified, randomly selecting just one variable from groups of correlated ones (see Table 1 for a complete list of variables used for each map set). As we compiled estimates of variability independently for each variable and map set (e.g. SD bio1 past, SD bio2 past, etc.), each user can define his own CSI, selecting the more interesting variables according to the case of study.The final CSI maps were obtained by summing the SD values of the variables selected and the subsequent outputs normalized (0 to 1) (Figs. 2–4). Histogram plots were represented with ggplot2 R package24 and maps were exported with ArcGIS v.10.2.2 (Esri, Redlands, California, USA 2014). The histograms were computed for these final CSI maps, which represent the frequency and distribution of CSI values. We presented the final CSI maps with two different colour ramp schemes with ArcGIS. The first consisted of defining equal interval breaks from 0 to 1. The second was based on defining 32 categories with different value breaks for past and future map sets according to the value frequency shown by the histogram plot, i.e. the category with the highest CSI values (no. 32) was 0.71–1 in the past map set and 0.356–1 in the future map set.Fig. 2Maps of Climate Stability Index (CSI) values for the past map set from Pliocene (3.3 Ma) to present (1979–2013), at 2.5 arc-min grid resolution. Colours range from blue for low standard deviation (SD) values, which represents areas with low climatic fluctuations (i.e, low values of CSI) during the period Pliocene–present, to red for high SD values, which shows areas where high climatic fluctuations would have taken place (i.e., high values of CSI). On the upper map, the colour ramp shows equal interval breaks. The histogram with frequency and distribution of CSI values is also shown. On the lower map, the colour ramp has been manually adjusted to a defined set of break values (see details in the text).Full size imageFig. 3Maps of Climate Stability Index (CSI) values for the future conditions (Shared Socioeconomic Pathways: SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5) from present (1970–2000) to future (2100), at 2.5 arc-min grid resolution. Colours range from blue for low standard deviation (SD) values, which represents areas with low climatic fluctuations (i.e, low values of CSI) from present to future, to red for high SD values, which shows areas where high climatic fluctuations would have taken place (i.e., high values of CSI). The colour ramp shows equal interval breaks. The histogram with frequency and distribution of CSI values is also shown for each future scenario.Full size imageFig. 4Maps of Climate Stability Index (CSI) values for the future conditions (Shared Socioeconomic Pathways: SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5) from present (1970–2000) to future (2100), at 2.5 arc-min grid resolution. Colours range from blue for low standard deviation (SD) values, which represents areas with low climatic fluctuations (i.e, low values of CSI) from present to future, to red for high SD values, which shows areas where high climatic fluctuations would have taken place (i.e., high values of CSI). The colour ramp has been manually adjusted to a defined set of break values (see details in the text).Full size image More