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Drainage area and branching ratio: a matter of scaleGeomorphological and ecological viewpoints on river networks generally differ owing to discordant definitions of the fundamental unit (the node) used to analyze them. From a geomorphological perspective, the determination of a river network entails the definition of an observational scale. Real river networks can be extracted from digital elevation models (DEMs) via algorithms for flow direction determination such as D8 (i.e., each pixel drains towards the lowest of its 8 nearest neighbors53). After the outlet location has been specified (and hence the upstream area A spanned by the river network), the first observational scale required is thus the pixel length l of the DEM, which defines the extent of a network node. A second scale is then needed to distinguish the portion of the drainage network effectively belonging to the channel network. The simplest but still widely used method53 defines channels as those pixels whose drainage area exceeds a threshold value AT. Hydrologically based criteria to determine the appropriate value for AT exist54; however, for the sake of simplicity, we here consider AT as a free parameter.BBTs and RBNs are random constructs, and as such they do not satisfy the optimality criterion of minimizing total energy expenditure, which is the fundamental physical process shaping fluvial landscapes. Furthermore, neither of these networks is a spanning tree, which is a key attribute of real fluvial landforms10: in fact, in both BBTs and RBNs, the extent of the drained domain is not defined. As a result, the drainage area at an arbitrary network node cannot in principle be attributed, unless by using the number of upstream nodes as a proxy. This has practical implications from an ecological viewpoint because drainage area is the master variable controlling several attributes of a river, such as width, depth, discharge, or slope3,55, which in turn impact habitat characteristics and the ecology of organisms therein56.In BBTs and RBNs, branching probability p has been defined35,38,45,46,47 as the probability that a network node is branching, i.e. connected to two upstream nodes. As such, the branching probability of a realized river network (be it a real river or a synthetic construct) could be evaluated as the ratio between the number of links NL constituting a network and the total number of network nodes N; if a unit distance between two adjacent nodes is assumed, the denominator equals the total network length. We note that the former definition of branching probability only holds in the context of the generation of a synthetic random network; it is in fact improper to refer to a “probability” when analyzing the properties of a realized river network. We clarify this aspect by introducing the concept of branching ratio pr for the latter definition (pr = NL/N). Moreover, in the case of BBTs, p and pr do not coincide (see Methods). Importantly, p and pr have no parallel in the literature on fluvial forms, nor do they refer to any of the well-studied measures of rivers’ fractal character.The choice of different observational scales for the same drainage network results in different values of NL and N, and hence of pr. Remarkably, the very same drainage network can result in river networks that virtually assume any value of pr (ranging from 0 to 1) and N (up to the upper bound A) depending on the choice of AT and A (the latter corresponding to a given l value when measured in the number of pixels; Fig. 1d–i); networks with low AT/A ratios result in high N (Fig. 2a), while networks with low AT result in high pr (Fig. 2b). Furthermore, pr does not identify the inherent (i.e., scale-independent) branching character of a given river network in relation to other river networks. In fact, by extracting different river networks at various scales (i.e., various AT values) and assessing the rivers’ rank in terms of pr, one observes that rivers that look more “branching” (i.e., have higher pr) than others for a given AT value can become less “branching” for a different AT value (Fig. 3). We therefore conclude that branching probability is a non-descriptive property of a river network, which by no means describes its inherent branching character, and depends on the observational scale.Fig. 2: Variation of N and pr as a function of observational scales for OCNs and real river networks.a Expected value of number of network nodes N as a function of threshold area AT and total drained area A (from Eq. (1)); the white dots indicate the values of AT and A used to generate the OCNs used in this analysis. b Expected value of branching ratio pr as a function of AT and A (from Eq. (1)); symbols as in a.Full size imageFig. 3: Values of branching ratio as a function of AT for the 50 real river networks analyzed in this study.a Natural values of pr in logarithmic scale. b z-normalized branching ratios (i.e., for each AT value, values of pr are normalized so that they have null mean and unit standard deviation), which better shows how rivers rank differently in terms of pr for different observation scales (i.e., AT). Lines connect dots relative to the same river. For visual purposes, rivers that rank first, second, second-to-last or last in at least one of the AT groups are displayed in colors; the other rivers are displayed in grey.Full size imageScaling is also crucial when looking at river networks from an ecological perspective. In this case, the relevant scale determining the dimension l of a node is the extent of habitat within which individuals (due to e.g. physical constrains) can be assigned to a single population57,58; the riverine connectivity and ensuing dispersal among these populations give rise to a metapopulation at the river network level. The specific spatial scale largely depends on the targeted species (e.g. being larger for fish than for aquatic insects), and it is conceivably much larger than (or, at least, it has no reason to be equal to) the pixel size of the DEM on which the river network is extracted. Since the evaluation of pr depends on the number of nodes N, which, in turn, is defined based on the scale length l, the resulting pr of a river network under this perspective would depend on the characteristics of the target taxa, which is inconsistent with the alleged role of pr as a scale-invariant property of river networks.Note also that using the ecological definition of l (i.e., spatial range of a local population) to discretize a real river network into N nodes, and from there calculate the branching ratio pr = NL/N, is problematic. Indeed, this would imply an elongation of all links shorter than l (which constitute a non-negligible fraction of the total links, under the assumption of exponential distribution of link lengths51), hence preventing a correct estimation of the connectivity patterns (i.e., distances between nodes) and the resulting ecological metrics of the river network (see section Ecological implications).From an ecological perspective, it could be reasonable to consider AT as a parameter expressing how a particular taxon perceives the suitable landscape, rather than a value to be determined from geomorphological arguments: for instance, large fishes inhabit wide and deep river reaches, and do not access small headwaters56. In this case, imposing a large AT would result in a coarser, less branching network constituted by few main channels (Fig. 1f, i), which could mimic the potentially available habitat for such species. Conversely, aquatic insects inhabit also small headwaters17,59, therefore their perceived landscape would resemble the finely resolved networks of Fig. 1d, g, characterized by low AT and higher (apparent) pr.Topology and scaling of river networks and random analoguesTo verify the topological (i.e., Horton’s laws on bifurcation and length ratios) and scaling (i.e., probability distribution of drainage areas) relationships of the different network types, we extracted from DEMs 50 real river networks encompassing a wide range of drainage areas (Fig. 4), and we generated 50 OCNs, 50 RBNs and 50 BBTs of comparable size (see Methods).Fig. 4: Location of real river basins used in the analysis.River basins are shown in dark grey; countries in light grey. Rivers’ numbering is sorted in ascending order according to drainage area values.Full size imageTypical values3,7,60 for the bifurcation ratio RB lie between 3 and 5, while length ratios (RL) range between 1.5 and 3.5. As expected, we observed that the real rivers and OCNs used in our analysis have RB and RL values within the aforementioned ranges (Fig. 5a, b). The same is true for RBNs, while the RB and RL values found for BBTs are lower than the typical ranges. This finding holds regardless of the scale (subsumed by AT) at which real river networks and OCNs are extracted (Supplementary Figs. 1 and 2). Remarkably, BBTs fail to satisfy Horton’s laws despite the statistical inevitability of such laws for any network argued by ref. 61. To this regard, we note that the networks analyzed by ref. 61 did not include constructs where all paths from the source nodes to the outlet have the same length, which is the defining feature of BBTs (Fig. 1a).Fig. 5: Comparison of topological and scaling properties of the different networks.a Scaling of number of network links Nω as a function of stream order ω for the various network types (rivers and OCNs obtained with AT = 20 pixels; RBNs and BBTs derived accordingly – see Methods). b Mean link length Lω (in units of l) as a function of ω. Networks used are as in panel a. c Scaling of drainage areas: probability P[A ≥ a] to randomly sample a node with drainage area A ≥ a as a function of a. The displayed trend lines are fitted on the ensemble values for the 50 network replicates, by excluding nodes with drainage area larger than 2000 pixels (cutoff value marked with a black solid line). The scaling coefficients β reported correspond to the slopes of the fitted trend lines. Extended details on all panels are provided in the Supplementary Methods.Full size imageWhile the power-law scaling of areas in OCNs (Fig. 5c) has an exponent β ≈ 0.45 that closely resembles the one found for the real rivers (β ≈ 0.46) and within the typically observed range8,10 β = 0.43 ± 0.02, drainage areas of RBNs scale as a power law with an exponent β ≈ 0.51, which departs from the observed range. Conversely, BBTs do not show any power-law scaling of areas. Scaling exponents of drainage areas fitted separately for each real river network yielded values in the range 0.36÷0.57 (Supplementary Table 1). In particular, we observed that these values tend to the expected range β = 0.43 ± 0.02 for increasing values of A, expressed in number of pixels (Supplementary Fig. 3), hence implying that highly resolved catchments are required in order to properly estimate β. Interestingly, the observed values of Horton ratios and scaling exponent β for RBNs are compatible with the values RB = 4, RL = 2, β = 0.5 predicted for Shreve’s random topology model3,60,62, which is actually equivalent to a RBN with infinite links.Ecological implicationsWe compared the different network types via two metrics that express the ecological value of a landscape for a metapopulation: the coefficient of variation of a metapopulation CVM and the metapopulation capacity λM. The coefficient of variation of a metapopulation63 is a measure of metapopulation stability (a metapopulation being more stable the lower CVM is), while the metapopulation capacity42,64 expresses the potential for a metapopulation to persist in the long run (persistence being more likely the higher λM is). Both measures are among the most universal metrics describing dynamics of spatially fragmented populations24,40. In order to assess the impact of the two landscape features mostly affecting metapopulation dynamics, i.e. spatial connectivity and spatial distribution of habitat patches, we calculated these metrics for the four network types under two different scenarios: uniform (CVM,U, λM,U) and non-uniform (CVM,H, λM,H) spatial distribution of habitat patch sizes. In the first scenario, CVM,U and λM,U assess stability and persistence (respectively) of a metapopulation solely based on pairwise distances between network nodes; in the second scenario, CVM,H and λM,H depend on the interplay between pairwise distances and spatially heterogeneous habitat availability (namely, downstream nodes being larger than upstream ones).We found that the values of CVM (be it derived with uniform (CVM,U) or nonuniform (CVM,H) distributions of patch sizes) obtained for OCNs match strikingly well those of real rivers (Fig. 6). These CVM values are consistently lower than those found for RBNs, while values of CVM for BBTs are even higher. Notably, this result holds for different values of AT (and hence different pr values) at which real rivers and OCNs are extracted (Fig. 6a–c; g–i), and for values of mean dispersal distance α (see Methods) spanning multiple orders of magnitude (Supplementary Figs. 4–7).Fig. 6: Comparison of values of metapopulation metrics across river network types and observational scales (AT).a–c CVM,U. d–f λM,U. g–i CVM,H. j–l λM,H. Boxplot elements are as follows: center line, median; notches, (pm 1.58cdot {{{{{{{rm{IQR}}}}}}}}/sqrt{50}), where IQR is the interquartile range; box limits, upper and lower quartiles; whiskers, extending up to the most extreme data points that are within ±1.5 ⋅ IQR; circles, outliers. Metapopulation metric values were obtained by setting α = 100 l. Note that in Eq. (1), given A = 40, 000, AT = 20 results in E[N] ≈ 4574, E[pr] ≈ 0.228; AT = 100 yields E[N] ≈ 2231, E[pr] ≈ 0.098; AT = 500 results in E[N] ≈ 1088, E[pr] ≈ 0.042.Full size imageFor a constant α value, the CVM of real rivers, OCNs and RBNs decreases as the resolution at which the network is extracted increases (i.e., AT decreases; see Fig. 6 and Supplementary Figs. 4–7). This is expected63, since a decrease in AT corresponds to an increase in N (Fig. 2a), leading to a decrease in CVM. Indeed, a larger ecosystem, constituted of more patches, has the potential to include a larger (and more diverse) number of subpopulations, which increases stability at a metapopulation level through statistical averaging–a phenomenon widely known as the portfolio effect65. We also found that BBT networks do not generally follow the above-described pattern of decreasing CVM with increasing N; rather, the CVM of BBTs increases with N when the mean dispersal distance α is set to intermediate to high values (Fig. 6 and Supplementary Figs. 5–7), and only when α is very low (e.g. α = 10 l as in Supplementary Fig. 4) and a uniform patch-size distribution is assumed does CVM,U follow the expected decreasing trend with increasing N.However, we need to warn against the conclusion that river networks with higher values of pr (and hence lower AT, see Fig. 2b) are inherently associated with higher metapopulation stability. Indeed, our result was obtained by changing the scale at which we observed the same river networks, and not by increasing the river networks’ size. If the number of network nodes (and, consequently, the branching ratio pr) is determined by the scale at which the landscape is observed, one cannot directly assume that any of such nodes is a node (or patch) in the ecological sense, i.e. the geographical span of a local population: the extent of such patches should be determined based on the mobility characteristics of the focus species, and should be independent of the scale at which the river network is observed. In contrast, we note that, if different river networks spanning different catchment areas (say, in km2) are compared, all of them extracted from the same DEM (same l and same AT in km2), then the larger river network will appear more branching (i.e., have larger pr). Indeed, by selecting catchments with larger A (in km2) for fixed l and AT (in km2), one moves towards the top-left corner of Fig. 2a, b (i.e., perpendicular to the level curves AT/A). The apparent higher “branchiness” of the river network with larger A will result in lower values of CVM; however, the higher metapopulation stability of the larger network will not be due to its (alleged) inherent more branching character, but only dictated by its larger habitat availability.We observed that metapopulation capacity λM values of OCNs (be it evaluated under uniform (λM,U) or non-uniform (λM,H) patch-size distribution assumption) are the closest to those of real rivers, while RBNs (and even more so BBTs) generally overestimate λM with respect to real rivers and OCNs (Fig. 6d–f; j–l). This result holds irrespective of the choice of AT and for intermediate to high values of α (Supplementary Figs. 5–7). When the mean dispersal distance is instead set to very low values (α = 10 l – Supplementary Fig. 4) and the river network is extracted at a high resolution (i.e., low AT), the metapopulation capacity of OCNs under assumption of uniform patch-size distribution (λM,U) is underestimated with respect to that of real rivers. A likely explanation for this apparent mismatch is that, for low values of AT, the number of nodes N tends to be somewhat higher for the extracted river networks used in this analysis than for OCNs (Supplementary Fig. 8), and the effect of the different dimensionality of real rivers and OCNs in the metapopulation capacity estimation tends to be more evident as the mean dispersal distance decreases. Interestingly, such mismatch is absent when a non-uniform patch size distribution is assumed, as λM,H values for OCNs match those for real rivers regardless of the mean dispersal distance value and the river network resolution (Fig. 6; Supplementary Figs. 4–7).The OCN construct encapsulates both random and deterministic processes, the former related to the stochastic nature of the OCN generation algorithm, and the latter pertaining to the minimization of total energy expenditure that characterizes OCN configurations. As such, OCNs reproduce the aggregation patterns of real river networks. From an ecological viewpoint, this implies that both pairwise distances between nodes and the distribution of patch sizes (expressed as a function of drainage areas, or of a proxy thereof such as the number of nodes upstream) are much closer to those of real networks than is the case for fully random synthetic networks as BBTs and RBNs. In particular, BBTs and (to a lesser extent) RBNs tend to underestimate pairwise distances with respect to real rivers and OCNs, as documented by a comparison of mean pairwise distances across network types (Supplementary Fig. 9a–c). Our analysis shows that the connectivity structure of these random networks (subsumed by the matrix of pairwise distances) is too compact with respect to that of real rivers, which leads to an overestimation of the role of dispersal in increasing the ability of a metapopulation to persist in the long run, but also an increased likelihood of synchrony among the different local populations, which results in higher instability.Comparison of patch size distributions among the network types expressed in terms of CVM,0 (i.e., the portion of CVM,H that uniquely depends on the distribution of patch sizes and not on pairwise distances) shows that, while for coarsely resolved networks (AT = 500) no clear differences in CVM,0 emerged, for highly resolved networks (AT = 20) BBTs heavily underestimate the CVM,0 of real rivers and OCNs, while RBNs slightly overestimate it (Supplementary Fig. 9d–f). As a result of the interplay of differences in distance matrices and patch size distributions, BBTs and (to a lesser extent) RBNs generally tend to overestimate the coefficient of variation of a metapopulation and the metapopulation capacity of real rivers and OCNs in both scenarios of uniform and non-uniform patch size distribution. The only exception to this trend occurs for the metapopulation capacity λM,H of very large BBTs (corresponding to AT = 20) in the case of very high dispersal distances (α = 1000 l – Supplementary Fig. 7): here, the patch-size effect (i.e., underestimation of CVM,0) predominates over the distance effect (i.e., overestimation of mean dij), resulting in an underestimation of λM,H with respect to real rivers and OCNs.Our results were derived under a number of simplifying assumptions. In particular, we acknowledge that, while the distance matrix of a landscape and the distribution of patch sizes have in general important implications for metapopulation dynamics, other factors not considered here, such as Euclidean between-patch distance48, fat-tailed dispersal kernel66 and density-dependent dispersal67 could also play a relevant role in this respect. However, it needs to be noted that, especially with regards to the assessment of the Moran effect in metapopulation synchrony (i.e., increased synchrony in local fluvial populations that are geographically close but not flow-connected48), the use of OCNs allows integration of Euclidean distances in a metapopulation model, while this is not possible for RBNs and BBTs, where Euclidean distances are not defined. Moreover, if a larger degree of realism is required for a specific ecological modelling study, such as heterogeneity in abiotic factors (e.g. water temperature or flow rates), the use of OCNs as model landscapes allows a direct integration of these variables, as they can conveniently be expressed as functions of drainage area3,55. In contrast, this is not possible for RBNs or BBTs, because only OCNs verify the scaling of areas (Fig. 5c), while RBNs and BBTs lack a proper definition of drainage areas.Our comparison of synthetic and real river networks showed that riverine metapopulations are more stable and less invasible than what would be predicted by random network analogues. Conversely, the use of OCNs as model landscapes allows capturing not only the scaling features of real rivers, but also drawing ecological conclusions that are in line with those that could be observed in real river networks. We thus support the use of OCNs as analogues of real river networks in theoretical and applied ecological modelling studies. While we found that BBTs are highly inaccurate in reproducing ecological metrics of real river networks and should be therefore discarded altogether in future modelling applications, RBNs show a certain degree of similarity with OCNs and real river networks in this respect; moreover, RBNs (as is the case for any random tree61) satisfy Horton’s laws on bifurcation and length ratios. A relevant advantage of RBNs over OCNs is that their generation algorithm is at least one order of magnitude faster49. Therefore, we acknowledge that RBNs could be considered as a suitable surrogate for real river networks as null models in cases where a large number of network replicates is required. To this end, we encourage researchers exploiting synthetic river networks (whether they be OCNs or RBNs) to always clarify the observational scales (that is, total area drained, size of a node, area drained by a headwater) subsumed by the synthetic network and which give rise to a certain complexity measure (i.e., branching ratio). Only in such a way could the predictions from these studies be compared with real river networks.In conclusion, our results advocate a tighter integration between physical (geomorphology, hydrology) and biological (ecology) disciplines in the study of freshwater ecosystems, and particularly in the perspective of a mechanistic understanding of drivers of persistence and loss of biodiversity. More

Animal husbandryCarukia barnesi polyps were available in culture from the James Cook University Aquarium, spawned from medusa originally collected near Double Island, North Queensland, Australia (16° 43.5′ S, 145° 41.0′ E) in 2014 and 20158. Populations exponentially increase through asexual reproduction8. Detached buds and swimming polyps were collected from the main culture, and transferred into 6-well tissue culture plates in natural filtered seawater. Plates were maintained in darkness to inhibit algae growth at 27 °C in a constant temperature cabinet. Buds and swimming polyps were left to develop and attach to well bottoms, at which point they were then fed freshly hatched Artemia nauplii and water changed 2–3 times per week. Lids remained attached to tissue culture plates to negate water evaporation and maintain a stable salinity. Polyps were maintained in this way for a minimum of 4 months before experiments began, with all individuals matured with the ability to asexually reproduce further buds. To preserve water quality15 polyps were starved for two days prior to experiment start and were not fed for the duration of the trials. One day prior to the experiment start, all immature buds and polyps were removed from wells, leaving approximately 5–10 mature polyps attached to the substrate for analysis.Preparation of reagentsReagentsSix chemicals were trialed in the current study to induce metamorphosis in C. barnesi polyps. Four indole containing compounds were chosen that have previously been trialed with other cubozoan species: 5-methoxy-2-methyl-3-indoleacetic acid, 5-methoxyindole-2-carboxylic acid, 2-methylindole16 and 5-Methoxy-2-methylindole15,16. Along with the retinoic X receptor 9-cis-retinoic acid and lugols solution.Indole compound treatmentsChemical concentrations of indoles documented in the literature were used to conduct preliminary concentration tests. Fifty mM stock solutions were prepared with 100% ethanol, which was diluted with filtered seawater to the desired experimental concentrations: 50 μM16, 20 μM and 5 μM15. Due to high fatality rates at all of these concentrations when used in this study on C. barnesi, all concentrations were diluted. Fifty mM stock solutions of 5-methoxy-2-methyl-3-indoleacetic acid, 5-methoxyindole-2-carboxylic acid, 2-methylindole and 5-Methoxy-2-methylindole were prepared with 50% ethanol (50% Milli-Q® water) and stored at − 20 °C. Fifty mM stock solutions were diluted with filtered seawater to the experimental concentrations of 5 μM, 1 μM, 0.5 μM, 0.1 μM and 0.05 μM. The carrier solution of 50% ethanol (50% Milli-Q® water) was diluted to the equivalent of the experimental concentrations listed above for use as a control, and incorporated into data as concentration 0. Seventeen ml of solution was added to polyps to fill each well of a 6-well plate.Iodine treatment (lugols solution)Aqueous iodine in the form of Lugols solution (0.37% iodine and 0.74% potassium iodide (sigma product information)) was prepared with equivalent concentrations of moles iodine/iodide: 1.5 μM, 3 μM, 6 μM, 12 μM and 24 μM. Filtered seawater only was used a control for this treatment and incorporated into data as concentration 0. 17 ml of solution was added to polyps to fill each well of a 6-well plate.Retinoid treatmentTo reduce ethanol associated fatality of polyps 0.015% ethanol in Milli-Q® water was used to prepare a 1 mM stock solution of 9-cis-Retinoic acid. The 1 mM stock solution was diluted with filtered seawater to the experimental concentrations of 5 μM, 1 μM, 0.5 μM, 0.1 μM and 0.05 μM. The carrier solution of 0.015% ethanol (Milli-Q® water) was diluted to the equivalent of the experimental concentrations listed above for use as a control, and incorporated into data as concentration 0. 17 ml of solution was added to polyps to fill each well of a 6-well plate.Metamorphosis trialsPrimary trialsExperimental concentrations of reagents were added to C. barnesi polyps growing in the wells of sterile 6-well tissue culture plates. One plate was used per chemical, per concentration, in which five wells functioned as replicates containing the chemical being trialed, whilst the sixth well contained only the control medium. Five concentrations were run for each of six chemicals; 30 plates in total.The filtered seawater the polyps were growing in was exchanged for the experimental chemical on day 0, and was not changed for the duration of the trial. Lids remained attached to tissue culture plates to negate water evaporation and hence salinity changes.Polyps in each well were photographed each day through a dissection microscope over a period of 34 days. Results were then recorded from the photographs, categorised (Fig. 6) as the number of polyps which displayed:Tentacle migration: one of the key signs of metamorphosis in this species, polyp tentacles merge, migrating to form four distinct corners in a square shape8.Detached medusa: a medusa formed and detached from the polyp, recorded regardless of health.Mobile detached medusa: a healthy medusa formed and detached from the polyp, with the ability to swim.Polyp survival: this was then used to calculate the number of polyps which survived the treatment which did not metamorphose.Optimisation trialThe optimal chemical and concentration was then deduced by choosing the combination that produced the largest percentage of healthy detached medusa, in this case 5-methoxy-2-methylindole at 1 μM. A final trial was then run with this to determine if length of chemical exposure could optimize healthy medusa yield. Three replicates of a minimum of five polyps were used per treatment, in which in 1 μM of 5-methoxy-2-methylindole (in seawater) was added to polyps for 24, 48, 72, 96 and 120 h, before the solution was changed to fresh seawater. A sea water only control was also run. The total number of healthy detached medusa were recorded each day.Data analysisAll statistical analysis was conducted in IBM SPSS Statistics Ver28. Graphs were produced in Microsoft Excel 2016 and OriginPro Graphing and Analysis 2021.Primary trialsThe effect of chemical, concentration and time was analysed using a repeated measures three-way ANOVA for four sets of data gathered during the metamorphosis process: percentage of polyps to display tentacle migration, percentage of polyps to have medusa detach, percentage of polyps to have healthy swimming medusa detach, percentage survival of polyps that did not metamorphose. Percentage data was arcsine square root transformed prior to analysis. Mauchly’s Test of Sphericity indicated that the assumption of sphericity had been violated on all four sets of data and therefore, a Greenhouse–Geisser correction was used.Optimisation trialDifferences in the mean percentage of healthy medusa produced at different exposure times was analysed using ANOVA. Differences between means were elucidated using a Post hoc Tukey pairwise comparison test (Tukey HSD alpha 0.05). More

Our study reveals zinc isotopes to be a promising trophic indicator in sharks and other fishes in general, similar to previous studies featuring both terrestrial and marine mammals9,10,11,12,13. We analysed the Zn isotope values for extant sharks spanning captive/aquarium and wild individuals from various localities and found close correspondence with their respective trophic level. Further, Zn concentration and isotope composition suggest preservation of this biological signal in fossil specimens with little diagenetic alteration. A survey of fossil shark teeth spanning the Miocene–Pliocene reveal similar δ66Zn values and variation as found in related (e.g., congeneric) extant sharks with similar dentition and ecology. Our δ66Zn results indicate high trophic levels for Otodus and perhaps a trophic change in C. carcharias, the great white shark.Zinc isotopes in extant sharks and teleostsAs with mammals9,10,11,12,13, bioapatite δ66Zn values in wild extant elasmobranchs and teleosts show overall lower values with increasing trophic level (Fig. 1; Supplementary Fig. 1). Both δ66Zn and δ15Ncoll correlate with FishBase17 trophic levels, despite differences in species’ geographic origin and tissue types sampled (Spearman’s correlation r = −0.87, p = 5.65E–16, n = 48 and r = +0.42, p = 1.47E–5, n = 40, respectively). There is no statistically significant relationship between bioapatite δ66Zn values and δ13Ccoll, but there is one between wild fish δ66Zn and δ15Ncoll values from the same tooth or individual (R2 = 0.28, p = 6.89E–4, n = 38; Supplementary Fig. 2). Both proxies thus generally reflect trophic levels. Large apex predatory sharks (e.g., Carcharodon carcharias, Isurus oxyrinchus, and Lamna ditropis) have significantly more negative δ66Zn values than lower trophic level teleosts and the plankton-feeding basking shark (Cetorhinus maximus). In particular, the shortfin mako shark (I. oxyrinchus) and great white shark (Carcharodon carcharias), both apex predators18,19, have much lower δ66Zn values than in any previously recorded extant vertebrate species (enameloid up to –0.71 and –0.63‰, respectively). These low δ66Zn values are likely due to the larger number of trophic levels in the marine ecosystem than in terrestrial food webs (terrestrial mammal enamel lies typically between 0 and +1.6‰9,11) and perhaps differences between marine and terrestrial Zn isotope baselines.Fig. 1: Zinc isotope (δ66Zn) composition of extant elasmobranch and teleost fish teeth and gill raker.Specimens come from off the coast of KwaZulu-Natal (KZN) South Africa, New Jersey (NJ), California (CA), North Carolina (NC), Iceland (IS), Norway (NO), Florida (FL), Cyprus (CY), Massachusetts (MA), Alaska and Israel. Aquarium sharks are from the New York (NY) and Tokyo (TYO) Aquariums and the Eilat (Israel) Underwater Observatory Park. Pisciculture S. aurata individuals are numbered and plotted individually to visualise the homogeneity among control-fed individuals compared to wild elasmobranchs and teleosts. Silhouettes are not to scale. Measurement uncertainty is indicated at the 2 SD level. Samples are colour-coded following their genus, regardless of locality. Source data are provided as a Source Data file.Full size imageAbsolute enameloid δ66Zn values vary by up to 1.26‰ among the extant species analysed from various oceanographic areas (Fig. 1). Our results also demonstrate large variability in enameloid δ66Zn values among extant sharks within the same region; for example, there is a 0.88‰ difference between mean values of Carcharodon carcharias and the bull shark (Carcharhinus leucas; Fig. 1) from KwaZulu-Natal (South Africa, KZN). In contrast, enameloid δ66Zn from the same species (e.g., Carcharodon carcharias, Carcharhinus obscurus) demonstrate a low isotopic variability, independent of geographic location (Fig. 1).We observe uniformity in the enameloid δ66Zn values of five gilt-head bream (Sparus aurata) individuals fed on a controlled fish pellet diet in pisciculture cages located offshore of Central Israel, with values within the measurement uncertainty of each other (–0.01 ± 0.01‰). As with δ66Zn, the δ15Ncoll and δ13Ccoll values are distinct from those of wild teleost individuals caught nearby in Haifa Bay, reflecting the artificial pelleted diet of the pisciculture individuals (Fig. 1, Supplementary Figs. 3, 4). Strongly contrasting the homogenous control fed S. aurata δ66Zn values, we observe a higher δ66Zn variability among (and even within) wild and aquaria elasmobranch individuals (fed with wild-caught fish and cephalopods). For instance, two teeth of a single tiger shark (Galeocerdo cuvier) individual (–0.52 and –0.27‰, Fig. 1) have a variability higher than the total variability among the three KZN G. cuvier individuals. Galeocerdo cuvier is well known for its highly opportunistic prey selection20. Therefore, the δ66Zn value of bioapatite is likely highly responsive to an individual’s diet at the time of tissue formation, and as shark teeth form and replace continuously, enameloid δ66Zn values can vary among teeth of a single individual. Thus, although fish can absorb Zn via their gills, waterborne Zn absorption appears to have a negligible effect on elasmobranch tooth δ66Zn values, in line with Zn incorporated into soft and skeletal tissues in natural environments being predominantly derived from dietary gastrointestinal uptake7,8.Carcharhinus enameloid δ66Zn values are high relative to sharks with similar bulk δ15Ncoll values, which contrary to the here analysed Carcharhinus species more regularly consume pelagic prey offshore, oceanic and on the continental shelf (e.g., Galeocerdo cuvier)21. This discrepancy may relate to Carcharhinus species inhabiting neritic waters where they feed primarily on demersal/benthic, freshwater-brackish-coastal prey22,23,24,25. While the diet of KZN G. cuvier and Carcharodon carcharias can also include reef-associated or demersal prey, pelagic organisms are typically more important by mass, especially in adult individuals20,26. Zinc isotope variability among marine organisms and their tissues is largely unknown, currently limiting our ability to identify specific food items based on shark enameloid δ66Zn values beyond generally observed trophic level effects. Whether higher Carcharhinus enameloid δ66Zn values relate to specific prey species (and trophic level) or general differences in basal organic matter source between a primarily neritic food web compared to a more open marine pelagic food web remains unclear (Supplementary Discussion 1). However, we observe no difference in δ13Ccoll values that imply a more terrestrial carbon signal in the KZN Carcharhinus species relative to sympatric species, arguing against differences in the basal organic matter source amongst the KZN shark species (Supplementary Fig. 3).A previous study on Arctic marine mammal bones suggested a higher geographic independence of δ66Zn values from baseline variability compared to δ13Ccoll and δ15Ncoll values13. Likewise, fish taxa with similar diet composition, habitat use and/or trophic level, have a similar range of bioapatite δ66Zn values regardless of their geographic locality (Fig. 1), indicating that δ66Zn may allow worldwide dietary and trophic level comparability with limited marine baseline variation. Further studies will need to expand our knowledge on δ66Zn variability in extant marine vertebrates as well as the effects of baseline on marine vertebrate enameloid δ66Zn values, especially compared to dentine δ13Ccoll and δ15Ncoll values. Nevertheless, the high taxa-specific and perhaps baseline-independent δ66Zn values suggest δ66Zn is an independent indicator of trophic level and an asset for present and past food web reconstructions in the marine realm.Deep-time zinc isotope preservation in fossil enameloidFossil enameloid has δ66Zn values and Zn concentrations ([Zn]) in the range of extant elasmobranch species, arguing against significant diagenetic modification (Figs. 2, 3, Supplementary Fig. 5). Fossil shark teeth examined herein are from Germany, Malta, Japan, North Carolina (USA) and Florida (USA) covering the Early Miocene (Burdigalian, 20.4–16.0 Ma), Miocene-Pliocene transition (Messinian-Zanclean boundary, ca. 5.3 Ma), and the Early Pliocene (Zanclean, 5.3–3.6 Ma; Fig. 2; Supplementary Note 2). Importantly, extant and fossil elasmobranch enameloid δ66Zn values (–0.71 to +0.28‰ and –0.83 to +0.27‰, respectively) differ from: (1) previously reported values of terrestrial mammal enamel (0 to +1.6‰);9,11 and (2) sedimentary carbonate δ66Zn values of the fossil sites (+0.34 to +0.49‰, Supplementary Fig. 6, Supplementary Table 1). These differences support a preserved biological signal in fossil enameloid.Fig. 2: Zinc isotope (δ66Zn) composition of fossil elasmobranch enameloid.Teeth are from the Early Pliocene of Japan, North Carolina (NC) and Florida (FL), Pliocene to Miocene transition of Florida, the Early Miocene of North Carolina, Germany and Malta. For more details on the sample background, see Supplementary Data 1, Supplementary Note 2. Silhouettes are not to scale. Measurement uncertainty is indicated at the 2 SD level. Samples are colour-coded following their genus, regardless of locality. Source data are provided as a Source Data file.Full size imageFig. 3: Zinc isotope (δ66Zn) composition of fossil and extant elasmobranch enameloid of selected taxa combined from Figs. 1 and 2.Fossil teeth are from multiple locations and ages. Grey silhouettes indicate extant teeth. The boxes for n  > 5 represent the 25th–75th percentiles (with the median as a horizontal line) and the whiskers show the 10th–90th percentiles. Box plots (and n) do not include aquarium teeth (open squares). Otodus spp. includes all O. chubutensis (dark blue) and O. megalodon teeth (light blue) analysed and samples are otherwise colour-coded following their genus. Silhouettes are not to scale. For more details on the samples, see Figs. 1 and 2 and Supplementary Data 1. Source data are provided as a Source Data file. Measurement uncertainty is indicated at the 2 SD level.Full size imageWe observe the same within tooth Zn spatial concentration pattern in extant and Miocene tiger shark (Galeocerdo spp.) teeth, with Zn being more enriched in the outer enameloid than close to the enameloid-dentine junction. If significant diagenetic Zn exchange had occurred throughout the enameloid, this original Zn concentration pattern would not be preserved in the fossil tooth (Supplementary Fig. 7). Additionally, both extant and fossil shark enameloid show the same variation in [Zn] according to their taxonomy, with carcharhiniforms generally having higher [Zn] than lamniforms (Supplementary Fig. 5), again arguing against significant diagenetic enameloid Zn exchange. For the European Miocene sites, δ18OP analyses were also conducted on a subset of teeth, where their enameloid appears to be generally well-preserved as suggested by δ18OP values demonstrating species-specific relative in-vivo temperature ranges as expected compared to the habitat use of equivalent modern species27 (Supplementary Fig. 8).To discern the effects of diagenetic Zn alteration, we compare visually pristine appearing enameloid with areas sampled along fractures and dentine of the same tooth (Supplementary Figs. 6 and 9, Supplementary Table 2). Our results demonstrate that the diagenetic Zn exchange in fractured enameloid leads to higher δ66Zn values than in the pristine enameloid of the same tooth, whereas we observe no differences in enameloid δ66Zn profiles of modern teeth (Supplementary Figs. 9 and 10, Supplementary Table 3). Likewise, the diagenetically more susceptible fossil dentine shows higher δ66Zn values as reflected by a significantly higher and more variable dentine-enamel δ66Zn offset (+0.78 ± 0.33‰, n = 13) than observed for extant teeth (+0.22 ± 0.1‰, n = 23; Supplementary Discussion 2, Supplementary Figs. 6 and 11). For the fossil enameloid shown here, in-vivo δ66Zn values must be at least as low as their current values, indicating limited to no alteration. Consequently, δ66Zn analysis of fossil enameloid can enable deep-time dietary reconstructions.The homogeneity in δ66Zn values for the same species or genera independent of locality and geological age is a remarkable observation (Figs. 2, 3), not only limiting the likelihood of Zn diagenetic alteration but also arguing for minimal variability in habitat-specific food web baselines or a strong homogenisation of δ66Zn values at low trophic levels. There are still some limitations, such as the absence of reported δ66Zn values of marine non-mammalian vertebrates for comparison outside this study, the limited sample size for some species, and uncertainties regarding Zn isotope baseline variability. However, our extensive δ66Zn dataset includes not only multiple species from different localities and periods with distinct differences in dietary Zn uptake among extinct elasmobranch species, but also direct overlap in extant and fossil δ66Zn values of the same genus and/or lifestyle. This spatial and temporal coherence suggests that it may be possible to use the same interpretative framework on extant and fossil elasmobranch assemblages globally (Figs. 1, 2, 3), and our remaining discussion is based on this assumption.Zinc isotopes and ecology of Miocene-Pliocene sharksAbsolute and relative δ66Zn values among some taxonomic groups show no statistical variation with geologic age and locality (e.g., Carcharias spp., Galeocerdo spp.), indicating relatively stable trophic levels and ecological niches throughout time and space. For example, most extinct elasmobranchs with a slender tearing, grasping tooth morphology (e.g., Carcharias) have δ66Zn values that can be directly compared to modern equivalents (e.g., Carcharias taurus, Isurus oxyrinchus, Lamna ditropis). This type of dentition and corresponding tooth morphology are adapted to restrain small, active prey—like fish and cephalopods28,29,30. However, there are differences among the δ66Zn values for these types of elasmobranchs within the Early Miocene of Germany, with Mitsukurina lineata and Pseudocarcharias rigida having higher mean δ66Zn values compared to Araloselachus cuspidatus (Fig. 2). Indeed, post hoc Tukey pairwise comparisons draw out A. cuspidatus as distinct from most species for the Germany (Early Miocene) assemblage, including those with a similar grasping tooth morphology (Supplementary Table 4). Our δ66Zn values indicate that A. cuspidatus was likely a higher trophic level piscivore than M. lineata and P. rigida, supported by the larger tooth size of A. cuspidatus.Zinc isotope values within the Galeocerdo lineage show no statistical variability with age nor locality, suggesting tiger sharks occupied a similar trophic level and ecological role in the marine ecosystem since at least the Early Miocene (Fig. 3). Notably, our results imply that the increase in body size from G. aduncus to the modern G. cuvier did not change its overall trophic level, which is in line with the highly similar tooth morphology between the two species31.For Carcharhinus, the Early Miocene Malta assemblage is drawn out as statistically different from extant wild Carcharhinus spp. (Supplementary Table 5). Still, Carcharhinus spp. in both extant and fossil assemblages always have higher mean δ66Zn values than other sympatric predatory sharks and are drawn out as statistically different from sympatric shark species in each fossil assemblage (Figs. 2, 3, Supplementary Tables 6–8). Based on similarities in tooth morphology and δ66Zn values among extant and extinct Carcharhinus spp., we suggest that extinct taxa also primarily occupied a neritic-coastal habitat feeding upon demersal-benthic prey22,23,24,25. For the Carcharhinus teeth from Malta, this interpretation is supported by lower δ18OP values than sympatric species, indicating a higher water temperature or lower salinity: i.e., a shallow and/or brackish water habitat (Supplementary Fig. 8). Consequently, the uniformly higher δ66Zn values of extant and fossil Carcharhinus spp. indicate the consumption of food items distinct from other measured sympatric species already during the Early Miocene and Early Pliocene.Absolute δ66Zn values for Otodus spp., along with values relative to sympatric species, indicate megatooth sharks were apex predators feeding at a very high trophic level (Figs. 2, 3). In all Early Miocene assemblages, mean O. chubutensis δ66Zn values are among the lowest compared to sympatric species, including the lowest bioapatite δ66Zn value measured to date (–0.83‰). Mean O. chubutensis δ66Zn values are as low as extant Carcharodon carcharias (respectively, –0.57 ± 0.18‰, n = 19 and –0.57 ± 0.05‰, n = 4). Noteworthy, Games-Howell pairwise comparisons indicate the lower extant C. carcharias δ66Zn values as distinct from most fossil Carcharodon populations, possibly indicating a dietary shift in the Carcharodon lineage (Supplementary Table 9). Early Pliocene values from O. megalodon from Japan also demonstrate very low mean δ66Zn values (–0.62 ± 0.11‰, n = 5) that are statistically different from the Atlantic O. megalodon populations sampled from Florida and North Carolina, which have higher mean δ66Zn values (respectively, –0.34 ± 0.11‰, n = 11; –0.38 ± 0.11‰, n = 7; Fig. 2, Supplementary Table 10).Possible explanations for the observed spatial and temporal variability in Otodus and Carcharodon δ66Zn values in our study are differences in prey consumption (and trophic level) or baseline variation. Additionally, we cannot rule out other factors such as interpretive limitations due to sample sizes. For example, extant C. carcharias can exhibit some degree of dietary individuality32, yet we only have δ66Zn data from two individuals (4 teeth) from two localities. Still, the low δ66Zn values in both extant C. carcharias compared to other extant sharks is in line with the generally high trophic level estimates of this species18. Particularly for O. megalodon from Japan where we have only one species analysed, we cannot exclude the possibility of either differences in δ66Zn baseline or regionally different prey species. However, the absence of significant δ66Zn differences within many taxa amongst locations and geological ages implies negligible differences in δ66Zn food web baselines (Figs. 2, 3). Therefore, the observed spatial and temporal variability in δ66Zn values likely demonstrates true dietary differences amongst Otodus and Carcharodon populations both geographically and temporally, with important implications for each species’ feeding ecology and evolution both on a local and global scale.Otodus and Carcharodon in the Early Miocene are represented by O. chubutensis and C. hastalis, respectively, with statistically significant higher mean δ66Zn values from the latter (Figs. 3, 4, Supplementary Tables 11, 12). The mean δ66Zn value for all O. chubutensis is the lowest of all mean values recorded in our fossil shark dataset (Fig. 3), suggesting that O. chubutensis could occupy a higher trophic position than C. hastalis. Importantly, differences between δ66Zn values of O. chubutensis and C. hastalis do not appear related to a different ratio of juveniles to adults in either species, as our results do not record an ontogenetic diet shift (Supplementary Fig. 12). We observe no correlation between the total body length of Otodus spp., Carcharodon spp. and their respective δ66Zn values (Supplementary Fig. 12), likely, because each examined specimen had already surpassed the body size for which ontogenetic dietary shifts, if any, occur.Fig. 4: Results from post-hoc Games-Howell pairwise comparisons of δ66Zn values of enameloid from fossil and extant Otodus spp. and Carcharodon spp.All assemblages and ages are combined for a given species, except for extant C. carcharias. Extant C. carcharias teeth are indicated with grey silhouettes. a Includes all O. megalodon populations, whereas (b) excludes the Japanese (Pacific) population, focusing on Atlantic and Tethys/Paratethys populations only. The boxes for n  > 5 represent the 25th–75th percentiles (with the median as a horizontal line), and the whiskers show the 10th–90th percentiles. Significance level is indicated by “*” (p value < 0.05), “**” (p value < 0.005), “***” (p value < 0.0005) and “****” (p value < 0.00005). Measurement uncertainty is indicated at the 2 SD level. See also Supplementary Tables 11, 12. Otodus chubutensis (dark blue) and O. megalodon teeth (light blue) are coloured separately. All other samples are colour-coded following their genus. Source data are provided as a Source Data file. Silhouettes are not to scale.Full size imageWhen including only Otodus spp. from the Atlantic and Paratethys/Tethys regions, we observe a statistically significant difference between O. chubutensis and O. megalodon (Supplementary Table 12, Fig. 4b). During the Early Pliocene, the Otodus lineage represented by O. megalodon shows a considerable increase in the mean δ66Zn value for the Atlantic populations, hinting at a reduced trophic position for the megatooth shark lineage in the Atlantic. At the same time, the Early Pliocene C. carcharias remains at the same trophic level as C. hastalis (Figs. 2–4, Supplementary Tables 11, 12). Although the extant sample size is limited, our results are intriguing because the mean δ66Zn value for extant C. carcharias places it at a trophic level that would be higher than the Atlantic Early Pliocene O. megalodon (Figs. 3, 4, Supplementary Table 11, 12).Extant Carcharodon carcharias is a predatory shark whereby larger individuals regularly feed on high trophic level marine mammals33. Although Neogene Carcharodon and Otodus were likely opportunistic in their prey selection similar to many extant apex predatory sharks33, fossil evidence of bite marks suggests that both taxa fed largely on marine mammals such as cetaceans (mysticetes and odontocetes) and pinnipeds1,2,4,34,35,36,37,38. However, in the majority of cases, it remains unclear if these feeding events on mammals document active hunting or scavenging and how important each prey taxa were to their overall diet. Early Pliocene C. carcharias and O. megalodon δ66Zn data suggest that lower trophic level mammal prey such as mysticetes (and perhaps herbivorous sirenians) may have been an important food item for both species. Mysticetes are filter-feeders and likely to have higher tissue δ66Zn values than piscivorous odontocetes or pinnipeds, similar to the higher δ66Zn values in the plankton-feeding extant Cetorhinus maximus compared to piscivorous sharks (Fig. 1). Bite marks on Late Miocene–Early Pliocene mysticetes bones from both Carcharodon carcharias and O. megalodon1,4,34,38 corroborate at least occasional feeding events.Now extinct small- and medium-sized mysticetes (e.g., Cetotheriidae and various small-sized Balaenidae and Balaenopteridae) were abundant during the Early Pliocene39,40 and were thus available as prey for large sharks, i.e., Otodus megalodon4 and Carcharodon carcharias1. In contrast, Early Miocene cetacean fossils are dominated by toothed cetaceans, where the Early Miocene European and North American sites sampled in this study lack any mysticete remains41,42,43,44. The Early Miocene Otodus (and modern C. carcharias) lower δ66Zn values (higher trophic level) may partly be related to the lack of lower trophic level mammals (e.g., mysticetes) available as prey. Mysticetes became more abundant following a diversity plateau during the mid-Miocene39,45. Subsequently mysticetes remains become more prominent in the Late Miocene to Early Pliocene fossil assemblages from North Carolina and Florida studied herein43,44, where mysticetes were, together with other mammals (e.g., odontocetes), possibly preyed upon by O. megalodon and C. carcharias.For the Early Pliocene of North Carolina, where we have δ66Zn values for both Otodus megalodon and Carcharodon carcharias, our results suggest largely overlapping trophic levels for both species. Feeding at the same trophic level does not necessarily imply direct dietary competition, as both species could have specialised on different prey with similar trophic levels. However, at least some overlap in food items between both species is likely, as also indicated by fossil bite marks1,4,34,38. Extant predatory sharks typically feed on a wide range of food items33, and there is evidence for generalist feeding, as well as, in some cases, specialisation at lower trophic levels for extant C. carcharias32. Higher dietary individuality and the opportunistic nature of apex predators are possible explanations for the range of δ66Zn values observed in both species (–0.61 to –0.04‰ in Pliocene North Carolina).The extinction of Otodus megalodon could have been caused by multiple, compounding environmental and ecological factors46,47, including climate change and thermal limitations48, the collapse of prey populations4 and resource competition with Carcharodon carcharias15 and possibly other taxa not examined here (e.g., carnivorous odontocetes). The δ66Zn results presented here indicate the potential of trophic change, where we find evidence for a decrease in the mean trophic position from O. chubutensis to O. megalodon in the Atlantic and an increase in trophic position for C. carcharias from the Early Pliocene to its extant form. If these trophic dynamics are accurate, then there is a possibility for the competition of dietary resources between these two shark lineages15. Our results also support the hypothesis of Otodus size-driven co-evolution and co-extinction with mysticetes4, indicated, at least for the Atlantic assemblage, by a shift towards lower trophic level prey from the Early Miocene to the Early Pliocene within the Otodus lineage. In general, our study demonstrates δ66Zn to be a powerful, promising tool to investigate the trophic ecology, diet, evolution, and extinction of fossil marine vertebrates. More

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