SCIENCE ADVANCES | RESEARCH ARTICLE ENVIRONMENTAL STUDIES Copyright © 2021 The Authors, some The global ocean size spectrum from bacteria to whales rights reserved; exclusive licensee American Association Ian A. Hatton1,2*†, Ryan F. Heneghan2,3†, Yinon M. Bar-On4, Eric D. Galbraith2,5 for the Advancement of Science. No claim to It has long been hypothesized that aquatic biomass is evenly distributed among logarithmic body mass size classes. original U.S. Government Although this community structure has been observed regionally, mostly among plankton groups, its generality has Works. Distributed never been formally tested across all marine life over the global ocean, nor have the impacts of humans on it been under a Creative globally assessed. Here, we bring together data at the global scale to test the hypothesis from bacteria to whales. We find Commons Attribution that biomass within most order of magnitude size classes is indeed remarkably constant, near 1 gigatonne (Gt) License 4.0 (CC BY). wet weight (1015 g), but bacteria and large marine mammals are markedly above and below this value, respectively. Furthermore, human impacts appear to have significantly truncated the upper one-third of the spectrum. This dramatic alteration to what is possibly life’s largest-scale regularity underscores the global extent of human activities. INTRODUCTION biomass across size classes. These factors include metabolism (16–23), In 1972, Sheldon et al. (1) published measurements of marine trophic growth efficiency (19–25), encounter rates or consumption plankton abundance spanning about six orders of magnitude in body (18, 26–28), predator-prey mass ratios (19–24, 26, 28–30), rates of mass (from ~0.6 to 100 m in body length), collected at approxi- growth (16, 17, 19, 22, 25–30), birth or reproduction (26–28), and mately 80 Atlantic and Pacific stations in a circumnavigation of the mortality (16, 17, 25–30). Many of these variables exhibit robust Americas. At each station, the total biomass of all individuals was allometric scaling relations with body size (31–34), but which com- approximately evenly distributed across logarithmic size classes (1). bination of variables ultimately dominate the maintenance of the On the basis of these planktonic observations, they boldly hypothe- size-spectrum across the diversity of marine taxa remains an open sized that “to a first approximation, roughly equal concentrations of question. More generally, a great diversity of adaptive traits, from material occur at all particle sizes within the range from 1 m to life history and resource encounter strategies to mobility and sensory about 106 m, i.e., from bacteria to whales.” Although Sheldon et al. ability, depends on organisms “being the right size” (14, 31, 33, 34). (1) were focused on the distribution of biomass at the regional scale, This suggests that not all size classes are created equal and that their study had immediate global implications. Yet, this extraordinary certain sizes should be selectively advantaged or disadvantaged, hypothesis has never been formally tested globally across the astro- challenging the idea of an evenly distributed size spectrum. Knowing nomical range in body masses it encompasses nor has its possible the community structure across the full size range of marine life is alteration by human impacts been examined at the whole-ocean scale. thus key to strengthening size spectrum theory and is needed for a Since Sheldon et al.’s seminal work (1), the distribution that re- broader understanding of biosphere functioning and human impacts sults from aggregating individuals, regardless of species identity, into on the global ocean (13, 15, 35). size bins has become known as the size spectrum or Sheldon spec- Despite nearly 50 years of empirical and theoretical work, research trum, among other names (2). Sheldon et al.’s hypothesis has been has been dominated by regional studies and has been limited to widely validated at local and regional scales, mostly among pelagic much smaller size ranges than the 23 orders of magnitude originally plankton groups (1–6), but occasionally extending up to fish (7, 8), conjectured [but see (36)]. Empirical size spectra have typically as well as in freshwater systems (8–11). These studies have often averaged a range in body mass of six orders of magnitude and have reported notable similarity in the exponents of these distributions not exceeded 16 (5, 7, 8, 10) (table S3). A major challenge to com- (fig. S2 and table S3) (1–3, 5, 7, 12). Although there are many ways to parisons over these disparate size scales is posed by the extremely represent the size spectrum (2), these exponents are typically near −1 different spatial scales over which measurements must be made. for the relation between the logarithm of numerical abundance across Whereas bacteria and small plankton can be estimated in a small logarithmic size classes, equivalent to an exponent near 0 for biomass water sample, the largest fish and mammals can actively range over across log size classes (2) (Materials and Methods). thousands of kilometers, and only the global scale unambiguously These empirical findings have inspired a rich literature on size captures the full spatial range of all marine organisms. Furthermore, spectrum theory [see recent reviews; (2, 12–15)]. Existing explana- although human activities are known to have locally altered the tions for the size spectrum are predominantly based on variations shape of many size spectra (2, 12, 15, 37, 38), the extent to which these of predator-prey interactions and tend to rely on a combination activities may have affected the whole-ocean size spectrum has not of two or more lower level factors to account for the distribution of been investigated. Here, we make use of advances in global ocean observation and recent meta-analyses to test Sheldon’s original hypothesis from bac- 1 Max Planck Institute for Mathematics in the Sciences, Leipzig 04103, Germany. teria to whales at the global scale. We evaluate this hypothesis in a 2 Institut de Ciència i Tecnologia Ambientals (ICTA), Universitat Autonoma de Barcelona, Barcelona, Spain. 3School of Mathematical Sciences, Queensland Uni- “pristine” state, before industrial-scale human capture of fish and versity of Technology, Brisbane, QD 4000, Australia. 4Department of Plant and marine mammals (pre-1850), based on a combination of marine Environmental Sciences, Weizmann Institute of Science, 76100 Rehovot, Israel. ecosystem models and prior published historical reconstructions. 5 Department of Earth and Planetary Sciences, McGill University, Montreal, QC H3A We compare the pristine to present-day size spectrum based on 0E8, Canada. *Corresponding author. Email: i.a.hatton@gmail.com published estimates of direct human impacts and population de- †These authors contributed equally to this work. clines (see Materials and Methods). Given the diversity of taxa and Hatton et al., Sci. Adv. 7, eabh3732 (2021) 10 November 2021 1 of 12 SCIENCE ADVANCES | RESEARCH ARTICLE observational scales, we tailored our methods to the available data are estimated from >220,000 water samples, geographically distributed for each group. For example, phytoplankton are estimated globally as shown in Fig. 1A (black points), and interpolated over the whole using satellite images of surface chlorophyll, with algorithms designed ocean based on environmental correlates. The biomass of fish, which to estimate total depth-integrated biomass. Heterotrophic bacteria aggregate, migrate, and can escape capture, is challenging to estimate and all zooplankton groups, from single cells to large crustaceans, from point samples but are nonetheless intensively “sampled” by commercial fisheries; so, we use two independent global process models constrained by global catch data (39, 40) (table S5). Last, given that large marine mammals can individually range across A Sample points and total biomass 25 100 225 whole ocean basins, we compile global population estimates for g/m2 most marine mammal species (n = 82) and use body size allometry and geographic ranges to estimate the remainder (n = 44; fig. S9; see Materials and Methods). Our approach allows us to estimate the biomass of 12 major groups (aggregated into 5 groups in the figures) over approximately 33,000 1° grid points of the global ocean. The total group biomasses are broadly concordant with prior global compilations of particular groups, as shown in tables S1 and S2 (41–43). We partition each group biomass into order of magnitude body mass size classes over their respective size ranges, based on published size distributions (table S3), or if unknown, we partition biomass uniformly across the group size range and test this assumption with alternative distri- B Ocean size-frequency distribution butions and sensitivity analysis (figs. S11 and S12) (44). For each group and size class, we estimate a logarithmic 95% confidence f(x) ~ x 1.04 interval (CI), representing a multiplicative fold uncertainty. We outline our data sources, methods for estimating pristine, and present-day biomass, as well as the various sources of uncertainty Number of individuals (count) in Materials and Methods and the Supplementary Materials (44), and report here the most robust overall results. RESULTS We find that the reconstructed pristine global ocean size spectrum is largely consistent with Sheldon et al.’s original hypothesis (Fig. 1B), particularly in the epipelagic (the upper, sunlit portion of the ocean). The least squares regression fit to log abundance versus log size Mammals class is close to the long-hypothesized value of −1 (−1.04, 95% CI: Fish −1.05 to −1.02) and exhibits remarkable regularity. This regularity Zooplankton derives from the fact that we are aggregating organisms over very Autotrophs large spatial extents and size classes and representing the relation Bacteria over an enormous 23 orders of magnitude, over which even large residual variation is undetectable. This pattern indicates that biomass is generally not dominated by Body mass (g) any best adapted size, as is evident when abundance is transformed to biomass (Fig. 2A). However, our results show exceptions at the Fig. 1. The global ocean size spectrum. (A) The black mapped points are extremes: Bacteria and whales diverge from the uniformity in n = 226,405 sample locations for measurements of heterotrophic bacteria and biomass, which are more obvious when displayed on a linear scale zooplankton. Autotrophs were estimated from satellite imagery of surface chlorophyll (Fig. 2B). Whereas all other groups sum to approximately 1 gigatonne and fish from global process models constrained by catch data. Marine mammals (Gt) wet weight (1015 g) of biomass in each order of magnitude size bin, are estimated from species global population estimates, and their biomass is not the size bins dominated by bacteria and whales are notably different. included on the map. Biomass (g/m2; wet weight) of each group is summed over all Although there is considerable uncertainty in our estimates (Fig. 2A) groups in each 1° region of the ocean (only biomass in the upper 200 m is shown (44), these differences are more pronounced and significant when here). (B) Total ocean biomass (wet weight) is partitioned across relevant size classes we consider the size spectrum over the entire water column (g, wet weight) for each group to estimate the global size spectrum. This is shown (cross-shading in Fig. 2), with bacteria dominating the biomass in as the total number of individuals in each order of magnitude size class over the the cold, dark ocean. Mesopelagic nekton are also relatively abun- ocean’s epipelagic and continental shelves (upper ~200 m), giving an exponent of −1.04 (95% CI: −1.05 to −1.02). The gray confidence band includes biomass un- dant, leading to a peak at 0.01 to 1 g, but these estimates are prone certainty in each size class (Fig. 2 A) and uncertainty in the size distribution of each to large uncertainties (41, 42, 44), and we hesitate to draw a strong group (Fig. 2C, i). Bin colors show the relative fraction of each group on a linear conclusion about this portion of the spectrum. Sensitivity analysis axis [no relation to y axis or to the biomass in (A)]. Further details are in Materials shows that the overall size spectrum slope is robust to both the choice and Methods. of group biomass distributions and the possible broad variations in Hatton et al., Sci. Adv. 7, eabh3732 (2021) 10 November 2021 2 of 12 SCIENCE ADVANCES | RESEARCH ARTICLE A Biomass spectrum, log scale B Biomass spectrum, linear scale C Slope variation 103 i. Mean Global biomass (Gt; 1015 g) Entire depth Mammals 7 Upper 200 m = 0.04 10 - - - - - - Fish 500 6 - - - - - - - - - - - - - Zooplankton - - Autotrophs 5 Frequency Bacteria 1 0 –0.1 –0.05 0 0.1 4 - - - 0.05 - ii. Mean 3 - - - 40 - - - - - - - - - - - = 0.04 0.1 - 2 - - - 20 1 - 0 0 10 5 105 10 5 –1 0 1 10 10 1 10 10 1 105 –0.5 0.5 Body mass (g) Slope value Fig. 2. The pristine ocean biomass spectrum. Total estimated historic ocean biomass in each order of magnitude size class is approximately 1 Gt (gigatonnes or petagrams = 1015 g), with exceptions at either extreme. Biomass is shown in the upper 200 m of the ocean (colored) and extending to the seafloor (hatched colors represent the group that dominates below the epipelagic; bacteria dominate <10−11 g, and mesopelagic fish dominate size classes 10−3 to 103 g). (A) Global ocean biomass is shown on a logarithmic scale with logarithmic 95% CIs on epipelagic biomass. Bin colors show the relative fraction of each group (no relation to y axis). (B) Biomass estimates in (A) are shown on a linear scale to highlight differences of bacteria and whales from the overall trend. (C) Frequency histograms of biomass spectrum slopes for (i) resampled data incorporating uncertainty in both biomass [shown in (A)] and the size distribution of each group (n = 10,000 simulations) and (ii) prior published slope values for n = 325 measured biomass spectra (from 47 separate studies; note the difference in x axis from C, i). biomass within our uncertainty bounds (slope 95% CI = ±0.043; DISCUSSION Fig. 2C, i, and figs. S11 and S12) (44). Slope estimates are also robust Our estimated reconstructions of the pristine ocean biomass suggest to different fitting methods (table S7) and binning schemes (fig. S11). a robust law-like property of marine systems that appears to hold Last, our data allow us to approximate size spectra over most 1° lat-lon across nearly all marine life. These estimates imply that biomass is regions of the ocean, and although we are less confident in these nearly invariant across logarithmic size classes but diverges at the ~33,000 slope estimates, given the patchiness in the data and lack of extremes with a relatively higher abundance of bacteria and lower some important major groups, our data suggest that size spectra abundance of whales. These divergences mark a departure from slopes may be similar across global environmental gradients (fig. S13). what might be considered a strong interpretation of the Sheldon Our analysis also shows that the whole-ocean pattern is not hypothesis. Moreover, the cumulative impacts of historical fishing immune to human impacts. Despite marine mammal and wild fish and whaling appear to have resulted in major alterations to the catches amounting to <3% of annual human food consumption (44), present-day size spectrum. We discuss the theoretical and applied the previously reported cumulative impacts of industrial fishing and implications of these findings. whaling (45–48) are notable when viewed within the context of the global size spectrum. Fish >10 g in size and marine mammals are likely Implications for theory to have been reduced in biomass by about 2 Gt (~60% reduction; Much of the current size spectrum theory has focused on particular Fig. 3A), and the largest size classes appear to have experienced a groups such as plankton or fish, typically using body mass allometries near 90% reduction in biomass since 1800 (Fig. 3B). We also esti- for those groups to estimate key variables of the theory. Although mate potential climatic impacts that could occur over the next several size spectrum theories make predictions for the slope based century. To do so, we use published impacts on major groups from only on a small number of variables, such as metabolic scaling and high emission–projected changes in climate [representative con- predator-prey body mass relations (16, 18, 19, 21, 25), these predic- centration pathway (RCP) of 8.5; (49–51)] and assume that current tions depend on the scaling exponents of the presumed underlying fishing effort remains constant (Fig. 3B). These estimates suggest body mass allometries (16–18, 21, 27–29) or require that particular that fishing and whaling could have already had a considerably combinations of exponents sum to one for dimensional reasons greater impact among large size classes than will climate change (16, 17, 25). Since the size spectrum apparently holds over nearly all over the coming decades. Although there are considerable uncertain- eukaryotes, the question may be raised as to whether the body mass ties in these projections, it is clear that the direct impacts of fishing allometries, which have been used to explain the size spectrum, and whaling have markedly altered the ocean biomass spectrum. show the same consistency over this vast size range. In contrast with We find that the upper one-third of the biomass spectrum has what is widely assumed, predator-prey mass ratios are extremely been severely truncated and the whole-spectrum slope significantly variable, with up to six orders of magnitude residual variation in altered (Fig. 3C). any given size class (fig. S14) (52–54), and metabolism does not scale Hatton et al., Sci. Adv. 7, eabh3732 (2021) 10 November 2021 3 of 12 SCIENCE ADVANCES | RESEARCH ARTICLE has pointed out that humans are now the top predator in the marine A Major group biomass Pre 1850 ecosystem, having extracted most of the predatory fish and mam- 8 Present 2020 mals that previously occupied the upper ranges of the size spectrum Biomass (Gt) Projected 2100 (57). This raises the question: Do humans now play the same role previously played by the predators we have removed? Have 4 we simply inserted ourselves into the marine size spectrum and now act as a functionally equivalent top predator? The answer is 0 clearly no. Although human biomass is now among the largest of any single B Human impacts on size classes vertebrate species (at approximately 0.4 Gt), it remains unexpectedly small relative to the marine biomass that has been lost from the 100 Fishing to present largest size classes as a direct result of fishing and whaling (~2.7 Gt; % Loss Climate projection Fig. 3A). Furthermore, we can estimate the metabolic energy asso- 50 ciated with the lost biomass spectrum using empirical metabolic scaling relations for fish and mammals. As detailed in Materials and 0 Methods, we estimate that the lost biomass spectrum (pink hatched 10 105 area in Fig. 3C) would have previously dissipated energy (in units of C Impacts on the biomass spectrum biomass) amounting to as much as 14 Gt/year (12 Gt/year, if we only consider fish). This represents a lost metabolic demand that is 10 Pre 1850: y = 0.64 x 0.04 two orders of magnitude greater than the ~0.1 Gt/year of biomass Present: y = 0.29 x 0.08 energy obtained through fishing [and not exceeding ~0.2 Gt/year; (58)]. Clearly, humans have not merely replaced the ocean’s top predators but have instead, through the cumulative impact of the Biomass (Gt) past two centuries, fundamentally altered the flow of energy through the ecosystem. Further work is necessary to understand how this massive alteration of biomass flow may be affecting ocean eco- system functioning. In summary, our results provide evidence that the pristine size spectrum regularities previously observed at the local scale among particular groups are largely preserved at the global scale across all groups, as hypothesized by Sheldon et al. (1) half a century ago. The fact that biomass is so evenly distributed across such a vast size 10 10 10 5 1 105 range raises questions about the generality of existing size spectrum Body mass (g) theory, demanding renewed effort to uncover the dominant under- lying processes. At the same time, our analysis has quantified a Fig. 3. Direct human impacts on ocean biomass. (A) Estimated biomass in the major impact of humanity on the distribution of biomass across ocean’s upper 200 m is compared across major groups at three time periods: pre-1850 size ranges, highlighting the degree to which human activities in the (hatched bars), current levels (solid bars), and projected to 2100 (lighter shading). Anthropocene have altered life at the global scale. (B) Direct human impacts are estimated across size classes and show progressively more extreme impacts above 10 g (we do not consider possible indirect impacts on bacteria and plankton groups). (C) These impacts have altered the shape of the biomass spectrum, with the current-day regression (2020; dashed gray line) having MATERIALS AND METHODS a significantly steeper slope than the pre-1850 regression (solid black line; pristine, To construct the global ocean size spectrum and assess human as in Fig. 2). Hatched pink area is called the lost biomass spectrum. impacts, we drew on a diverse assemblage of data using methods tailored to the data available for different taxonomic groups and following a number of simplifying assumptions. Here, we summarize as 3/4 with body size but closer to one (fig. S15) (33, 34, 55, 56). our data sources and methodology for estimating the biomass of each Near-proportional metabolic scaling, for example, significantly major functional group (heterotrophic bacteria, phytoplankton, alters the predictions of several of the theories that rely upon it, zooplankton, fish, and mammals; Table 1), as well as the assump- yielding predicted slopes that differ significantly from the observed tions and limitations associated with reconstructing pristine ocean slope by −0.2 (18, 28) to +0.25 (20, 21, 23), depending on the theory. biomass. We describe how these estimates are used to build the While this may be insufficient to falsify these theories, it suggests global marine size spectrum, by partitioning biomass across rele- that size spectrum theory may need to be questioned in light of new vant size classes for each of 12 major groups. We outline the various evidence. More broadly, the size spectrum appears more general sources of uncertainty and how we estimate the 95% CI of our biomass and consistent than many of the individual-level processes and estimates for each functional group. We also detail our approach to allometries presumed to be its cause. estimate human impacts on the size spectrum through animal hunting and climate change. Full details of our approach are in the Supplementary Human impacts on energy flow Materials, including all data and referenced sources, as well as source Our results place the global loss of marine animals due to human code, allowing our analysis to be reproduced and updated as new consumption within the context of the size spectrum. Prior work data become available (https://doi.org/10.5281/zenodo.5520055). Hatton et al., Sci. Adv. 7, eabh3732 (2021) 10 November 2021 4 of 12 SCIENCE ADVANCES | RESEARCH ARTICLE Table 1. Summary of pristine ocean biomass estimates, data sources, and methods among groups. Estimated pristine ocean biomass (wet weight; 1 Gt =1015 g) are compared across major groups for the epipelagic (top 200 m) and full depth to the seafloor. Because depth-resolved estimates of fish and mammals were not available, these taxa were roughly allocated to top and full depth categories. Fold uncertainty is a multiplicative 95% CI on biomass. These biomass estimates are consistent with other global meta-analyses across major groups (20, 41–43, 67) and were used to partition biomass across the body size range to build the global ocean size spectra in Figs. 1 and 2. GLM, generalized linear model; SST, sea surface temperature. Biomass Gt Body mass Uncertainty Data sources and methods summary Major group Top Full range g 200 m depth ( (n is number of measurements) n = 47,254 samples from (60-62 Heterotrophic bacteria 10-14 10-11 3.7 14.5 3.9 with chlorophyll, SST and bathymetry to interpolate globally. Picophytoplankton 10-14 10-11 2.2 2.2 3.2 n = 39,402 chlorophyll a MODIS-Aqua satellite data averaged over 2002-2016. Nanophytoplankton 10-12 10-8 1.8 1.8 3.2 Biomass of each phytoplankton group was calculated using satellite chlorophyll, based on empirical equations from (72, Microphytoplankton 10-9 10-5 1.4 1.4 3.2 73, 82-84 ). Data also from (41-43). Nanozooplankton 10-13 10-10 1.21 2.5 6.5 Global estimates (not spatially resolved) from (41, 42, 69). Microzooplankton 10-11 10-5 2.3 4.8 6.5 n = 3866 samples from (64 ). GLM with sample n = 176,042 from COPEPOD (63 ) & depth, chlorophyll Mesozooplankton 10-6 10 4.1 10.9 7.7 n = 1509 samples from (65 ). and SST for global Macrozooplankton 10-3 103 0.24 1.5 11 n = 23,815 from MAREDAT (66 ). interpolation. Two independent data-constrained global marine ecosystem 10-3 107 5.5 5.5 5 models (39, 40) forced with Earth system model inputs in 20, 41). 10-2 103 0 5.4 3 Global estimates (not spatially resolved) from (41, 42, 75) n = 126 species global population estimates (not spatially Mammals 104 109 0.44 0.44 5 resolved) from IUCN (47), and meta-analyses of (48, 67). The size spectrum can be represented in many ways. In Fig. 1B, measurements of individual cell size were taken from five studies we show the relation between the logarithm of numerical abundance covering pelagic and coastal regions (44). Phytoplankton biomass versus logarithmic size class, obtaining a slope near −1. As we show across all groups were derived from sea surface temperature and in Fig. 2, this is equivalent to a slope near 0 for log biomass versus satellite chlorophyll a measurements, obtained from monthly clima- log size class. Alternatively, we can normalize our size classes by tologies of MODIS-Aqua (Moderate Resolution Imaging Spectro- dividing by their width, which gives a normalized abundance spec- radiometer aboard the Aqua spacecraft, 4-km resolution) from trum with a slope near −2 and a normalized biomass spectrum with 2002 to 2016, and aggregated to a 1° spatial resolution. Zooplankton a slope near −1 (2, 13). Furthermore, size spectra can be represented biomass across all groups except nanozooplankton derive from a as a probability density function (exponent near −2), a complementary total of >200,000 biomass samples aggregated from four sources, cumulative distribution function, or rank-size relation [exponent most notably COPEPOD and MAREDAT (63–66). Fish biomass near −1; i.e., Zipf’s law; (59)]. It is also important to recognize that was estimated from two data-constrained global ecosystem models Sheldon et al. (1) used octave size classes (powers of 2) in terms of [BiOeconomic mArine Trophic Size-spectrum model (BOATS) body mass but plotted these size classes in terms of equivalent spheri- (39) and FishErIes Size and functional TYpe model (FEISTY) (40)]. cal diameter (ESD). If size class is instead based on log ESD, then log Mammal biomass was estimated from 126 species global population abundance versus log ESD gives an expected exponent near −3 (44). estimates deriving from the International Union for Conservation of Nature (IUCN) (47) and meta-analyses (48, 67). In addition, for Data sources building generalized linear models for bacteria and zooplankton Our data sources are summarized in Table 1. All raw data, comprising groups, we used bathymetry data for each 1° region of the global more than 290,000 samples of abundance or biomass of particular ocean from General Bathymetric Chart of the Oceans, as well as annual taxonomic groups at various ocean locations and depths, are included average chlorophyll a and sea surface temperature from MODIS-Aqua. in the Supplementary Materials and our source code (https:// doi.org/10.5281/zenodo.5520055). In addition, we provide our Reconstructing pristine biomass biomass predictions for each spatially resolved major group for each 1° To estimate pristine biomass before industrial-scale fishing and latitude and longitude region of the ocean (fig. S1), amounting to whaling (circa 1850), we consider only the direct impacts of animal >33,000 biomass estimates for each of eight spatially resolved groups capture on the extracted fish and mammal groups. We have not (Table 1). considered the many possible indirect impacts, including trophic Bacteria abundance data were obtained from >47,000 sample cascades, changes in bioenergetic pathways, or habitat loss, and so measurements deriving from three sources (60–62), and ~500 in situ we do not attempt to estimate possible indirect changes to the various Hatton et al., Sci. Adv. 7, eabh3732 (2021) 10 November 2021 5 of 12 SCIENCE ADVANCES | RESEARCH ARTICLE groups of bacteria, plankton, and mesopelagic fish, or nonmesopelagic surface temperature, and chlorophyll a measurements were used as fish less than 10 g in size, and assume these groups have remained environmental predictor variables. For nanozooplankton, we were the same through time. This represents an important but unavoid- unable to find a sample source with which to generate a global sta- able source of uncertainty. tistical model, so we used an aggregate estimate of biomass for this Reconstructions of pristine fish biomass are also subject to con- group and partitioned biomass across its size range (42). Since no siderable uncertainty. For our estimates of fish (which includes true uncertainty bound was provided for nanozooplankton estimates, we fish, cephalopods, and benthic invertebrates), we relied on two spa- use the uncertainty range calculated for microzooplankton, which tially resolved marine ecosystem models that predict fish biomass overlaps taxonomically with the nanozooplankton. For bacteria and from environmental parameters (39, 40). These models were built zooplankton groups, we follow the approach of (41, 42) in reporting independently and are each constrained with recent fishery harvest our uncertainty interval, which derives from (i) the standard error data. For the pristine estimates used here, the models were each run from 1000 bootstrap predictions of mean global abundance or bio- without fishing and forced with preindustrial environmental inputs mass from the statistical model and (ii) the SD of the log-transformed from an Earth system model (CESM-BGC1) for the decade 1850–1860. sample data on which the statistical model was fit (44). The resulting biomass estimates derived from these simulations are Phytoplankton necessarily dependent on the assumptions of the two models and To estimate global phytoplankton biomass, we used annual average the Earth system model used to force them. Despite the inherent satellite chlorophyll a observations from MODIS-Aqua, from uncertainties, both models produce global-scale patterns in catch and 2002 to 2016, and empirical equations of chlorophyll a with depth biomass consistent with current-day empirical estimates (table S1) and by functional type, to calculate the global biomass of pico-, (20, 41, 42) and yield pristine biomass estimates within a factor of nano-, and microphytoplankton. Our estimate of total phytoplankton two of one another (table S5). biomass includes both autotrophs and mixotrophs, since both of To estimate pristine marine mammal biomass, we used current these groups contain chlorophyll a and so are represented in satellite global population estimates, adding estimates of population declines, estimates. To convert satellite chlorophyll a observations to phyto- obtained from the IUCN (47) or else took the upper CI values ob- plankton biomass, we first split total satellite surface chlorophyll a tained from multiple present-day global abundance estimates, when in each 1° region into pico-, nano-, and microphytoplankton there were only qualitative reports of declines. For many of the largest chlorophyll a using equations from (72). These equations model the whales, we relied on pristine reconstructions from (48). In the ab- nonlinear shifts in the relative proportions of each group—in regions sence of any data on pristine estimates or population declines, we of low chlorophyll a, picophytoplankton tend to dominate the assumed that pristine and present-day global populations are the biomass, and in regions of high chlorophyll a, the larger nano- and same (n = 47 of 126 species; see data S1). microphytoplankton tend to dominate. We converted surface chlorophyll a into total chlorophyll in the water column in each 1° Estimating major group biomass region using an empirical equation in (72) and, finally, converted Below, we summarize our methods for estimating biomass for total chlorophyll a into carbon and, last, wet biomass following (73). each major group. A full description is available in the Supplemen- We obtained the cumulative 95% CI by multiplying the reported tary Materials. multiplicative 95% CIs from each empirical equation (44). Heterotrophic bacteria and zooplankton Fish Our data sources for heterotrophic bacteria abundance did not dis- The major group we have called “fish” include epipelagic, meso- tinguish between bacteria and archaea, so we include both of these pelagic, and demersal organisms as well as some benthic organisms groups in our heterotrophic bacteria biomass estimate. These are that are not included in zooplankton data. Hence, our fish group often just referred to as bacteria; photosynthetic bacteria are included includes true fish (bony and cartilaginous) and invertebrates of the in phytoplankton. Bacterial abundance was multiplied by mean same size range (mostly cephalopods). To calculate total fish biomass, bacteria cell size to estimate global biomass. We did not find a we estimate nonmesopelagics and mesopelagics separately. statistically significant difference in mean bacteria cell size between We estimate biomass of epipelagic and demersal fish, cephalopods, coastal and open ocean samples, so we assumed a single mean indi- and large benthic invertebrates using spatially resolved estimates vidual bacteria cell size across the global ocean (fig. S4) (44). To derived from two process-based global marine ecosystem models estimate total zooplankton biomass, we split zooplankton into four (39, 40). These models were built independently, are each comprehen- groups defined by their linear size ranges: nano (0.8 to 5 m), micro sive in their spatial coverage and size range, and both constrained (5 to 200 m), meso (200 m to 2 cm), and macro (0.2 to 10 cm) with fishery catch data. The first estimate comes from the BOATS (43, 68). Nano- and microzooplankton cover protists groups such (39), a size-based global model that represents harvested organisms as heterotrophic flagellates, dinoflagellates, ciliates, and juvenile (including epipelagic and demersal fish, squid, and benthic inverte- mesozooplankton (64, 69). Mesozooplankton covers groups such as brates) from 10 g to 100 kg, using average temperature in the top copepods, larvaceans, amphipods, and giant rhizaria (65, 70). Macro- 75 m with integrated primary production in the water column as zooplankton includes groups such as chaetognaths, euphausiids, environmental inputs. The second estimate comes from the FEISTY tunicates, fish larvae, ctenophores, and cnidaria (71). (40), which represents the global biomass of epipelagic and demersal Global estimates of abundance for bacteria and biomass for each fish and benthic invertebrates from 1 mg to 125 kg. This model zooplankton group (micro-, meso-, and macrozooplankton, as well estimates biomass of functional types, with sea surface temperature, as all other animals that pass through a zooplankton life stage, but zooplankton carbon concentration, and particulate organic carbon excluding nanozooplankton) were calculated using generalized linear flux to the sea floor as environmental inputs. models fit to log-transformed sample measurements from across We used publicly available output from these models to derive the world’s oceans (n = 226,405; Fig. 1A). Bathymetry, satellite sea our global biomass estimates from simulations where each model is Hatton et al., Sci. Adv. 7, eabh3732 (2021) 10 November 2021 6 of 12 SCIENCE ADVANCES | RESEARCH ARTICLE forced with environmental inputs from the CESM-BGC1 Earth Boundaries of the “Sheldon hypothesis” system model (both models’ output available at https://www.isimip. There are conceptual uncertainties in delineating the physical and org/about/marine-ecosystems-fisheries/). For each model, we cal- taxonomic boundaries of what should be included to test the con- culated their global average biomass using the decadal average from jecture raised by Sheldon et al. (1). In particular, the question arises 1850 to 1860 from simulations of pristine ocean biomass with no of whether to include all ocean depths, estuaries, benthic and sedi- fishing. We chose this decade because it was the furthest in the past ment species, seabirds, etc. Sheldon et al. made measurements of that both models have been run through, and it is far enough back mostly the pelagic environment in the upper water column, which in time that anthropogenic climate impacts are not discernible from characterizes most empirical studies of size spectra up to the present existing climate variability (74). To obtain the biomass of fish with (summarized in table S3) (5). We have thus tried as closely as possible body sizes greater than 100 kg, we used the scaling relationship to reproduce this analysis globally, over all taxa, but our estimates of between biomass and body size from (20) to define the relationship fish biomass also include demersal fish and large benthic organisms between biomass and body size as a power function with an average over the continental shelves. We have also excluded brackish waters exponent of −0.06 (assuming an average ecosystem trophic transfer and mangrove ecosystems, as well as species such as seabirds that do efficiency of 0.125 and an average predator-prey mass ratio of 1000). not physically reside in the ocean. Although we have thus focused The fish component of this biomass was then calculated by sub- on the epipelagic, we show results that include biomass estimates tracting mammal biomass, which was estimated separately (see down to the seafloor in Fig. 2 and Table 1. “Mammals” section). To calculate the uncertainty range for our esti- Measurement error mates of epipelagic and demersal fish biomass, we follow the ap- There are various kinds of measurement errors associated with proach of (42), taking the 90% CI of global fish biomass from (20) the estimation of each major group. For example, phytoplankton as representative of this uncertainty range. estimates from satellite imagery of surface chlorophyll a concentra- Mesopelagic fish live in the mesopelagic zone (200 to 1000 m) of tions require well-calibrated ground truthing and reproducible the global ocean. Although difficult to sample directly, these fish can relationships between chlorophyll across each phytoplankton group be detected by the reflectance of acoustic signals from sonar, and (76). Zooplankton biomass samples have been taken with dozens of this reflectance can be used to estimate their biomass (75). For our different gear types and mesh sizes but cannot capture very small or estimate of mesopelagic fish biomass, we used results from (75), who large zooplankton as reliably (63), and it is difficult to evaluate the developed a model to estimate global estimates of mesopelagic fish effects of zooplankton avoidance, aggregation, and diurnal migra- biomass from acoustic surveys, accounting for uncertainties in the tion (77). Fish biomass is particularly difficult to estimate over the body structures of mesopelagic fish (44). global ocean, and although our marine ecosystem models are con- Mammals strained by global catch data, there are large uncertainties in harvest Marine mammal biomass was estimated from species-specific surveys data due to underreported and illegal catches (58). Last, mammal for the majority of all known marine mammal species. Population biomass derives from visual observation at the sea surface and in data of varying quality exist for more than two-thirds of all approx- breeding grounds, with unequal observational effort across regions imately 126 extant species of marine mammals, with nearly all current and species (47). We did not explicitly attempt to deal with measure- estimates of marine mammals taken from the IUCN (47) (n = 87). ment error and assumed that our data sources are the best available, We estimated “prewhaling” population counts by taking larger valued and the specific studies from which they derive had attempted to abundance estimates or upper CIs when extensive capture levels have deal with these measurement issues. More generally, we do not ex- been reported or else from expert opinion or modeling studies (n = 83). pect these errors to significantly bias our final analysis, which aggre- For most species of whales, we relied on the historic reconstruction gates a great number of measurements into relatively coarse order estimates in (48). When no additional information was available of magnitude size classes (44). beyond current estimates (n = 47 species), we assumed pristine num- Geographic bias bers were the same as exist currently. We believe this approach is With the exception of phytoplankton, which derives from satellite more likely to underestimate pristine abundance than overestimate it data with uniform global coverage and is averaged over more than a in most instances, but the values provided are among the most com- decade, all other groups are not uniformly sampled over the global plete tallies of currently available data for marine mammal biomass. ocean or at different depths. As shown in Fig. 1A, sampled observa- Estimates of marine mammal uncertainty is obtained from addi- tions of heterotrophic bacteria and the various zooplankton groups tional species population data from multiple additional sources, are patchy, with far fewer samples in the southern hemisphere. We summarized in the mammal dataset—available in the Supplementary attempted to correct this geographic bias by using generalized linear Materials, which includes minimum, mean, and maximum values models that interpolate biomass over the global ocean using environ- for 115 marine mammal species—and drawn from 275 primary mental predictor variables (chlorophyll a, sea surface temperature, published sources (67). Given the necessarily limited knowledge of and bathymetry), which are consistent in their coverage globally (44). the prewhaling period, we assumed the uncertainty range for pristine Major group biomass mammal biomass to be slightly more than double the range of our For each major group, we estimated global biomass uncertainty, calculated present-day mammal biomass [from 2.2 to 5; (44)]. represented as a multiplicative 95% CI around the average biomass estimate (Fig. 2A). Following the approach of (41, 42), we report Sources of uncertainty these uncertainty ranges as multiplicative fold changes (×/÷) from There are several kinds of uncertainty associated with our recon- the mean, rather than additive changes (±). We elected to use a structions of the pristine size spectrum and its present-day structure. multiplicative factor to represent uncertainty because the distribu- Below, we list the kinds of uncertainties and how we attempted to tion of sample data is best approximated by a log-normal distribu- deal with each. tion, and the geometric mean (i.e., the arithmetic mean on log scale) Hatton et al., Sci. Adv. 7, eabh3732 (2021) 10 November 2021 7 of 12 SCIENCE ADVANCES | RESEARCH ARTICLE will give an estimator that is more robust to outliers, particularly with biomass spectrum slopes that ranged from −0.03 (MLE) to −0.04 when data are sparse (41, 42). Given the range of source methods we (RMA), as summarized in table S7. We also investigated the use of use to estimate biomass, our calculations of 95% CI were not the alternative binning of biomass, such as half order of magnitude, and same for all groups, such that uncertainty bounds are not strictly found this also had very little effect on the overall slope (fig. S11). comparable across different methodologies. Nonetheless, our mean biomass and uncertainty ranges for each group are consistent with Fishing and climate projections those from other global biomass studies that use different method- To estimate the impacts of fishing on the size spectrum, we use two ologies (20, 41–43, 67) (table S1). Full methods to calculate uncer- estimates (45, 46), focusing on the depletion caused by industrial tainties for each group are given in the Supplementary Materials. fishing up until the early 2000s. We combined these two estimates Major group size distributions for the fraction of fish >10 g remaining from pristine fish biomass While most size distributions within plankton groups are well studied [58% inferred from (46) and 33% inferred from (45)] by taking their and similar [i.e., approximately even biomass across log size classes; geometric mean, giving a value of 44% of fish >10 g remaining. We table S3; (5)], relatively little is known of the overall size distributions therefore calculated the size spectrum slope that would be consistent of heterotrophic bacteria, fish, and mammals. For mammals, we with the 44% depletion among the fraction >10 g, assuming that fish used average species body mass with each global population count, ≤10 g have not been significantly affected by current harvesting in thus avoiding the need for any assumptions of their size distributions. the global average. This assumes that the slope has thus steepened For groups where less is known about the size distribution, we used by −0.17 for all fish >10 g (44). an even biomass across log size classes as a starting point and tested In addition to steepening in the size spectrum due to fishing, there this assumption by sensitivity analysis with randomly generated have also been significant declines in large mammals, particularly size distributions (see “Building the size spectrum” section). We find whales. We compiled both prewhaling and current abundance for that the particular size distribution within major groups has very little more than two-thirds of all ~126 included species of marine mammals. effect on the overall global size distribution (Fig. 2C, i, and fig. S12). These data are derived from over 275 primary sources and drawn from meta-analyses of (48, 67), as well as expert opinion and com- Building the size spectrum pilation from (47). These data suggest that among the smallest marine To construct the abundance and biomass spectra in Figs. 1 and 2, mammals (10 to 100 kg), only 47% remain, but progressively smaller we partitioned the global biomass estimates for each major group fractions characterize the larger size classes, with possibly only 25% across their relevant size classes (Table 1). Biomass was assigned of mammals remaining in the 10- to 100–metric ton (MT) size class to relevant group size classes in different ways, depending on the and only 3% of blue whales, making up the largest size class (47, 48). group, as described above. It is important to note that given the nature Combining the global estimates of fish reductions (45, 46) with those of the data, macrozooplankton, for example, may include fish larvae, of marine mammals (47, 48, 67), we calculated the percentage lost and mesozooplankton may contain juvenile species of what are in each size class (Fig. 3B) and the resulting shape of the global bio- otherwise macrozooplankton. For mammals, on the other hand, mass spectrum (Fig. 3C) (44). we used global population estimates for each species and associated We compare fishing and whaling impacts up to the present with these numbers to a mean species body mass. We do not expect indi- combined projected future fishing and climate change impacts across vidual versus species mean values of body size to bias our results over the entire size spectrum. To assess combined fishing and climate order of magnitude size classes. impacts to the end of the 21st century, we assume that the impacts Most research over the past 50 years has revealed that the bio- of fishing and climate on biomass are additive, with little nonlinear mass distribution within major groups is approximately invariant interaction between them (50). We also assume that the cumulative across log size class (Fig. 2C, ii, shows the distribution of slopes over historical fishing impacts are maintained into the future, such that 325 size spectra from 47 different studies; see also table S3). We thus effective fishing effort remains approximately constant. Projected assumed an even distribution of biomass across log size classes in climate change impacts are obtained from Earth system model sim- each group and then tested the sensitivity of this assumption to ulations that estimate the changes in ocean temperature, circulation different size distributions. We randomly allocated group biomass patterns, and biogeochemical cycling that will result from a given across log size classes where total group biomass itself is also drawn future trajectory of atmospheric greenhouse gases. Here, we use the at random from a log-normal distribution centered on the mean worst-case scenario trajectory, RCP of 8.5. Rather than relying on a biomass with SD obtained from the 95% CI fold uncertainty for single model, we take the mean estimate from the 10 climate models 10,000 simulations. Our sensitivity analysis shows that even quite that participated in the fifth simulation round of the climate model extreme variation in group size distribution still yield overall biomass intercomparison project (CMIP5), as analyzed by (80). spectrum slopes very near our reported value of −0.04, with little Estimated changes in phytoplankton, zooplankton, and fish bio- variation, as shown in Fig. 2C, i (see also fig. S12). For the top 200 m, mass were calculated using ecosystem modules that were run in a fully we obtained a normal distribution of slope values with mean of −0.049 coupled mode with the ocean modules (49–51), and we assumed uni- and SD of 0.021, thus giving a 95% CI for the slope of the average form changes across each group’s respective size ranges. Unlike the global biomass of −0.085 to −0.003. Across the entire water column, case for the preceding groups, there are no global process models avail- we obtain a normal distribution with mean of −0.056 and SD of 0.020, able for marine mammals. Instead, we use the model of (51), combined giving a 95% CI for the slope of −0.095 to −0.017 (fig. S12). with the mean projected sea surface temperature increase from the Although we report best-fit parameters from ordinary least squares 10 CMIP5 climate models. 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