Philippa Kaur

The upside-down jellyfish, Cassiopea sp. produces several hydrodynamic effects capable of altering the ecosystem which it inhabits. Not only do Cassiopea produce feeding currents capable of turning over the water column above them several times per hour3, they are also capable of releasing interstitial porewater from the benthos5. The rate of porewater release, on the order of mL h−13, is capable of increasing water column NH4 levels by almost 30% under certain conditions3. In this study, we investigated two hypothetical mechanisms for this porewater release, and found that a combination of the morphology of the bell and the pulsing behavior of the jellyfish was responsible for releasing porewater from directly below the bell via a suction-pumping mechanism.The Bernoulli hypothesis4, a low-pressure zone surrounding the animal due to a velocity gradient between the substrate boundary and the incurrent flow of the Cassiopea sp. feeding current, predicted porewater release from the substrate surface surrounding the perimeter of the animal. While porewater is entrained from the perimeter of the bell into the feeding current4 lateral expulsion of porewater due to the suction pump mechanism would produce a visually similar flow of porewater. A horizontal flow of water does occur near the bottom1, but this flow is restricted to a narrow region near the bell and velocities were low compared to the vertical excurrent jet (Fig. 4). To test the effect of Bernoulli’s principle, we measured the effect on porewater release rates of an impermeable ring-shaped barrier surrounding the animal in order to inhibit benthic-pelagic fluid flux other than directly under the animal (Fig. 2A) using labeled fluorescein per the methods of Durieux et al.3, which were adapted from those of Jantzen et al.5 (Fig. 2). If the Bernoulli mechanism contributed to porewater liberation this treatment should have reduced the porewater release rate, but the release rates observed were not significantly different from the control treatment (2.23 mL h−1 ± 1.27 s.d., Fig. 2D).The suction pumping hypothesis5, a mechanism using the exumbrellar cavity as a suction pump that draws porewater vertically upward beneath the bell and then expels it laterally, would expect to see the majority of porewater released from directly under the bell of Cassiopea sp. This mechanism is supported by bell morphology5 and the appearance of deep porewater at the benthic surface of the exumbrellar cavity5. In our, an impermeable disk was placed underneath the animal to obstruct the flow predicted by the suction pump hypothesis (Fig. 2B). Additionally, we made a 6 mm perforation in the bells of the jellyfish to interfere with the ability to form the sub-ambient pressure in the exumbrellar space necessary for suction pumping to occur (Fig. 2C). Both treatments resulted in a significant decrease in porewater liberation, with flows indistinguishable from the absence of any animal (Fig. 2D), supporting the suction-pumping hypothesis.Since the suction pumping mechanism requires pressure fluctuations in the exumbrellar space, we also directly measured the water pressure below the jellyfish. The initiation of the power stroke of bell pulsation coincides with a sudden decrease in water pressure in the exumbrellar space (Fig. 3A,B) of a mean magnitude of 43.4 Pa (± 13.6 s.d.). These pressure fluctuations appear to be unaffected by animal size (Fig. 3D,E), although the rate of porewater release is known to scale with bell diameter3. Note that the muscles responsible for bell contraction in Cassiopea sp. are roughly 2-dimensional sheets13 with a thickness of one cell14 and therefore the cross-sectional area also does not scale with diameter. Our experiments were performed on smooth acrylic rather than sand, so that the conditions here were optimal for the formation of a tight seal with the bottom. However, the magnitude of this difference is likely to be small, as Cassiopea sp. produce copious amounts of mucus, which can compensate for small-scale surface roughness. In addition, the duration of each individual bell pulse is short1, so given the fine pore size of a sand or mud substrate, it is unlikely that subambient pressure would have the opportunity to dissipate enough to affect the high suction impulse produced.While not statistically significant, bell perforation did lead to data suggesting a decrease in exumbrellar pressure fluctuations (Fig. 3C), which could explain the reduction in porewater release observed (Fig. 2C). The fact that some pressure fluctuation was seen despite a complete lack of porewater release suggests that a minimum magnitude of pressure fluctuation might be necessary for suction pumping to occur. Furthermore, the effect may have been reduced by the ability of injured Cassiopea to produce copious amounts of mucus, which could have acted to minimize the impact of bell perforation. These parallel lines of reasoning firmly suggest that suction-pumping is, in fact, the dominant mechanism by which Cassiopea sp. release porewater.The suction-pumping mechanism for the release of porewater has broad-ranging ecological implications. Release rates should increase additively with population density, and the rate of bell pulsation should correlate with the rate of porewater liberation. The additive relationship to population density is important, since Cassiopea can occur at high densities of up to 100 animals m−23. Furthermore, while the Bernoulli mechanism predicted that interstitial water movement would be limited to the upper layers of the benthos, the suction pump mechanism has the potential to release porewater from deeper sediment strata. This deep flushing should expand the oxygen penetration depth downward, affecting factors such as respiration and sediment stability15. Given the fact that Cassiopea are capable of moving along the substrate5,16 this also means that the oxygen penetration depth is likely to fluctuate over time, favoring organisms that are able to adapt their metabolism or are able to relocate themselves17.Given that porewater at the field site in Long Key, Florida, from which the animals in this study were collected, has mean ammonium concentrations of 72 μM, 160 times higher than the surrounding water column11, any benthic-pelagic coupling mechanisms in this habitat could alter nitrogen dynamics, especially given the fact that many marine primary producers preferentially take up ammonium, the most reduced state of nitrogen available, as a nitrogen source18. Cassiopea sp. animal size and population densities are known to correlate with anthropogenic disturbances, and it is suggested that this is due to an increase in nutrient availability in these areas6. In addition to prey capture, Cassiopea sp. could be supplementing their nitrogen demand through the release of nutrient-rich interstitial porewater, from which Cassiopea sp. can directly absorb ammonium and other nutrients such as phosphate and trace metals5. In fact, jellyfish presence significantly reduced porewater ammonium levels near the animal5, suggesting that nutrient-rich porewater was replaced by down-welling low-nutrient surface water. The observed benthic locomotion of Cassiopea5,16 may be a mechanism to avoid remaining in locations where they have depleted this nutrient resource3. It has been reported that Cassiopea sp. affect benthic nutrient transport on a more general level, increasing ammonium uptake and decreasing nitrate uptake of the bottom sediments19. Water column nutrient levels also varied significantly between presence and absence of Cassiopea sp., and also between light and dark treatments in the presence of Cassiopea sp.20. The addition of jellyfish increased the efflux of ammonium from the benthos during the dark treatments, but reduced ammonium concentrations in the water column during light treatments20. It is entirely possible that absorption of nutrients by Cassiopea sp.5 in order to meet daytime metabolic demand resulted in the animals reducing water column ammonium concentrations in these experiments20.In addition, Cassiopea sp. have been shown to increase spatial heterogeneity of interstitial oxygen and nutrient fluxes20, making it comparable to other biogenic processes like bioturbation. Bioturbation typically oxygenates the upper layers of substrate, increasing the nitrification zone21, and also increases 3-dimensional heterogeneity of oxygen and nutrient concentrations, allowing for more complex nutrient dynamics21. The transport of interstitial porewater from specific regions under individual jellyfish could well produce a similar effect. The porewater release rates can also be compared to that of abiotic processes, such as wind-wave driven flow over sediment wave ripples, which have been shown to liberate porewater at rates of up to 140 L m−2 day−1, or three orders of magnitude greater than diffusion alone, on shallow, exposed coastlines such as beaches22. Environmental mixing would be lower in the sheltered mangrove habitats where Cassiopea sp. are found, since at our study site wind wave height was reduced from 5.4 cm in the bay to 0.07 cm in the mangroves3. In these coastal habitats, the sediment often acts as a nutrient sink, causing certain nutrients to become limiting to primary producers. Some fringe mangrove forests along coastlines in both Florida and Belize have been shown to be N-limited, for example23,24. If these nutrients are then released back into the water column, they potentially increase primary productivity in the system occupied by Cassiopea sp. Depending on the system, this could either increase production or cause eutrophication, potentially altering productivity on a local or regional scale, as has been observed when nutrients are released from the benthos by winds25 or bioturbation26.The mechanics of suction-pumping also imply that interstitial porewater release rate will correlate with bell pulse rate. Pulse rate correlates with water temperature (Fig. 5B), which would suggest that Cassiopea sp. can release greater quantities of nutrient-rich porewater during the summer months. This was confirmed by a recent study on the related species, Cassiopea medusa from Lake Macquarie, Australia8. By extension, our model suggests that pulsing, and therefore porewater release, should cease entirely below 18ºC. In fact, at our site in Lido Key, population densities of Cassiopea sp. declined rapidly once water temperatures dropped this low (Fig. 6). This same temperature of 18 °C was determined independently to be the threshold at which Cassiopea sp. polyp feeding was inhibited10. As such, it is likely that winter minimum temperatures of 18ºC represent a limiting condition on Cassiopea sp. range expansion. Studies on Cassiopea medusa, suggested thermal stress and bell degradation at 16 °C8. As global climates warm, we can expect both a poleward shift of Cassiopea sp. Range9,27 and an increase in transport rates of porewater and its associated benthic nutrients throughout this range, leading to increased productivity, and potentially exacerbating eutrophication in some regions.We determined that a suction-pumping mechanism is responsible for the interstitial porewater release by Cassiopea, suggesting that release rates are independent of population density, but affected by pulse rate. The potential role of bell pulse rate was investigated further, and we found correlations between bell pulse rate and both animal size and water temperature. As a result, we expect that porewater liberation would demonstrate seasonal variations, with lower rates during the winter and reaching a maximum during the summer months. Cassiopea are able to release nutrient-rich porewater in the shallow quiescent habitats they inhabit, and through their feeding current mix these nutrients throughout the water column. Since this effect varies seasonally, it is likely that further study will show that these jellyfish are responsible for a complex system of nutrient dynamics in their ecosystem. More

Traditional ecological footprint consumption accountsTo truly reflect the ecological footprint and ecological carrying capacity of Dongying city, according to the lifestyle and consumption of Dongying city and with reference to Shandong Province Statistical Yearbook and Dongying City Statistical Yearbook, the biologically productive land is divided into arable land, forestland, grassland, water, construction land and fossil energy land, and the main consumption items of each category are shown in Fig. 3.Figure 3Traditional ecological footprint consumption accounts in Dongying city. This paper uses the carbon footprint to improve the fossil energy footprint of the traditional ecological footprint.Full size imageNPP-based correction of ecological footprint parametersThe 30 m land use of the study area was resampled to 500 m, consistent with the resolution of MOD17A3H after pre-processing with MRT and other tools. Correction of ecological footprint parameter factors in Dongying City for 2015, 2018 and 2020 based on the annual average NPP of vegetation (Table 1). This method is faster and more accurate than other methods, and the implementation of NPP calculations from the vegetation light energy use efficiency (LUE) framework to correct ecological footprint parameters is more applicable and accurate than other methods.Table 1 Average annual net primary productivity per land type in the Yellow River Delta.Full size tableYield factorThe formula for calculating the yield factor for arable land in the Yellow River Delta refers to NFA 2016:$$left{ {begin{array}{*{20}c} {Y_{j1} = frac{{Sigma A_{W} }}{{Sigma A_{N} }}} \ {A_{N} = frac{{P_{N} }}{{Y_{N} }}} \ {A_{W} = frac{{P_{N} }}{{Y_{W} }}} \ end{array} } right.$$
(1)
In Eq. (1), ({Y}_{j1}) is the yield factor of the arable land in the study area, ({A}_{N}) is the harvested area ( culture area ) of agricultural products of category (N) in the study area, ({A}_{W}) is the area required to produce an equivalent amount of this type of agricultural product based on the world average yield, ({P}_{N}) is the production of agricultural products of category (N) under the region, ({Y}_{N}) is the average yield of agricultural products of category (N) under the region, and ({Y}_{W}) is the world average production of a category of agricultural products.The NPP products from MODIS supported by remote sensing were used as the base data to correct the yield factors of woodlands and grasslands in the study area under the ecological footprint model.$$Y_{{{text{j}}2}} = overline{{NPP_{local} }} /overline{{NPP_{global} }}$$
(2)
In Eq. (2), ({Y}_{mathrm{j}2}) is the yield factor for woodland and grassland in the study area, ({NPP}_{local}) is the average annual net primary productivity of woodland and grassland in the study area in the corresponding year, and ({NPP}_{global}) is the global average NPP of woodland and grassland in the corresponding year, referring to Amthor et al.24.In addition, most of the land for construction comes from cropland, so the yield factor for construction land is the same as that for cropland25. The yield factors for the watershed were derived from the Wackernagel and Rees26 study.Balancing factorThe NPP model for provincial hectares was applied to the municipal scale. Among them, the NPP of four biologically productive lands, namely cropland, woodland, grassland and water, was weighted and summed to obtain the annual average NPP within the city area.$$overline{NPP} = frac{{mathop sum nolimits_{j} left( {A_{j} times NPP_{j} } right)}}{{mathop sum nolimits_{j} A_{j} }}$$
(3)
In Eq. (3), (overline{NPP }) is the average net primary productivity of arable land, forestland, grassland and water in Dongying, ({A}_{j}) is the area of land in category (j), and ({NPP}_{j}) is the average annual NPP of productive land in category (j).Balancing factors for arable land, woodland, grassland and water in the Yellow River Delta.$$R_{j} = frac{{NPP_{j} }}{{overline{NPP} }}$$
(4)
In Eq. (4), ({R}_{j}) is a balancing factor.The sites for construction are located in areas suitable for agricultural cultivation or directly occupy arable land, so the potential ecological productivity of urban construction land is the same as that of arable land, and therefore the equilibrium factor for construction land is equal to that of arable land27.Ecological footprint principles and improvementsEcological footprint modelEcological footprint model includes ecological footprint, ecological carrying capacity and ecological deficit. As the study area is within the city limits and the statistics have their own characteristics, adjustments have been made to the methodology for calculating the national ecological footprint accounts28. Based on the biological consumption account, the ecological footprint can be calculated for any land use type.$$EF = frac{P}{{Y_{N} }} times R_{j} times Y_{j}$$
(5)
In Eq. (5), (P) is the number of biologically productive land harvesting consumption items in a category, and ({Y}_{N}) is the average production of consumption Item (N) in the region. The ecological footprint of the construction land is measured based on the area of human infrastructure land and is equal to its ecological carrying capacity.Ecological carrying capacity is the determination of the maximum carrying capacity of an ecosystem for human activity, expressed as the sum of the biologically productive land area available in an area.$$EC = N times ec = N times sum left( {a_{j} times R_{j} times Y_{j} } right)$$
(6)
In Eq. (6), (EC) is the ecological carrying capacity per capita, and ({a}_{j}) is the per capita area of biologically productive land of category j in the region. According to the recommendations of the World Commission on Environment and Development, 12% of the ecological carrying capacity should also be deducted for biodiversity conservation. The population figures for the study area were obtained from the statistical yearbook and the seventh national census data. According to the recommendations of the World Commission on Environment and Development, 12% of the ecological carrying capacity should also be deducted for biodiversity conservation.An ecological deficit is the interpolation of the ecological footprint and ecological carrying capacity.$$ED = EF – EC$$
(7)
When (ED >0) indicates an ecological deficit, the ecological environment has exceeded the carrying capacity. Conversely, when (ED More

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Brazil’s new government aims to achieve zero deforestation in the Amazon rainforest. This welcome initiative should be extended to the Cerrado, the world’s most biodiverse woodland savannah.
Competing Interests
The authors declare no competing interests. More

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Goal and scope of the studyThe goal of this study was to assess the planetary footprints of GHG mitigation strategies for the global production of plastics. To calculate planetary footprints, we apply LCA in combination with the planetary boundaries framework as proposed by ref. 22. As GHG mitigation strategies, we consider recycling, bio-based production and production via CCU, and compare their planetary footprints to the planetary footprints of fossil-based plastics. We use a bottom-up model covering >90% of global plastic production for 2030 (and 2050, Supplementary Information, section 3). The bottom-up model builds on the plastic production system from ref. 10 and includes plastic production, the supply chain and the disposal of plastics at the end of life.Functional unitIn LCA, the functional unit quantifies the functions of the investigated product system. In this study, the function of the product system is the production and disposal of >90% of global plastics. To cover >90% of global plastics, we define the functional unit as the yearly global production and disposal of 14 large-volume plastics (summarized in Supplementary Table 5). We estimated the yearly production volumes for 2030 and 2050 based on the production volumes in 2015 and the annual growth rates shown in Supplementary Table 5.Our assessment includes plastic disposal. However, the production and disposal of plastics do not necessarily occur in the same year. For instance, while polyolefins used for plastic packaging have an average lifetime of 6 months, the average lifetime of polyurethane used in construction is 35 years11. Including the lifetime of plastics, and hence, the temporal difference between production and disposal, would lead to an increasing plastic stock. An increasing stock, in turn, represents a carbon sink during the production year that appears to enable the production of net-negative GHG emission plastics based on biomass or CCU. However, the plastic stock is not a permanent carbon sink, which would be required for producing net-negative GHG emission plastics55. To avoid misleading conclusions about net-negative bio- and CCU-based plastics, we assign the planetary footprints from disposal to the year of plastic production. Thereby, we conservatively assess the planetary footprints of plastics.In addition, we address the challenge highlighted in ref. 56 that the increasing demand for plastics renders determining the absolute sustainability of plastics difficult. We meet this challenge by assuming a steady-state production system with a recurring functional unit in the same amount every year. We thereby analyse discrete scenarios with constant consumption levels for plastics. Therefore, our conclusions depend on the accuracy of the demand forecasts and apply only to the production volumes considered.System boundariesWe use cradle-to-grave system boundaries, including plastic production and supply chain, potential recycling and final disposal at the end of life. Assessing the use phase of plastics is not possible because of a lack of data. The versatile properties of plastics result in a wide range of applications that cannot be represented in a single study. Furthermore, it would be necessary to consider not only the emissions of the use phase (probably relatively small) but also the system-wide environmental consequences of using plastics in each application compared to other materials. Thus, a consequential assessment of the plastic use phase is desirable but beyond the scope of this study.The plastics supply chain includes several intermediate chemicals such as monomers, solvents or other reactants. The bottom-up model covers the production of all intermediate chemicals in the foreground system. As a background system, we use aggregated datasets from the LCA database ecoinvent. A list of all intermediate chemicals and all aggregated datasets can be found in Supplementary Information, section 1. In addition, the foreground system of the bottom-up model does not include environmental impacts from infrastructure and transportation because of a lack of data. However, we consider the environmental impacts of infrastructure and transportation from other industrial sectors by aggregated datasets, for example, from electricity generation and biomass cultivation.The bottom-up model includes the best available fossil-based technologies and the following technologies for plastic disposal and virgin production based on biomass and CCU.Plastic waste disposalThe bottom-up model includes three options for plastic waste disposal: landfilling, incineration with energy recovery and recycling. Plastic waste can occur in several forms: as sorted fraction of municipal solid waste, as mixed plastics and residues from sorting, and as residues from mechanical recycling. For all fractions, we include waste incineration with energy recovery and landfilling.Landfilled plastic waste is assumed to degrade by approximately 1% of the contained carbon, which is in line with the ecoinvent database45. Mechanical recycling is only modelled for sorted fractions of packaging waste owing to impurities of mixed and non-packaging wastes. In contrast, chemical recycling can be applied to all plastic fractions. In this study, we model chemical recycling as pyrolysis to refinery feedstock, that is, naphtha. The pyrolysis has yields of 29 to 69% depending on the type of plastic (details in Supplementary Information, section 1). Furthermore, we include options for chemical recycling of plastic waste to monomers, which are still early-stage technologies. To derive the minimal necessary recycling rate in Fig. 5, we apply an optimistic scenario with a 95% yield of chemical recycling processes following common modelling in life-cycle inventories of chemicals (Supplementary Information, section 3)57. All calculations are constrained to maximum recycling rates of 94% as the remaining 6% are assumed to be the minimal landfilling rate until the middle of the century11. The assumption is based on historical trends in end-of-life treatment of plastics.Bio-based productionBio-based GHG mitigation is frequently discussed in the literature and is often associated with competition with the food industry58. To avoid competition with the food industry, the bottom-up model is restricted to lignocellulosic biomass as feedstock, that is, energy crops, forest residues and by-products from other industrial biomass processes (for example, bagasse). In this study, unless mentioned otherwise, we model biomass as energy crops because of their potential for large-scale application (Supplementary Information, section 3). However, we conduct a sensitivity analysis for other lignocellulosic biomass sources to assess the sustainability of bio-based plastics in more detail.For each biomass type, we account for the carbon uptake during the biomass growth phase by giving a credit corresponding to the biomass carbon content. We do not consider land use change emissions as current literature lacks an assessment of land use change effects on other Earth-system processes besides climate change.For biomass processing, we include the following high-maturity processes: gasification to syngas and fermentation to ethanol, and the subsequent conversion to methanol and ethylene (Supplementary Table 1). Methanol and ethylene can be further converted to propylene and aromatics, which all together represent the building blocks for all plastics in this study.CCU-based productionCCU-based plastic production particularly requires CO2 and hydrogen. For CO2 supply, we consider CO2 capture from highly concentrated point sources within the plastics supply chain. Highly concentrated point sources include the conventional fossil-based processes, ammonia production, steam methane reforming, ethylene oxide production, the bio-based processes for ethanol and syngas, and plastic waste incineration. Capturing from processes within the plastics supply chain is limited by the amount of CO2 emitted by these processes and avoids the corresponding emissions. For these processes, we considered the energy demand for compressing the CO2 with 0.4 MJ of electricity59. For waste incineration, we consider a decrease in energy output when capturing CO2. All further CO2 sources are conservatively approximated by direct air capture. For 1 kg CO2 captured via direct air capture, we include an uptake of 1 kg of CO2 equivalent while considering the energy demand of 1.29 MJ electricity and 4.19 MJ heat60.Hydrogen for CCU is produced by water electrolysis, with an overall efficiency of 67%61. Previous studies have already shown that renewable electricity is required for CCU to be environmentally beneficial13. Thus, we conduct a sensitivity analysis for multiple electricity technologies to assess their influence on the sustainability of CCU-based plastics (Supplementary Information).For CCU-based production, we include high-maturity technologies, such as CO2-based methanol and methane, as well as subsequent production of olefins and aromatics (Supplementary Table 1). We do not consider CCS as an additional scenario, as fossil resources and storage capacities are ultimately limited. Therefore, CCS may serve as an interim solution for GHG mitigation but stands in contrast to long-term sustainability as the goal of this study.Pathway definitionWe assess nine pathways for the plastics industry towards sustainability. Pathway 1 is fossil-based plastic production (current recycling rate of 23%) that serves as a reference. We also include two pathways that combine all circular technologies: Pathway 2, which minimizes the climate change impact (climate-optimal), and pathway 3, which minimizes the maximal transgression of the share of SOS of the plastics industry (balanced) (Fig. 2). To assess the impact of switching from fossil to renewable feedstocks, we introduce pathway 4, which is bio-based, and pathway 5, which is CCU-based (Fig. 3). Pathways 4 and 5 include the current recycling rate of 23%. In addition, we introduce three pathways with the maximum recycling rates of 94%: pathway 6, in which the remaining virgin production is based on fossil resources; pathway 7, in which it is based on biomass; and pathway 8, in which it is based on CO2 (Fig. 3). Pathway 9 combines biomass, CCU and recycling, and additionally includes chemical recycling of polymers to monomers to calculate the minimal recycling rate to achieve sustainable plastics (Fig. 5).The planetary boundaries frameworkWe follow the recommendations for absolute environmental sustainability assessment in ref. 29 and choose the planetary boundaries framework for the assessment. The planetary boundaries framework suits the goal of the study best because of its precautionary principles for the definition of environmental thresholds, the SOS. We assess eight of the nine Earth-system processes suggested in ref. 21, namely, climate change, ocean acidification, changes in biosphere integrity, the biogeochemical flow of nitrogen and phosphorus (referred to as N cycle and P cycle), aerosol loading, freshwater use, stratospheric ozone depletion, and land-system change. We do not assess the Earth-system process of novel entities since neither control variables nor the boundary itself is yet adequately defined22. We consider the global boundaries for the Earth-system processes in line with the scope of this study. These global boundaries and the corresponding calculation of planetary footprints are subject to assumptions and thus incorporate uncertainty (Supplementary Information, section 2).For the two subprocesses for climate change (namely, atmospheric CO2 concentration and energy imbalance at the top-of-atmosphere), we only consider the energy imbalance at the top-of-atmosphere quantified by radiative forcing. We focus on radiative forcing, as the control variable is more inclusive and fundamental, and the global limits are stricter than for atmospheric CO2 concentration21. Thereby, we conservatively assess climate change.Biosphere integrity is divided into functional and genetic diversity of species. Preserving functional diversity ensures a stable ecosystem by maintaining all ecosystem services. We assess the functional diversity of species using the method proposed in ref. 18. The method covers the mean species abundance loss caused by the two main stressors, direct land use and GHG emissions, as a proxy for the biodiversity intactness index. Genetic diversity provides the long-term ability of the biosphere to persist under and adapt to gradual changes of the environment21. Genetic diversity is often approximated by the global extinction rate. However, using the global extinction rate does not fully cover variation of genetic composition, resulting in high uncertainties when quantifying genetic diversity18. Thus, we focus on functional diversity.Downscaling of the safe operating spaceAs the plastics industry accounts for only a fraction of all human activities, we assign a share of the SOS to plastics. The plastics industry should operate within its assigned share to be considered environmentally sustainable. To assign a share of SOS to the plastics industry, we apply utilitarian downscaling principles. Utilitarian downscaling principles are tailored to maximize welfare in society29. We approximate welfare by consumption expenditure on plastics as an economic indicator for consumer preferences and human needs62. An extensive discussion on the other downscaling principles and their implications can be found in Supplementary Information.Although the final consumption expenditures on plastics are negligible, the industry consumes plastics to produce other goods and services. Accordingly, plastics are produced mostly in the upstream supply chain to support the final consumption of other goods and services. Thus, consuming other goods and services induces plastic production. To account for this inducement of plastic production, we used the total global plastic production xplastics to represent the global intermediate and final consumption expenditure on plastics. For this purpose, we use the gross output vector x of the product-by-product input–output table of EXIOBASE for the year 2020 (ref. 63). To calculate the share of SOS of the plastics industry, we divide the total global plastic production xplastics by the gross world product. The gross world product equals the total global final consumption expenditure. Analogously, we also consider the end-of-life treatment of plastics to be consistent with the system boundaries of the environmental assessment.We estimate the share of SOS for the plastics industry for 2030 and 2050 based on data for the year 2020. Accordingly, we assume that the market share of the plastics industry and, therefore, its share of SOS do not change in the coming years despite the increasing production volume of plastics. Thereby, we implicitly assume that all industries grow equally economically. Alternatively, economic forecasting models could estimate future market shares of plastics. However, applying economic forecasting models is complex, and the results would still be highly uncertain, especially if industry pursues low-carbon technology pathways. Therefore, estimating future market shares is beyond the scope of this study.Technology choice modelTo calculate the planetary footprint of plastics, we use a bottom-up model of the plastics industry. The model builds on the technology choice model (TCM) that allows for linear optimization of production systems27. The TCM represents the production system based on the following elements: technologies, intermediate flows, elementary flows and final demands. Ref. 27 describes each element in detail.The TCM is based on the established computational structure of LCA64. This structure arranges the data that represent the physical production system in the technology matrix A and the elementary flow matrix B. In the technology matrix A, columns represent technologies, and rows represent intermediate flows. Therefore, the coefficient aij of the A matrix corresponds to an intermediate flow i that is either produced (aij  > 0) or consumed (aij  More

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