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    Circadian regulation of diel vertical migration (DVM) and metabolism in Antarctic krill Euphausia superba

    Vertical migration
    We performed two separate vertical migration experiments (Fig. 1A,B). In the first one (Fig. 1A) a group of 45 krill was exposed to LD for 48 h. In the second one (Fig. 1B) a group of 41 krill was exposed to LD for 24 h followed by constant darkness (DD) for 48 h. During LD, lights were turned on at 6:00 (corresponding to Zeitgeber Time 0 or ZT0). Light intensity gradually increased until 12:00 (ZT6) and then decreased gradually until 18:00 (ZT12), when the lights were turned off. During DD, lights were turned off at all times. In both experiments, krill could move freely within a vertical column tank (200 cm height × 50 cm diameter) filled with chilled and filtered seawater (Supplementary Fig. S1). No food was offered at any time during the experiments and an acclimation period of three days (LD, no food) was provided before each experiment. We used an infrared (IR) camera system to monitor DVM during light and dark phases and estimated the variation in mean krill depth over time. We tested the presence of rhythmic patterns using the RAIN algorithm, which allows the detection of rhythms of any period and waveform23.
    Figure 1

    Vertical migration patterns of krill exposed to LD and LD-DD. (A) Vertical migration patterns of krill exposed to LD for 48 h. X-axis indicate the Zeitgeber Time (ZT) given in hours from each event of lights-on (6:00), corresponding to ZT0. Y-axis indicate the mean krill depth in cm (n = 45). Error bars represent SEMs. White and grey rectangles represent alternation of light and dark phases. For each experimental day, results of the RAIN analysis test for the presence of rhythmic oscillations are reported (T = period of oscillation; p = p-value). (B) Vertical migration patterns of krill exposed to LD for 24 h followed by 48 h in DD. X-axis represent the time in hours from the beginning of the run. For the first 24 h, time is given in ZT, with ZT0 corresponding to lights-on (6:00). For the following 48 h, time is given in Circadian Time or CT, with CT0 corresponding to subjective lights-on in DD (6:00). Y-axis indicate the mean krill depth in cm (n = 41). Error bars represent SEMs. White, grey and light grey rectangles represent alternation of light, dark and subjective light phases respectively. For each experimental day, results of the RAIN analysis test for the presence of rhythmic oscillations are reported (T = period of oscillation; p = p-value). The figure was generated using the plot function in the “graphics” package (version 3.6.3, https://www.rdocumentation.org/packages/graphics) in R (RStudio version 1.0.136, RStudio Team 2016).

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    Clear rhythmic oscillations were detected in both experiments. When krill were exposed to LD, they displayed rhythmic vertical migration with a period of about 24 h. Peak upward migration occurred towards the second half of the light phase. In the first experiment (Fig. 1A), RAIN detected a period of oscillation of 24 h (p-value = 3.5e−07) in day 1 and a period of 23 h (p-value = 5.4e−08) in day 2, with peak upward migration at ZT9 in both days. In the second experiment (Fig. 1B), RAIN detected a period of 24 h (p-value = 4.2e−04) in day 1, when krill were exposed to LD, with peak upward migration at ZT8.
    Krill DVM in the field displays mostly a nocturnal migratory pattern, characterized by upward migration during the night and downward migration during the day6,11. Therefore, we were at first surprised to observe the opposite DVM pattern in the lab, with upward migration during the day (i.e. light phase) and downward migration during the night (i.e. dark phase). However, previous studies on Drosophila already revealed that circadian behaviors might differ significantly between wild and laboratory populations of the same species24. Physical constriction, exposure to artificial light regimes and feeding schedules and deprivation of ecological interactions may have a profound impact on the behavior of captured animals25. In the aquarium, krill are fed mostly during the day. This, in association with the absence of predators, might have led to the reversal of the DVM rhythm. In addition, in order to avoid interaction with rhythmic cues related to food, krill were briefly starved before and during the experiment. Previous studies suggested that starved zooplankton might become more attracted towards light sources26,27. This may have contributed to stimulate the upward movement observed during the light phases. Additional observations of DVM with (A) krill accustomed to different feeding schedules (e.g. krill fed during the night) and (B) starved krill exposed to illuminated dark phases (DL or LL) might help to clarify these points.
    After we switched to DD conditions (Fig. 1B), during the first day we did not observe any significant rhythm. This might not necessarily imply that no rhythmic migration occurred. In fact, individual krill might have been still rhythmic, but they might have not been synchronized with each other due to the absence of the LD entraining cue or Zeitgeber. A similar phenomenon has already been reported for wild zooplankton in the Arctic and Antarctic during periods of continuous illumination in summer (i.e. during midnight sun)28,29. At that time of the year, in the Arctic, the local populations of Calanus finmarchicus and C. glacialis did not display any net DVM as revealed by backscatter data, but unsynchronized individual migrations were registered instead29. Implementation of individual tracking methods to apply in the lab during DVM monitoring under extreme photoperiodic conditions including constant darkness (DD) and constant light (LL) would allow further insight into this aspect.
    During the second day of DD exposure, RAIN detected a period of 12 h (p-value = 2.3e−02), with a first peak of migration in the early subjective light phase (CT29) and a second peak in the early dark phase (CT41). This suggested that in free-running conditions an endogenous rhythm of vertical migration might emerge with a period of about 12 h. This is in agreement with previous studies of swimming activity, oxygen consumption, enzyme activity and transcription in krill exposed to DD16,18,22 and strongly suggests that the endogenous clock in krill is characterized by a free-running period significantly shorter than 24 h.
    Oxygen consumption
    An endogenous rhythm of activity occurring at the organismic level might contribute to the occurrence of DVM in zooplankton19,30. This might apply to krill as well, since they are known to display daily rhythms in metabolism and physiology15,16. Therefore, we monitored daily rhythms of oxygen consumption in krill exposed to LD and DD and associated them with the observed DVM patterns. Due to technical limitations, we could not monitor oxygen consumption directly within the vertical migration tank. We used individual krill incubated in 2 L Schott bottles filled with oxygen-saturated chilled and filtered seawater instead. We followed the decrease in pO2 over a period of 48 h and tested the presence of rhythmic consumption patterns using the RAIN algorithm. Clear rhythmic oscillations were detected in both conditions.
    In LD, two out of six tested animals (33%) displayed rhythmic oxygen consumption (Fig. 2A,B). Both individuals displayed clear oscillations in the circadian range (i.e., approx. 24 h period): the first one (krill#4, Fig. 2A) displayed a period of 21 h in day 1 (p-value = 1.9e−04) and 24 h in day 2 (p-value = 3.7e−02), while the second one (krill#6, Fig. 2B) displayed a period of 24 h in both days (day 1, p-value = 5.3e−11; day 2, p-value = 3.9e−11). The oscillation was always strongly synchronized to the LD cycle, with peak oxygen consumption occurring at ZT11 (day 1) and ZT12 (day 2) in krill#4 (Fig. 2A) and ZT12 (day 1) and ZT13 (day 2) in krill#6 (Fig. 2B), corresponding to the light/dark transitions. Considering that the animals were incubated within a small volume of water (2 L) and their ability of swim freely might have been severely reduced, changes in swimming activity might not have greatly contributed to the oxygen uptake oscillation. Therefore, this could be interpreted as the result of an internal metabolic oscillation instead. This would support the hypothesis that an internal rhythm of activity might contribute to DVM in krill, even if the mechanisms still remain unknown. In the Calanoid copepod Calanus finmarchicus similar oscillations of oxygen consumption were interpreted as a metabolic anticipation of DVM19.
    Figure 2

    Oxygen consumption patterns of krill exposed to LD. (A,B) In both panels, X-axis represents time given as Zeitgeber Time or ZT measured in hours. ZT0 corresponds to each event of lights-on (6:00). Y-axis represents residual oxygen consumption expressed in mg/L. Positive values indicate increase of oxygen consumption, whereas negative values indicate decrease of oxygen consumption. Black points represent raw data points. Black solid line represents the model fit obtained by applying a GAM to the residual oxygen consumption over time. Red-shaded areas represent the 95% confidence interval around the GAM model’s fit. White and grey rectangles represent alternation of light and dark phases. For each experimental day, results of the RAIN analysis test for the presence of rhythmic oscillations are reported (T = period of oscillation; p = p-value). The figure was generated using the plot function in the “graphics” package (version 3.6.3, https://www.rdocumentation.org/packages/graphics) in R (RStudio version 1.0.136, RStudio Team 2016).

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    In DD, four out of seven tested animals (57%) displayed rhythmic oxygen consumption (Fig. 3A–D). Three of them (krill#3, #4 and #7, Fig. 3B–D) showed a period of about 24 h. The peak of oxygen uptake was advanced compared to LD and occurred during the subjective light phase. Krill#3 (Fig. 3B) displayed a period of 23 h in day 1 (p-value = 1.0e−07) and 24 h in day 2 (p-value = 4.2e−06), with peak oxygen consumption at CT11 and CT34. Krill#4 (Fig. 3C) displayed a period of 21 h in day 1 (p-value = 2.0e−05) and 24 h in day 2 (p-value = 1.6e−06), with peak consumption at CT9 and CT28. Krill#7 (Fig. 3D) displayed a period of 24 h in day 2 (p-value = 2.2e−07), with peak consumption at CT28. A fourth individual (krill#2, Fig. 3A) displayed a period of 12 h in day 1 (p-value = 1.7e−03), with a first peak of consumption at CT3 during the early subjective light phase and a second peak 12 h later (CT15) during the early dark phase. The general advance of the oxygen uptake peak observed in krill#3, 4 and 7 together with the 12 h rhythm displayed by krill#2 suggested that in free-running DD conditions a process of period shortening similar to the one observed for DVM might occur also for oxygen consumption. Previous studies suggested that in krill similar 12 h free-running endogenous rhythms might occur also at the level of metabolic gene expression and enzymatic activity16. This, together with the recent analysis of krill circadian transcriptome revealing a significant 12 h free-running oscillation at the molecular level, strongly suggests that a short endogenous period of oscillation might characterize the circadian clock of Antarctic krill.
    Figure 3

    Oxygen consumption patterns of krill exposed to DD. (A–D) In all panels, X-axis represents time given as Circadian Time or CT measured in hours. CT0 corresponds to first subjective lights-on event (6:00). Y-axis represents residual oxygen consumption expressed in mg/L. Positive values indicate increase of oxygen consumption, whereas negative values indicate decrease of oxygen consumption. Black points represent raw data points. Black solid line represents the model fit obtained by applying a GAM to the residual oxygen consumption over time. Red-shaded areas represent the 95% confidence interval around the GAM model’s fit. Light grey and grey rectangles represent alternation of subjective light and dark phases respectively. For each experimental day, results of the RAIN analysis test for the presence of rhythmic oscillations are reported (T = period of oscillation; p = p-value). The figure was generated using the plot function in the “graphics” package (version 3.6.3, https://www.rdocumentation.org/packages/graphics) in R (RStudio version 1.0.136, RStudio Team 2016).

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    The relatively small percentages (33% in LD and 57% in DD) of individual krill showing significant rhythmic oxygen consumption might have been related to the small sample size in our experiment (n = 6 in LD and n = 7 in DD). However, additional measurements of krill oxygen consumption performed using the same methods in LD and DD on larger samples (n = 10), on board of RV Polarstern during Antarctic expedition PS 112 (March to May 2018), displayed similar percentages of rhythmic individuals (3 out of 10 or 30% in LD, and 4 out of 10 or 40% in DD) (Supplementary Figs. S2A–C and S3A–D). Interestingly, the on-board analyses revealed the same tendency to develop shorter periods of oscillation in DD (krill#7: T = 12 h, p-value = 8.5e−04; krill#9: T = 17 h, p-value = 8.3e−08) (Supplementary Fig. S3C,D). Also, on-board measurements in LD displayed almost a reversed phase of oscillation compared to those in the lab, with peak oxygen consumption occurring at the beginning of the light phase, around ZT4 (Supplementary Fig. S2A–C). It is tempting to speculate that this might be related to the reverse DVM pattern observed in the lab. Unfortunately, we do not have the corresponding DVM measurements from the field to support this hypothesis. Additional field observations of krill rhythms of oxygen consumption in association with DVM would help to clarify how these two phenomena might be related to each other.
    Dissection of putative circadian oscillators in krill brain and eyestalks
    It might be possible that the DVM rhythm and the metabolic oscillation observed in krill were under the influence of separated circadian oscillators. This was suggested by the different responses displayed by DVM and oxygen consumption in DD. While DVM showed a complete shift to a 12 h rhythm, oxygen consumption only showed an advance in the peaking time.
    Previous studies on the circadian system of Crustaceans identified multiple oscillators located in the head and along the body31. In particular, a model has been proposed where the circadian oscillators in the head are situated in the brain, in the eyestalks and in the retinae of the compound eye (Supplementary Fig. S4)31. To investigate this hypothesis we compared, for the first time, daily patterns of clock genes expression in brain and eyestalks tissue of krill exposed to LD and DD. Krill were sampled within a 72-h time-series, 9 animals were collected every four hours. During the first 24 h (ZT0-24), krill were exposed to LD, while during the remaining 48 h (CT0-48) krill were exposed to DD. We dissected brain and eyestalks tissue (Supplementary Fig. S5) and measured relative changes in clock-related mRNAs over time during the first day in LD (ZT0-24) and during the second day in DD (CT24-48) (Supplementary Table S1). We used RAIN to check for rhythmic oscillations within tissue.
    Clear rhythms of oscillation were found in both tissues. In LD, the core clock components in the brain displayed an antiphase relationship between positive (clk-cyc) and negative (per-tim) regulators, with clk-cyc peaking around ZT16-20 (clk: T = 24 h, p-value = 4.86e−07; cyc: T = 24 h, p-value = 2.28e−12) and per-tim peaking around ZT4 (per: T = 24 h, p-value = 2.99e−05; tim: T = 24 h, p-value = 1.31e−11) (Fig. 4A). In the eyestalks such antiphase relationship was not present and most clock genes showed upregulation during the dark phase (ZT16-24) (Fig. 4B). The antiphase relationship is a typical feature of the circadian clock and is well-known from studies on model organisms like Drosophila and mouse2. So far, previous studies on krill failed to demonstrate a clear antiphase relationship between positive and negative regulators21,22. This was discussed as a non-canonical feature of krill circadian clock, as observed before in other Crustacean species32,33. However, our results suggest that this might be related to the specific tissue analyzed. In fact, previous works focused mostly on the eyestalks or on the full head21,22, possibly failing to detect the antiphase oscillation in the brain. This indicates that separate oscillators might be present in the brain and the eyestalks of krill, as already suggested for other Crustaceans31, and suggests that the central pacemaker might be located in the brain. The oscillator in the eyestalks, where all clock genes displayed upregulation during the dark phase, seems to be mostly influenced by the external photoperiod and might be considered as a peripheral oscillator.
    Figure 4

    Comparison of daily patterns of clock genes expression in LD between brain and eyestalk tissues. (A, B) Heatmaps representing up- (in yellow) and down- (in blue) regulation of clock genes expression over time in the brain (A) and eyestalks (B) of krill exposed to LD. For gene names abbreviations please see Supplementary Table S1. Zeitgeber Time (ZT) given in hour from time of lights-on (6:00), corresponding to ZT0, is indicated below each column of the heatmaps. Heatmaps were generated using the heatmap.2 function in the “gplots” package (version 3.0.4, https://github.com/talgalili/gplots) in R (RStudio version 1.0.136, RStudio Team 2016).

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    As in LD, also in DD different patterns of regulations were observed in the brain and in the eyestalks (Supplementary Fig. S6A,B). In the brain, clk, cyc and per, three of the core clock components, displayed a marked tendency towards a shortening of the oscillation period (Fig. 5A–C). Clk shifted from 24 to 12 h (p-value = 1.31e−16), cyc from 24 to 16 h (p-value = 2.48e−10) and per from 24 to 12 h (p-value = 4.05e−07). In the eyestalks, only per showed a similar tendency, shifting from 24 h (p-value = 3.69e−06) to 16 h (p-value = 2.36e−13) (Fig. 5D). This again suggested that separated oscillators might be present in krill brain and eyestalks. The shortening of clock gene oscillation period observed in DD in the brain and, to a lesser extent, in the eyestalks, together with the short (12–16 h) oscillation period registered for cry2 across all tissues and conditions (brain LD: T = 12 h, p-value = 2.4e−08; brain DD: T = 12 h, p-value = 1.4e−04; eyestalk LD: T = 12 h, p-value = 3.2e−05; eyestalk DD: T = 16 h, p-value = 6.1e−13) (Supplementary Fig. S7A,B), is in agreement with previous observations of krill clock gene expression in DD22 and strongly indicates that krill endogenous circadian period might be significantly shorter than 24 h also at the molecular level.
    Figure 5

    LD-DD shortening of the oscillation period in the core clock genes clk, cyc and per. (A–C) Line-plots representing changes in expression levels over time for the clock genes clk (A), cyc (B) and per (C) in LD (blue) and DD (red) in the brain, and for the clock gene per (D) in LD (blue) and DD (red) in the eyestalks. Time intervals are reported on the x-axis. For LD, Zeitgeber Time (ZT) is used, given in hours from the time of lights-on (6:00). For DD, Circadian Time (CT) is used, given in hours from the beginning of the subjective light phase (6:00). Mean gene expression levels (n = 7) are reported on the y-axis as mean Relative Quantities (RQ), indicating the average normalized expression levels of the target clock genes relative to the expression levels of the selected internal and external reference genes at each time interval. Error bars represents SEMs (n = 7). Results of the RAIN analysis test for the presence of rhythmic oscillations are reported (T = period of oscillation; p = p-value). A schematic representation of the light/dark cycle is given below the graphs. For LD, withe rectangles indicate light phases, grey rectangles indicate dark phases. For DD, light grey rectangles indicate subjective light phases, grey rectangles indicate dark phases. The figure was generated using the plot function in the “graphics” package (version 3.6.3, https://www.rdocumentation.org/packages/graphics) in R (RStudio version 1.0.136, RStudio Team 2016).

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    The presence of separated oscillators in krill might help to coordinate different aspects of daily rhythmicity on different levels including physiology (e.g. oxygen consumption) and behavior (e.g. DVM). This might allow a flexible regulation of daily rhythms in response to local changes in environmental conditions driven by temporary and/or seasonal factors including photoperiod, food availability and presence/absence of predators among others.
    Adaptive significance of the short endogenous free-running period in krill
    The tendency in krill to display a 12 h endogenous free-running period might represent a circadian adaptation for living at high latitudes, where the photoperiodic signal displays strong seasonal variability16,22. Surveys from plants and insects along broad latitudinal gradients indicate that high-latitude species tend to have shorter endogenous periods compared to low-latitude ones34. The reasons why this happens are not fully understood yet, but it has been proposed that the short endogenous period might help the clock to entrain to a wider range of photoperiods34. Indeed, krill displayed rhythmic clock gene activity during the midnight sun in summer, suggesting that their clock can successfully entrain to extremely long photoperiods17,35. However, exposition to similar extreme photoperiods in the laboratory apparently caused the disruption of the clock, suggesting that in the field krill might switch to alternative Zeitgebers (i.e. entraining cues) to entrain the clock when photoperiod becomes extremely long/short (e.g. midsummer/midwinter)36.
    From an ecological perspective, having a short endogenous period might help krill to adapt to different environmental scenarios. In the presence of overt day/night cycles, the clock would entrain to the photoperiod and promote daily rhythms with a period of approx. 24 h, like for example the nocturnal DVM pattern usually observed during spring and autumn. This would help krill to anticipate the day/night cycle and maximize the costs/benefits balance between time spent feeding at the surface and time spent hiding in deeper water layers. At the same time, the clock would promote 24 h oscillations in krill metabolism and physiology and coordinate phases of high and low activity with phases of upward and downward migration during DVM.
    On the other hand, in the absence of overt day/night cues, for example during summer and winter, the clock would tend to shift towards the free-running period and promote daily rhythms with a period shorter than 24 h. Observations of krill DVM in the field during winter are scarce, due to the harsh weather conditions which characterize the Southern Ocean at that time of the year. Much of the rhythmic biology of krill during winter still remains unknown. At the same time, field observations of krill DVM and swimming activity during summer suggest that a de-synchronized, “around-the -clock”, individual migratory movement might be present instead18,28. According to some studies, frequent shallow individual migrations could occur during summer as a result of a hunger-satiation mechanism, triggered by the abundant primary production occurring in the surface layers37. To get further insight into these aspects, first we would need to perform additional laboratory studies and field observations of krill rhythmic functions (oxygen consumption, swimming activity, DVM) under extreme photoperiods (LL-DD in the lab, summer–winter in the field). Second, laboratory and on-board trials with krill exposed to different food concentrations (low-medium–high) and different photoperiods (LD-DD-LL) could be used to study the interaction between food and light cues in the emergence of “opportunistic” rhythmic responses. More

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    Divalent heavy metals and uranyl cations incorporated in calcite change its dissolution process

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    The global biological microplastic particle sink

    For this study we use the University of Victoria Earth System Climate Model (UVic ESCM) version 2.940,41,42. The UVic ESCM is an intermediate-complexity earth system model with a resolution of 1.8(^circ ) latitude by 3.6(^circ ) longitude and 19 ocean depth levels. The surface ocean level is 50 m deep. The model contains a two dimensional energy moisture-balance model of the atmosphere, as well as representations of sea ice, ocean circulation and sediments, and terrestrial carbon. The particular biogeochemical version used here includes three phytoplankton functional types, namely diazotrophs (DZ), mixed phytoplankton (PH), and small phytoplankton and calcifiers (CO)43. The model pre-industrial climate has been previously described43, as has its response to business-as-usual atmospheric (hbox{CO}_2) forcing44. The following sections describe the MP model. A model schematic is presented in Fig. 6.
    Figure 6

    Microplastic model schematic. Marine snow is produced as a fixed fraction of the free detritus (DET) pool. MP aggregates with this marine snow, entering the (hbox{MP}_A) (marine snow entrained MP) pool. (hbox{MP}_A) held in aggregates sinks at the aggregate rate, with a fraction reaching the seafloor considered to be lost from the ocean. Detrital remineralisation releases the (hbox{MP}_A) from marine snow aggregates at the rate of detrital remineralisation. MP is also grazed by zooplankton and excreted into a pellet-bound (hbox{MP}_Z) pool. Pellet-bound (hbox{MP}_Z) sinks and is released back to the free MP pool at the rate of detrital remineralisation, but some is also lost at the seafloor. Details on the biogeochemical aspects of the model are previously described43.

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    Model description
    The base model43 was modified in order to quantify the roles of two of the three theorised biological export pathways on MP (aggregation in marine snow and zooplankton ingestion; for now, we neglect an explicit representation of biofouling29). We distinguish between detritus that becomes faecal pellets, and the physical aggregation of marine snow, by introducing a new faecal pellet tracer to divert 50% of zooplankton particulate losses into a separate detrital pool27. For simplicity, this new pellet detrital pool has the same sinking parameterisation as the original detritus. Using the same sinking rates for both detrital classes produces ocean biogeochemistry that is identical to the previously published versions of the model. In the model, plastic particles only interact passively with marine snow (they do not, for example, modify aggregate sinking rates), but they interact actively with zooplankton grazing (described below). Plastic particles have been observed to both increase and decrease the sinking rates of marine snow21,22 and decrease the sinking rates of faecal pellets20,38, but for simplicity and as a first approximation we neglect these effects in our model.
    Three MP compartments are introduced; “free” (unattached) microplastic (MP), microplastic aggregated in marine snow ((hbox{MP}_A)), and microplastic in zooplankton faecal pellets ((hbox{MP}_Z)). All MP are considered to represent particles within a biologically active size range, but this size (and the particles’ composition) is never made explicit. These assumptions could bias modelled MP towards polymer types favoured by generic zooplankton34 and particle sizes in the lower end33,34 of the defined range of microplastic size. However, our parameter sensitivity testing in the Supplemental Information tests various fractional uptake rates that implicitly consider size and particle composition in how biologically “active” the MP pool is. As with all model ocean tracers, microplastic concentrations (MP) vary according to:

    $$begin{aligned} frac{dmathrm {MP}}{dt} = T + S(mathrm {MP}) end{aligned}$$
    (1)

    With T including all transport terms and S representing all source minus sink terms. The source and sink terms for free microplastic are:

    $$begin{aligned} S(mathrm {MP}) = Emis – S(mathrm {MP}_A) – S(mathrm {MP}_Z) + w_p frac{delta mathrm {MP} times F_R}{delta z} end{aligned}$$
    (2)

    Microplastic is emitted to the ocean (Emis) along coastlines and major shipping routes using a scaling against regional (hbox{CO}_2) emissions (a dataset provided with the standard UVic ESCM version 2.9 package download), in order to approximate degree of industrialisation and population density in this first version of this model. The rate of emission is a proportion of the total annual plastic waste generation ((F_T))45. For now, abiotic degradation of macroplastics as a source of microplastics to the ocean is neglected to keep the model simple and focus on biological transport. The MP then exchanges with the marine snow ((hbox{MP}_A)) and zooplankton faecal pellet ((hbox{MP}_Z)) pools. A fast particle rising rate ((w_p)) of 1.9 cm per second46 is prescribed to a fraction ((F_R)) of the free MP in each grid cell below the surface level as an approximation of positive buoyancy. An alternative approach would be to assign a uniform rise rate to all MP particles, and to subject the value of the rise rate to sensitivity testing. However, a weakness of this alternative approach is that the many types of plastic in the ocean have different characteristic buoyancies, which could produce unique particle pathways18. In this alternative approach it would be more appropriate to explicitly simulate multiple MP types in the model (which we sought to avoid in this first modelling effort for the sake of simplicity). Nevertheless, we conducted a sensitivity test using several different rise rates, and the effect of reducing the mean rise rate was similar to reducing the fraction assigned a rise rate.
    In the current model version there are no abiotic breakdown rates (i.e., photo-degradation39) or respiration losses47 removing MP from circulation.
    MP is modelled to aggregate in marine snow as:

    $$begin{aligned} S(mathrm {MP}_A) = A_{upt} – A_{rel} – w_Dfrac{delta mathrm {MP}_A}{delta z} end{aligned}$$
    (3)

    MP particles are taken up ((A_{upt})) via a Monod function applied to the rate of marine snow formation (sources of detritus; (D_A) in nitrogen units, multiplied by an aggregation fraction, (F_A)) in order to approximate an increased likelihood of MP/marine snow encounter with increasing MP concentrations that approaches a level of saturation at high MP concentrations:

    $$begin{aligned} A_{upt} = frac{mathrm {MP}}{k_P + mathrm {MP}} times source(D_A) times F_A end{aligned}$$
    (4)

    The uptake constant ((k_P)) is subjected to sensitivity testing, as is the fraction of marine snow aggregation ((F_A)). In this parameterisation, the aggregation of MP in marine snow represents the net uptake of MP into aggregates by both aggregation and biofouling processes. Biofouling occurs mostly in the upper 50 m35, which is the entire surface layer grid cell in our model. The entrainment-release cycle of biofouling is implicit in our parameterisation via the microbial loop, which is temperature-dependent. Sensitivity testing of the (k_P) and (F_A) parameters therefore represent testing of the net aggregation due to non-zooplankton biological aggregation effects. MP is released ((A_{rel})) from marine snow at the rate of detrital remineralisation ((mu _D)). This rate is temperature-dependent and results in higher rates of release in the low latitudes.

    $$begin{aligned} A_{rel} = mu _D mathrm {MP}_A end{aligned}$$
    (5)

    A particle sinking term ((w_D)) applies to marine snow-associated MP, and has the same value as sinking detritus. The base unit of all MP tracers is number of plastic particles. As a first approximation we assume that all marine snow aggregates forming from free detritus have the characteristic of diatom aggregates (8.8 (upmu )g C per aggregate48). Model detritus in mmol N is converted to mmol C using Redfield stoichiometry, which is then converted to (upmu )g C to calculate the maximum number of aggregates. The maximum number of aggregates is then multiplied by the aggregation fraction (F_A), to calculate (hbox{MP}_A) source and sink rates. MP is conserved for all MP tracers when surface flux balances sedimentary loss rate. What fraction of MP particles reaching the seafloor via aggregate and faecal pellet ballasting are returned to the water column ((F_B)) is tested. For simplicity and as a first approximation, detritus ballasted by calcite, and calcite43, are assumed to not aggregate with microplastic.
    Similarly, for MP associated with zooplankton, sources and sinks are:

    $$begin{aligned} S(mathrm {MP}_Z) = P_{upt} – P_{rel} – w_Dfrac{delta mathrm {MP}_Z}{delta z} end{aligned}$$
    (6)

    The calculation of MP particle ingestion rate ((P_{upt})) is the same as for other food sources37. A grazing preference ((psi _{MP})) for MP is subjected to sensitivity testing. This sensitivity testing implicitly examines effects such as biofouling altering the grazing preference of zooplankton for MP. It is assumed that 100% of ingested MP will be egested as faecal pellets and released ((P_{rel})) to the “free” MP pool at the rate of faecal pellet remineralisation, with no plastic remaining in the gut and no plastic being metabolised by the zooplankton. Ingesting MP also results in a reduced zooplankton carbon uptake rate19, with implications for primary and export production (although, Redfield ratios are conserved). Pellet-bound (hbox{MP}_Z) is considered to sink at the rate of faecal pellets ((w_D)).
    Plastic is eaten by zooplankton in this model. The Holling II grazing formulation37 is extended to include MP. Grazing of MP ((G_{MP})) is calculated as:

    $$begin{aligned} begin{aligned} G_{MP}&= mu _Z^{max} times Z times mathrm {MP}times R_{M:P}times R_{F:MP}times R_{N:F}times psi _{MP}\&quad times ,(psi _{CO}CO+psi _{PH}PH+psi _{DZ}DZ+psi _{Detr_{tot}}Detr_{tot}\&quad +,psi_{Z}Z+psi _{MP}mathrm {MP}times R_{M:P}times R_{F:MP}times R_{N:F} + k_Z)^{-1} end{aligned} end{aligned}$$
    (7)

    The maximum potential grazing rate ((mu _Z^{max})) is scaled by zooplankton population (Z) and MP availability (MP), and weighted by a food preference ((psi _{MP})), total prey (CO, PH, DZ, (hbox{Detr}_{{tot}})), and Z representing the food sources described in44 and a half saturation constant for zooplankton ingestion ((k_z)). Grazing preferences must always sum to 1 in the model, so sensitivity testing of (psi _{MP}) requires that all grazing preferences must also be adjusted. This is done by varying (psi _{MP}) but requiring (psi _{DZ}) always be set to 0.1 (on the basis that diazotrophs are a poor food source, and to minimize disruption to the nitrogen cycle). The remaining allowance is equally split by the other (psi ) terms. The calculation occurs in N units, so MP is first converted to grams of MP using the MP particle-to-mass conversion of 236E3 tonnes MP = 51.2E12 particles MP ((R_{M:P}))4. It is assumed that 1 g MP will roughly replace 1 g of food (at Redfield ratios; (R_{N:F}) is the conversion from mol Food to mol N) in the zooplankton’s diet, and MP is thus converted to mmol N for the grazing calculation. However, we subject this ratio ((R_{F:MP})) to sensitivity testing. Zooplankton uptake of plastic is therefore:

    $$begin{aligned} P_{upt} = frac{G_{MP}}{R_{M:P}times R_{F:MP}times R_{N:F}} end{aligned}$$
    (8)

    MP particles are released from faecal pellets via remineralisation, which occurs at the same rate as the remineralisation of aggregates:

    $$begin{aligned} P_{rel} = mu _D mathrm {MP}_Z end{aligned}$$
    (9)

    Model forcing
    The model was integrated at year 1765 boundary conditions (including agricultural greenhouse forcing and land ice) for more than 10,000 years until equilibration was achieved. From year 1765 to 1950, historical (hbox{CO}_2) concentration forcing, and geostrophically adjusted wind anomalies are applied. From 1950 to 2100 the model is forced with a combination of historical (hbox{CO}_2) concentration forcing (to 2000) and a business-as-usual high atmospheric (hbox{CO}_2) concentration projection RCP8.549,50. MP emissions start from 2 million metric tonnes in year 1950 (a total plastic waste generation estimate45), increasing at a rate of 8.4% per year. (hbox{CO}_2) and MP forcing is summarized in Fig. 7. It has been estimated that about 4% of total plastic waste generated enters the ocean30, but that the microplastic mass found at the sea surface represents only about 1% of the annual plastic input to the ocean4. We test a range of input fractions (see Table 2), after applying a mass conversion from tonnes to number of MP particles4. Using a considerable over-estimation of MP pollution rate also implicitly accounts for abiotic degradation of larger plastics.
    Figure 7

    Model forcing from years 1950–2100. Atmospheric (hbox{CO}_2) follows RCP8.5 (panel a). Plastic flux into the ocean is assumed to be some fraction of the total historical and projected plastic waste generation estimate (panel b), with a continuing rate of increase of 8.4% per year45, converted to MP particles using a mass conversion4. Previous estimates of actual total plastic mass flux into the ocean is only about 4% of the total plastic waste generation30, with the MP fraction being a small proportion of that.

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    Table 2 Microplastic model parameters and range tested.
    Full size table

    Experimental setup
    A 700-member Latin Hypercube51 was used to test the microplastic parameter space of the model using the forcing described in the previous section. While biological model parameters might also influence microplastic uptake and transport, we limited our initial tests to the new parameters introduced above. A range of values was prescribed to the parameters listed in Table 2, in which the parameter space was randomly sampled with a normal distribution. The objective was to see what can be learned about plastic accumulation in the ocean, when very little is known about plastic/particle interactions and basic processes are still poorly understood. An analysis of the full Latin Hypercube parameter search is provided as Supplemental Information.
    We adopted an incremental approach to increasing model complexity. We started with a control Hypercube where biology was not allowed to take up plastic, in order to first test the physical parameters ((F_T) and (F_R), the fraction of total annual plastic produced entering the ocean as MP, and the fraction assigned a rise rate, respectively). One hundred simulations were performed in this configuration, with the results analysed in the Supplemental Information. We next included passive plastic aggregation in marine snow (MP plus the (hbox{MP}_A) tracer) in a 300 simulation Hypercube, spread across the (k_P) (marine snow uptake coefficient) parameter space (0–1, 1–100, 100–1000 particles (hbox{m}^{-3}), each with 100 Hypercube simulations) in a normal distribution. These 300 simulations explored the 5 relevant MP model parameters: (F_T), (F_R), (F_A) (marine snow aggregation fraction), (k_P), and (F_B) (fractional return to ocean at the seafloor). These results are also provided in the Supplemental Information. Finally, we added active zooplankton-associated plastic (MP, plus (hbox{MP}_A) and (hbox{MP}_Z) tracers) as a third 300-individual Hypercube set. This third Hypercube is similarly split across the (k_P) parameter space in a normal distribution, but with the addition of grazing parameters (psi _{MP}) (MP grazing preference) and (R_{F:MP}) (the food to MP substitution ratio; 7 parameters in total). More

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    On the interpretability of predictors in spatial data science: the information horizon

    Meaningless predictors and spatial dependence
    The variogram range of the GRF predictors has a strong influence on model validations. Figure 6 shows the increase in the cross-validation (R^2) with increasing ranges for all three study sites. The maximum prediction accuracy is reached when the range of the structurally meaningless predictors (e.g. the GRFs) is similar to the range of the soil properties. This is also the reason why meaningless predictors, with respect to a structural relationship to a soil property, such as photographs of faces or paintings, can produce accurate evaluation statistics.
    The effect is more stable when 100 GRFs are used, compared to only 10 GRFs for each range of spatial dependence. That is, when using 100 GRFs, relatively accurate model validations are already reached using lower scale predictors compared to using only 10 GRFs. However, cross-validation accuracy can be relatively high when the variogram ranges of the 10 GRFs are long and thus better resemble the effects of EDFs.
    Figure 6

    Influence of the variogram ranges of Gaussian Random Fields (GRF) on predictive accuracy. Blue: (R^2) values for models based on 100 GRFs; gold: (R^2) values for models based on 10 GRFs; red: variogram range of the corresponding soil property.

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    We can therefore accept the first two hypotheses: using enough but totally meaningless predictors with similar or longer ranges of spatial dependence than that of the response variable, can result in models that produce high predictive accuracies, however, with zero descriptive accuracy. Both, GRFs and EDFs are spatial but not environmental predictors. So, we can “interpolate” with only a few but very large-scale random predictors. But when we interpolate, we cannot interpret. And when the predictors are not completely linear as EDFs, which is the case for GRFs with random meaningless variations between the sample locations, smoothing between the sample points, which is the concept behind interpolation, is not guaranteed. Hence, using GRFs or otherwise meaningless predictors is neither a structural model nor an interpolation model in the classical sense, and therefore must be rejected in principle.
    Reference models and prediction accuracy
    The prediction accuracies of the different models are presented in Fig. 7. Figure 8 shows the corresponding maps.
    Figure 7

    Modelling cross-validation accuracies (represented by the coefficient of determination, (R^2)) for all approaches and datasets (GMS: Gaussian mixed scaling, EDF: Euclidean distance fields, GRF: Gaussian random fields models with 100 or 10 predictors).

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    Figure 8

    Modelling results. The first row shows the reference models (GMS: Gaussian mixed scaling, EDF: Euclidean distance fields). The other three rows show the models based on 100 Gaussian random fields (GRF) with different variogram ranges.

    Full size image

    Generally, the GMS models produced the best results. This could be an effect of the number and structure of the predictors, which is larger compared to the merged restricted GMS + EDF dataset, and thus possibly an effect of overfitting to the dependence structure of the data23.
    Models with EDFs generally performed better than models with the restricted GMS. Hence, the spatial dependence of soil properties cannot be described by the constrained GMS dataset. There is an increase in prediction accuracy when using the EDFs together with the restricted GMS dataset (except for the Meuse dataset), which could be an indicator for non-stationarity.
    In terms of prediction accuracy, modelling with GRFs produced relatively high predictive accuracies (Fig. 7).
    The information horizon—descriptive accuracy and relevance
    Generally, the descriptive accuracy is strong if there is a causal relationship25 between the response and a predictor. The descriptive accuracy can also be high if there are associations among variables as usually inferred by statistical analysis, which can suggest potential causal relationships1.
    Provided that the relevance of the predictors is given and the algorithm or method to generate the data is valid15, 17, the results of this study indicate that the descriptive accuracy is high if the range of spatial dependence of a predictor is equal or smaller than the range of the response variable. However, predictive accuracy can increase when predictors with longer ranges than the range of the environmental property are included, possibly due to non-stationarities in the environmental process4,26 or effects of anisotropy. Therefore, one should remove only those predictors from multiscale approaches15,17,27,28,29,30 with variogram ranges that are long with respect to the size of the study area and if their information content is below a certain minimum (Fig. 4).
    If, on the other hand, predictors show ranges of about the diagonal length of the entire study area, then they resemble the properties of the EDFs (Fig. 5) and their ranges are too long to lend themselves to interpretation. In these cases, predictors behave indistinguishably from purely spatial predictors, although they might still be interpretable in some situations.
    In summary, these results confirm our third hypothesis, and show that the primary information horizon is located somewhere between the range of the variogram of the soil property and a certain minimal variation of the predictors across the study site.
    Beyond the information horizon—descriptive uncertainty and contextual complexity
    We recently showed that when finer to coarser scales are successively removed from a set of all scales of a GMS modelling, prediction accuracy usually remains high, even if only the coarsest scales remain in the model4. In cases where the prediction accuracy decreases, we can assume that (i) structural information is lacking, that (ii) interpolation is not the appropriate method, or that (iii) the spatial dependence of the coarse scale GMS predictors are not suitable for interpolation, e.g. if all these coarse scale predictors only show a trend in one direction, for example in X direction only instead of X and Y direction.
    We also found an increase in prediction accuracy beyond the range of the variogram of soil properties in GMS and similar approaches4,15,26, when successively adding coarser scales. There are two explanations. First, not all original terrain properties show exactly the same original scale or range, which is due to the convolution functions and the general approaches to calculate terrain properties (e.g. first and second order derivatives, i.e. slope and curvature). Second, this effect might be related to non-stationarity, where coarse-scale predictors can help to “divide” the study area into zones. We tested this here by combining the restricted set of GMS predictors, which are within the information horizon, with EDFs. In all cases prediction accuracy increased. Hence, there is obviously some spatial dependence present, resulting from predictor interactions on very coarse scales or long ranges, which are beyond the information horizon, inferable by the size of the study area. In these cases, there will be some uncertainty in the descriptive accuracy when using predictors that show information contents below a certain minimum of spatial variation.
    Looking specifically at the three study sites we see complex soil property formation processes due to interactions of predictors at different scales. This contextual complexity has to be taken into account when interpreting environmental predictors beyond the information horizon, as discussed above.
    In Piracicaba very coarse-scale predictors are important27. The soil formation system, however, is rather simple. It is based on rock formation, strike and dip, and subsequent erosion. In this case coarse scale terrain indicators for aspect are good proxies to differentiate between the two different types of parent material, even though they resemble properties of EDFs. In such cases partial dependence models should be applied to aide interpretation27.
    The silt content in Rhine-Hesse is controlled by local silt translocation31, which occurred in the last glacial period of the Pleistocene epoch (Würm glaciation) and which was modulated by interactions of climate and terrain. This can be described in terms of a teleconnected system32 and can be mapped by terrain only, which then serves as a proxy for that system26,27. Similar to Piracicaba, interpretations of predictors with very large ranges and relatively low information content can be reasonable. However, the descriptive uncertainty is higher compared to predictors that fall within the information horizon.
    The situation for Meuse is different due to a different dominant process system. The zinc content is driven by flooding events. Therefore, different and more relevant predictors, such as the distance to the river Meuse, should be used in this case9. We see that EDFs perform better compared to the mixed dataset (GMS restricted + EDF). This shows that the multiscale terrain predictors are not relevant, but represent noise, and can therefore serve at most as vague proxies. Another problem resulting in such an effect could be algorithmic issues related to feature selection within the Random Forests model, which in some specific cases might occur in relation to autocorrelated predictors33, or to effects due to fitting noise5.
    Interestingly, in all cases the GMS models perform better compared to the mixed dataset (GMS restricted + EDF). This can be either due to a higher number of predictors in the GMS approach or relevant structural predictors beyond the information horizon.
    Generally, the interpretation of environmental predictors beyond the edge of the information horizon needs specific care and is afflicted with more uncertainty. More