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To capture the first-order characteristics of the distribution of eDNA shed by mesopelagic species, we used a mechanistic model with one spatial dimension (the vertical dimension). It treats migrating organisms as a continuous point source of eDNA and simulates temporal evolution of the eDNA concentration vertical profiles in a one-dimensional ocean with climatological conditions. Horizontal variation of the distribution of eDNA shed by mesopelagic species is not considered in this study. The point source in the model represents a number of individuals within a single species. The simulation includes relevant eDNA transport processes using a vertical Price-Weller-Pinkel (PWP) dynamical module42. We use this model to first explore the sensitivity of eDNA concentration profiles to a variety of biological and physical parameters and to assess vertical and temporal variability of the eDNA concentration. Table 1 outlines the parameters, separated by type, and ranges of values for each parameter used in the sensitivity analysis (see “Sensitivity analysis” section below) and in a case study of how the model can be used to determine the percent of individuals that migrate (see “Application to ecological questions” section below). We then discuss how the mechanistic model can be used in conjunction with field sampling to test ecological hypotheses, highlighting how analysis of eDNA concentration profiles can provide information regarding where and when organisms are located in the water column. Finally, we comment on implications of this work and how the model can be used to both design and interpret observations.Table 1 Parameters separated by category.Full size tableModel overviewGoverning equationsTo maintain simplicity and also provide a more realistic scenario where both settling and neutrally buoyant eDNA particles28 are considered, we assume that the eDNA material at any given time in the system consist of eDNA particles of two size classes. Here, large eDNA particles are on the order of 10 s of µm to 1 mm and represent materials such as fecal pellets, chunks of tissue, or gametes that would be subject to both settling and physical breakdown over time. Small eDNA particles are on the order of 0.1 µm to 10 s of µm and would be any eDNA shed from an organism that has a density such that they are near-neutrally buoyant including extracellular eDNA or forms such as sperm, urine, blood, or single cells. This size class of small particles is so small that we can neglect their settling. In practice, these two size fractions of eDNA would be captured using the common method of filtering water through a < 1 µm pore size filter43. Both small and large particles in the model are subject to the same eDNA decay rate constant and large particles break down over time into small particles.The equation describing the change of eDNA concentration in the form of large particles is:$$begin{aligned} frac{partial {C_{LP}}}{partial {t}} = - w_vfrac{partial {C_{LP}}}{partial {z}} + frac{partial {}}{partial {z}}left( kappa _zfrac{partial {C_{LP}}}{partial {z}}right) - kC_{LP} - delta C_{LP} + w_sfrac{partial {C_{LP}}}{partial {z}} + hat{S_{LP}} end{aligned}$$ (1) where (C_{LP}) is the concentration of large eDNA particles, (w_v) is the vertical velocity [L/T] with a positive value pointing upward, (kappa _z) is the vertical diffusivity [L(^{2})/T], k is the first order decay rate constant [1/T], (delta) is the breakdown rate of particles [1/T], (w_s) is the settling rate of eDNA [L/T], and (hat{S_{LP}}) is the shedding rate of new large eDNA particles.Similarly, the equation describing the temporal evolution of the concentration of small particles of eDNA, (C_{SP}), is:$$begin{aligned} frac{partial {C_{SP}}}{partial {t}} = - w_vfrac{partial {C_{SP}}}{partial {z}} + frac{partial {}}{partial {z}}left( kappa _zfrac{partial {C_{SP}}}{partial {z}}right) - kC_{SP} + delta C_{LP} + hat{S_{SP}} end{aligned}$$ (2) where the parameters are the same as Eq. (1). Note that there is no settling term in Eq. (2) as small eDNA particles are assumed to be neutrally buoyant and that the (delta) term in Eq. (2) has the opposite sign as that in Eq. (1), reflecting eDNA volume conservation during the breaking-down of the large particles into small particles.Physical modelThe 1-D vertical model is implemented in MATLAB. The physical module is based on a previously published 1-D model of physical processes in the mixed layer42 and is modified to include the relevant organism and eDNA parameters. The model spans from the surface down to 1500 m deep with a vertical resolution of 0.5 m and has a time step of 10 s. Each simulation runs for a total of 90 days, representing one of the four seasons: summer (July, August, September - JAS), fall (October, November, December - OND), winter (January, February, March - JFM), and spring (April, May, June - AMJ). The model has a zero-gradient open boundary condition at the bottom. The model is forced on the surface by climatological, 8-hourly meteorological conditions from the NCEP/NCAR Reanalysis at a location in the Northeast Atlantic Ocean (37.047(^circ) N, -71.25(^circ) W). Inputs include air temperature, short wave radiation, long wave radiation, precipitation, air pressure, air humidity, and winds. The wind stress and heat fluxes are calculated using the bulk formulae44.The initial vertical distribution of the temperature and salinity in the model are seasonal climatological profiles obtained from the NCEI World Ocean Atlas 2018 at a site in the Northwest Atlantic slope sea (39.125(^circ) N, −70.875(^circ) W; north of the Gulf Stream). The model also simulates the influences of vertical mixing and advection on the temperature, salinity and eDNA particles. The mixing influence is incorporated by prescribing synthetic vertical profiles of vertical diffusivity that combines observed seasonal mean mixed layer depth45 and simulated seasonal mean vertical diffusivity profile from an operational model46, both at a site in the Northwest Atlantic slope sea (see Supplemental Text S1 and Supplemental Fig. S1). Vertical advection profiles are set to increase linearly from 0 ms(^{-1}) at the surface to the maximum value of ((10^{-4}) ms(^{-1})) at 200 m and then decrease linearly back to 0 ms(^{-1}) at 400 m (Supplemental Fig. S2). This prescribed advection profile does not change seasonally and represents enhanced vertical motions associated with sub-mesoscale processes in the upper water column (e.g.,47). Note that the result of this study is not sensitive to the prescribed vertical profiles of diffusivity or vertical velocity (see below).The physical parameters that will be adjusted in this study include: the initial temperature and salinity profiles, the mixed layer depth, the vertical diffusivity profile, and the vertical velocity profile (see Ocean parameters in Table 1).Organism movementThis study focuses on eDNA shed by vertically migrating organisms living in the mesopelagic ocean. For simplicity, we assume the organisms reside at the constant depth of 500 m during the day and the constant depth of 50 m during the night. These depths fall within the range of where migrating organisms are found at these times41,48. As the objective of this study is to develop a qualitative understanding of the vertical distribution of the eDNA concentration, the exact depth a particular mesopelagic species resides at in the daytime is not crucial. Organisms begin migrating to the surface two hours before sunset, and the upward migration ends one hour after sunset. The time of sunset and sunrise are determined seasonally using NOAA’s ESL solar calculator for the year 2019 at 42.35(^circ) N, −71.05(^circ) W. Both upward and downward migrations are assumed to be in constant speed, and the migration times do not change within each season (Fig. 2).Figure 2Representative organism migration curves for each season. Migration times change with sunrise and sunset for each season. This illustration assumes that 50% of individuals migrate. The shading shows the percentage of individuals with black indicating 100%, i.e., all organisms, and grey indicating 50%. These numbers vary among the simulations.Full size imageThe migration parameters that can be adjusted in the model include: daytime residing depth, nighttime residing depth, the start and end times of migrations (and thus duration), the percent of individuals that migrate, and the layer thickness (i.e., “width” of school). (See Organism parameters in Table 1). In this study, we focus on the start and end times of migrations (and thus duration) and the percent of individuals that migrate.eDNA parametersWe assume organisms are continuously shedding eDNA, and the shedding rate is fixed in time in each simulation. The eDNA then remains in the water column, where it is subject to transport and decay as described by Eqs. (1) and (2). Although several studies have characterized eDNA shedding rates of different marine organisms29,49,50, shedding rates are highly variable across studies and have high error associated with them, likely due to high temporal variability29. Here, we use a constant shedding rate of 1 mass unit per time step (10 seconds). Note that this study focuses on the relative vertical distribution of the eDNA concentration and its temporal variability, rather than its absolute value. The particle size distribution of eDNA (and the breakdown rate of large to small particles) and the settling rate of eDNA are largely unknown and expected to be time-varying28. Here we use a breakdown rate of fecal pellets to apply to large eDNA particles breaking down into small eDNA particles51. The most well characterized parameter of eDNA is decay rate, which several studies have characterized as a function of water temperature29,49. The upper and lower limits of the decay rate have also been well established29,31. Finally, there are currently no estimates of eDNA settling rates. We use values of marine snow settling rates52 to apply to large eDNA particles that are subject to settling in the model.The eDNA-related parameters that are adjusted in this mechanistic model include: settling rate of large particles; ratio of large particles to small particles that are shed by an organism; eDNA breakdown rate (large particles to small particles); the eDNA decay rate. (See eDNA parameters in Table 1). Note that shedding rates in the model do not change over the course of each simulation.Sensitivity analysisA series of 90-day simulations were carried out with altered values of the aforementioned parameters to examine the sensitivity of the eDNA vertical distribution to the parameters. Table 1 provides a list of the parameters that were adjusted in the sensitivity analysis. Note that the diffusivity profile (both the shape of the profile and the mixed layer depth), the temperature profile (which impacts the eDNA decay rate), and the daytime length (which impacted migration times) all change with the season. Other sensitivity parameters include vertical advection, settling rate of large particles, the ratio of large to small eDNA particles shed by organisms, and the percent of individuals that migrate. A total of 972 simulations were conducted with the following sets of parameters: 4 mixing profiles (one for each season), 3 vertical advection profiles (upwelling, downwelling, none), 3 settling rates of large eDNA particles, 3 decay rate constant scenarios (two constant values representing high and low values in the literature31, one temperature-dependent rate29 for each season, Supplemental Fig. S3), 3 scenarios for the percent of individuals that migrate, and 3 ratios of large to small eDNA particles shed by the organisms.In order to assess the impact of the parameters on the eDNA profiles, several metrics were defined. First, the water column was divided into three sections: surface layer (0–100 m), mid-depth (100–450 m), and deep water (450–550 m), based on our representative daytime and nighttime depths (500 m and 50 m) used for the simulations. For each simulation, the mean and maximum eDNA concentration in each depth bin was recorded. Also, the cumulative eDNA concentration in each depth bin was normalized to calculate the proportion of eDNA in each depth bin at any given time during the simulation. For each simulation, the mean and standard deviation of the proportion of eDNA in each depth bin were calculated over the course of the 90 day simulation.A first-order comparison of the vertical length scales of eDNA transport by different processes were conducted. Here, we use a time scale of eDNA decay, T(_{90}), i.e., the time it takes for 90% of the released eDNA to decay, to determine the vertical length scale of each process. In particular, we would like to estimate, the vertical distances eDNA is transported by advection, mixing, and settling before 90% of the released eDNA has decayed, L(_{mix}), L(_{advect}) and L(_{settling}), respectively. These quantities are defined mathematically as,$$begin{aligned} T_{90} = frac{-ln(0.1)}{k_{avg}} end{aligned}$$ (3) $$begin{aligned} L_{mix} = sqrt{kappa _v T_{90}} end{aligned}$$ (4) $$begin{aligned} L_{advect} = w_{vm} T_{90} end{aligned}$$ (5) $$begin{aligned} L_{settle} = w_s T_{90} end{aligned}$$ (6) where (k_{avg}) is the average decay rate constant [T(^{-1})] for the whole water column over the 90 day simulation, (kappa _v) is the maximum vertical diffusivity coefficient [L(^{2})T(^{-1})] , (w_{vm}) is the maximum vertical velocity [LT(^{-1})] , and (w_s) is the settling rate [LT(^{-1})]. Note that because k is temperature dependent, the value of the decay rate constant will change both vertically (e.g., deeper water will be colder and have a lower decay rate constant) and temporally (e.g., at a given depth, the water temperature will be warmer in the middle of the day and thus will have a higher decay rate constant).Application to ecological questionsAfter obtaining a first-order understanding of the eDNA concentration profile and the impact of the parameters on the eDNA distribution, we ran another set of model simulations to examine if vertical and temporal eDNA concentration variability can shed light on an ecological question regarding what percentage of individuals within the same species migrate on a daily basis. To do this, for each season, all parameters were held constant except for the percent of individuals that migrate, P(_{m}). In each season, the value of P(_{m}) varies from 0 to 100% with an increment of 10%. A total of 44 such simulations (4 seasons x 11 percent migrate scenarios) were carried out. We then compared mean and maximum eDNA concentrations in the surface layer (0–100 m) to those in the deep water (450 to 550 m), and examined the relationship between the surface-to-deep ratios and P(_{m}). More

Modelling approachWe used the PISCES-v2 biogeochemical model, attached to the Nucleus for European Modelling of the Ocean version 4.0 (NEMO-v4) general ocean circulation model29. PISCES-v2 includes five nutrients pools (nitrate, ammonium, phosphate, silicic acid and dissolved iron), dissolved oxygen, the full carbon system and accounts for two phytoplankton (nanophytoplankton and diatoms) and two zooplankton types (microzooplankton and mesozooplankton). Bioavailable nitrogen in our simulations is considered to be the combination of nitrate and ammonium. Its nitrogen cycle includes nitrogen fixation, nitrification, burial, denitrification in both the water column and sediments, and coupled nitrification–denitrification. Nitrogen isotopes were integrated within PISCES-v2 for the purposes of this study, using nine new tracers (Supplementary Note 1). Horizontal model resolution varied between ~0.5° at the equator and poles, and 2° in the subtropics, whereas vertical resolution varied between 10 and 500 m thickness over 31 levels.We conducted simulations under both preindustrial control and climate change scenarios. The preindustrial control scenario from 1801 to 2100 maintained preindustrial greenhouse gas concentrations and only included internal modes of variability. The climate change simulation from 1851 to 2100 included natural variability, prescribed changes in land use, as well as historical changes in concentrations of greenhouse gases and aerosols until 2005, after which future concentrations associated with RCP8.5 were imposed30. The biogeochemical model (PISCES-v2) was run offline from the physical model (NEMO-v4) using monthly transports and other physical conditions generated by the low resolution version of the IPSL-CM5A ESM57.Experiments were initialized from biogeochemical fields created from an extensive spin-up of 5000 years under repeat physical forcing, followed by a 300-year simulation under the preindustrial control scenario. The preindustrial control simulation used in analysis was therefore the final 300 years of a 5600-year spin-up involving two repeat simulations of the preindustrial control scenario. We utilized a global compilation of δ15NNO320 supplemented with recent data to assess the isotopic routines in the model and conducted a thorough model-data skill assessment at replicating observed patterns in space (Supplementary Note 2 and Supplementary Figs. 1–3).Anthropogenic nitrogen depositionThe effect of increasing aeolian deposition of nitrogen was assessed in our simulations. Preindustrial nitrogen deposition was prescribed as the preindustrial estimate at 1850, whereas the historical to future deposition was created by linear interpolation between preindustrial (1850) and modern/future fields (2000, 2030, 2050 and 2100). These fields were provided by Hauglustaine et al.8. However, the rapid rise between 1950 and 2000 was maintained, such that 60% of the increase between the preindustrial and modern fields occurred after 1950 (Supplementary Fig. 4).The historical rise in anthropogenic nitrogen deposition was assessed by including it in additional simulations under both preindustrial control and climate change scenarios. Four initial experiments were therefore conducted: preindustrial control; preindustrial control plus anthropogenic nitrogen deposition; climate change; and climate change plus anthropogenic nitrogen deposition.Global model experimentsWe undertook four initial simulations to quantify the impacts of anthropogenic climate change and nitrogen deposition: a preindustrial control simulation from 1801 to 2100; a full anthropogenic scenario from 1851 to 2100; a climate change-only scenario without the increase in anthropogenic nitrogen deposition from 1851 to 2100; and a nitrogen deposition scenario without anthropogenic climate change from 1851 to 2100. Anthropogenic effects to nitrogen cycling were quantified by comparing mean conditions over the final 20 years of the twenty-first century (2081–2100) with mean conditions over the final 20 years of the preindustrial control simulation, whereas effects on nitrogen isotopes were quantified by comparing mean conditions over the final 20 years of the twenty-first century (2081–2100) with mean conditions over the historical period (1986–2005) from the same simulation.To understand the direct and indirect effects of climate change, we undertook two additional idealized simulations. First, we imposed temperature changes on biogeochemical rates, while maintaining ocean circulation associated with the preindustrial control scenario, to assess the direct effects of warming on biogeochemical processes. Second, we imposed the preindustrial control temperature field on biogeochemical processes, while altering the circulation in line with the climate change scenario, to assess the indirect effects of climate change (i.e., how changing circulation alters substrate supply to biogeochemical reactions). Each experiment was run from 1851 to 2100 and without the anthropogenic increase in atmospheric nitrogen deposition, parallel with the full climate change simulation.Agreement between the climate change simulation without anthropogenic nitrogen deposition was quantified using a pixel-by-pixel correlation analysis using Spearman’s rank correlation based on the non-parametric nature of the two-dimensional fields used for comparison. Fields were euphotic zone nitrate, twilight zone δ15NNO3, euphotic zone δ15NPOM, and vertically integrated NPP, zooplankton grazing, nitrogen fixation, water column denitrification and sedimentary denitrification.Depth zonesWe assessed changes in biogeochemical variables related to nitrogen cycling in two depth zones defined by light. The euphotic zone was defined by depths between the surface and 0.1% of incident irradiance as recommended by Buesseler et al.42. The twilight zone was also defined using light, as advocated by Kaartvedt et al.58. Depths between 0.1% and 0.0001% of incident irradiance defined the twilight zone. These definitions typically returned euphotic zone thicknesses of 137 ± 23 m (mean ± SD), and twilight zone thicknesses of 233 ± 37 m. The boundary between these depth zones were deepest in oligotrophic tropical and subtropical waters, and were shallowest in equatorial and temperate waters (Supplementary Fig. 7).Time of emergenceToE calculations determined when anthropogenic, anomalous trends emerged from the noise of background variability. ToE was calculated at each grid cell within both the euphotic and twilight zones (depth-averaged) and using annually averaged fields of ocean tracers. We therefore ignored temporal trends and variability at seasonal and sub-seasonal scales. Raw time series were first detrended and normalized using the linear slope and mean of the preindustrial control experiment, such that the preindustrial control time series varied about zero, while anomalous trends in experiments with climate change and/or nitrogen deposition deviated from zero. These detrended and normalized time series were smoothed using a boxcar (flat) moving average with a window of 11 years to filter decadal variability (Supplementary Fig. 12). Differences with the preindustrial control experiment were then computed.To determine whether the differences with the preindustrial control experiment were anomalous, we calculated a measure of noise from the raw, inter-annual time series of the preindustrial control experiment (1801–2100). A signal emerged from the noise if it exceeded 2 SDs, a threshold that represents with 95% confidence that a value was anomalous and is therefore a conservative envelope to distinguish normality from anomaly16.Furthermore, we required that anomalous values must consistently exceed the noise of the preindustrial control experiment until the end of the simulation (2100) to be registered as having emerged. Temporary emergences were therefore rejected, making our ToE estimates more conservative. A graphical representation of this process is shown in Supplementary Fig. 12.Isolating biogeochemical 15NO3 fluxesWe analysed the biogeochemical fluxes of 15NO3 and NO3 into and out of each model grid cell within the twilight zone, to determine whether the trends in δ15NNO3 were related to biogeochemical or physical changes. Fluxes of 15NO3 and NO3 included a net source from nitrification (NO3nitr) and net sinks due to new production (NO3new) and denitrification (NO3den). Although nitrification did not directly alter the 15N : 14N ratio in our simulations, the release of 15NO3 and NO3 by nitrification conveyed an isotopic signature determined by prior fractionation processes that produce ammonium (NH4). These processes include remineralization of particulate and dissolved organic matter, excretion by zooplankton and nitrogen fixation. The isotopic signatures of these processes were thus included implicitly in NO3nitr. For each grid cell, we calculated the biogeochemical tendency to alter δ15NNO3 based on the ratio of inputs minus outputs:$${Delta} {delta }^{15}{{{{{{rm{N}}}}}}}_{{{{{{rm{NO3}}}}}}}=left(frac{{,{!}^{15}{{{{{rm{N}}}}}}{{{{{rm{O}}}}}}}_{3}^{{{{{{rm{nitr}}}}}}}-{,{!}^{15}{{{{{rm{N}}}}}}{{{{{rm{O}}}}}}}_{3}^{{{{{{rm{new}}}}}}}-{,{!}^{15}{{{{{rm{N}}}}}}{{{{{rm{O}}}}}}}_{3}^{{{{{{rm{den}}}}}}}}{{,{!}^{14}{{{{{rm{N}}}}}}{{{{{rm{O}}}}}}}_{3}^{{{{{{rm{nitr}}}}}}}-{,{!}^{14}{{{{{rm{N}}}}}}{{{{{rm{O}}}}}}}_{3}^{{{{{{rm{new}}}}}}}-{,{!}^{14}{{{{{rm{N}}}}}}{{{{{rm{O}}}}}}}_{3}^{{{{{{rm{den}}}}}}}}-1right)cdot 1000$$
(1)
This calculation excluded any upstream biological changes and circulation changes that might have altered δ15NNO3.0D water parcel modelWe simulated the nitrogen isotope dynamics in a recently upwelled water parcel during transit to the subtropics by building a 0D model. The model simulates state variables of dissolved inorganic nitrogen (DIN), particulate organic nitrogen (PON) and exported particulate nitrogen (ExpN), as well as their heavy isotopes (DI15N, PO15N and Exp15N) in units of mmol N m−3 over 100 days given initial conditions and constants listed in Supplementary Table 1.$$frac{Delta {{{{{rm{DIN}}}}}}}{Delta t}=-{{{{{mathrm{N}}}}}}_{{{{{{rm{uptake}}}}}}}+{{{{{mathrm{N}}}}}}_{{{{{{rm{recycled}}}}}}}$$
(2)
$$frac{Delta {{{{{rm{PON}}}}}}}{Delta t}={{{{{mathrm{N}}}}}}_{{{{{{rm{uptake}}}}}}}-{{{{{mathrm{N}}}}}}_{{{{{{rm{recycled}}}}}}}-{{{{{mathrm{N}}}}}}_{{{{{{rm{exported}}}}}}}$$
(3)
$$frac{Delta {{{{{rm{ExpN}}}}}}}{Delta t}={{{{{mathrm{N}}}}}}_{{{{{{rm{exported}}}}}}}$$
(4)
$$frac{Delta {{{{{rm{DI1}}}}}}{}^{15}{{{{{rm{N}}}}}}}{Delta t}=-{}^{15}{{{{{rm{N}}}}}}_{{{{{{rm{uptake}}}}}}}+{}^{15}{{{{{rm{N}}}}}}_{{{{{{rm{recycled}}}}}}}$$
(5)
$$frac{Delta {{{{{rm{PO}}}}}}{}^{15}{{{{{rm{N}}}}}}}{Delta t}={}^{15}{{{{{rm{N}}}}}}_{{{{{{rm{uptake}}}}}}}-{}^{15}{{{{{rm{N}}}}}}_{{{{{{rm{recycled}}}}}}}-{}^{15}{{{{{rm{N}}}}}}_{{{{{{rm{exported}}}}}}}$$
(6)
$$frac{Delta {{{{mathrm{Exp}}}}}{}^{15}{{{{{rm{N}}}}}}}{Delta t}={}^{15}{{{{{rm{N}}}}}}_{{{{{{rm{exported}}}}}}}$$
(7)
First, the model calculates maximum potential growth rate of phytoplankton (μmax) in units of day−1 (Eq. 8) using temperature and then finds nitrogen uptake (Nuptake, Eq. 10) using PON and limitation terms for nitrogen (Nlim, Eq. 9), light (Llim, Supplementary Table 1) and iron (Felim, Supplementary Table 1).$${mu }_{{{max }}}=0.6,{{{{{rm{da}}}}}}{y}^{-1}cdot {e}^{Tcdot {T}_{{{{{{rm{growth}}}}}}}}$$
(8)
$${{{{{mathrm{N}}}}}}_{{{{{mathrm{lim}}}}}}=frac{{{{{{rm{DIN}}}}}}}{{{{{{rm{DIN}}}}}}+{{{{{mathrm{K}}}}}}_{{{{{{rm{DIN}}}}}}}}$$
(9)
$${{{{{mathrm{N}}}}}}_{{{{{mathrm{uptake}}}}}}={mu }_{max }cdot {{{{{mathrm{L}}}}}}_{{{{{mathrm{lim}}}}}}cdot ,min ({{{{{mathrm{Fe}}}}}}_{{{{{mathrm{lim}}}}}},{{{{{mathrm{N}}}}}}_{{{{{mathrm{lim}}}}}})cdot {{{{{mathrm{PON}}}}}}$$
(10)
At a constant temperature of 18 °C, μmax is equal to ~1.9 day−1. Limitation terms for light and iron are set as constant and are used to prevent unrealistically high nitrogen uptake when nitrogen is high, such as occurs immediately following upwelling in the high-nutrient low-chlorophyll regions of the tropics. Fractionation by phytoplankton is calculated assuming an open system21, in this case where nitrogen can be lost through export of organic matter. To calculate the fractionation associated with uptake (15Nuptake, Eq. 11), we multiply the total nitrogen uptake (Nuptake, Eq. 10) by the heavy to light isotope ratio (({r}_{{{{{{rm{DIN}}}}}}}^{15}), Eq. 12) and the fractionation factor (εphy, Supplementary Table 1), which is converted from units of per mil (‰) to a fraction relative to one. This fractionation factor (εphy) is constant at 5‰ but is decreased towards 0‰ by the nitrogen limitation term (Nlim, Eq. 9), such that when nitrogen is limiting to growth, the fractionation during uptake decreases (last term on the right-hand side approaches 1).$${}^{15}{{{{{rm{N}}}}}}_{{{{{{rm{uptake}}}}}}},=,{{{{{mathrm{N}}}}}}_{{{{{{rm{uptake}}}}}}}cdot {r}_{{{{{{rm{DIN}}}}}}}^{15}cdot left(1-frac{{{{{mathrm{N}}}}}_{{{{{mathrm{lim}}}}}}cdot {varepsilon }_{{{{{{rm{phy}}}}}}}}{1000}right)$$
(11)
$${r}_{{{{{{rm{DIN}}}}}}}^{15},=,frac{{{{mathrm{DI}}}}^{15}{{{{{{rm{N}}}}}}}}{{{{{{rm{DIN}}}}}}}$$
(12)
At each timestep, a fraction of the PON pool becomes detritus (Eq. 15) and this detritus is instantaneously recycled back to DIN or exported to ExpN and removed from the water parcel. The amount of detritus produced per timestep is calculated as the sum of linear respiration (Eq. 13) and quadratic mortality (Eq. 14) terms, where Presp (units of day−1), Kresp (units of mmol N m−3) and Pmort (units of (mmol N m−3)−1 day−1) are constants (Supplementary Table 1).$${{{{{rm{Respiration}}}}}},=,{{{{{mathrm{P}}}}}}_{{{{{{rm{resp}}}}}}}cdot {{{{{rm{PON}}}}}}cdot frac{{{{{{rm{PON}}}}}}}{{{{{{rm{PON}}}}}}+{{{{{mathrm{K}}}}}}_{{{{{{rm{resp}}}}}}}}$$
(13)
$${{{{{rm{Mortality}}}}}},=,{{{{{mathrm{P}}}}}}_{{{{{{rm{mort}}}}}}}cdot {{{{{rm{PON}}}}}}^{2}$$
(14)
$${{{{{rm{Detritus}}}}}},=,{{{{{rm{Respiration}}}}}},+,{{{{{rm{Mortality}}}}}}$$
(15)
Once we know the fraction of PON that becomes detritus at any given timestep, we must solve for the fraction of that detritus that becomes DIN through recycling (Eq. 17), and that which becomes ExpN through export (Eq. 18). The fraction of detritus that is recycled back into DIN is temperature dependent (Eq. 16), with higher temperatures increasing rates of recycling above a minimum fraction set by frecmin (Supplementary Table 1). The relationship with temperature is exponential, similar to phytoplankton maximum growth (μmax), but the degree of increase associated with warming is scaled down by a constant factor equal to Trec (Supplementary Table 1). The fraction that is exported to ExpN is the remainder (Eq. 18).$${f}_{{{{{{rm{recycled}}}}}}}={f}_{{{{{{rm{recmin}}}}}}}+{T}_{{{{{{rm{rec}}}}}}}cdot {e}^{Tcdot {T}_{{{{{{rm{growth}}}}}}}}$$
(16)
$${{{{{mathrm{N}}}}}}_{{{{{{rm{recycled}}}}}}}={{{{{rm{Detritus}}}}}}cdot {f}_{{{{{{rm{recycled}}}}}}}$$
(17)
$${{{{{mathrm{N}}}}}}_{{{{{{rm{exported}}}}}}}={{{{{rm{Detritus}}}}}}cdot (1-{f}_{{{{{{rm{recycled}}}}}}})$$
(18)
The major fluxes of Nuptake, Nrecycled and Nexported are now solved for. All that remains is to calculate the isotopic signatures of the recycling (Eq. 19) and export (Eq. 20) fluxes. These, similar to 15Nuptake (Eq. 11), are solved by multiplying against a standard ratio of heavy to light isotope (({r}_{{{{{{rm{PON}}}}}}}^{15}), Eq. 21).$${}^{15}{{{{{rm{N}}}}}}_{{{{{{rm{recycled}}}}}}}={{{{{mathrm{N}}}}}}_{{{{{{rm{recycled}}}}}}}cdot {r}_{{{{{{rm{PON}}}}}}}^{15}$$
(19)
$${}^{15}{{{{{rm{N}}}}}}_{{{{{{rm{exported}}}}}}}={{{{{mathrm{N}}}}}}_{{{{{{rm{exported}}}}}}}cdot {r}_{{{{{{rm{PON}}}}}}}^{15}$$
(20)
$${r}_{{{{{{rm{PON}}}}}}}^{15}=frac{{{{{{rm{PO}}}}}}{}^{15}{{{{{rm{N}}}}}}}{{{{{{rm{PON}}}}}}}$$
(21)
Finally, we calculate the δ15N values of the major pools in the model (DIN, PON and ExpN) as output (Eqs. 22–24). We assume in this model that the major pools of DIN, PON and ExpN represent the total amount of the light isotope (14N), whereas the DI15N, PO15N and Exp15N pools represent the relative enrichment in 15N compared to a standard ratio. For simplicity, we make the standard ratio equal to 1. Therefore, taking the ratio of the DI15N to DIN pools and subtracting one returns the isotopic signature. Multiplying this by 1000 converts this signature to per mil units (‰).$${delta }^{15}{{{{{{rm{N}}}}}}}_{{{{{{rm{DIN}}}}}}}=left(frac{{{{{{rm{DI}}}}}}{}^{15}{{{{{rm{N}}}}}}}{{{{{{rm{DIN}}}}}}}-1right)cdot 1000$$
(22)
$${}^{15}{{{{{rm{N}}}}}}_{{{{{{rm{PON}}}}}}}=left(frac{{{{{{{rm{PO}}}}}}}^{15}N}{{{{{{rm{PON}}}}}}}-1right)cdot 1000$$
(23)
$${}^{15}{{{{{rm{N}}}}}}_{{{{{{rm{ExpN}}}}}}}=left(frac{{{{{mathrm{Exp}}}}}{}^{15}{{{{{rm{N}}}}}}}{{{{{{rm{ExpN}}}}}}}-1right)cdot 1000$$
(24) More

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Study setupSix adults and six elderly, who were included in a previously conducted in vivo GOS intervention study [11], donated their faecal material for the current study (Fig. S1) at their first visit or at least 4 weeks after the intervention period. Each participant defecated into a stool collector (Excretas Medical BV, Enschede, the Netherlands). Directly after defecation, faecal material was divided into two portions. A small portion (~0.5 g) was frozen immediately. The remaining faeces was anoxically cryo-conserved and used as inoculum for the in vitro incubations. The viability of different microbial groups in the anoxically cryo-conserved faecal material was determined with propidium monoazide (PMA) dye. The in vitro incubations lasted for 24 h with samples collected in duplicate to compare microbiota composition, carbohydrate degradation and metabolite production between age groups (adults vs elderly). The degrading capacity for two typical bifidogenic carbohydrates, i.e., GOS and 2′-FL, was determined for the microbiota of all six adults and six elderly and compared to a non-carbohydrate control. To further extend these experiments, we also studied the degradation of other typical bifidogenic carbohydrates, i.e. FOS, inulin, and IMMP, using the faecal inocula of three adults and three elderly for which sufficient material was still available.ParticipantsThe six adults (20–30 yrs) and six elderly participants (70–85 yrs) of the intervention study [11] were randomly contacted and participated in the current study, who differed significantly in age, but not in sex, BMI, alcohol consumption, smoking, medication use or dietary fibre intake (Table 1). None of the participants took acid inhibitors (e.g., proton pump inhibitors), nor antibiotics 90 days prior to the study, nor did any of the participants have a chronic disorder or major surgery, as these factors potentially could have limited participation, completion of the study, or interfered with the study outcomes. Detailed description of the inclusion and exclusion criteria has been provided previously [11]. Subject codes as shown in the results were randomly assigned in the data analysis phase and cannot be traced back to individual subjects without the specific randomization key. The study was approved by the medical Ethics Committee of the Maastricht University Medical Center+ and registered in the US National Library of Medicine (http://www.clinicaltrials.gov) with the registration number NCT03077529 [11].Table 1 Characteristics of adults (n = 6) and elderly (n = 6) included in this study.Full size tableDietary intakeParticipants in the current study completed the dietary records on 3 consecutive days, after instructed to record their food, beverage and dietary supplement intake based on standard household units. Their nutrient intake was analyzed using the online dietary assessment tool of The Netherlands Nutrition Centre (www.voedingcentrum.nl).CarbohydratesFive different carbohydrates, i.e., GOS, 2′-FL, FOS, inulin and IMMP were used as sole carbon sources in this study. GOS and the human milk oligosaccharide 2′-FL (Fucα1-2Galβ1-4Glc) were kindly provided by Friesland Campina (Amersfoort, The Netherlands). In order to mimic the actual portion of GOS utilized by intestinal microbiota, purified GOS with  0.05) to explain the observed difference, using the prc function in the vegan package [30]. As for the metabolite data, redundancy analysis (RDA) in combination with Monte Carlo permutation was performed to assess to what extent explanatory variables, i.e., incubation time, subject- and carbohydrate-specificity, could explain the overall variation in metabolite data, using the rda function in the vegan package [30]. To assess the effect of age group (adult vs elderly) on the degradation of carbohydrates/concentration of metabolites during incubation, we analyzed the data using two-way mixed ANOVA, with one between-subjects factor (age group) and one within-subjects factor (incubation time), using the anova_test function in the rstatix package [31]. False discovery rate (FDR) correction according to the Benjamini–Hochberg procedure was applied for multiple testing when applicable. A corrected P value < 0.05 was considered to indicate significant difference. More

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