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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.
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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

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.

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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

In this study, we generated a new time-series dataset to investigate the response of dark-synchronized MT+ cultures to SIP− filtrate (6 time points, 0–9 h, Fig. 2a) and to compare expression patterns with two existing datasets on the response of MT− to SIP+ [16, 18] (4 time points, 0–10 h, Fig. 2b). Here, we first report the results of a conventional DE analysis for each dataset separately. Next, we use these results to discover genes or biological processes related to sexual reproduction, either based on their predicted functional annotation or the current literature. Finally, we integrate the results of both the novel and publicly available datasets in an integrative analysis that aims at identifying key genes involved in either a single or both mating types.
Fig. 2: Transcriptional responses induced by SIP treatment of Seminavis robusta.

a Multidimensional scaling (MDS) plot for MT+ expression data (0 h–9 h), and (b) MDS plots of two MT− expression datasets (0 h–3 h and 10 h, respectively). Distances between samples in the MDS plot approximate the log2 fold changes of the top 500 genes. c Number of significant DE genes between control and SIP treated cultures for each time point in both mating types. Each dataset was analyzed on a 5% overall FDR (OFDR) level, i.e., the fraction of false positive genes over all rejected genes. The color represents mating type (MT+: red, MT−: blue) and the shade denotes direction of change (dark: downregulated after SIP treatment, light: upregulated after SIP treatment). d Number of significantly enriched GO terms on a 5% FDR level for each time point. The color represents mating type (MT+: red, MT−: blue). A high number of GO terms are discovered in the early time points for MT+, in comparison to the number of DE genes.

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General transcriptional response and identification of key SIP responsive genes
Multidimensional scaling plots of the RNA-seq data (Fig. 2a, b) showed that in both mating types the dark-to-light transition and time since illumination were the major drivers of gene expression change throughout the experiments. However, as time progresses, the effect of SIP becomes more pronounced. This is supported by DE analysis showing that the number of significant genes increased markedly at later time points (Fig. 2c). Overall, most genes are significantly DE in only a single time point on a 5% overall FDR (OFDR) level (Supplementary Fig. 1B). Combined, on a 5% OFDR level, 4037 genes are DE in response to SIP treatment for MT+, while 5486 genes are found to be DE in MT− in the first 3 h and 6079 genes after 10 h. The stronger response during the first 3 time points in MT− versus MT+ may be the result of the use of a chromatographic fraction of SIP+ for MT− while MT+ cultures were treated with a SIP− containing filtrate. Gene sets for many biological processes were significantly enriched in the conventional lists of DE genes: a total of 1081 and 740 enriched biological process terms were discovered for the response to sex pheromones in MT+ and MT−, respectively (Fig. 2d, Supplemenatry Fig. 2).
We discovered key genes by developing a statistical integrative analysis workflow that is capable of testing for equivalent, i.e., non-DE, expression between conditions. Coupling equivalence testing in one mating type with DE calls in the other allowed for the discovery of key genes exhibiting mating type specific responses to SIP, while DE calls in both datasets found key genes responsive in both mating types. This workflow revealed 52 key genes responding to SIP in both mating types (SRBs), 12 genes uniquely responding in MT+ (SRPs) and 70 genes uniquely responding in MT− (SRMs) (Fig. 3a, Supplementary Figs. 3, 4, 5). Similar to the conventional DE analysis, the response of MT− was more pronounced compared to MT+, likely due to technical differences such as different protocols for pheromone administration. Remarkably, while in MT− we discovered a comparable number of down- and upregulated SRMs, we only found upregulated SRPs and SRBs, possibly indicating that sexual processes induced by SIPs are mainly driven by the induction of key genes rather than the downregulation of inhibitory genes (Fig. 3a).
Fig. 3: Visualization and main results of the integrative workflow.

a Schematic representation of the integrative workflow indicating how SIP responsive genes with a shared response (SRBs) or mating type specific response (SRPs, SRMs) were discovered. Non-responsive genes consist of genes that are equivalently expressed after SIP treatment versus control, or that are very lowly/not expressed (filtered). A log fold change (LFC) cutoff of ±log(3) was used to define responsive (differentially expressed) genes and equivalent genes. At the right side of the panel, log2 fold changes of SRMs, SRPs and SRBs in both mating types are plotted. Each gene is plotted for the time point at which they are differentially expressed. Genes which were not expressed (“filtered”) in the non-responsive mating type are plotted as diamonds. The red horizontal lines represent the fold change cutoff used to determine equivalence and differential expression. The number of discovered genes is indicated in the top left corner of each plot. b Expression of a selection of SIP responsive genes (SRMs, SRPs, SRBs). For each gene, counts per million (CPM) are plotted as a function of time for both mating types. The data points correspond to gene expression of the replicates in each time point and the solid line represents the mean. Data points and lines are colored according to condition, i.e., black for control condition and orange for SIP treatment. c Expression of the five genes belonging to the gene family of SRP12 (Sro2882_g339270). Data are presented in the plots in the same manner as in (b).

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In what follows we will discuss in more detail the genes and pathways that are responding to SIP in both mating types or uniquely in one mating type and link these changes to physiological events in the mating process. In each section, we first discuss key genes highlighted by the integrative analysis (Fig. 3), after which we discuss results from the conventional DE analysis, focussing on selected biological processes (Fig. 4).
Fig. 4: Gene expression of Seminavis robusta genes involved in mating-related processes.

a Heatmap of genes related to mitotic and meiotic cell cycle progression, which are differentially expressed (DE) in both mating types in the conventional DE analysis. Each gene is plotted for control and SIP treated conditions in both S. robusta mating types. Genes are specified as row names and are scaled relative to the mean expression, amounting to counts per million (CPM) standardized to zero mean and unit variance for each gene in each mating type separately. Blue indicates low expression, while red indicates high expression. b Expression of genes related to diproline synthesis and reactive oxygen species (ROS) production, which are significantly DE in only one mating type in the conventional DE analysis. CPM are plotted as a function of time for both mating types. The data points correspond to gene expression of the replicates in each time point while the solid line represents the mean. Data points and lines are colored according to condition, i.e., black for control condition and orange for SIP treatment. P5CS = Δ1-pyrroline-5-carboxylate synthetase; P5CR = Δ1-pyrroline-5-carboxylate reductase.

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Responses to SIP conserved in both mating types
Integrative analysis reveals key genes responsive in both mating types
A large fraction (22/52) of SRBs, i.e., key genes with a strong response to SIP in both mating types, lack any functional annotation and homology to sequenced genomes of other diatoms (Supplementary Table 2), suggesting that the molecular mechanisms underlying early mating are highly species-specific. The remaining 30 SRBs can be linked to energy metabolism, ROS signaling and meiosis, amongst others. Pyruvate kinase (Sro373_g129070) and isocitrate dehydrogenase (Sro492_g153950), respectively involved in glycolysis and the citric acid cycle, are strongly upregulated in both mating types (Fig. 3b), suggesting an increased energy demand. Interestingly, pyruvate kinase is also upregulated during gametogenesis in the brown alga Saccharina latissima [26] and the parasite Plasmodium berghei [27]. In addition, two enzymes from the pentose phosphate pathway (PPP) are among the SRBs: transketolase (Sro524_g159900) and transaldolase (Sro196_g083630) (Supplementary Fig. 3). The PPP generates NADPH, a reductive compound needed in various metabolic reactions and involved in detoxification of ROS by regenerating glutathione [28, 29]. Furthermore, one SRB encoding a heme peroxidase (Sro1252_g256250) exhibited strong upregulation upon SIP treatment (Fig. 3b). Upregulation of heme peroxidases was also reported during sexual reproduction in other eukaryotes, e.g., mosquitoes (Anopheles gambiae) [30] and fungi [31, 32]. Heme peroxidases promote substrate oxidation in various metabolic pathways and are essential for the detoxification of ROS [33], suggesting that ROS signaling plays a role in the response to SIP, as seen in the green algae Volvox carteri, where high ROS levels trigger sex [34]. Finally, a highly expressed SRB encodes a transmembrane protein containing an Epidermal Growth Factor-like (EGF-like) domain (Sro65_g036830, Fig. 3b), with potential orthologs encoded in pennate and centric diatoms including P. tricornutum and T. pseudonana (BLASTp, E  More