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Study species and pre-cultivationTo create the mesocosm communities, we selected nine herbaceous grassland species that are native to and widespread in Central Europe (Supplementary Table 9), where they can also co-occur. The species were Alopecurus pratensis L., Diplotaxis tenuifolia (L.) DC., Lolium perenne L., Poa pratensis L., Prunella vulgaris L., Sinapis arvensis L., Sonchus oleraceus L., Vicia cracca L., Vicia sativa L. To increase generalizability54, the species were selected from three functional groups (grasses, annual forbs, perennial forbs), and they represent five families.Seeds were obtained from different sources (Supplementary Table 9). For the transplanted-seedling community (see section ‘Experimental lay-out), seedlings were pre-cultivated in a greenhouse of the Botanical Garden of the University of Konstanz. As the species require different times for germination, they were sown on different dates (Supplementary Table 10) to ensure that seedlings of all species were at a similar developmental stage at transplantation. Seeds were sown separately per species in plastic trays filled with potting soil (Einheitserde®, Pikiererde CL P). The greenhouse had a regular day-night rhythm of c. 16:8 hours, and its ventilation windows automatically opened at 21 °C during the day and at 18 °C during the night. Two days before transplanting, the seedlings were placed outdoors to acclimatize. For the sown community, we sowed a seed mixture of the nine study species directly into the outdoor mesocosm pots.Experimental setupGlobal change treatmentsWe imposed six global change treatments: climate warming, light pollution, microplastic pollution, soil salinization, eutrophication, and fungicide accumulation, all of which frequently occur in the environment. These GCFs were chosen because they differ in their nature (i.e., physical, chemical), are likely to differ in their mode of action and effect direction21, and can be easily implemented. Each of the six GCFs have been shown to impact plants and their environment when applied on their own10,13,17,19,20,55,56,57,58,59,60. Furthermore, all of the chosen GCFs are likely to continue to increase in magnitude or extent in the near future61,62,63,64,65. For the climate-warming treatment, we used infrared-heater lamps (HS-2420; 240 V, 2000 W; Kalglo Electronics Co., Bethlehem, USA) set to 70% of their maximum capacity to achieve an average temperature increase of 2.0 °C (±SD = 0.2 °C) at plant level. This is within the range of temperature increases predicted by the RCP 4.5 scenario for the year 2100 [+1.1 − 2.6 °C; 63]. For the light-pollution treatment, we used LED spotlights (LED-Strahler Flare 10 W, IP 65, 900 lm, cool white 6500 K; REV Ritter GmbH, Mömbris, Germany), which were switched on daily from 9 pm to 5 am, corresponding to the times of sunset and -rise. The average light intensity was 24.5 lx at ground level, which is within the range of light intensities found below street lights, and matches the light intensities used in other light-pollution experiments14,56. For the microplastic pollution treatment, we used granules (1.0–2.5 mm diameter) of the synthetic rubber ethylene propylene diene monomer (EPDM Granulat, Gummi Appel GmbH + Co. KG, Kahl am Main, Germany) at a concentration of 1% (w/w, granules/dry soil, approximately corresponding to 1.5% v/v). EPDM granules are, for example, used in artificial sport turfs, from where they easily spread into the surroundings, and have been used previously to investigate the effects of microplastics on plants18. The chosen concentration is well within the range of concentrations used in previous studies18,66,67, and is at the low to intermediate range of concentrations found in sites polluted with plastics68. For the soil-salinization treatment, dissolved NaCl was added to the soil. Soil salinity is commonly measured as electrical conductivity, with a conductivity between 4 and 8 dS m−1 considered to be moderately saline69. For the experiment, we used a salinity of 6 dS m−1. To maintain a more or less constant salinity level, electrical conductivity was measured weekly, and, if required, adjusted by adding dissolved NaCl. For the eutrophication treatment, 3 g of a dissolved NPK fertilizer (Universol® blue oxide, ICL SF Germany & Austria, Nordhorn, Germany) was added per pot. For N, this corresponds to an input of 100 kg N ha−1, comparable to the yearly amounts of atmospheric N deposition in large parts of Europe52 and the yearly nitrogen input on agricultural field in the European Union70. To ensure a more or less constant nutrient availability during the experiments, we split total fertilizer input into three applications (directly after, 3 weeks after, and 6 weeks after starting the experiments) of 1 g fertilizer per pot per application. In addition, to avoid severe nutrient limitation in the other pots, all pots (irrespective of the eutrophication treatment) received basic fertilization. This was applied four times to the transplanted-seedling-community pots and five times to the sown community pots, with 0.2 g fertilizer per pot per application. For the pesticide treatment, we used the fungicide Landor® CT (Syngenta Agro GmbH, Maintal, Germany). This fungicide was chosen because it contains three azoles as active agents, which belong to the most widely used class of antifungal agents71. To each pot in this treatment, we added 1.5 μl fungicide dissolved in water (1‰). This corresponds to 60% of the maximum amount that should be used per hectare of cropland. A summary of the levels of the individual GCFs used in our experiment is provided in Supplementary Table 8.Combinations of simultaneously acting GCFsTo examine the potential effects of the numbers of simultaneously acting GCFs, we created five levels of increasing GCF numbers. These levels were: zero (i.e., the control without any GCF application), one (single), two, four and six GCFs. For the one-, two- and four-GCF levels, there were six different combinations, so that each of these levels included either six different GCFs in case of the one-factor, or six different GCF combinations in case of the two- and four-GCF levels. In the six-GCF level, all six factors were combined, so that there was only one combination. To avoid potential biases due to unequal representation of the different GCFs in each GCF-number level, we created the GCF combinations randomly but with the restriction that each GCF was present in an equal number of combinations for each GCF-number level (i.e., each GCF was included once in GCF-number levels 1 and 6, respectively, twice in GCF-number level 2, and four times in GCF-number level 4; Supplementary Table 11).Experimental lay-outThe experiment was conducted outdoors in the climate-warming-simulation facility of the Botanical Garden of the University of Konstanz, Germany (N: 47°69’19.56”, E: 9°17’78.42”). Twenty of the 2 m × 2 m plots of this facility were used for our experiment. As the climate-warming and light-pollution treatments could not be applied to each individual pot separately, we applied those treatments at the plot level. Therefore, we assigned four of the 20 plots to the climate-warming treatment, four plots to the light-pollution treatment and four plots to both climate-warming and light-pollution treatment combination. Each plot had a 145 cm high metal frame. The eight plots assigned to the climate-warming treatment were equipped with a 1.80 m long, horizontally hanging infrared-heating lamp at the top of the metal frame (i.e., at 145 cm above soil level). The heating lamp slowly oscillated along its longitudinal axis to ensure uniform heating of the whole 2 m × 2 m plot. The eight plots assigned to the light-pollution treatment, each had a LED spotlight attached to one of the sides of the metal frame at a height of 120 cm. To reduce illumination of the neighboring plots, light-pollution was only applied to the outer plots of the climate-warming-simulation facility (Supplementary Fig. 5), and LEDs were pointing away from the inner plots and were equipped with lamp shades made of black plastic pots (18 cm × 18 cm × 25.5 cm). Furthermore, to reduce the light intensity to a realistic light-pollution level (24.5 lx) as found below street lights, we covered the spotlight with a layer of white cloth (Supplementary Fig. 6). For further details on the artificial light treatment, see Supplementary Fig. 7.To create mesocosms with the transplanted-seedling and sown communities, we filled 10-L pots (CEP- Container, 10.0 F, Burger GmbH, Renningen-Malmsheim, Germany) with a mixture of 40% potting soil (see above), 40% quartz sand (0.5–0.8 mm), and—to inoculate the substrate with a natural soil community—20% top soil excavated from a seminatural grassland patch in the botanical garden. In total, the experiments with the transplanted-seedling and sown communities, each included 120 pots (i.e., 20 treatment combinations × six replicates × 2 experiments = 240 pots in total; see Supplementary Table 11), which were distributed across the 20 plots. To prevent leakage of fertilizer or salt solutions, each pot was placed onto a plastic dish. To reduce differences due to environmental variation within plots, the positions of pots within each plot were re-randomized every 14 days. Plants were watered regularly to avoid drought stress and to avoid differences in soil moisture due to application of fertilizer- and salt-solutions.For the sown community, we randomly distributed five seeds of each of the nine species on the substrate in each pot on 3 July 2020. For the transplanted-seedling community, two seedlings of each of the nine species were transplanted into each pot (i.e., 18 seedlings per pot) according to a fixed pattern (Supplementary Fig. 8) on 6 July 2020. Since there were a few seedlings missing for S. arvensis (six seedlings) and V. cracca (four seedlings), we re-sowed these species in germination trays on 6 July 2020. On 13 July 2020, dead seedlings, and the missing seedlings for S. arvensis were replaced. Since V. cracca took longer to germinate, the missing seedlings were transplanted on 17 July 2020.MeasurementsTo investigate the effects of single-GCFs and their number on the sown and transplanted-seedling communities, we used plant biomass as an indicator for plant performance72. As it was impossible to disentangle the roots, we only used aboveground biomass. On 14 and 15 September 2020, i.e., 10 weeks after transplanting, we harvested the transplanted-seedling communities. On 28 and 29 September, i.e., twelve weeks after sowing, we harvested the sown communities. For both community types, we harvested the plants separately by species. The harvested plants were stored in paper bags, dried at 70 °C for at least 72 hours and weighed.Statistical analysisAll analyses were done in R 3.6.273. As the transplanted-seedling and sown communities were harvested at different times, we treated them as separate experiments, and therefore analyzed them separately (but see the subsection “Community type specific responses” below).Community aboveground biomassTo analyze the effects GCF number on plant-community productivity, we fitted linear mixed-effects models separately for the transplanted-seedling and sown communities, using the lmer function in the “lme4” package74. Total aboveground biomass per pot was the response variable. To improve normality of the residuals, biomass of the transplanted-seedling and sown communities was square-root- and natural-log-transformed, respectively. We included GCF number as a continuous fixed variable. To account for non-independence of pots in the same GCF combination and of pots in the same plot, GCF combination and plot were included as random effects. The effects of the individual GCFs on biomass production were also assessed by fitting linear mixed-effects models, using only the data of the control and single-GCF treatments, and including GCF identity as fixed effect.Community compositionTo assess potential effects of single-GCFs and GCF number on the final composition of the transplanted-seedling and sown communities, we first assessed variation in species composition, based on biomass proportions, among pots using principal component analysis (PCA) [rda function of the “vegan” package75,]. For each PCA (Supplementary Fig. 1), we extracted the PC1 and PC2 values, which together explained more than 65% of the variation in community composition and included them as response variables in separate linear mixed models, as described above for community biomass.To evaluate whether GCF number affects the diversity and evenness of plant communities, we calculated the Shannon index (H)76, using the diversity function in the “vegan” package, and evenness index (J)77 based on species biomass proportions. Subsequently, the single-GCF and GCF-number effects on diversity and evenness of the sown and transplanted-seedling communities were analyzed using linear mixed-effects models, or—if adding random effects did not improve the model—more parsimonious linear models78,79. For all models, we used type II analysis of variance (ANOVA) tests (Anova function in the “car” package) to assess the significance of fixed effects.Hierarchical diversity-interaction modelingWhen there is a significant GCF-number effect, this could reflect that with increasing numbers of co-acting GCFs, there is a higher chance that it will include a GCF with a strong and dominant effect (i.e., sampling or selection effects). However, it could also be that the GCF-number effect is driven by interactions among the GCFs, and the effects of these interactions could be GCF-specific or general. As our experiment does not include all possible combinations of GCFs, it does not allow to test the contributions of each possible multi-way GCF interaction. Therefore, to gain insights into whether the GCF identities and specific or general GCF interactions underlie the significant GCF-number effects, we applied the hierarchical diversity-interaction modeling framework of Kirwan et al.80. This framework was originally developed for estimating contributions of species identities and their interactions to ecosystem functions, but we here applied it to GCF identities and interactions. For each of the response variables showing a significant GCF-number effect, we ran five hierarchical models specifying different assumptions about the potential contributions of individual GCFs and their interactions to the GCF-number effect, and compared them using likelihood ratio tests (Fig. 4). For these analyses, the data of the control treatment (i.e., GCF number zero) was excluded. Each of the five models specified different assumptions about the potential contributions of individual GCFs and their interactions to the GCF-number effect. The first model is the null model, which assumed that there were no GCF-specific contributions (i.e., all GCFs contributed equally) and that there were no contributions of GCF interactions. Therefore, the null model only included the centered sum of the GCFs of each treatment (M) as fixed effect. M accounts for differences in ‘initial abundances’ of GCFs—meaning that the other model terms are interpreted based on the average initial abundance—and was also included in the four other models80. This way, we could include the GCFs’ relative proportions in each GCF combination, instead of just considering GCF presence, while taking into account that, with increasing GCF number, the relative proportion of each individual GCF is automatically reduced. In the second model, the GCF identities (i.e., their proportions in the respective GCF combination) were added, assuming that individual GCFs contribute differently to the effect of GCF number. In the third model, separate-pairwise interactions between the GCFs were added, considering that, in addition to contributions of individual GCFs, specific pairwise interactions contributed to the GCF-number effect. In the fourth model, the average GCF-interaction model (which is also called the evenness model in Kirwan et al. 2009), the separate-pairwise GCF interactions were replaced by an average interaction effect. Thus, the average GCF-interaction model assumed equivalent contributions of all pairwise GCF interactions. In the fifth model, the additive GCF-specific interaction contributions model, the average interaction effect of the fourth model was replaced by average GCF-specific interaction effects. This model assumed that each GCF’s contribution to a pairwise interaction remains constant. For the calculation of the average GCF-specific and average interaction effect, we used the equations provided by Kirwan et al.80. For each of the response variables, we generally included the same random terms as in the main analyses of the GCF-number effect. However, as this resulted in singularity warnings for some of the hierarchical diversity-interaction models, e.g., those for species diversity and evenness measures, we used for these cases linear models instead of linear mixed models.Fig. 4: Hierarchical diversity-interaction-modeling framework to assess contributions of GCF identities and GCF interactions to GCF-number effects.The framework was adapted from Kirwan et al.80. The null model assumes equivalent contributions of all GCFs and no interactions between them. The subsequent models assume more complex effects of how the individual GCFs and their interactions determine the GCF-number effects. The questions that can be answered by comparing specific models are depicted next to the arrows connecting the two models.Full size imageCommunity type-specific responsesAs the transplanted-seedling and sown communities were harvested at different times, we treated them as separate experiments, and therefore analyzed them separately. However, to test explicitly whether both community types differed in their responses to single-GCFs and GCF number, we also analyzed them jointly. To this end, we fitted linear mixed-effects models for each response variable including GCF number (or single-factor treatments), community type and their interaction as fixed effects (Supplementary Table 5).Final number of plants per speciesTo test for effects of individual GCFs and GCF number on species presence, i.e., the number of individuals per species present at harvest, we fitted generalized linear mixed-effects models for the transplanted-seedling and sown communities separately. We included the survival rate (number of individuals present at harvest divided by the number of planted/sown individuals) as response variables. For the models testing the effects of GCF number, we included GCF combination, species, pot, and plot as random effects. For the models testing the effects of single-GCFs, the same random effects were included, except for GCF combination. Specific random effects were removed from the model if their incorporation resulted in singular fit warnings due to low variation. We assessed the effects of individual GCFs or GCF number using type III ANOVA tests (Anova function in the “car” package, Supplementary Table 7).Eutrophication effectsIn addition to the general assessment of individual GCF effects in the hierarchical diversity-interaction models, we specifically assessed the effects of eutrophication. This was done because eutrophication had the strongest effect on productivity as individual GCF, and this might also have dominated the GCF-number effect, indicating a sampling effect. To this end, we added a binary-coded variable to include information on whether eutrophication was included in the different GCF combinations. Subsequently, we fitted linear mixed-effects models for all response traits that were affected by GCF number. In these models, we included GCF number, community type, eutrophication, and the respective two-way interactions as fixed effects, and plot and GCF combination as random effects. Effects of fixed factors were assessed using type III ANOVA tests (Anova function in the “car” package; Supplementary Table 6).Reporting summaryFurther information on research design is available in the Nature Portfolio Reporting Summary linked to this article. More

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Overall frameworkCells in our model are arranged along independent radial files, with each cell in one of either the proliferation, enlargement-only, wall thickening, or mature zones, depending on the distance of the cell’s centre from the inside edge of the phloem and the time of year. Only cells that contribute to the formation of xylem tracheids are treated explicitly. A daily timestep is used, on which cells in the proliferation and enlargement-only zones can enlarge in the radial direction if these zones are non-dormant, and on which secondary-wall thickening can occur in the wall thickening zone. Cells in the proliferation zone divide periclinally if they reach a threshold radial length. Cell-size control at division is intermediate between a critical size and a critical increment22. Mother cells divide asymmetrically, with the subsequent relative growth rates of the daughters inversely proportional to their relative sizes. Size at division and asymmetry of division are computed with added statistical noise22, and therefore the model is run for an ensemble of independent radial files with perturbed initial conditions.Equations and parametersCell enlargement and divisionCells in the proliferation and enlargement-only zones, when not dormant, enlarge in the radial direction at a rate dependent on temperature and relative sibling birth size. A Boltzmann-Arrhenius approach is used for the temperature dependence30:$$mu={mu }_{0}{e}^{frac{{E}_{a}}{k}left(frac{1}{{T}_{0}}-frac{1}{T}right)}$$
(1)
where μ is the relative rate of radial cell growth at temperature T (μm μm−1 day−1), μ0 is μ at temperature T0 (=283.15 K), Ea is the effective activation energy for cell enlargement, k is the Boltzmann constant (i.e. 8.617 x 10−5 eV K−1), and T is temperature (K). μ0 was calibrated to an observed mean radial file length at the end of the elongation period dataset23 (Table 1; see “Observations”), and Ea was calibrated to an observed temperature dependence of annual ring width dataset31 (Table 1; Supplementary Fig. 4; see “Observations”).Table 1 Model parameters calibrated to observationsFull size tableRadial length of an individual cell then increases according to:$${{Delta }}{L}_{r}={L}_{r}({e}^{epsilon mu }-1)$$
(2)
where ΔLr is the radial increment of the cell (μm day−1), Lr is the radial length of the cell (μm), and ϵ is the cell’s growth dependence on relative birth size, given by22:$$epsilon=1-{g}_{asym}{alpha }_{b}$$
(3)
where gasym is the strength of the dependence of relative growth rate on asymmetric division (Table 2; unitless), and αb is the degree of asymmetry relative to the cell’s sister22 (scalar):$${alpha }_{b}=frac{{L}_{r}{,}_{b}-{L}_{r}{,}_{b}^{sis}}{{L}_{r}{,}_{b}+{L}_{r}{,}_{b}^{sis}}$$
(4)
where Lr,b is the radial length of the cell at birth (μm) and ({L}_{r}{,}_{b}^{sis}) is the radial length of its sister at birth (μm), which are calculated stochastically22:$${L}_{r}{,}_{b}={L}_{r}{,}_{d}(0.5-{Z}_{a})$$
(5)
$${L}_{r}{,}_{b}^{sis}={L}_{r}{,}_{d}(0.5+{Z}_{a})$$
(6)
where Lr,d is the length of the mother cell when it divides (μm) and Za is Gaussian noise with mean zero and standard deviation σa (Table 2; −0.49 ≤Za≤ 0.49 for numerical stability).Table 2 Parameters used in the model that are taken directly from literatureFull size tableLength at division is derived as22:$${L}_{r}{,}_{d}=f{L}_{r}{,}_{b}+{chi }_{b}(2-f+Z)$$
(7)
where f is the mode of cell-size regulation (Table 2; unitless), χb is the mean cell birth size (Table 3; μm), and Z is Gaussian noise with mean zero and standard deviation σ (Table 2).Table 3 Parameters used in the model that are calculated from observationsFull size tableThe first cell in each radial file is an initial, which produces phloem mother cells outwards and xylem mother cells inwards. It grows and divides as other cells in the proliferation zone, but on division one of the daughters is stochastically assigned to phloem or xylem, the other remaining as the initial. The probability of the daughter being on the phloem side is fphloem (Table 3).Cell-wall growthBoth primary and secondary cell-wall growth are influenced by temperature, carbohydrate concentration, and lumen volume. A Michaelis-Menten equation is used to relate the rate of wall growth to the concentration of carbohydrates in the cytoplasm:$${{Delta }}M=frac{{{Delta }}{M}_{max}theta }{theta+{K}_{m}}$$
(8)
where ΔM is the rate of cell-wall growth (mg cell−1 day−1), ΔMmax is the carbohydrate-saturated rate of wall growth (mg cell−1 day−1), θ is the concentration of carbohydrates in the cell’s cytoplasm (mg ml−1), and Km is the effective Michaelis constant (mg ml−1; Table 1).The maximum rate of cell-wall growth, ΔMmax, is assumed to depend linearly on lumen volume (a proxy for the amount of machinery for wall growth), and on temperature as in Eq. (1):$${{Delta }}{M}_{max}=omega {V}_{l}{e}^{frac{{E}_{aw}}{k}left(frac{1}{{T}_{0}}-frac{1}{T}right)}$$
(9)
where ω is the normalised rate of cell-wall mass growth (i.e. the rate at T0; Table 1; mg ml−1 day−1), Vl is the cell lumen volume (ml cell−1), and Eaw is the effective activation energy for wall building (eV; Table 1). ω and Km were calibrated to an observed distribution of carbohydrates23 (see next section). Eaw was calibrated to an observed temperature dependence of maximum density31 (Table 1; see “Observations”).Lumen volume is given by:$${V}_{l}={V}_{c}-{V}_{w}$$
(10)
where Vc is total cell volume (ml cell−1) and Vw is total wall volume (ml cell−1). Cells are assumed cuboid and therefore Vc is given by:$${V}_{c}={L}_{a}{L}_{t}{L}_{r}/1{0}^{12}$$
(11)
where La is axial length (μm; Table 2) and Lt is tangential length (μm; Table 3). Vw is given by:$${V}_{w}=M/rho$$
(12)
where M is wall mass (mg cell−1) and ρ is wall-mass density (Table 2; mg[DM] ml−1).Cells in the proliferation and enlargement-only zones only have primary cell walls. ΔMmax (Eq. (9)) is therefore given the following limit:$${{Delta }}{M}_{max}=min ({{Delta }}{M}_{max},rho {V}_{{w}_{p}}-M)$$
(13)
where ({V}_{{w}_{p}}) is the required primary wall volume:$${V}_{{w}_{p}}={V}_{c}-({L}_{a}-2{W}_{p})({L}_{t}-2{W}_{p})({L}_{r}-2{W}_{p})/1{0}^{12}$$
(14)
where Wp is primary cell-wall thickness (Table 3; μm).Carbohydrate distributionThe distribution of carbohydrates across each radial file is calculated independently from the balance of diffusion from the phloem and the uptake into primary and secondary cell walls. The carbohydrate concentration in the phloem is prescribed at the mean value observed across the three observational dates in23, as described below in “Observations”, and the resulting concentration in the cytoplasm of the furthest living cell from the phloem is solved numerically. The inside wall of this cell is assumed to be impermeable to carbohydrates and therefore provides the inner boundary to the solution. It is assumed that the rate of diffusion across each file is rapid relative to the rate of cell-wall building, and therefore concentrations are assumed to be in equilibrium on each day. Carbohydrate diffusion between living cells is assumed to be proportional to the concentration gradient:$${q}_{i}=({theta }_{i-1}-{theta }_{i})/eta$$
(15)
where qi is the rate of carbohydrate diffusion from cell i − 1 to cell i (mg day−1) and η is the resistance to flow between cells (calibrated to the observed distribution of carbohydrates23, see next section; Table 1; day ml−1).As it is assumed that carbohydrates cannot diffuse between radial files, at equilibrium the flux into a given cell must equal the rate of wall growth in that cell plus the wall growth in all cells further along the radial file away from the phloem. From this it can be shown that the equilibrium carbohydrate concentration in the furthest living cell from the phloem in each radial file is given by:$${theta }_{n}={theta }_{p}-eta mathop{sum }limits_{i=1}^{n}mathop{sum }limits_{j=i}^{n}{{Delta }}{M}_{j}$$
(16)
where θp is the concentration of carbohydrates in the phloem (Table 3; mg ml−1) and n is the number of living cells in the file (phloem mother cells are ignored for simplicity). The rate of wall growth in each cell depends on the concentration of carbohydrates (Eq. (8)), and therefore θn must be found that results in an equilibrium flow across the radial file. This is done using Brent’s method41 as implemented in the “ZBRENT” function42.Zone widthsThe widths of the proliferation, enlargement-only, and secondary wall thickening zones vary through the year, and are fitted to observations on three dates23 (see Supplementary Fig. 2 and “Observations”). Linear responses to daylength were found, which are therefore used to determine widths for the observational period and later days:$${z}_{k}={a}_{k}+{b}_{k}{{{{{{{rm{dl}}}}}}}};{{mathrm{DOY}}}ge 185$$
(17)
where zk is the distance of the inner edge of the zone from the inner edge of the phloem (μm), k is proliferation (p), secondary wall thickening (t), or enlargement-only (e), ak and bk are constants (Table 3), dl is daylength (s), and DOY is day-of-year. The proliferation zone width on earlier days when non-dormant was fixed at its DOY 185 width (assuming this to be its maximum, and that it would reach its maximum very soon after cambial dormancy is broken in the spring). During dormancy, the proliferation zone width is fixed at its value on DOY 231 (the first day of dormancy23). The enlargement-only zone width prior to DOY 185, the first observational day, is assumed to be a linear extension of the rate of change after DOY 185. The wall-thickening zone width plays little role prior to DOY 185 at the focal site, and so was set to its Eq. (17) value each earlier day. On all days the condition zt≥ze≥zp is imposed, and zone widths cannot exceed their values at 24 h daylength (necessary for sites north of the Arctic circle). Supplementary Figure 2 shows the resulting progression of zone widths through the year, together with the observed values.DormancyProliferation was observed to be finished by DOY 23123, and so the proliferation and enlargement-only zones are assumed to enter dormancy then. Release from dormancy in the spring is calculated using an empirical thermal time/chilling model33. It was necessary to adjust the asymptote and temperature threshold of the published model because the heat sum on the day of release calculated from observations in Sweden (see “Observations”) was much lower than reported for Sitka spruce buds in Britain in the original work:$${{{{{{{{rm{dd}}}}}}}}}_{req}=15+4401.8{e}^{-0.042{{{{{{{rm{cd}}}}}}}}}$$
(18)
where ddreq is the required sum of degree-days (°C) from DOY 32 for dormancy release and cd is the chill-day sum from DOY 306. The degree-day sum is the sum of daily mean temperatures above 0 °C, and the chill-day sum is the number of days with mean temperatures below 0 °C. Dormancy can only be released during the first half of the year.Simulation protocolsEach simulation consisted of an ensemble of 100 independent radial files. Each radial file was initialised by producing a file of 100 cells with radial lengths χb(1+Za), allowing these to divide once, ignoring the second daughter from each division, and then limiting the remaining daughters to only those falling inside the proliferation zone on DOY 1. Values for ϵ (the relative growth of daughter cells) and Lr,d (the radial length at division) were derived for each cell. The main simulations were conducted at the observation site in boreal Sweden (64.35°N, 19.77°E) over 1951–1995 to capture the growth period of the observed trees23. Results are mostly presented for 1995 when the observations were made. Simulations for calibration of the effective activation energies (i.e. Ea and Eaw) were performed at 68.26°N, 19.63°E in Arctic Sweden over 1901–200431. Daily mean temperatures for both sites were derived from the appropriate gridbox in a 6 h 1/2 degree global-gridded dataset43.ObservationsObservations of cellular characteristics and carbohydrate concentrations23 were used to derive a number of model parameters, and to test model output (model calibration and testing were performed using different outputs). According to the published study we used, samples were cut from three 44 yr old Scots pine trees growing in Sweden (64°21’ N; 19°46’ E) at different times during the growing season. 30 μm thick longitudinal tangential sections of the cambial region were made, and the radial distributions of soluble carbohydrates measured using microanalytical techniques23. Cell sizes, wall thicknesses, and positions in their Fig. 123, an image of transverse sections on three sampling dates, were digitised using “WebPlotDigitizer”44. These, together with the numbers of cells in each zone and their sizes given in the text of that paper, were used to estimate zone widths, which were then regressed against daylength to give the parameters for Eq. (17) (Table 3), mean cell size in the proliferation zone on the first sampling date (used to derive χb; Table 3), mean cell tangential length (Table 3), and final ring width (used to calibrate μ0; Table 1). The thickness of the primary cell wall (Table 3) was derived by plotting cell-wall thickness against time and taking the low asymptote.The distributions of carbohydrates along the radial files on the last sampling date for “Tree 1” and “Tree 3” (results for “Tree 2” were not shown for this date) shown in Fig. 2 of the observational paper23 were calculated. The masses for each of sucrose, glucose, and fructose in each 30 μm section were digitised using the same method as for cell properties and then summed and converted to concentrations, with the results shown in Supplementary Figure 5. Mean observed carbohydrate concentrations and cell masses at four points were used to calibrate values for the η, ω, and Km parameters in Table 1. Calibration was performed by minimising the summed relative error across the observations.The calibration target for the effective activation energy for wall deposition (i.e. Eaw) was the observed relationship between maximum density and mean June-July-August temperature over 1901-2004 in northern Sweden31 (Supplementary Fig. 3), and for the effective activation energy for cell enlargement the relationship between ring width and temperature (i.e. Ea) target was the same study (Supplementary Fig. 4). These observations were made on living and subfossil Scots pine sample material from the Lake Tornesträsk area (68.21–68.31°N; 19.45–19.80°E; 350–450 m a.s.l.) using X-ray densitometry for maximum density, and standardised to remove non-climatic information31.Reporting summaryFurther information on research design is available in the Nature Portfolio Reporting Summary linked to this article. More