Philippa Kaur

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Direct injection method for ethylene and acetylene δ13C analyses by GC-C-IRMSFollowing the direct injection approach of classical ISARA12 with a few modifications, ARA samples with high ethylene yield ( > 500 ppmv) in 10% v/v acetylene were manually injected into a Thermo Scientific Trace GC Ultra-Isolink with an Agilent HP-PLOT/Q  capillary GC column (30 m, i.d. = 0.32 mm, f.t. = 20 μm) and a combustion reactor connected to a Thermo Scientific Delta V Plus isotope ratio mass spectrometer (GC-C-IRMS; Fig. 1a). Modifications include the replacement of silver ferrules in the GC oven with Valcon polymide (graphite reinforced polymer) ferrules to limit memory effects from acetylene. The combustion reactor was oxidized with pure oxygen for 1 h before each run and brief (15 min) seed oxidations were performed between measurement batches (i.e., required every ~ 6–8 ethylene injections, ~ 4–6 acetylene injections) to regenerate reactor oxidation capacity and minimize drift of δ13C values. See Supplementary Table S1a online for additional instrument settings.Ethylene Pre-Concentration (EPCon) methodARA samples with  More

Thermal requirements to develop PDWe examined the response of a wide spectrum of European grapevine varieties to XfPD infection in three independent experiments conducted in 2018, 2019, and 2020. Overall, 86.1% (n = 764) of 886 inoculated plants, comprising 36 varieties and 57 unique scion/rootstock combinations, developed PD symptoms 16 weeks after inoculation. European V. vinifera varieties exhibited significant differences in their susceptibility to XfPD (Supplementary Table S1). All varieties, however, showed PD symptoms to some extent, confirming previous field observations of general susceptibility to XfPD9,12,37. We also found significant differences in virulence (χ2 = 68.73, df = 1, P = 2.2 × 10−16) between two XfPD strains isolated from grapevines in Majorca across grapevine varieties (Supplementary Fig. S1). Full details on the results of the inoculation tests are available in “Methods”, Supplementary Note 1, Supplementary Table S1 and Supplementary Data 1.Growing degree days (GDD) have traditionally been used to describe and predict phenological events of plants and insect pests, but rarely in plant diseases58. We took advantage of data collated in the inoculation trials together with temperature to relate symptom development to the accumulated heat units at weeks eight, 10, 12, 14, and 16 after inoculation (Supplementary Data 1). Rather than counting GDDs linearly above a threshold temperature, we consider Xf ’s specific growth rate in vitro within its cardinal temperatures. The empirical growth rates come from the seminal work by Feil & Purcell38 shown in the inset of Fig. 1a. This Arrhenius plot was transformed, as explained in Supplementary Note 2A, to obtain a a piece-wise function f(T) Eq. (1). Our model and risk maps are based on f(T) (red line in Fig. 1a) because it provides the best fit to the experimental data when compared with the commonly used Beta function (blue line) for representing the thermal response in biological processes59,60. This Modified Growing Degree Day (MGDD) profile Eq. (1) enables to measure the thermal integral from hourly average temperatures, improving the prediction scale of the biological process61. MGDD also provides an excellent metric to link XfPD growth in culture with PD development as, once the pathogen is injected into the healthy vine, symptoms progression mainly depends upon the bacterial load (i.e., multiplication) and the movement through the xylem vessel network, which are fundamentally temperature-dependent processes38,62. Moreover, MGDD can be mathematically related to the exponential or logistic growth of the pathogen within the plant (Supplementary Note 2B).Fig. 1: Climatic and transmission layers composing the epidemiological model.a MGDD profile fitted to the in vitro data of Xf growth rate in Feil & Purcell 200138. The original Arrhenius plot in Kelvin degrees (inset) was converted to Celsius, as explained in (Supplementary Note 2A), to obtain the fit shown in the main plot red line; the blue line represents the fit with a Beta function. b Correlation between CDD and the average ({T}_{min }) of the coldest month between 1981 and 2019. Plotted black dots (worldwide) and yellow dots (main wine-producing zones) depict climatic data from 6,487,200 cells at 0.1∘ × 0.1∘ resolution, spread globally and retrieved from ERA5-Land dataset. The red solid line depicts the fitted exponential function for worldwide data and the blue solid line for main vineyard zones. c Nonlinear relationship between MGDD (red line) and CDD (blue line) and the likelihood of developing chronic infections. Black dots depict the cumulative proportion of grapevine plants in the population of 36 inoculated varieties showing five or more symptomatic leaves at each of the 15 MGDD levels (see Supplementary Information). Vertical bars are the 95% CI. d Combined ranges of MGDD and CDD on the likelihood of developing chronic infection. e Transmission layer in the dynamic equation (1) of the SIR compartmental model. f Relationship between the exponential growth of the number of infected plants with the risk index and their ranks.Full size imageInterannual infection survival in grapevines plays a relevant role when modelling PD epidemiology. In our model, we assumed a threshold of five or more symptomatic leaves for these chronic infections based on the relationship between the timing and severity of the infection during the growing season and the likelihood of winter recovery38,39,42. This five-leaf cut-off was grounded on: (i) the bimodal distribution in the frequency of the number of symptomatic leaves among the population of inoculated grapevines (Supplementary Fig. S1), whereby vines that generally show less than five symptomatic leaves at 12 weeks after inoculation remain so in the following weeks, while those that pass that threshold continue to produce symptomatic leaves, and (ii) the observed correlation between the acropetal and basipetal movement of Xf along the cane (Supplementary Fig. S1). The likelihood of developing chronic infections as a function of accumulated MGDD among the population of grapevine varieties was modelled using survival analysis with data fitted to a logistic distribution ({{{{{{{mathcal{F}}}}}}}}({{{{{rm{MGDD}}}}}})). A minimum window of MGDD = 528 was needed to develop chronic infections (var. Tempranillo), about 975 for a median estimate, while a cumulative MGDD  > 1159 indicate over 90% probability within a growing season (red curve in Fig. 1c and “Methods”).Next, we intended to model the probability of disease recovery by exposure to cold temperatures. Previous works had specifically modelled cold curing on Pinot Noir and Cabernet Sauvignon varieties in California as the effect of temperature and duration39 by assuming a progressive elimination of the bacterial load with cold temperatures42. In the absence of appropriate empirical data to formulate a general average pattern of winter curing among grapevine varieties, we combined the approach of Lieth et al.39 and the empirical observations of Purcell on the distribution of PD in the US related to the average minimum temperature of the coldest month, Tmin, isolines41. To consider the accumulation of cold units in an analogy of the MGDD, we searched for a general correlation between Tmin and the cold degree days (CDDs) with base temperature = 6 ∘C (see “Methods”). We found an exponential relation, ({{{{{rm{CDD}}}}}} sim 230exp (-0.26cdot {T}_{min })), where specifically, CDD ≳ 306 correspond to ({T}_{min } < -1.{1},^{circ }{{{{{rm{C}}}}}}) (Fig. 1b). To transform this exponential relationship to a probabilistic function analogous to ({{{{{{{mathcal{F}}}}}}}}({{{{{rm{MGDD}}}}}})), hereafter denoted ({{{{{{{mathcal{G}}}}}}}}({{{{{rm{CDD}}}}}})), ranging between 0 and 1, we considered the sigmoidal family of functions (f(x)=frac{A}{B+{x}^{C}}) with A = 9 × 106, B = A and C = 3 (Fig. 1c), fulfilling the limit ({{{{{{{mathcal{G}}}}}}}}({{{{{rm{CDD}}}}}}=0)=1), i.e., no winter curing when no cold accumulated, and a conservative 75% of the infected plants recovered at ({T}_{min }=-1.{1},^{circ }{{{{{rm{C}}}}}}) instead of 100% to reflect uncertainties on the effect of winter curing.MGDD/CDD distribution mapsMGDD were used to compute annual risk maps of developing PD during summer for the period 1981–2019 (see “Methods”). The resulting averaged map identifies all known areas with a recent history of severe PD in the US corresponding to ({{{{{{{mathcal{F}}}}}}}}({{{{{rm{MGDD}}}}}}) , > , 90 %) (i.e., high-risk), such as the Gulf Coast states (Texas, Alabama, Mississippi, Louisiana, Florida), Georgia and Southern California sites (e.g., Temecula Valley) (Fig. 2a), while captures areas with a steep gradation of disease endemicity in the north coast of California (({{{{{{{mathcal{F}}}}}}}}({{{{{rm{MGDD}}}}}} , > , 50 % )). Overall, more than 95% of confirmed PD sites (n = 155) in the US (Supplementary Data 2) fall in grid cells with ({{{{{{{mathcal{F}}}}}}}}({{{{{rm{MGDD}}}}}}) , > , 50 %).Fig. 2: Average thermal-dependent maps for Pierce’s disease (PD) development and recovery in North America and Europe.PD development during the growing season based on average ({{{{{{{mathcal{F}}}}}}}}({{{{{rm{MGDD}}}}}})) estimations between 1981 and 2019 in North America (a) and Europe (b) derived from the results of the inoculation experiments on 36 grapevine varieties. Large differences in the areal extension with favourable MGDDs can be observed between the US and Europe. The winter curing effect is reflected in the distribution of the average ({{{{{{{mathcal{G}}}}}}}}({{{{{rm{CDD}}}}}})) for the 1981–2019 period in the United States (c) and Europe (d). A snapshot of the temperature-driven probability of chronic infection averaged for the 1981–2019 period is obtained from the joint effect of MGDD and CDD in North America (e) and Europe (f). Warmer colours indicate more favourable conditions for chronic PD and the dashed line highlights the threshold of chronic infection probability being 0.5.Full size imageThe average MGDD-projected map for Europe during 1981–2019 spots a high risk for the coast, islands and major river valleys of the Mediterranean Basin, southern Spain, the Atlantic coast from Gibraltar to Oporto, and continental areas of central and southeast Europe (Fig. 2b). Of these, however, only some Mediterranean islands, such as Cyprus and Crete, show ({{{{{{{mathcal{F}}}}}}}}({{{{{rm{MGDD}}}}}}) , > , 99 %) comparable to areas with high disease incidence in the Gulf Coast states of the US and California. Almost all the Atlantic coast from Oporto (Portugal) to Denmark are below suitable MGDD, with an important exception in the Garonne river basin in France (Bordeaux Area) with low to moderate MGDD (Fig. 2b).Figure 2a shows how the area with high-risk MGDD values extends further north of the current known PD distribution in the southeastern US, suggesting that winter temperatures limit the expansion of PD northwards9. A comparison between MGDD and CDD maps (Fig. 2a vs. Fig. 2c, Fig. 2e) further supports the idea that winter curing is restricting PD northward migration from the southeastern US. However, consistent with growing concern among Midwest states winegrowers on PD northward migration led by climate change63, we found a mean increase of 0.12% y−1 in the areal extent with CDD  0.075) in 22.3% of the vineyards in Europe. However, no vineyard is in epidemic-risk zones with a high-risk index and only 2.9% of the vineyard surface is at moderate risk (Supplementary Table S8). The areas with the highest risk index (r(t) between 0.70 and 0.88) are mainly located in the Mediterranean islands of Crete, Cyprus and the Balearic Islands or at pronounced peninsulas like Apulia (Italy) and Peloponnese (Greece) in the continent (Fig. 6a and Supplementary Table S8). Most vineyards are in non-risk zones (42.1%), whereas 35.6% are located in transition zones with presently non-risk but where XfPD could become established in the next decades causing some sporadic outbreaks. In Supplementary Data 4 and Supplementary Table S8, we provide full details of the total vineyard areas currently at risk for each country and region.Fig. 6: Intersection between Corine-land-cover vineyard distribution map and PD-risk maps for 2020 and 2050.Data were obtained from Corine-land-cover (2018) and the layer of climatic suitability forP. spumarius in Europe from35. The surface of the vineyard contour has been enlarged to improve the visualisation of the risk zones and disease-incidence growth-rate ranks. a PD risk map for 2019 and its projection for 2050 (b). Blue colours represent non-risk zones and transient risk zones for chronic PD (R0  More

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National negotiators inked a deal to protect nature in the early hours of 19 December in Montreal.Credit: Julian Haber/UN Biodiversity (CC BY 2.0)

Despite earlier signals of possible failure, countries around the world have cemented a deal to safeguard nature — and for the first time, the agreement sets quantitative biodiversity targets akin to the one that nations set seven years ago to limit global warming to 1.5–2 ºC above pre-industrial levels.In the early hours of 19 December, more than 190 countries eked out the deal, known as the Kunming-Montreal Global Biodiversity Framework, during the COP15 international biodiversity summit in Montreal, Canada. A key target it sets is for nations to protect and restore 30% of the world’s land and seas globally by 2030, while also respecting the rights of Indigenous peoples who depend on and steward much of Earth’s remaining biodiversity. Another target is for nations to reduce the extinction rate by 10-fold for all species by 2050.
10 startling images of nature in crisis — and the struggle to save it
Steven Guilbeault, the Canadian environment minister, described COP15 as the most significant biodiversity conference ever held. “We have taken a great step forward in history,” he said at a plenary session where the framework was adopted.At several points during the United Nations summit, which ran from 7–19 December, arguments over details threatened to derail a deal. In the final hours of negotiations, the Democratic Republic of the Congo (DRC) objected to how the framework would be funded. Nonetheless, Huang Runqiu, China’s environment minister and president of COP15, brought the gavel down on the agreement.Negotiators from several African countries, which are home to biodiversity hotspots but say they need funding to preserve those areas, thought that China’s presidency strong-armed the deal. Uganda called it “fraud”. A source who spoke to Nature from the African delegation, and who asked not to be named to maintain diplomacy, said the negotiating process was not equitable towards developing countries and that the deal will not enable significant progress towards stemming biodiversity loss. “It was a coup d’état,” they say. However, a legal expert for the Convention on Biological Diversity — the treaty within which the framework now sits — told COP15 attendees that the adoption of the framework is legitimate.Concerns and disappointmentsScientists and conservation groups have welcomed the deal, emphasizing that there has never been an international agreement to protect nature on this scale. Kina Murphy, an ecologist and chief scientist at the Campaign for Nature, a conservation group, says, “It’s a historic moment for biodiversity.”

Huang Runqiu, China’s environment minister and president of COP15, brought the gavel down on the biodiversity deal, despite objections from representatives of the Democratic Republic of the Congo.Credit: Julian Haber/UN Biodiversity (CC BY 2.0)

But some concerns and disappointments remain. For one, the deal lacks a mandatory requirement for companies to track and disclose their impact on biodiversity. “Voluntary action is not enough,” says Eva Zabey, executive director of Business for Nature, a global coalition of 330 businesses seeking such a requirement so that firms can compete on a level playing field. Nevertheless, it sends a powerful signal to industry that it will need to reduce negative impacts over time, says Andrew Deutz, an environmental law and finance specialist at the Nature Conservancy, a conservation group in Arlington, Virginia.In addition, the deal is weak on tackling the drivers of biodiversity loss, because it does not specifically call out the most ecologically damaging industries, such as commercial fishing and agriculture, or set precise targets for them to put biodiversity conservation at the centre of their operations, researchers say.
Can the world save a million species from extinction?
“I would have liked more ambition and precision in the targets” to address those drivers, says Sandra Diaz, an ecologist at the National University of Córdoba, in Argentina.The deal is not legally binding, but countries will have to demonstrate progress towards achieving the framework’s goals through national and global reviews. Countries failed to meet the previous Aichi Biodiversity Targets, which were set in 2010 and expired in 2020; scientists have suggested that this failure occurred because of a lack of an accountability mechanism.With the reviews included, the framework “is a very good start, with clear quantitative targets” that will allow us to understand progress and the reasons for success and failure, says Stuart Pimm, an ecologist at Duke University in Durham, North Carolina, and head of Saving Nature, a non-profit conservation organization.A long time comingScientists have estimated that one million species are under threat because of habitat loss, mainly through converting land for agriculture. And they have warned that this biodiversity loss could threaten the health of ecosystems on which humans depend for clean water and disease prevention, and called for a new international conservation effort.
Crucial biodiversity summit will go ahead in Canada, not China: what scientists think
The new agreement took 4 years to resolve, in part because of delays caused by the COVID-19 pandemic (the summit was supposed to take place in Kunming, China, in 2020), but also because of arguments over how to finance conservation efforts. Nations finally agreed that by 2030, funding for biodiversity from all public and private sources must rise to at least US$200 billion per year. This includes at least $30 billion per year, contributed from wealthy to low-income nations. These figures fall short of the approximately $700 billion that researchers say is needed to fully safeguard and restore nature, but represents a tripling of existing donations.Low- and middle-income countries (LMICs), including the DRC, had called for a brand-new, independent fund for biodiversity financing. Lee White, environment minister from Gabon, told Nature that biodiversity-rich LMICs have difficulty accessing the Global Environment Facility (GEF), the current fund held by the World Bank in Washington DC, and that it is slow to distribute funds.But France and the European Union strongly objected to a new fund, arguing it would take too long to set up. The framework instead compromises by establishing a trust fund by next year under the GEF. The final agreement also calls on the GEF to reform its process to address the concerns of LMICs.Progress without drastic changeAnother sticking point during negotiations was how to fairly and equitably share the benefits of ‘digital sequence information’ — genetic data collected from plants, animals and other organisms. Communities in biodiversity-rich regions where genetic material is collected have little control over the commercialization of the data, and no way to recoup financial or other benefits from them. But countries came to an agreement to set up a mechanism to share profits, the details of which will be worked out by the next international biodiversity summit, COP16, in 2024.Overall, the deal marks progress toward tackling biodiversity loss, but it is not the drastic change scientists say they were hoping for. “I am not so sure that it has enough teeth to curb the activities that do most of the harm,” Diaz says. More

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

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