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In-flight dosing system
The system used in this work is detailed in Fig. 1. It can be broken down into three primary modules: (1) a “coarse tracking” system that uses a pair of stereoscopic cameras to identify the three dimensional location of a target subject, which is passed on to (2) the “fine tracking” system that uses a single higher speed camera and a fast scanning mirror (FSM) to keep the target in the middle of the field of view (FOV) of the camera using a proportional-integral-derivative (PID) control loop, and (3) the laser dosing system that fires the laser pulse, which is co-aligned with the fine tracking system to ensure the laser pulse is accurately applied to the subject even while it is moving. For both the coarse and fine tracking systems, subjects are identified by the size of their silhouettes generated from near infrared LED back-illumination or reflection. As demonstrated in Fig. 1b, the subject cages were 20 cm cubes constructed from clear acrylic, but with the side facing the tracking and dosing systems made of borosilicate glass, placed two meters away from the FSM. A high-speed video camera (Vision Research Phantom) was set up to record a small subset of experiments at 2000 frames per second as well. For all experiments, each cage contained only a single subject to be illuminated, or “dosed,” with the laser, and conditions were set such that a subject could be dosed only when it was at least 2.5 to 5 cm away from any wall of the cage to ensure the subject was flying normally, rather than taking wing or alighting.
Figure 1

Schematics and images of in-flight dosing setup. (a) Schematic (not to scale) of primary dosing system components and communication lines among them. Note that the mirror control and 3D position subsystems were run on separate kernels within the same PC. (b) Image of complete system setup including the test cage location, LED backlighting, and control electronics. Cameras for coarse and fine tracking, the fast scanning mirror (FSM), and dosing laser path are contained in the white circle and better seen in (c) close-up image of core tracking and dosing system components and alignment among them. Red line represents fine tracking image path, green line the dosing laser path (laser not shown), and yellow line the combined fine tracking and dosing laser path.

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Prior to commencing the laser dosing experiments, a number of parameters were defined to analyze the results, as detailed in Table 1 and Fig. 2. The key outcome, in line with our previous study15 and with WHO guidelines on insecticide treatments17, was whether the subjects were alive or disabled (i.e. dead or moribund) 24 h after the treatment. To characterize how well the subjects were tracked during the laser pulse, the tracking error was defined as how far the insect’s centroid was from the center of the fine tracking camera’s FOV. Other parameters defined in Table 1 relate to the “occlusion factor,” or how much of the laser beam’s energy (assuming a Gaussian profile) overlapped with the target’s outline, as demonstrated in Fig. 2. From the coarse tracking system’s output of xyz position of the target, we could also define velocity, speed, and both linear and angular acceleration of the subjects before, during, and after the laser pulse.
Table 1 Definitions of all parameters tracked or calculated for each in-flight dosing event.
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Figure 2

Representative fine tracking camera images of A. stephensi silhouettes. In each frame, the approximate outline of the thorax and abdomen is drawn (thick black lines) according to a set pixel intensity threshold. The centroid of this region is then calculated (intersection of red crosshairs) and compared with the center of the camera’s field of view (green dot) to determine the current tracking error and provide input to the fine tracking PID loop controlling the direction of the scanning mirror. The green circle around the green dot represents the spot size of the laser (2.5 mm diameter for all images shown here); occlusion factor represents how much of this laser spot (assuming a Gaussian profile) overlaps with the body of the subject. The images in (a) demonstrate a typical time course for a single subject in 1 ms intervals, and those in (b) show representative depictions of tracking errors ranging from 1 to 5 pixels for various subjects.

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Initial results with 532 nm laser
Initial experiments were conducted with A. stephensi subjects and a 532 nm laser (Verdi, Coherent) using parameters for power (3 W), pulse duration (25 ms), and laser spot diameter (2.5 mm) that were defined in our previous work15 as an optimal combination of potential cost and mortality performance. As seen in Supplemental Video 1, the system could be quite effective in disabling a flying mosquito with these parameters. Of note from the video, along with flight tracking data for numerous trials (not shown), the 25 ms pulse duration appeared to be short enough that the mosquitoes did not perceptibly alter their flight pattern during the pulse to throw off the tracking algorithm. From Fig. 3a,b, though, the initial system did not have consistent enough tracking performance, such that survival of the subjects was almost entirely dictated by how well the fine tracking system kept the target near the center of its FOV. From this initial experiment on a sample of 80 subjects, we set limits for mean and maximum tracking error during the laser pulse as 2 and 3 pixels, respectively, where each pixel represents ~ 250 μm. Figure 3c,d demonstrates that the system was able to achieve and maintain this performance after modifying the PID loop parameters, and that there was no longer any association between tracking performance and mortality at these conditions. These criteria were evaluated and assured for all mortality data reported in this manuscript (i.e. a Kruskal–Wallis test indicated no significant differences in tracking errors among subjects that survived or were disabled by the laser pulses). Further, Supplemental Fig. S1 shows that flight behavior, in particular speed and linear acceleration, did correlate with tracking accuracy, but that the system was able to meet the noted tracking requirements even at the extremes of flight behavior that could be observed in this study given the restricted flight volumes (though the typical values seen here largely align with available data for other Anopheles mosquitoes18,19).
Figure 3

Influence of mean and maximum tracking errors on mortality outcomes. Initial mortality outcomes using LD90 conditions with a 532 nm laser from previous anesthetized work showed strong correlation with (a) mean and (b) maximum tracking errors over the 25 ms pulse duration. After setting and achieving new tracking error targets of less than 2 pixels mean and 3 pixels max (see Fig. 2b for depictions of overlap between the laser spot and the subject for various error magnitudes), identical experiments no longer showed any correlation with (c) mean or (d) maximum tracking errors. Moribund and dead outcomes were grouped in (c) and (d), labeled “Disabled,” and subsequent experiments since they both represent functional kills and are grouped as such in WHO guidelines for insecticide trials.

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Mortality results were analyzed as in Fig. 4. Each data point represents the mortality outcomes (i.e. percentage of targets that were dead or moribund at 24 h, assuming acceptable control mortality  2 × that of the other experiments at 445 or 532 nm. Note that this greater LD90 fluence value for the smaller spot still represented a lower pulse energy than required for the larger spots given the spot size differential.
Table 2 List of in-flight dosing experimental conditions and resulting LD90 fluence values for A. stephensi subjects.
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Figure 5

Dose–response curves for all experiments from Table 2, other than the two constant pulse energy tests. The x-axis is plotted on a log scale to allow clear visualization of the curves at both low and high fluence values. Individual data points and error bars not shown for the sake of clarity. The intersections of the dashed horizontal line at 90% mortality with the dose–response curves indicate the LD90 points, which are also presented in Table 2, along with pseudo R2 values for the logistic regression fits.

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Dosing with near infrared wavelengths
Two near infrared (NIR) laser sources were examined as well—a custom constructed 1,064 nm (1 μm) fiber laser with a maximum output of 30 W and a commercial 1,570 nm (1.5 μm) fiber laser (IPG Photonics) with a maximum deliverable output of 11 W. The right-hand side of Fig. 5 shows the dose–response curves for these laser sources in addition to those using visible wavelengths. All of the infrared experiments resulted in significantly higher LD90 fluence levels compared with the visible lasers, and given the log scale of Fig. 5, varying experimental conditions with the 1 μm source led to comparatively larger changes in LD90 compared with the visible sources. As with the blue diode, the small spot (1.5 mm) had the highest LD90 fluence, but unlike the visible lasers, the larger spot (4 mm) offered a lower LD90 fluence compared with the baseline 2.5 mm. For the 1.5 μm source, there was insufficient mortality at the maximum power available from this source with a 2.5 mm spot and 25 ms pulse duration, so Fig. 5 shows a curve using slightly longer pulse durations to make up the additional fluence required. From the available data, it appears that the LD90 fluence levels for the 1 μm and 1.5 μm sources are at least at reasonably comparable levels.
Effects of longer pulse durations with lower power
We then further explored the effects of increasing the pulse duration to determine whether this could relax the optical power required from the laser source, given that laser cost is correlated with output power. Figure 6a,b show the results for the 532 nm and 1,064 nm sources, respectively, with spot diameters of 2.5 mm and pulse duration set to 25, 50, or 100 ms. In all cases, the optical power was adjusted according to the pulse duration to supply a constant pulse energy, and therefore fluence at approximately the LD75 level determined from previous experiments, which was chosen to ensure a low likelihood of any data point being 100% mortality (i.e., a saturated signal). As evidenced from Fig. 6a and Table 3, at 532 nm there was a significant drop off in mortality at the longer pulse durations, although the effect is smaller going from 50 to 100 ms compared with the initial drop from 25 to 50 ms. Similar, but smaller magnitude effects were seen with the 1 μm source in Fig. 6b and Table 3. Supplemental Fig. S2 shows that the tracking accuracy for these experiments somewhat mirrors the mortality performance, with a notable decrement from 25 to 50 ms but no significant change from 50 to 100 ms.
Figure 6

Mortality results for experiments with constant pulse energy achieved by proportionally adjusting the power according to pulse duration (25, 50, and 100 ms). Dosing was performed with both the (a) 532 nm and (b) 1,064 nm lasers, both using a 2.5 mm spot size, and set to the approximate LD75 fluence value from the dose–response curves (solid curves with dashed line 95% confidence intervals of logistic regression fit) from the corresponding 25 ms experiments. Error bars on individual points represent 95% confidence intervals of exact binomial probabilities. Statistical differences among mortality at the various pulse durations summarized in Table 3. The slight offsets on the x axis in (a) stem from slight changes in the beam spot size as a function of power.

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Table 3 Results of χ2 tests for mortality equivalence among experiments with constant pulse energy but varied amounts of power and pulse duration (25, 50, and 100 ms).
Full size table

Comparing dosing performance across other insects
Using the same system and procedures, experiments were also run on SWD and ACP subjects as a way of cursorily exploring laser-insect interaction for species of interest besides A. stephensi. For SWD, a full dose–response curve was created for the 1 μm laser with typical exposure settings (2.5 mm spot diameter and 25 ms pulse duration). The LD90 fluence from this work was 8.6 J/cm2, compared with 12.9 J/cm2 for A. stephensi under the same conditions. Tracking performance on SWD subjects was comparable to that for A. stephensi, given that flight parameters such as speed and acceleration were comparable as well. With ACP subjects, inducing them to fly in the cages was very difficult. As such, we could not process a sufficient number of subjects to create a proper dose–response curve. Based on the limited data available, and as demonstrated in Supplemental Video 2, the system as set for the mosquito LD90 condition with the 1 μm laser, 2.5 mm spot diameter and 25 ms pulse duration was effective in tracking and disabling the ACP subjects, despite their very different flying behavior (greater speeds and accelerations, limited durations) relative to the other test species.
Longer range dosing system demonstration
As a final proof of principle test, a long-range version of the system from Fig. 1 was configured. This system worked at a distance of 30 m instead of 2 m, facilitated primarily by modifying the optics used for the coarse and fine tracking systems. Given the reduced flexibility of this system, it was only used with the 1 μm laser with a 2.5 mm spot diameter and 25 ms pulse duration. Rather than acquiring new dose–response curves, which was impractical given the setup’s location in a building ~ 30 km away from the insect-housing chamber, we verified the efficacy of the system using the LD90 conditions established by short-range dosing. Supplemental Video 3 shows this system dosing an A. stephensi subject from the same stock as used for short-range testing, and Supplemental Video 4 shows the same for a wild-sourced Culex pipiens mosquito obtained in a local pond. Note that the wild C. pipiens was substantially larger in size than the lab-reared A. stephensi. In all of the limited number of tests of this system for both species (10 A. stephensi and 5 C. pipiens), the mortality rate was 100%. More

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Total P and available P
Fertilizer application significantly (P  0.05). The highest increase in available P concentration in NPK + S treatment observed in the 60–100 cm soil depth, with the increase of 111% and 115% in 60–80 cm and 80–100 cm soil depths, respectively, over CK treatment.
Figure 2

Effect of long-term application of chemical fertilizer, organic manure, and straw on total phosphorus (P) and available P concentrations. * indicates significant difference at P  3.6%) was associated with OM treatment, especially at the 0–20 and 20–40 cm soil depths (Fig. 3). The PAC values under NPK, NPK + S and OM treatments increased by 7.6%, 4.5% and 11.5% in the 0–20 cm soil depth and 4.2%, 1.3%, and 5.8% in 20–40 cm soil depth, respectively as compared to the CK treatment. However, PAC value for soil depth below 40 cm showed the trend, NPK  More

NEWS AND VIEWS
09 September 2020

How can the decline in global biodiversity be reversed, given the need to supply food? Computer modelling provides a way to assess the effectiveness of combining various conservation and food-system interventions to tackle this issue.

Brett A. Bryan &

Brett A. Bryan is at the Centre for Integrative Ecology, Deakin University, Melbourne, Victoria 3125, Australia.
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Carla L. Archibald

Carla L. Archibald is at the Centre for Integrative Ecology, Deakin University, Melbourne, Victoria 3125, Australia.

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Nature is in trouble, and its plight will probably become even more precarious unless we do something about it1. Writing in Nature, Leclère et al.2 quantify what might be needed to reverse this deeply worrying path while also feeding people’s increasingly voracious appetites. The authors’ answer is to team ambitious conservation measures with food-system transformation in the hope of reversing the trend of global terrestrial biodiversity loss.

By nature, we mean the diversity of life that has evolved over billions of years to exist in dynamic balance with Earth’s biophysical environment and the ecosystems present. Nature contributes to human well-being in many ways, and the services it provides, such as carbon sequestration by plants or pollination by insects, could impose a vast cost if lost3. Although the slow and long-term decline of Earth’s biodiversity4 is often overshadowed by climate change, and more recently by the COVID-19 pandemic, the loss of biodiversity is no less of a risk than those posed by the other challenges. Many would argue that the effect of biodiversity losses could surpass the combined impacts of climate change and COVID-19.
More and more, the realization is growing that, as a planet, we are what we eat. Human demand for food is accelerating with the ever-increasing global population (projected to approach 10 billion by 2050), and each successive generation is wealthier and consumes more resource-intensive diets than did the previous one5. Trying to balance this rapidly rising demand against the limited amount of land available for crops and pasture sets agriculture and nature (Fig. 1) on a collision course6. As Leclère and colleagues show, a bold and integrated strategy is required immediately to turn this around.

Figure 1 | A bean field bordering a rainforest reserve near Sorriso, Brazil.Credit: Florian Plaucheur/AFP/Getty

Taking a long view out to the year 2100, Leclère et al. present a global modelling study assessing the ability of ambitious conservation and food-system intervention scenarios to reverse the decline, or, as they call it, “bending the curve”, of biodiversity losses resulting from changes in agricultural land use and management. Projections of future land use and biodiversity are uncertain, and when these models are combined, this uncertainty is compounded. One of the great innovations of Leclère and colleagues’ work is in embracing this uncertainty by combining an ensemble of four global land-use models and eight global biodiversity models and measuring the performance of future land-use scenarios in terms of higher-level model-independent metrics such as the amount of biodiversity loss avoided.
Importantly, the study also included a baseline (termed BASE) scenario — the world expected without interventions — and Leclère et al. used this to gauge the effectiveness of the intervention scenarios. Although it is not a focus of the paper, it’s worth pausing to ponder the sobering picture painted by this business-as-usual future largely bereft of birdsong and insect chirp.
Choosing to act now can make a difference to nature’s plight. Most (61%) of the model combinations run by the authors indicated that implementing ambitious conservation actions led to a positive uptick in the biodiversity curve by 2050. Such conservation actions included: extending the global conservation network by establishing protected nature reserves; restoring degraded land; and basing future land-use decisions on comprehensive landscape-level conservation planning. This comprehensive conservation strategy avoids more than half (an average of 58%) of the biodiversity losses expected if nothing is done, but also leads to a hike in food prices.

When conservation actions were teamed with a range of equally ambitious food-system interventions, the prognosis for global biodiversity in the model was improved further. Including both supply- and demand-side measures, these approaches included boosting agricultural yields, having an increasingly globalized food trade, reducing food waste by half, and the global adoption of healthy diets by halving meat consumption. These combined measures of conservation and food-systems actions avoided more than two-thirds of future biodiversity losses, with the integrated action portfolio (combining all actions) avoiding an average of 90% of future biodiversity losses. Almost all models predicted a biodiversity about-face by mid-century. These food-system measures also avoided adverse outcomes for food affordability.
Leclère and colleagues’ work complements the current global climate-change scenario framework (tools for future planning by governments and others, including scenarios called shared socio-economic pathways, which integrate future socio-economic projections with greenhouse-gas emissions), and represents the most comprehensive incorporation of biodiversity into this scenario framing7 so far. However, a major limitation of the present study is that it does not consider the potential impact of climate change on biodiversity. This raises an internal inconsistency because, on the one hand, the baseline scenario considers land-use, social and economic changes under approximately 4 °C of global heating by 21008, yet, on the other hand, it does not consider the profound effect of warming on plant and animal populations and the ecosystems they comprise9. Also absent from the models were other threats to biodiversity, including harvesting, hunting and invasive species10. Although Leclère and colleagues recognized these limitations and assigned them a high priority for future research, unfortunately for us all, omitting these key threats probably means that the authors’ estimates of biodiversity’s plight and the effectiveness of integrated global conservation and food-system action are overly optimistic. To truly bend the curve, Leclère and colleagues’ integrated portfolio will need to be substantially expanded to address the full range of threats to biodiversity.
Although the models say that a better future is possible, is the combination of the multiple ambitious conservation and food-system interventions considered by Leclère et al. a realistic possibility? Achieving each one of the conservation and food-system actions would require a monumental coordinated effort from all nations. And even if the global community were to get its act together in prioritizing conservation and food-system transformation, would such efforts come in time and be enough to save our planet’s natural legacy? We certainly hope so.

doi: 10.1038/d41586-020-02502-2

References

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Díaz, S. et al. Science 366, eaax3100 (2019).

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Leclère, D. et al. Nature https://doi.org/10.1038/s41586-020-2705-y (2020).

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Butchart, S. H. M. et al. Science 328, 1164–1168 (2010).

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Springmann, M. et al. Nature 562, 519–525 (2018).

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Kok, M. T. J. et al. Biol. Conserv. 221, 137–150 (2018).

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Leclère, D. et al. Towards Pathways Bending the Curve of Terrestrial Biodiversity Trends Within the 21st Century https://doi.org/10.22022/ESM/04-2018.15241 (Int. Inst. Appl. Syst. Analysis, 2018).

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Warren, R., Price, J., Graham, E., Forstenhaeusler, N. & VanDerWal, J. Science 360, 791–795 (2018).

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Driscoll, D. A. et al. Nature Ecol. Evol. 2, 775–781 (2018).

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Tree-ring data
We used tree-ring records from over 210,000 trees of 110 species, distributed globally in habitats ranging from the tropics to the Arctic region over more than 70,000 sites (Supplementary Fig. 1, Supplementary Table 1). The largest publicly available data source from which we used data is the International Tree-Ring Data Bank (ITRDB, https://www.ncdc.noaa.gov/data-access/paleoclimatology-data/datasets/tree-ring). These were complemented with other datasets to maximize the number of records for each species and to fill in spatial gaps. A particularly large tree-ring dataset used in our analyses is the National Forestry Inventory data from the Ministère des Forêts de la Faune et des Parcs from Quebec, Canada52,53 (hereafter NFI-Quebec). This data consists of a complete set of ring-width data from 156,711 trees from 79.381 sites across the province of Quebec. Field tree-ring data were collected according to specific standard protocols52,53, which consisted of selection of up to nine trees in each plot, with 3–5 trees ( >91 mm diameter at breast height, DBH) randomly selected, 1–2 selected from the largest trees, and 1–2 from trees closest to the mean tree diameter of the plot52,53. From selected trees one core per tree was collected. Tropical tree-ring data were compiled from the ITRDB and from unpublished and published records26,27,54,55. For species with larger sample sizes, we distinguished between tree-ring data from trees that died naturally before the moment of sampling and trees that were alive at the moment of sampling, allowing us to test the assumption that living tree ages can be used to estimate trees natural lifespans (see section “Trade-off estimates and assessment of possible artefacts”). Part of these dead tree data were obtained from the ITRDB by selecting tree-ring records of which the last measured ring width was dated to before AD1900. We assumed that most of these trees must have been dead at the time of sampling as no records were collected before 1900. In addition, we compiled published dead tree data from refs. 21,56, and used subfossil tree-ring data from refs. 57,58. Supplementary Table 1 provides an overview of the datasets, and full details of each dataset are available online as supplemental info.
Various data controls and selection procedures were used to assure high confidence in our dataset. Where possible we tried to identify duplicate records, i.e., multiple cores taken from the same individual tree. This is only a problem for ITRDB, but not for the NFI-Quebec dataset where only one core per tree existed, or for datasets from co-authors. We thus merged ITRDB records that had identical ID′s except for the last character of their ID (e.g. 01a, 01b, or ID1-1, ID1-2, etc). From the ITRDB, we only used species for which we could obtain data from a minimum of 3 different sites with at least 20 records each, and only selected species that had a minimum total of 100 separate ring width series. We excluded those sites from the ITRDB that showed relative even age structures, and are thus unlikely to represent old-growth populations that provide robust estimates of trees’ maximum lifespans. To this end, we calculated for each ITRDB site the coefficient of variation in tree ages (CVAge = StandDevAge/ MeanAge × 100) and excluded sites with a CVAge lower than 10%. A large subset of ITRDB-data from 46 species has previously been inspected for data quality by co-author S. Voelker59. In this subset of data, each ring width series was manually re-aligned by cambial age (i.e., ring number from pith), providing more reliable estimates of tree ages. For the datasets that were not acquired from the ITRDB, we used slightly different criteria. From NFI-Quebec, we used all available sites, excluding those that were classified with evidence of recent management (commercial thinning or clear-cutting) and where fire or insect disturbances destroyed more than 25% of the forest cover.
For estimates of species-level early growth rates and lifespans (cf. Fig. 1a), we included only species with a minimum of 30 records, as lower sample size is unlikely to provide good approximations of tree life spans. This resulted in the inclusion of 110 species, with a median sample size of 305 trees and 12 sites per species. To assess within-species relationships between early growth and tree lifespan, we included 82 species. As a general rule, we included only species with more than a total of 150 trees and from at least 3 sites. About half of our species had more than 300 tree records (see Supplementary Information).
To assess what minimum sample size is needed to get a representative estimate of the true maximum age of a species or a site, and to evaluate how sample size affected estimates of trade-offs between early growth and longevity, we randomly resampled 500 times varying sample sizes—from 25 to 600 trees—from a subset of 11,752 Picea mariana trees from NFI-Quebec sites located north of 50.7°N. Comparison of the maximum ages of these random subsets of trees with the true observed maximum ages shows that a sample size of 100 trees results in 99.4% of the cases in maximum age estimates larger than the 95th percentile of the original dataset, and in 67.2% of the cases in ages larger than the 99th percentile original age (Supplementary Fig. 2a, b). As more than 70% of the species had at least 100 trees we thus assumed that for most species, the estimates of their lifespan were close to true lifespans. We used this same approach to assess how sample size affected the estimate of the trade-offs (i.e., estimation of the negative exponential decay constant; see next section for details). This analysis showed that sample size of 300 trees (corresponding to median sample sizes for trade-off analysis), leads to mean errors in the estimated slope of 12% (Supplementary Fig. 2c). Thus, for most species we achieve relatively accurate estimates of the trade-off strength. Low sample sizes for some species will nevertheless result in small errors of the mean slope, but we expect that positive and negative errors will cancel out against each other. Indeed, we do not observe a specific bias towards over- or under-estimation for low sample sizes, as the mean exponential decay constant for a simulated sample size of 150 trees is very similar to that observed (i.e., −0.409 versus −0.399).
Trade-off estimates and assessment of possible artefacts
The strength of the trade-offs between growth and tree lifespan was assessed for each species using a 95th quantile regression between mean early growth rate and the natural logarithm of age using the QUANTREG package in R60, as

$$begin{array}{*{20}{c}} {{{log}}(A_{(95{mathrm{th}},{mathrm{quantile}})}) = a + b cdot overline {{mathrm{RW}}} } \ {{mathrm{or}}} \ {{mathrm{Lifespan}} approx A_{left( {95{mathrm{th}},{mathrm{quantile}}} right)} = {mathrm{exp}},left( {a + b cdot overline {{mathrm{RW}}} } right)} end{array}$$
(1)

where A is age of the tree, (overline {{mathrm{RW}}}) is the mean ring width over the first 10 years. The constant b describes the negative exponential decay constant (i.e., exponential rate of decrease of tree lifespan with increasing early growth rate). This quantile regression fit results in similar estimates of the maximum ages of trees as the 95th percentile ages in binned early growth rate categories (see Supplementary Fig. 3a–c). Note that in contrast the maximum diameter does not vary strongly between slow and fast-growing trees (Supplementary Fig. 3d). We chose a relative short period, the first ten years, for estimating early growth as our study included some relative short-lived species. Previous studies have found similar results when using longer periods (50 years)56, and we expect no substantial difference using different early growth periods as tree growth is usually strongly auto-correlated in time61.
To assess trade-off strengths within species, we calculated the mean decay constant (b, Eq. 2) for each species using relative age, A/max(A), and relative mean early ring width, (overline {{mathrm{RW}}})/max((overline {{mathrm{RW}}})). Maximum of A and (overline {{mathrm{RW}}}) are species level maxima. The mean slope calculation across all species was weighted by the cube root of the sample size to account for the large differences between species in sample size, and confidence of the trade-off estimates.
While these relationships suggest true trade-offs, they may also be affected (or even driven by) the approaches or analytical methods used here. In particular, we here evaluate the effect of the following four possible artefacts on our results; (1) the use of living trees to estimate tree lifespans, (2) effect of recent growth increases on early growth-age relationship, (3) effects of pith offsets and wood decay on early growth-age relationship, (4) sampling artefacts, such as disproportionate selection of large trees.
(1)
Use of living trees: our analysis includes mostly trees that were sampled when still alive, and may thus not be representative for the true lifespan trees may achieve. To assess to which degree use of living trees may affect our results, we analyse and compare the trade-off strengths of trees that died before 1900 to living trees for 12 species with sufficient data availability (minimum of 150 dead and 150 living trees). As the slopes of dead and living trees do not differ significantly (Supplementary Fig. 5f, g, paired t-test exponential decay coefficient, t = −0.1095, p = 0.915, n = 12), we conclude that 95th quantile regressions on living trees can be used to approximate tree lifespan.

(2)
Effect of recent growth increases: recent growth stimulation of trees due e.g. to CO2 fertilisation, warming in higher latitudes, and/or nitrogen deposition, may result in observation of a trade-off. This is because recent increases in growth will lead to higher early growth rates for young trees compared to old trees, resulting in a negative relationship between early growth and tree age. The comparison of trade-off strength of dead versus living trees provides strong evidence that this effect does not drive the trade-off. In addition to this, we use a data driven forest simulation (see section “Examining the effects of growth stimulation on forest dynamics”) to assess how growth increases affect estimations of the trade-off strength. In this simulation, we used the actual tree-ring data to simulate realistic growth increases of Picea mariana tree-ring trajectories in response to high latitude warming. By sampling from these trajectories at the end of the growth increase period (i.e., year 350), and in a period without any recent growth increases (i.e., year 600, see Fig. 3e), we establish that growth increases result in only a small over-estimation of the trade-off, decreasing the exponential decay coefficient from −0.37 to −0.44 (see Supplementary Fig. 9c). Thus, it is unlikely that recent growth stimulation is the cause for the negative relation between early growth and tree lifespan.

(3)
Pith offset: tree-ring data, especially those acquired from ITRDB, may miss the innermost sections due to incomplete cores, decayed centres, or imperfect increment borer alignment. Missing rings will result in underestimation of tree ages and inaccurate early growth rates estimation and could thus affect the estimated relationship between early growth and lifespan. However, ring widths in most species decrease with tree age and size17, and even trees showing constant wood production with age, will show decreasing ring width because of geometry. Thus early growth in these samples will underestimate true growth rates and would most likely weaken the observed trade-off, rather than strengthening it. A comparison of species present in both the NFI-Quebec and the ITRDB datasets confirms this. The NFI-Quebec dataset was less affected by pith offset problems, as the trees were carefully screened and trees with substantial differences between cumulative ring widths and field diameters were excluded. Yet, we find that slopes were more negative for NFI-Quebec compared to ITRDB (mean b of −0.25 for Quebec vs. −0.10 for ITRDB, two-sided paired t.test, t = 2.49, p = 0.047, n = 7 species) and pith offsets thus do not explain the relationship. This comparison also shows that estimates of the strength of the trade-offs between early growth and longevity inferred from ITRDB data are probably conservative, as the Quebec data can be considered to be of higher quality, and were collected according to standard protocols. In contrast, data from the ITRDB may contain incomplete series and were collected for unknown purposes, and these issues probably weaken trade-offs in the ITRDB.

(4)
Sampling biases: one potential bias in our dataset may arise due to the tendency of tree-ring studies to sample predominantly large trees in the field (i.e., big tree selection bias62,63,64). This may result in a negative relationship between early growth and tree age, as young slow-growing trees tend to be underrepresented in the tree-ring sample (i.e., have not reached the field minimum size threshold yet), compared to fast-growing young trees that are much larger, and therefore more likely to be sampled. This effect would reduce the number of trees with slow early growth and young ages in the tree-ring sample (i.e., trees in the lower left-hand corner of the early growth-lifespan graphs, cf. Supplementary Fig. 6a), and results in overestimation of the 95th percentile age estimates for slow-growing trees. Our approach to estimate to which degree this bias affected our estimates of growth-lifespan trade-offs was as follows. We first used the tree-ring NFI-Quebec data of Picea mariana, combined with plot data from Quebec to reconstruct a new artificial tree-ring dataset with a size frequency distribution identical to the population size frequency distribution for this species in Quebec (Supplementary Fig. 6b). For each tree of Picea mariana sampled for their tree-rings we know the early growth rate and age, and also the complete diameter- and age-trajectory up to the year of sampling. From these data, we resampled for each size class (in bin widths of 2 cm) the same number of trees as that observed in the field. By doing this we filled in the lacking data of trees smaller than 91 mm, and created a new artificial tree-ring dataset that had an identical size structure to that observed in the field. We know the mean growth rate over the first ten years and the age at which each individual tree reached the diameter of their respective size class, and could thus reconstruct the early growth rate versus tree age graphs for the full population, including the smaller size classes which were missing from our original tree-ring sample. We then compared the early growth -lifespan relationship for the complete population to that of the trees larger than 91 mm, mimicking the NFI-Quebec field collection protocol. This shows that the exponential decrease is marginally larger (b = −0.505 compared to −0.470 for trees >91 mm) and that the intercept is lower (159 years compared to 220 for trees >91 mm) when sampling all trees compared to only trees with diameters >91 mm (Supplementary Fig. 6). Hence, the use of a minimum size threshold (91 mm) in the NFI from Quebec results in a slight underestimation of the trade-off (by ~7%) for the Picea mariana dataset. We also resampled from this artificial dataset the 10% largest trees, to mimic a hypothetical standard tree-ring sampling scenario that only samples the largest trees. Such a sampling scenario resulted in a decay constant of −0.432, thus again causing a small underestimation of the true trade-off. This simulation proves that the trade-off is not a result of a sampling bias.

Possible environmental drivers of the trade-offs
We evaluated whether the observed trade-off between early growth and tree lifespans could be caused by covariance of growth and lifespan with climate, soil or competition. Temperature variation for example reduces tree growth and lifespan in various species (cf. Fig. 2a, b). To this end, we calculated site-level mean early growth rates and the maximum tree age for a set of species covering different geographic regions (North America, Europe and Quebec). For Quebec, we combined multiple nearby locations to obtain a minimum of 30 trees per site, as sample sizes were low for each location. Site-level mean annual temperature and precipitation was obtained from WorldClim65. We then assessed for nine different species the effect of temperature and precipitation on site-level mean early life growth and maximum tree age using major axis regression from the package smart-366. These analyses confirm that early life growth is positively related to temperature for all nine species studied, and that lifespan decreases significantly with temperature for seven out of nine species (see Fig. 2a, b). Using linear mixed effect models with species as random factor (nlme-package-R67), we find that across all nine species, mean early life growth increases on average by 0.11 mm for each degree temperature increase, while lifespan decreases by 13 years for each degree temperature increase. Precipitation has no significant effect on early life growth or tree lifespan.
To disentangle whether lifespan decreases are a direct effect of temperature increases, or due to increases in early life growth, mixed effect models were run for all nine species that simultaneously included temperature and mean early life growth rate as explanatory variables for variation in tree lifespan. To account for species differences in growth and age, we used relative mean early ring width ((overline {RW})/max((overline {RW}))), and relative maximum age (A/max(A)), and used species as a random factor with random intercepts for both early life growth and temperature. This analysis shows that mean early life growth is a stronger predictor of tree lifespans than temperature (t-value early growth = −7.2, p  , D_0} end{array}} right..$$
(4)

Here b = 0.025, k = 3 × 10−11 and D0 = 91 mm, which is the minimum sampling diameter used for the NFI-Quebec. The rationale to set the mortality below D0 to zero in this model is that the trees sampled for tree rings did all survive to this diameter (as only trees with diameters >91 mm were cored). Thus, only by setting mortality to zero for trees , A_0} end{array}} right.,$$
(5)

with a = 0.021 and b = 0.0000015. Analogous to the diameter-dependent mortality model, we set mortality to zero for trees younger than 74 years (A0), which is the age at which the average Picea mariana tree reaches 91 mm in diameter (D0).
We next created a 600 year sequence of annually seeded, 1250 member, tree cohorts. Each member of a cohort is a randomly selected tree diameter growth trajectory derived from the tree-ring cores, extended in time to an age of 500 years. Short growth trajectories were extended by using the mean growth of the 10 oldest trees that had a similar ring width in the first ten years of growth. To this end all early mean ring width was grouped into six equal early ring width classes.
All trees of this so-constructed tree cohort set live, by construction, exactly 600 years. Realistic age structures were realised by sequentially (year-on-year and tree-by-tree) assigning death to trees where a random number generator identified those individuals  smaller than μ(D) or μ(A). To test the realism of this procedure, we compared the predicted and observed tree age versus early ring width relationship—or i.e. the growth-longevity trade-off. The slope of the relationship for the diameter-dependent mortality model μ(D) is very close to observed (Supplementary Fig. 9a), and is thus a realistic representation of the observed mortality process and justifies its use to examine the effect of a growth stimulation on standing stocks. In contrast, we find that the age-dependent mortality model μ(A) does not result in a significant trade-off between early growth and tree lifespan (Supplementary Fig. 9b), providing an ideal comparison for models that fail to incorporate the observed trade-offs.
To mimic growth stimulation, we boosted growth of trajectories from year t0 = 300 year onwards of the 600 year sequence of cohorts, while exposing the trajectories over the entire 600 year period to the mortality algorithm just described. We stimulated growth rate, (overline {{mathrm{RW}}}) (mm year−1) from year t0 = 300 year onwards according to

$$overline {{mathrm{RW}}_{stim}} left( t right) = overline {{mathrm{RW}}} left( t right) cdot exp left( {lambda left( A right) cdot delta Tleft( t right)} right),$$
(6)

and

$$delta Tleft( t right) = left{ {begin{array}{*{20}{c}} {frac{{overline {dT} }}{{dt}} cdot left( {t – t_0} right),} & {t – t_0 ,150 yrs) as younger trees are more sensitive to temperature increases than older trees (Supplementary Fig. 9d), and use an exponential model of the form

$$overline {{mathrm{RW}}} left( {A,,T} right) = a cdot {mathrm{exp}}left( {lambda left( A right) cdot delta T} right),$$
(8)

where a is a constant, λ(A) is the exponential increase rate for age class [A, A+ δA] and δT = (T − 0) (°C). We then used the exponential growth increase with temperature for each age band, λ(A), to estimate the relationship between tree age and λ(A) (Supplementary Fig. 9e). In all cases the age modulation of the stimulus is

$$lambda left( A right) = left{ {begin{array}{*{20}{c}} {0.0000132 cdot A^2-0.00291 cdot A + 0.229,} & {A , < ,135} \ {0.07,} & {A , ge ,135} end{array}} right..$$ (9) Finally, we compared the effect of growth stimulation on forests dynamics against simulation without growth increases (baseline) for the two different mortality models. We also performed one simulation where we multiplied the full growth series by 2, as a representation of the effect of growth stimulation on a faster-growing species. Finally, we evaluated for each simulation the mean ring width growth, the stem mortality rate, the age of the largest (75th percentile) trees that died and the change in the total basal area stock over time for the full population. For the stem mortality and the basal area stocks, we calculate and present the change in dynamics of the growth stimulation scenario relative to the baseline scenario without growth stimulation. All analyses and simulations were performed using R-studio, version 0.99.90370. Maps in SI figures were produced using the ggmap function from the R-package ‘ggplot2’71 More