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Ethics statement
The work was carried under the ethical Permit Number VARELY/711/2016 issued by the regional environmental centre of Finland. Every possible effort was made to minimise disturbance.
Field system set-up
The study was performed in a farmland area in Southern Finland, near Lammi Biological Station (61° N, 25° E). We selected the lapwing as the study species, a common breeder in the study area. This ground nesting medium-sized farmland bird is listed as IUCN Near Threatened globally but Endangered within Europe17. The main threat to the species is agricultural intensification, and particularly the destruction of nests in arable land due to large scale mechanical operations, such as sowing17. In Finland, as in many other countries, a fraction of lapwing nests on arable land are located by volunteers, and their protection secured. However, locating these nests is highly time consuming and challenging, and most nests are left unprotected, and likely destroyed, every spring18.
We selected nine field parcels with a total of 22 lapwing nests in 2016, and three field parcels with nine nests in 2017. Study field parcels were intensively searched for nests by experienced observers during the week preceding the start of the recording work (see below), and individual nest locations were recorded with a hand-held GPS (model Garmin GPSmap 62 s, position accuracy ~ 3 m). Overall five of the field parcels were represented by ploughed fields (with irregular substrate owing to the upper soil being turned over) and seven by unploughed fields (direct sowing or winter cereals). Flight routes were constructed and saved in MapPilot 1.5.1 (Drones Made Easy, San Diego, USA) for areas around nests that covered approximately 0.5–1 ha (see Fig. 4). A drone cruised along the pre-programmed route, each flight lasting approximately 6–10 min (the time was constrained by the drone battery). Flights were done between 5-25.5.2016 and 16-18.5.2017 at altitudes of 15 or 25 m above ground level. Distance between transects was approximately 7 m for flights at 15 m of altitude and 12 m for flights at 25 m of altitude. We aimed to achieve a minimum of at least one flight over each field at each altitude (15 and 25 m) and each period of the day (07—11 a.m. and 14—20 p.m.). Overall, 54 flights were completed in 2016 and 19 in 2017. Thermal images were acquired by using a DJI Phantom 3 Advanced quadcopter with a FLIR Tau 2, 336 * 256 pixel, 9 mm lens thermal camera mounted on it. To ensure quality, thermal images were continuously saved during flights directly to a USB stick using a ThermalCapture unit (TeAx Technology GmbH, Wilnsdorf, Germany). Image acquisition occurred with the camera pointed in nadir position. Temperature, cloud cover, air humidity and wind speed data for each flight were accessed afterwards through Airdata.com service. In all circumstances, the incubating adult left the nest as we approached the edge of the field before the start of the drone flight.
Figure 4

Schematic representation of the key steps of this study, from extensive nest search at selected fields (A), to flying the drone carrying the thermal sensor along a pre-programmed route over the field (B), preparing the thermal images by extracting the coordinates of the box drawn around the nest (C), and finally applying a neural network deep learning algorithm to classify images as having or not having a nest (D). The satellite image in (A) and (B) is taken from Google maps (www.google.it/maps, map data: Google). Figure created in Microsoft Office PowerPoint 2016 (www.microsoft.com).

Full size image

Deep learning algorithm for nest identification
To automatically classify images as having or not having a nest, we trained a deep learning model (more details in extended methods in Supplementary information) to detect nests while minimising the occurrence of false positives (hereafter false presences) and false negatives (hereafter false absences). In doing so, we choose a convolutional neural network (CNN) approach19 and YOLOv3 training program20, as done in a similar study3.
We selected all images with nests in them (positive images, n = 1969) from each flight, and a larger number of randomly selected images without a nest (negative images, n = 3,469). We manually labelled all positive images using software ImageJ 1.8.021 with bounding boxes, which coordinates were then indexed by corresponding image names to be used by the YOLOv3. Next, we split the set of positive images into a training set and a test set by randomly selecting 70% of the flights (and all associated images) for training, and using the remaining 30% of flight images for testing. Selection was done at the flight rather than the image level to avoid that similar images from the same flight would be used in both training and testing, causing testing results to be positively biased.
Training was executed for 800 epochs, whereby an epoch is defined as the entire dataset passing forward and backward through the neural network (training program available at http://github.com/ultralytics/yolov3). After training was completed, a weights file was generated, which included the final value stored by each neuron, represented by floating point numbers in series. We then developed a program which read the configuration file of the YOLOv3 architecture and constructed the network according to the architecture specified in PyTorch implementation. Developing our own program was done to increase flexibility of expanding functionalities without interrupting unfamiliar code flow. The program read the trained weights file in series and stored the values to proper neurons, resulting in the construction of a deep learning model specifically for nest detection. This was then used to validate and test all the trained weight files to select the best model.
Through the testing, an output value was produced representing the confidence that an image included a nest. Values close to zero indicate that an image contained no nests with a high confidence, while values close to one that an image included a nest with a high confidence. In the cases where multiple spots appeared as possible nests, the overall confidence for that image was taken from the spot with the highest confidence values.
Performance of the neural network in discriminating images as having a nest or not was assessed by means of calculating four standard evaluation metrics for these types of systems: Precision, recall (propensity to avoid false positives and false negatives, respectively), accuracy (overall discrimination accuracy) and F1 score (the harmonic mean of precision and recall; more details in extended methods in Supplementary information). Performance was evaluated separately for the training and for the testing parts of the system.
Statistical analyses
We quantified the effect of environmental factors on the performance of the deep learning algorithm. We ran two separate analyses, one focused on factors affecting occurrence of false presences (i.e. the algorithm erroneously identifies an image without a nest as having a nest), and one on factors affecting occurrence of false absences (algorithm erroneously identifies an image with a nest as not having a nest). As the response of the former model we used the confidence as given by the algorithm for all the test images known to have no nest in them (values close to one indicate high probability of false presence). This model used data from images without a nest from all available flights (n = 3,469 images from 73 flights, as these were not used for training). The response for the false absence model was the confidence of the test images (n = 497 images with a nest from the 30% flights, n = 14 flights, not used for training) to having no nest in them (values close to one indicate high probability of false absence). Because the response variable is a proportion, we used beta regression with logit link. In each model we also included flight identity as a random factor to account for pseudo-replication stemming from multiple images per flight.
Models were run using the glmmTMB package22 in R version 3.6.123. Covariates considered are: air temperature (hereafter temperature), cloud cover, wind speed, air humidity (hereafter humidity), drone height (either 15 or 25 m above ground level) and substrate type (two classes: ploughed or un-ploughed). These variables are deemed potentially relevant in affecting the nest visibility in thermal images, and consequent performance of the deep learning algorithm. Air temperature, humidity, cloud cover and wind speed may reduce the thermal contrast between a nest (warm) and the remaining landscape, and create heterogeneous thermal landscape that hampers nest detection24. Moreover, ploughing alters the physical structure of the substrate, making it rougher and more heterogeneous, with many physical objects that may resemble a nest shape, thereby affecting nest detection accuracy. Drone height may affect detection accuracy due to the decreasing size and sharpness of a nest at higher altitudes.
Prior to analyses, we checked for outliers and ran variance inflation (VIF) analyses to assess the collinearity level between covariates. For the false presence model, humidity had a high VIF value of 3.9 being strongly correlated to temperature (R = − 0.7) and was excluded from following analyses. For the false absence model, humidity and wind speed had high VIF (28.8 and 2.3, both correlated with temperature, R = − 0.9 and 0.7, respectively), and were excluded from analyses. The remaining covariates had a VIF  More

Test-case species
Perca fluviatilis (Actinopterygii, Percidae) is a common widely spread Eurasian species living in freshwater and brackish habitats49. Its economic (high market value) and recreational (i.e. fishing) interests have led to the development of its RAS (i.e. recirculating aquaculture systems) farming since the 1990’s49. Perca fluviatilis is among the most interesting species for the development of inland aquaculture in Europe49. However, despite its economic potential, the production is still limited. This is mainly due to major bottlenecks, especially in first-life stages, such as low growth rate, low survival rate, and high cannibalism rate49. This highlights the potential interest of re-starting new domestication programmes. An intraspecific differentiation was already showed for this species in standardised conditions (e.g. growth19,50, behaviour16, development51).
Biological material collection and pre-experiment rearing conditions
Population sampling and rearing conditions were adapted from Toomey et al.16. Egg ribbons (one ribbon corresponding to one female) were obtained during the May 2018 and May 2019 spawning seasons from four lakes (Appendix S1): Valkea-Müstajärvi (VAL; 2018; Finland; 61° 13′ 08″ N, 25° 07′ 05″ E), Iso-Valkjärvi (ISO; 2018; Finland; 60° 57′ 21″ N, 26° 13′ 3″ E), Geneva (GEN; 2019; France; 46° 22′ 7.20″ N, 6° 27′ 14.73″ E), and Balaton (BAL ; 2019 ; Hungary ; 46° 54′ 23.375″ N, 18° 2′ 43.119″ E). We chose these populations since a phenotypic differentiation is known between the Finnish and Geneva populations16 while genetic specificities of central Europe populations have been already observed52,53. After transportation, 13–19 egg ribbons per lake were incubated at the experimental platform of aquaculture (Unit of Animal Research and Functionality of Animal Products, University of Lorraine, Vandœuvre-lès-Nancy, France) at 13 °C in incubators (110 × 64 × 186 cm; one population per incubator to avoid potential disease transmission between populations, one to two incubators per population) containing nine racks each (45 × 7 × 12 cm). Each incubator had its own temperature control and recirculated water system (flow rate of 4 m3 h−1). Water was UV-sterilized. Temperature (13.0 ± 0.4 °C) and oxygen rate (10.0 ± 0.5 mg L−1) were checked daily while pH (8.0 ± 0.2) was monitored three times a week (± standard error). Ammonium and nitrite concentrations (lower than 0.05 mg L−1) were measured three times a week until hatching. Light intensity was 400 lx at the water surface. Photoperiod was 12L:12D (12 h of light and 12 h of darkness).
Experimental rearing protocol
Two independent experimental phases were performed: phase I from hatching until the end of weaning (i.e. transition from live feed to inert pellets; 26 days post-hatching, dph) and phase II from 27 dph until the end of nursery, at 60 dph. The larval period was split in two phases in order to ensure availability of larvae across the whole larval period since there is a very high mortality rate during first-life stages. Because wild egg ribbons are not available the same time for all populations (i.e. asynchronous spawning seasons) and in order to prevent potential pathogen transmission, all populations were reared in independent structures. Since there are increasing concerns about the epizootic disease Perhabdovirus in Europe49, all populations were tested for the occurrence of this virus (Laboratoire Département d’Analyses du Jura, Poligny, France). All results were negative to the presence of the Perhabdovirus.
Regarding phase I, larvae from the different egg ribbons of each population were mixed after hatching and transferred to three green (RGB: 137, 172, 118) internal-wall 71 L cylindro-conical tanks (three replicates per population; RAS) at a density of 50 larvae L−1. Photoperiod was 12L:12D (simulation of dawn and dusk for 30 min) and light intensity was 400 lx at the water surface. Temperature was gradually increased during the first 2 weeks to 20 °C (1 °C day−1). Larvae were hand-fed with newly hatched Artemia nauplii (Sep-Art, INVE; seven times a day, every 1 h 30 from 8.30 am to 5.30 pm) from 3 days post-hatching until at 16 dph, which corresponds to the beginning of the weaning (i.e. transition from live feed to inert dry artificial diet) period. At 16 dph, Artemia ration was decreased by 25% every 3 days and dry feed ration (BioMar, 300 µm until 21 dph, then 500 µm) was increased by the same ratio. After 25 dph, larvae were fed with dry feed ad libitum (BioMar 500 µm, then 700 µm at 44 dph until 60 dph). At 26 dph, the larvae left in the cylindro-conical tanks were removed in order to start phase II.
Regarding phase II, after hatching, larvae left (i.e. not sampled for phase I) were held in 2 m3 tanks (RAS). The same conditions as phase I were used (temperature, light intensity, feeding, and photoperiod regimes). At 27 dph, these larvae were transferred to the three cylindro-conical tanks in order to start phase II at a density of 19 larvae L−1. Light intensity was 80 lx at water surface, all else remaining the same as phase I (except for density).
During the two phases, oxygen concentration (8.5 ± 2.3 mg L−1) and temperature (20.0 ± 0.6 °C) were checked daily in all tanks (± standard error). Ammonium and nitrite concentrations (means inferior to 0.05 mg L−1) and pH (7.7 ± 0.6 mg L−1) were monitored three times a week (± standard error). Tanks were cleaned daily after first feeding and dead individuals were removed every morning.
Larviculture performance assessment
A trait is considered in this study at the replicate level. Each trait value is obtained from the mean of individual values.
Survival and development traits
Survival rate is one of the key traits contributing to the success of larviculture production49,54. Because of fast decomposition of dead larvae, it was not possible to count dead larvae during the first 5 days post-hatching. Consequently, the daily count of dead larvae was only performed in phase II. Therefore, survival rate in phase I was calculated for each cylindro-conical tank thanks to the final count of larvae using the following formula: Nf × 100/(Ni − Ns), where Nf is the final number of fish counted at the end of phase I, Ni the initial number of fish, and Ns the number of fish sampled along the phase (i.e. for behaviour experiments, see below). For phase II, the Bergot survival rate55 was used since it takes into account the number of fish removed for sampling and the daily mortality. Two traits related to the development of individuals and essential for larviculture were considered49: swim bladder inflation rate and deformity rate. Swim bladder inflation rate was estimated at the end of each experimental phase (following the protocol used in Jacquemond56; 20 g L−1 of sea salt and 70 mg L−1 of MS-222): 100 × (SB + /Nf) with SB + the number of larvae with swim bladder and Nf the final number of larvae. Deformity rate was estimated in the final counting of each experimental phase using the following formula: 100 × (Nm/Nf) with Nm the number of deformed larvae (only visible column deformities) and Nf the final number of larvae counted. Finally, the volume of the yolk sac was also evaluated at 1 day post-hatching since it reflects the quantity of nutritional reserves available before exogenous feeding49. It is calculated using the following formula: π/6 × YSL×YSH2, where YSL is the length of the yolk sac and YSH the height of the yolk sac57.
Behavioural traits
The ability of a biological unit to be efficiently produced in intensive conditions (i.e. intensive farming is an increasing trend in the aquaculture development) also depends on (1) inter-individual relationships, (2) inter-individual distances, and (3) activity16. Indeed, tolerance to conspecifics in a restricted area is essential for production since it can impact individual welfare58. Highlighting populations which present a cohesive group structure would be advantageous. Nevertheless, living in group is not costless because it can trigger aggressive behaviours which can lead to uneven competition for food, mortalities, stress, or immune suppression16. Therefore, both inter-individual distances and inter-individual interactions need to be considered. Finally, activity is also important since it contributes to the total energetic budget16. Furthermore, less active individuals could contribute to decrease the occurrence of inter-individual contacts and subsequent potential aggressive interactions.
Regarding aggressive interaction quantification, aggressiveness was calculated for phase II using the formula : 100 × (Ni − (Nf + Nd + Ns) + Nc)/(Nf − Ns) with Ni the initial number of larvae, Nf the final number of larvae, Nd the sum of dead larvae counted daily, Ns the number of sampled larvae, and Nc the number of truncated or enucleated (enucleation being a specific indicator of aggressiveness in perch16) larvae among the dead ones (not possible in phase I since it was not possible to count dead larvae during the first 5 days post-hatching due to fast decomposition; in addition, no truncated or enucleated individuals were recorded for phase I).
Regarding the evaluation of inter-individual distances and activity, the detailed protocol is available in Toomey et al.16. Briefly, for each population, three replicates for each cylindro-conical tank were performed (nine replicates per population) over 2 days for phase I (25 and 26 dph) and phase II (44 and 45 dph). For each population, 90 individuals (n = 30 per cylindro-conical tank, 10 individuals per replicate) were sampled and transferred to three aquaria (58 L; light intensity of 80 lx light intensity, 20 °C). After one night of acclimatisation, populations were tested per groups of ten individuals in circular arenas (30 cm diameter, 1.5 cm of water depth, 10 lx) to study inter-individual distances and activity16. After 30 min acclimatisation, individuals were filmed for 30 min. After the experiment, individuals were euthanized (overdose of MS-222) and kept in formalin 4% for later length measurements. Larvae tested in the circular arenas from ISO, VAL, BAL, and GEN were respectively 14.05 ± 0.55 mm, 12.90 ± 0.62 mm, 10.62 ± 0.47 mm, and 11.81 ± 1.01 mm during phase I and 26.74 ± 1.67 mm, 26.28 ± 1.99 mm, 19.24 ± 1.22 mm, and 12.26 ± 0.45 mm during phase II (± standard error). Analyses were performed using the ImageJ software59. Images were extracted from videos at 5-min interval (six images per video). For each image, coordinates of individuals were noted using the middle point between the eyes. The mean of inter-individual distances was evaluated per replicate. It corresponds to the mean of distances between a focal fish and all the other fish of the group and it is an indicator of the group cohesion. Detailed calculation is available in Colchen et al.60. Activity was analysed in ImageJ. Every 5 min, one image per second was extracted for six consecutive seconds. For each image, coordinates of each individual were noted. This allowed calculating distance swam every second during the 5 s. The mean allowed obtaining for each individual the mean distance swam per second. From these values, we were able to calculate an average activity per replicate.
Growth traits
Growth traits are important in larviculture production, more particularly the length at hatching, specific growth rate, and growth heterogeneity49. To evaluate these traits, 30 larvae per population (i.e. ten larvae per cylindro-conical tank) were sampled the first and last days of each experimental phase, euthanized with an overdose of MS-222, and kept in formalin 4%. For phases I and II, larvae were measured using ImageJ (± 0.01 mm). For phase II, larvae were also individually weighted (± 0.1 mg; not possible in phase I due to the imprecision of measure at 1 day post-hatching). Since specific growth rate (SGR) is a trait of interest at the end of larviculture, it was calculated only in phase II using the following formula: SGR = 100 × (ln(Xf) − ln(Xi)) × ∆T−1 where Xi and Xf are respectively the average initial and final weight/length and ∆T the duration of phase II. Final growth heterogeneity was calculated for both phases in the following way: CVXf/CVXi in which CV is the coefficient of variation (100 × standard deviation/mean) and Xi and Xf the initial and final weight/length, respectively.
Statistical analyses
All statistical analyses were performed in R 3.0.361 to assess if there were statistical differences (p value  More

Monthly climatic variables
Our dataset is based on simulations of monthly mean temperature (°C), precipitation (mm month−1), cloudiness (%), relative humidity (%) and wind speed (m s−1) of the HadCM3 general circulation model6,12,13. At a spatial grid resolution of 3.75° × 2.5°, these data cover the last 120,000 years in 72 snapshots (2,000 year time steps between 120,000 BP and 22,000 BP; 1,000 year time steps between 22,000 BP and the pre-industrial modern era), each representing climatic conditions averaged across a 30-year post-spin-up period. We denote these data by

$$begin{array}{c}{T}_{{rm{HadCM3}}}(m,t),;{P}_{{rm{HadCM3}}}(m,t),;{C}_{{rm{HadCM3}}}(m,t),\ {H}_{{rm{HadCM3}}}(m,t),;{W}_{{rm{HadCM3}}}(m,t),end{array}$$
(1)

where (m=1,ldots ,12) represents a given month, and (tin {T}_{{rm{120}}{rm{k}}}) represents a given one of the 72 points in time for which simulations are available, denoted ({T}_{{rm{120}}{rm{k}}}).
We downscaled and bias-corrected these data in two stages (Fig. 1). Both are based on variations of the Delta Method14, under which a high-resolution, bias-corrected reconstruction of climate at some time t in the past is obtained by applying the difference between modern-era low-resolution simulated and high-resolution observed climate – the correction term – to the simulated climate at time t. The Delta Method has previously been used to downscale and bias-correct palaeoclimate simulations, e.g. for the widely used WorldClim database9. A recent evaluation of three methods commonly used for bias-correction and downscaling15 showed that the Delta Method reduces the difference between climate simulation data and empirical palaeoclimatic reconstructions overall more effectively than two alternative methods (statistical downscaling using Generalised Additive Models, and Quantile Mapping). We therefore used this approach for generating our dataset.
Fig. 1

Method of reconstructing high-resolution climate. Yellow boxes represent raw simulated and observed data, the dark blue box represents the final data. Maps, showing modern-era climate, correspond to the datasets represented by the bottom three boxes.

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Downscaling to ~1° resolution
A key limitation of the Delta Method is that it assumes the modern-era correction term to be representative of past correction terms15. This assumption is substantially relaxed in the Dynamic Delta Method used in the first stage of our approach to downscale the data in Eq. (1) to a ~1° resolution. This involves the use of a set of high-resolution climate simulations that were run for a smaller but climatically diverse subset of ({T}_{120k}). Simulations at this resolution are very computationally expensive, and therefore running substantially larger sets of simulations is not feasible; however, these selected data can be very effectively used to generate a suitable time-dependent correction term for each (tin {T}_{120k}). In this way, we are able to increase the resolution of the original climate simulations by a factor of ~9, while simultaneously allowing for temporal variability in the correction term. In the following, we detail the approach.
We used high-resolution simulations of the same variables as in Eq. (1) from the HadAM3H model13,16,17, available at a 1.25° × 0.83° resolution for the last 21,000 years in 9 snapshots (2,000 year time steps between 12,000 BP and 6,000 BP; 3,000 year time steps otherwise). We denote these by

$$begin{array}{c}{T}_{{rm{HadAM3H}}}(m,t),;{P}_{{rm{HadAM3H}}}(m,t),;{C}_{{rm{HadAM3H}}}(m,t),\ {H}_{{rm{HadAM3H}}}(m,t),;{W}_{{rm{HadAM3H}}}(m,t),end{array}$$

respectively, where (tin {T}_{21k}), represents a given one of the 9 points in time for which simulations are available, denoted ({T}_{{rm{21}}{rm{k}}}).
For each variable (Xin {T,P,C,H,W}), we considered the differences between the medium- and the high-resolution data at times (tin {T}_{21k}) for which both are available,

$$Delta {X}_{{rm{HadAM3H}}}^{{rm{HadCM3}}}(m,t),:={X}_{{rm{HadAM3H}}}(m,t)-{X}_{{rm{HadCM3}}}^{ boxplus }(m,t),$$

where the ( boxplus )-notation indicates that the coarser-resolution data was interpolated to the grid of the higher-resolution data. For this, we used an Akima cubic Hermite interpolant18, which (unlike a bilinear interpolant) is smooth but (unlike a bicubic interpolant) avoids potential overshoots. For each (tin {T}_{120k}) and each (tau in {T}_{21k}),

$${X}_{{rm{HadCM3}}}^{ boxplus }(m,t)+Delta {X}_{{rm{HadAM3H}}}^{{rm{HadCM3}}}(m,tau )$$
(2)

provides a 1.25° × 0.83° resolution downscaled version of the data ({X}_{{rm{HadCM3}}}(m,t)) in Eq. (1). The same is true, more generally, for any weighted linear combination of the Δ({X}_{{rm{HadAM3H}}}^{{rm{HadCM3}}}(m,tau )), which is the approach taken here, yielding

$$X{{prime} }_{ sim {1}^{circ }}(m,t),:={X}_{{rm{HadCM3}}}^{ boxplus }(m,t)+mathop{underbrace{sum _{tau in {T}_{21k}}w(t,tau )cdot Delta {X}_{{rm{HadAM3H}}}^{{rm{HadCM3}}}(m,tau )}}limits_{{rm{time-variable}},{rm{correction}},{rm{term}}},$$
(3)

where ({sum }_{tau in {T}_{21k}}mathop{overbrace{w(t,tau )}}limits^{ge 0}=1) for any given (tin {T}_{125k}). We discuss the choice of an additive approach for all climatic variables later on. Crucially, in contrast to the classical Delta Method – which, for all (tin {T}_{125k}), would correspond to (w(t,{rm{present}},{rm{day}})=1) and (w(t,tau )=0) otherwise (cf. Eq. (5)) –, the resolution correction term that is added to ({X}_{{rm{HadCM3}}}^{ boxplus }(m,t)) in Eq. (3) need not be constant over time. Instead, the high-resolution heterogeneities that are applied to the medium-resolution HadCM3 data are chosen from the broad range of patterns simulated for ({T}_{21k}). The strength of this approach lies in the fact that the last 21,000 years account for a substantial portion of the range of climatic conditions present during the whole Late Quaternary. Thus, by choosing the weights (w(t,tau )) for a given time (tin {T}_{125k}) appropriately, we can construct a ({T}_{21k})-data-based correction term corresponding to a climatic state that is, in a sense yet to be specified, close to the climatic state at time t. Here, we used atmospheric CO2 concentration, a key determinant of the global climatic state19, as the metric according to which the (w(t,tau )) are chosen; i.e. we assigned a higher weight to Δ({X}_{{rm{HadAM3H}}}^{{rm{HadCM3}}}(m,tau )) the closer the CO2 level at time (tau ) was to that at time t. Specifically, we used

$$w{prime} (t,tau )=frac{1}{{({{rm{CO}}}_{2}(t)-{{rm{CO}}}_{2}(tau ))}^{2}},$$

and rescaled these to (w(t,tau )=frac{w{prime} (t,tau )}{{sum }_{tau in {T}_{21k}}w{prime} (t,tau )}) (Supplementary Fig. 1). In the special case of (tin {T}_{21k}), we have (w(t,t)=1) and (w(t,tau )=0) for (tau ne t), for which Eq. (3) simplifies to

$$X{{prime} }_{ sim {1}^{circ }}(m,t)={X}_{{rm{HadAM3H}}}(m,t)quad {rm{for}},{rm{all}},tin {T}_{21k}.$$

Formally, the correction term in Eq. (3) corresponds to an inverse square distance interpolation of the Δ({X}_{{rm{HadAM3H}}}^{{rm{HadCM3}}}) with respect to CO220. We also note that, for our choice of (w(t,tau )), the correction term is a smooth function of t, as would be desired. In particular, this would not the case for the approach in Eq. (2) (unless (tau ) is the same for all (tin {T}_{125k})).
The additive approach in Eq. (3) does not by itself ensure that the derived precipitation, relative humidity, cloudiness and wind speed are non-negative and that relative humidity and cloudiness do not exceed 100% across all points in time and space. We therefore capped values at the appropriate bounds, and obtain

$$begin{array}{lll}{T}_{ sim {1}^{circ }}(m,t) & := & T{{prime} }_{ sim {1}^{circ }}(m,t),\ {P}_{ sim {1}^{circ }}(m,t) & := & {rm{max }}left(0,P{{prime} }_{ sim {1}^{circ }}(m,t)right),\ {C}_{ sim {1}^{circ }}(m,t) & := & {rm{min }}left(100 % ,{rm{max }}(0 % ,C{{prime} }_{ sim {1}^{circ }}(m,t))right),\ {H}_{ sim {1}^{circ }}(m,t) & := & {rm{min }}left(100 % ,{rm{max }}(0 % ,H{{prime} }_{ sim {1}^{circ }}(m,t))right),\ {W}_{ sim {1}^{circ }}(m,t) & := & {rm{max }}left(0,W{{prime} }_{ sim {1}^{circ }}(m,t)right).end{array}$$
(4)

Supplementary Fig. 2 shows that this step only affects a very small number of data points, whose values are otherwise very close to the relevant bound.
Bias-correction and downscaling to 0.5° resolution
In the second stage of our approach, we applied the classical Delta Method to the previously downscaled simulation data. Similar to the approach in Eq. (3), this is achieved by applying a correction term, which is now given by the difference between present-era high-resolution observational climate and coarser-resolution simulated climate, to past simulated climate. This further increases the resolution and removes remaining biases in the data in Eq. (4).
Since our present-era simulation data correspond to pre-industrial conditions (280 ppm atmospheric CO2 concentration)6,12,13, it would be desirable for the observational dataset used in this step to be approximately representative of these conditions as well, so that the correction term can be computed based on the simulated and observed climate of a similar underlying scenario. There is generally a trade-off between the quality of observation-based global climate datasets of recent decades, and the extent to which they reflect anthropogenic climate change (which, by design, is not captured in our simulated data) – both of which increase towards the present. Fortunately, however, significant advances in interpolation methods21,22,23 have produced high-quality gridded datasets of global climatic conditions reaching as far back as the early 20th century23. Thus, here we used 0.5° resolution observational data representing 1901–1930 averages (~300 ppm atmospheric CO2) of terrestrial monthly temperature, precipitation and cloudiness23. For relative humidity and wind speed, we used a global data representing 1961–1990 average (~330 ppm atmospheric CO2) monthly values24 due to a lack of earlier datasets. We denote the data by

$${T}_{{rm{obs}}}(m,0),;{P}_{{rm{obs}}}(m,0),;{C}_{{rm{obs}}}(m,0),;{H}_{{rm{obs}}}(m,0),;{W}_{{rm{obs}}}(m,0).$$

We extrapolated these maps to current non-land grid cells using an inverse distance weighting approach so as to be able to use the Delta Method at times of lower sea level. The resulting data were used to bias-correct and further downscale the ~1° data in Eq. (3) to a 0.5° grid resolution via

$$X{{prime} }_{0.{5}^{circ }}(m,t),:={X}_{ sim {1}^{circ }}^{ boxplus }(m,t)+mathop{underbrace{{X}_{{rm{obs}}}(m,0)-{X}_{ sim {1}^{circ }}^{ boxplus }(m,0)}}limits_{{rm{correction}},{rm{term}}},$$
(5)

where (Xin {T,P,C,H,W}). In particular, the data for the present are identical to the empirically observed climate,

$$X{{prime} }_{0.{5}^{circ }}(m,0)={X}_{{rm{obs}}}(m,0).$$

Finally, we again capped values at the appropriate bounds, and obtained

$$begin{array}{lll}{T}_{0.{5}^{circ }}(m,t) & := & T{{prime} }_{0.{5}^{circ }}(m,t),\ {P}_{0.{5}^{circ }}(m,t) & := & {rm{max }}left(0,P{{prime} }_{0.{5}^{circ }}(m,t)right),\ {C}_{0.{5}^{circ }}(m,t) & := & {rm{min }}left(100 % ,{rm{max }}(0 % ,C{{prime} }_{0.{5}^{circ }}(m,t))right),\ {H}_{0.{5}^{circ }}(m,t) & := & {rm{min }}left(100 % ,{rm{max }}(0 % ,H{{prime} }_{0.{5}^{circ }}(m,t))right),\ {W}_{0.{5}^{circ }}(m,t) & := & {rm{max }}left(0,W{{prime} }_{0.{5}^{circ }}(m,t)right).end{array}$$
(6a)

Similar as in the analogous step in the first stage of our approach (Eq. (4)), only a relatively small number of data points is affected by the capping; their values are reasonably close to the relevant bounds, and their frequency decreases sharply with increasing distance to the bounds (Supplementary Fig. 2).
In principle, capping values, where necessary, can be circumvented by suitably transforming the relevant variable first, then applying the additive Delta Method, and back-transforming the result. In the case of precipitation, for example, a log-transformation is sometimes used, which is mathematically equivalent to a multiplicative Delta Method, in which low-resolution past simulated data is multiplied by the relative difference between high- and low-resolution modern-era data14; thus, instead of Eq. (5), we would have ({P}_{0.{5}^{circ }}(m,t),:={P}_{ sim {1}^{circ }}^{ boxplus }(m,t)cdot frac{{P}_{{rm{obs}}}(m,0)}{{P}_{ sim {1}^{circ }}^{ boxplus }(m,0)}). However, whilst this approach ensures non-negative values, it has three important drawbacks. First, if present-era observed precipitation in a certain month and grid cell is zero, i.e. ({P}_{{rm{obs}}}(m,0)=0), then ({P}_{0.{5}^{circ }}(m,t)=0) at all points in time, t, irrespectively of the simulated climate change signal. Specifically, this makes it impossible for current extreme desert areas to be wetter at any point in the past. Second, if present-era simulated precipitation in a grid cell is very low (or indeed identical to zero), i.e. ({P}_{ sim {1}^{circ }}^{ boxplus }(m,0)approx 0), then ({P}_{0.{5}^{circ }}(m,t)) can increase beyond all bounds. Very arid locations are particularly prone to this effect, which can generate highly improbable precipitation patterns for the past. In our scenario of generating global maps for a total of 864 individual months, this lack of robustness of the multiplicative Delta Method would be difficult to handle. Third, the multiplicative Delta Method is not self-consistent: applying it to the sum of simulated monthly precipitation does not produce the same result as applying it to simulated monthly precipitation first and then taking the sum of these values. The natural equivalent of the log-transformation for precipitation is the logit-transformation for cloudiness and relative humidity, however, this approach suffers from the same drawbacks.
Minimum and maximum annual temperature
Diurnal temperature data are not included in the available HadCM3 and HadAM3H simulation outputs. We therefore used the following approach to estimate minimum and maximum annual temperatures. Based on the monthly HadCM3 and HadAM3H temperature data, we created maps of the mean temperature of the coldest and the warmest month. In the same way as described above, we used these data to reconstruct the mean temperature of the coldest and warmest month at a 1.25° × 0.83° resolution by means of the Dynamic Delta Method, yielding

$${T}_{ sim {1}^{circ }}^{{rm{coldest}},{rm{month}}}(t),{rm{and}},{T}_{ sim {1}^{circ }}^{{rm{warmest}},{rm{month}}}(t),$$

for (tin {T}_{120k}). We then used observation-based 0.5° resolution global datasets of modern-era (1901–1930 average) minimum and maximum annual temperature23, denoted

$${T}_{{rm{obs}}}^{{rm{min }}}(0),{rm{and}},{T}_{{rm{obs}}}^{{rm{max }}}(0),$$

to estimate past minimum and maximum annual temperature as

$$begin{array}{lll}{T}_{0.{5}^{circ }}^{{rm{min }}}(t) & := & {T}_{ sim {1}^{circ }}^{{rm{coldest}},{rm{month}}, boxplus }(t)+{T}_{{rm{obs}}}^{{rm{min }}}(0)-{T}_{ sim {1}^{circ }}^{{rm{coldest}},{rm{month}}, boxplus }(0),\ {T}_{0.{5}^{circ }}^{{rm{max }}}(t) & := & {T}_{ sim {1}^{circ }}^{{rm{warmest}},{rm{month}}, boxplus }(t)+{T}_{{rm{obs}}}^{{rm{max }}}(0)-{T}_{ sim {1}^{circ }}^{{rm{warmest}},{rm{month}}, boxplus }(0),end{array}$$
(6b)

respectively. This approach assumes that the difference between past and present mean temperature of the coldest (warmest) month is similar to the difference between the past and present temperature of the coldest (warmest) day. Instrumental data of the recent past suggest that this assumption is well justified across space (Supplementary Fig. 3).
Land configuration
We used a reconstruction of mean global sea level25 and a global elevation and bathymetry map26, interpolated to a 0.5° resolution grid, to create land configuration maps for the last 120,000 years. Maps of terrestrial climate through time were obtained by cropping the global data in Eq. (6a and b) to the appropriate land masks. Values in non-land grid cells were set to missing values, except in the case of below-sea-level inland grid cells, such as the Aral, Caspian and Dead sea.
Bioclimatic data, net primary productivity, leaf area index, biome
Based on our reconstructions of minimum and maximum annual temperature, and monthly temperature and precipitation, we derived 17 bioclimatic variables27 listed in Table 1. In addition, we used the Biome4 global vegetation model28 to compute net primary productivity, leaf area index and biome type at a 0.5° resolution for all (tin {T}_{120k}), using reconstructed minimum annual temperature, and monthly temperature, precipitation and cloudiness. Similar to a previous approach21, we converted cloudiness to the percent of possible sunshine (required by Biome4) by using a standard conversion table and applying an additional latitude- and month-specific correction. Since Biome4 estimates ice biomes only based on climatic conditions and not ice sheet data, it can underestimate the spatial extent of ice. We therefore changed simulated non-ice biomes to ice, and set net primary production and leaf area index to 0, in grid cells covered by ice sheets according to the ICE-6g dataset29 at the relevant points in time. Whilst our data represent potential natural biomes, and as such do not account for local anthropogenic land use, maps of actual land cover can readily be generated by superimposing our data with available reconstructions of global land use during the Holocene30. More

Distinctive temperature responses along a substrate gradient
Within the temperature range of ~14 to ~34 °C in our incubations, the observed AORs at the ambient substrate level (AORambient, see Methods) varied over 3 orders of magnitude, from 0.5 to ~4000 nM d−1, across a wide spectrum of ambient ammonium levels ranging from 14 nM to 96 μM (Fig. 1). Three different types of temperature response of AORambient patterns at estuarine, shelf, and sea basin stations were observed: (I) a positive response with a Topt of ≥34 °C (Fig. 1a, b); (II) a negative response, which has never been reported before, with a Topt of ≤14 °C (Fig. 1d–f); and (III) a dome-shaped response with a Topt of 20–29 °C (Fig. 1c, g–i).
The Type I pattern was observed at two of the three estuarine stations (JLR1 and JLR2, Fig. 1a, b) where ammonium concentrations were high (≥24 μM), and the AOR increased linearly as the temperature increased from 14 to 34 °C. In these cases, the Topt was equal to or higher than the maximum experimental temperature of 34 °C (Fig. 1a, b). The Type II pattern was observed at the shelf stations (N1, M1, and M2), where NH4+ concentrations ranged from 45 to 550 nM (Fig. 1d–f). In contrast to the Type I pattern, the Topt of the Type II pattern was equal to or lower than the minimum experimental temperature of 14 °C, showing a continuously decreasing AOR as temperature increased. The Type III pattern was observed at station JLR3 (outer estuary), N2 (shelf), N3 and J1 (basin), for which the Topt of the AOR varied from 20 to 29 °C, with rates decreasing toward both higher and lower temperatures (Fig. 1c, g–i). The NH4+ concentrations of the Type III stations ranged from 14 to 5000 nM. Nevertheless, the highest Topt values were observed at coastal sites with the highest ambient ammonium concentrations (Fig. 1).
Substrate regulates AOR and its thermal optimum temperature
For those stations with low ammonium concentrations, the AOR at in situ temperature increased when the substrate was enriched (AORenriched, additions of 2000 nM 15NH4+) (Fig. 1f, i). Meanwhile, the Topt of the AOR shifted significantly toward higher values (t test, p  Q10Vmax (Supplementary Fig. 2). This criterion was fulfilled in both J1 and JLR4 cases (Fig. 2c–f). We see the positive shift of Topt due to the ammonium addition (up to ~100 nM at J1 station and up to ~10 μM at JLR4) can be closely predicted (Fig. 3c, d; Supplementary Fig. 2). Overall, the DAMM model successfully predicts the entire thermal response curve, including rates and Topt, except when the manipulated temperatures exceed Topt-sat (Fig. 3; Supplementary Fig. 2). AOR drops significantly when temperature is greater than the Topt-sat, so heat-impaired biological enzyme activity27,28 might result in deviations from the relationship between Vmax (Km) values and temperature from the Arrhenius law.
Fig. 3: Validation plot for the rate predictions and observations.

a, b Scatter plot of the predicted rates via the Dual Arrhenius and Michaelis–Menten kinetics model (DAMM model) and the measured rates under different substrate concentrations and temperatures (below the optimum temperature in substrate-saturated conditions, Topt-sat). Linear regressions between the model predictions and the measurements are presented (two-sided t test was used to generate the p value (95% confidence) to measure the strength of correlation coefficient. p values are uncorrected). c, d The rate patterns (dots) against temperature under different substrate concentrations. Curves stand for the predicted rates derived from the DAMM model and the symbols represent the measured rates. The shades denote the uncertainty of model prediction. The dashed black vertical lines represent the Topt-sat. The measured rates in (a, c) are presented as mean values, instead of standard deviation the given bars indicate the variation range of two independent experiments. The measured rates in (b, d) and the predicted rates in (a–d) are expressed as the mean values ± SD (n = 10 in (a, c); n = 48 in (b, d); independent experiments).

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The substrate-dependent thermal optimum is attributable to the effect of temperature on biochemical kinetics and the structural stability of the enzymes. Increasing temperature promotes catalytic rate, thus, Vmax increases due to increasing kinetic energy of reactants and rates of collision, as well as higher structural flexibility of enzymes27,29. However, higher structural flexibility (lower stability) also results in active sites with a reduced ability for ligand recognition and binding, therefore, lower kinetic efficiency. Accordingly, one important physiological response of an organism to rising temperature will be a reduction in substrate affinity (Supplementary Table 2), and thus higher substrate demands (i.e. higher Km value)25,29,30,31. In other words, higher substrate levels help to compensate for enzyme structural stability losses and so promote growth rates at higher temperature. Note that some other microbes may respond differently to temperature, with Q10Km ≤ Q10Vmax for instance. This may lead to predictable yet unidirectional rate increases in response to warming (without substrate-regulated Topt) until the Topt-sat is reached, regardless of substrate changes.
Similarly, nutrient-dependent Topt has been reported for phytoplankton growth in pure cultures previously. For instance, Thomas et al.32 indicated that the Topt for growth of a marine diatom was a saturating function of major nutrient (nitrate and phosphate) concentration, and that the Topt could decrease by 3–6 °C at low concentrations relative to that at saturated nutrient levels. In addition to studies of pure cultures, field studies have also suggested that organisms may tolerate higher temperature stresses when nutrients are more abundant. For example, kelp (Laminaria saccarina) with high nitrogen reserves have more capacity for thermal adaptation33, while corals with symbionts limited by phosphate are more susceptible to heat-induced bleaching34. Although these examples are functionally and taxonomically distant from AOA and ammonia-oxidizing bacteria (AOB), strong similarities in substrate/nutrient regulation characteristics may imply a similar mechanism of enzymatic thermal responses between chemoautotrophs and photoautotrophs.
Nevertheless, the higher thermal optimum of AO in the estuarine system (e.g., JRL1, JLR2, and JLR3) than in the offshore environment (e.g., N3 and J1) can be explained by a substrate-regulated Topt. Note that field AOR represents explicitly the collective activity of the AO community composed of AOA and AOB, which may have distinctive thermal tolerances and affinities for substrate. Therefore, community structure very likely plays a role in modulating the thermal response patterns of community AOR in the field environments, in addition to substrate concentration.
Rate proportion and community thermal optimum
To further examine to what extent the community structure (proportions of AOA and AOB) might shape the thermal response patterns of community AOR observed in the field, we added allylthiourea (ATU) to inhibit the activity of AOB for rate discrimination (see Methods; Supplementary Discussions). Results showed that the inhibitory efficiency of AOR was gradually reduced with increasing offshore distance (Fig. 4). That is, from the estuary (JLR4, JLR1, JLR2, and JLR3) to the shelf (N1 and N2) and the sea basin (N3), the relative contribution of AOB to the community AOR dropped from as high as ~100% in the upper estuary down to ~70% in the shelf transition zone, and near 0% in the basin. Meanwhile, the AOA/AOB gene copies data (see Supplementary Methods) from estuary to sea basin (Fig. 4) also clearly show that the abundance of AOA relative to AOB increased exponentially with increasing offshore distance. A similar offshore pattern of community distribution was also observed in other regions, such as from the Pearl River estuary to the South China Sea35, and from the freshwater region of the Chesapeake Bay to the coastal and open ocean water column36. This pattern suggests that AOB strongly prefer substrate-replete niches, and vice versa for AOA20,37, agreeing well with our M–M experimental data that the substrate saturation condition for AOB-dominated water at JLR4 was several orders of magnitude higher than that for AOA-dominated water from J1 (Supplementary Table 2). The Km values of AOB in JLR4 varied from 7 to 55 μM in accordance with varying temperatures from 10 to 37 °C, while the Km values of AOA in J1 varied from 13 to 44 nM over a similar temperature range (Supplementary Table 2). Results were supportive of previous pure culture and field studies which showed the minimum ammonium demand for AOB is >1 μM and Km values range from 28 to 4000 μM38,39,40,41, while minimum ammonium demand and Km value for AOA are  Q10Vmax, which also results in a reduction in α during warming for both AOA and AOB. Yet, the relative reduction in AOA specific affinity as temperature increases is more significant (Fig. 5a), suggesting AOAs are more competitive in low temperature environments relative to AOBs, and so may not be favored in a warming ocean. On the other hand, the specific affinity of AOBs is insensitive to temperature change, suggesting their adaptation to nearshore environments with greater temperature fluctuation. The seaward gradient in temperature fluctuations and ammonium concentrations determine the nitrifier community, thus, thermal response pattern of community AOR observed in the field.
Fig. 5: Thermal response projections in near- and offshore regions.

a The thermal responses of specific affinity at the J1 and JLR4 stations. Data are expressed as the mean values ± SD (n = 10 in J1 station; n = 48 in JLR4 station; independent experiments). b Normalized warming-driven variations in ammonia oxidation rates. Rate changed (%) is relative to the ammonia oxidation rate (AOR) at in situ temperature. The mean increase (nearshore hollow dots) is denoted by the dashed line and the mean reduction (offshore, solid dots) is denoted by the solid black line. The shaded area represents the 4 °C increase in temperature mentioned in the IPCC study. Note that the stations where the surface salinities are lower than 32 are classified as nearshore station, and the others are classified as offshore stations. The data in (b) are presented as mean values, instead of standard deviation the given bars indicate the variation range of two independent experiments.

Full size image

To predict the trends of AOR in different geographic spaces in warming ocean, we compile the available marine AOR data to examine the AOR changes empirically. If we assume the biogeographic distribution of AO community remains unchanged and consider solely the warming effect on AOR relative to the onsite temperature, we found the thermal responses of AOR in nearshore and offshore are quite different (Fig. 5b). More specifically, the higher Topt of these AO communities in nearshore regimes allows ocean warming to promote coastal AOR when the temperature change increment is More

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Forest sites and soil sampling
The sites used in this study are part of a permanent network of existing mature forest plots across Europe established in 2011–2012 (see Baeten et al.54 for detailed descriptions). We included four sites ranging over a large climatic gradient: North Karelia (Finland), Białowieża (Poland), Râşca (Romania), and Colline Metallifere (Italy), which correspond to typical boreal forests, hemiboreal mixed broadleaved-coniferous, montane mixed beech, and Mediterranean thermophilous, respectively (Supplementary Table 1, Supplementary Fig. 1). At each site, we selected 30 m × 30 m forest plots dominated by either one tree species (monospecific stands) or by three co-dominating tree species, hereafter referred to as mixed stands, resulting in a total of 34 species combinations (species were considered co-dominant if they composed >15% of the stand; see Supplementary Data file 1 for plot and tree species information). Each site differed in total species numbers, species identity, and species combinations (Supplementary Table 1). There were two replicates per tree species for the monospecific plots of each site, except for Picea abies and Quercus robur, which were only replicated once and Betula pendula which had no mono-specific plot in Białowieża. There was a minimum of three mixed species plot replicates per site that were composed of any of the target species present at the site (Supplementary Table 1), i.e., the replicate mixed plots at each site did not necessarily have the same tree species combinations. There were 64 plots in total. The sampling design with the total plot number, their distribution over four forest ecosystems, and including a wide range of tree species is well suited to address the generality of our hypothesis that microbial responses to DRW cycles are modified by tree species mixing but poorly suited to identify site-specific patterns with plot numbers too limiting within specific sites for robust testing.
Within each plot, we selected five tree triplets, a triplet being a triangle of three tree individuals within a maximum distance of 8 m from each other and no obstructing tree individuals within the triangle. Each triplet was composed of either the same species in the monospecific stands (monospecific triplet) or the three tree species present in the mixed stands (mixed triplet). At the estimated tree individual size weighted (based on individual diameter at breast height) center within the triangle, we collected five soil cores from the topsoil (10 cm deep, 5.3 cm diameter) after the litter layer had been removed. The five soil cores were spaced at roughly 35 cm from each other circling the center point (approximate sampled area 50 cm × 50 cm). A depth of 10 cm was selected because it is the standard topsoil sampling depth in soil ecology, has the highest soil microbial activity, and is under the most influence from the plant community19. All soil cores from each sampling location (i.e., tree triplet) within a plot were then sieved together through a 2 mm sieve and air-dried immediately after sampling for transportation and experiment preparation.
Experimental design
The soils collected from the 64 forest plots at the four sites were split into six replicate microcosms, yielding a total of 384 microcosms that were housed at the Montpellier European Ecotron CNRS in Montpellier, France. Each microcosm contained 95 g dry weight of soil in a glass vial (soil volume 51–72 ml; air volume 259–279 ml), initially incubated at 80% of water holding capacity (WHC) using deionized water, 25 °C, no light, and 40% relative air humidity (the vials were covered with Parafilm® to allow gas exchange but to prevent soil desiccation) for 3 weeks to reactivate the microbial community (Supplementary Fig. 3). After this acclimation period, half of the microcosms (192, i.e., n = 3 per plot) was assigned to a drying-rewetting (DRW) treatment and the other half (192, i.e., n = 3 per plot) to a control treatment. Maximum microbial mineralization activity appears to be reached between 60% and 80% WHC55. We chose 80% to ensure soils were entirely and homogeneously humid; very sandy soils with a low WHC, such as those from the Polish site, were not completely wetted at the typically chosen 60% WHC. Each treatment replicate was housed in a 2 m3 individual growth chamber (n = 6). Within each chamber, the microcosms were randomly distributed on a single shelf and re-randomized weekly. The DRW treatment was defined as two DRW cycles while the soils in the control treatment were maintained at 80% WHC throughout the experiment (Supplementary Fig. 3). Water content was adjusted gravimetrically 2–3 times a week.
Due to the large latitudinal distribution and varying soil and climate conditions of the sites (Supplementary Table 1), the soil microbial communities do not necessarily have the same degree of drought history and adaptation56. We therefore applied a site-specific drought treatment representative of each of the four study sites, i.e., site-specific drought intensity and duration. We used the permanent wilting point as a water stress threshold indicator since there is not a known microbial equivalent. The permanent wilting point was measured using a pressure plate extractor (1500F2, Soilmoisture Equipment Corp., Santa Barbara, USA) at pF 4.2 (15.5 bar) for the plots with the fastest and slowest drying soils of each site. The soil drying speed, i.e., the number of days it took for the soil to dry from 80% WHC down to constant weight, was measured gravimetrically for each plot using a subsample of soil that was subsequently excluded from the experiment. We then averaged the permanent wilting point values per site and designated this average as the drought intensity: Colline Metallifere 11% H2O g−1 dry soil, Râşca 30%, Białowieża 12%, and North Karelia 12%. The beginning of the drought was considered the moment the soil water content arrived at this threshold. The drought duration was calculated using the forest drought history data from Grossiord et al.56 as the average annual number of days the relative extractable water (REW) dropped below 0.2 (unitless) over the 1997–2010 period. REW is the ratio of available soil water to maximum extractable water (i.e., WHC), ranging between the field capacity (REW 1.0) and the permanent wilting point (REW 0.0)56. Plants are in non-water limited conditions when REW is >0.4 and water limited when REW is 2 mm diameter) and fine roots (≤2 mm in diameter). Fine roots were further separated into tree and understory roots. Tree fine roots were further divided into dead (which are hollow, brittle, and dark-colored) and live fine roots, which were then sorted by species (based on distinct color, architecture, morphology, and mycorrhizal types) and subsequently further divided based on their functions into absorptive and transport roots66. Ectomycorrhizal root tips were counted on absorptive tree roots using a binocular. All absorptive tree fine-root samples were scanned with a flat-bed scanner (resolution of 800 dpi) and scans were then analyzed using WinRhizo (Regent Instruments, Quebec, Canada, 2009) to quantify root length, surface area, volume, and diameter. Coarse root samples were also scanned to obtain coarse root volume, which was used together with the stone mass to calculate fine-earth volume (cm−3) of each soil sample. Root samples were dried (minimum 72 h, 40 °C) and weighed. Carbon and nitrogen concentrations of milled absorptive fine-root samples were measured for samples pooled at the plot level using dry combustion (Elementar Vario El Cube). Absorptive root analysis results are provided in Supplementary Table 2. We chose absorptive root traits rather than the commonly used leaf traits to characterize functional trait characteristics of tree communities, because the majority of soil microorganisms are intimately associated to the rhizosphere and thus root traits67. CWM is a measure of the relative species abundance weighted trait values. FDis is a measure of the abundance weighted mean distance between the “trait space’ of individual species. Both indices were calculated with the same standard root chemical and morphological traits (Supplementary Table 2) using the R function ‘dbFD’ in the FD package (version 1.0-1268). Due to difficulties in differentiating between Quercus species in root samples from some of the Italian plots, we were unable to determine mean absorptive root trait values at the plot level. We therefore used mean root trait values at the site level calculated from the mono-specific stands. Although the root trait values were not at the plot level, we were still able to determine the CWM and FDis indices at plot level since the root traits values were reported to tree species relative abundance in each plot. The relative abundance of each tree species was calculated using the basal areas of the tree individuals used in the five plot tree triplets (three tree individuals per tree triplet). Within each plot, the basal areas of a tree species (including five or fifteen tree individuals depending on whether the plot was mixed or mono-specific, respectively) were summed and then reported to the total basal area of the 15 tree individual, giving the relative basal area of each tree species within each plot. In order to synthesize this data, we incorporated them in a principal component analysis (PCA) and extracted the first axis scores (explaining 52.8% of the variance; Supplementary Fig. 2). Although the evidence supporting a universal root economics spectrum (RES) for woody species is inconsistent69,70,71, we consider our PCA1 axis as an acquisitive to conservative trait gradient with lower scores represented acquisitive root traits (high N content, specific root length, and ectomycorrhizal colonization intensity) and higher scores represented conservative traits (large diameter and high tissue density). The FDis was calculated following Laliberté & Legendre64 based on all traits at the plot level. The mono-specific stands had a FDis value of zero, which limits FDis variability for half of the plots. Accordingly, there was one single FDis value per plot that was used in our statistical analyses.
Since soil microbial resistance and recovery are tied to soil parameters and resource availability17,18, we also included major topsoil parameters (0–10 cm) known to affect microbial activity and/or community composition (Supplementary Table 2) measured previously during the FunDivEurope project54 at the plot level. Similar to the CWM absorptive root traits, we incorporated the topsoil variables into a PCA using the function ‘prcomp’ from the factoextra package (version 1.0.662) and extracted the first axis scores (explaining 52.5% of the variance; Supplementary Fig. 2) for a synthetic soil parameter measure for each individual plot. High PC1 scores are associated with higher pH, carbon content, and clay content and lower bulk density, the inverse is correlated with low PC1 scores.
We used generalized mixed-effects linear models (two-sided) using the lme4 package (version 1.1–2172) to assess the effects of the DRW treatment and the influence of the tree species number on microbial C and N-related parameters. The root FDis, root CWM PC1, and soil PC1 variables were included with the treatment × tree species interaction as explanatory variables. For the response variables (instantaneous CO2 and N2O fluxes measured five times over the experiment and cumulative fluxes, DOC, and TDN leaching, qCO2, and resistance and recovery indices), extreme values were removed (±3 times the IQR of all values for each variable). The soil collection site and plot as well as the growth chambers used for the incubation were included as random variables with plot nested within site. We did not include any climatic variables from the different sites, because they were highly correlated to site, which was already a random effect in the model. The model structure was as follows: response variable ~ Root FDis + Root CWM PC1 + Soil PCA axis + Treatment * Tree species number * Flux measurement time + (1|Chamber) + (1 | Site/Plot). The “Flux measurement time” variable, which identifies the times the five flux measurements were taken (i.e., beginning, drought 1, rewetting 1, drought 2, rewetting 2; Supplementary Fig. 3), was used only in the models that looked at the temporal dynamics of CO2 and N2O fluxes. For the analysis of resistance and recovery indices, we did not keep the “Treatment” variable in the model since these indices were calculated using both the DRW and control treatment results (see above). Additionally, for the resistance and recovery indices, instead of a “Flux measurement time” variable, a “Cycle” variable was included to distinguish the microbial activity resistance and recovery of the first and second cycles; the “Cycle” result indicates the change between the first and second cycle. Model residuals were plotted to test for normality, and data was transformed (log2 or BoxCox) when normality was not met. We also verified for data homogeneity and model probability (Q–Q plots). In order to identify the most parsimonious model we used the R software (version 3.5.3) and the “dredge” function in the MuMIn package (version 1.43.673) which uses the lowest Akaike information criteria (AIC) to rank all possible models with all possible combinations of the explanatory variables in the full model.
The data presented here is tied to specific spatial and temporal ecological conditions (e.g., forest drought history, tree species presence, microbial community composition, and soil property heterogeneity) which are susceptible to change. This makes exact study replication challenging and underlines the importance of including a wide range of conditions (e.g., multiple forest types, tree species, tree species combinations, climatic conditions, and soil types) as done here in order to explore general, potentially reproducible, trends oppose to site-specific trends.
Reporting summary
Further information on research design is available in the Nature Research Reporting Summary linked to this article. More

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