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There were three methods of sampling the populations. For Methods 1 and 2, records were obtained by driving along the road transects, and stopping to score the age groups in herds within some 100 m of the road. There were three road transects, entirely in the administrative boundaries of Serengeti National Park and consistent every year (1962–2018), with records summed over the three for each data entry. Transect 1 was from Seronera (34.823°E, 2.428°S) west to Kirawira (34.208°E, 2.151°S; 120 km), Transect 2 from Seronera to Bologonja (35.173°E, 1.757°S; 115 km), and Transect 3 from Seronera to Olduvai Gorge (35.35°E, 2.993°S; 75 km) (Fig. 1). The first two transects were in similar savanna ecosystems, and comparison of samples from these two showed close similarity.
Fig. 1

Ungulate and ostrich sampling transects in the Serengeti ecosystem.

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The criteria for age classes in each species are given in Online-only Table 1. The sample was the herd within view (such as a group of impalas (Ae. melampus) or hartebeests (Al. buselaphus), which occur in discrete groups), or a subset of it if the herd was very large. One observer, using 8–10 x magnification binoculars, called out the age category while a recorder entered the records on data sheets. These were later entered digitally.
Two exceptions to this were the immense herds of migrant wildebeest (C. taurinus) and zebra (Eq. quagga). Because they were numerous and extensive, herds had to be sampled in a systematic way. A vehicle drove through the herds, stopping every half kilometer, where a 180 degree scan out to 100 m was conducted to count the sample within view. The transects were from the start to the end of the herd, with some being 30 km long through a single, continuous herd. Method 3 used aerial pictures of the herds to score age groups. Although the sampling protocol was different in the three methods (due to different distributions of each species) the same criteria for identifying age classes was used in all methods. All methods used either systematic or random sampling of the populations.
All species were either migrants, if the species shows seasonal variation in habitat, or residents, if the species remains in the same area of the park year-round. A notable exception to this is the wildebeest (C. taurinus). In fact, there were two populations of wildebeest, a large migrant herd and a small resident herd at the far western end of the ecosystem. These two were sampled separately and scored as either migrant or resident.
Method 1
This method was used in all sampling years for impala (Ae. melampus), Coke’s kongoni (Al. buselaphus), topi (D. lunatus), warthog (P. africanus), Defassa waterbuck (K. defassa), and zebra (Eq. quagga). Sampling years 1984–1994 for African buffalo (Sy. caffer), 1965–2012 for giraffe (G. camelopardalus), and 1964–2016 for wildebeest (C. taurinus).
Populations were sampled once or twice a year at specific times, depending on the availability of different age classes in the areas near transects. Because ungulates had different birth seasons samples were collected at two time periods, once in mid-year and once at year-end. Only one time period per year was used for each species. The early age group, “infants”, was sampled usually near the end of the rainy season (March–June) since many species give birth during the rainy season. For some species, there was a second sampling period (August-December) at the end of the dry season, to measure the survival of juveniles during this period of ecological stress. There are a few cases where more than two samples were obtained in a single year, so as to track the survival of the whole cohort throughout a year.
Method 2
This method was used in all sampling years for eland (T. oryx), elephant (L. africana), Grant’s gazelle (N. granti), ostrich (S. camelus), and waterbuck (K. defassa).
These species were sufficiently scarce that an adequate sample could not be obtained at specific times. For these, records were scored whenever the species was seen in a sampling period, and then records for all sampling periods of a single given year were summed. A special case was Thomson’s gazelle (Eu. thomsonii), which, although numerous, was scored only during one short time period (1992–1994) for the months of August and September.
Method 3
This method was used in sample years 1965–1973 for African buffalo (Sy. caffer), and 1926–1933 for giraffe (G. camelopardalus tippelskirchi), wildebeest (C. taurinus), and zebra (Eq. quagga). The area covered was in all cases within the Serengeti ecosystem. Buffalo and giraffe were only found in the savanna, while wildebeest were sampled when they were on the plains. Flights were made systematically over the area, wildebeest was sampled using photographs at regular intervals, buffalo and giraffe were sampled when they were encountered.
The third method, applied only in the very early years, used aerial photographs to identify age classes and females. The same criteria for identifying age classes was used as those for Methods 1 and 2 (Online-only Table 1), with an emphasis on the shape and size of horns for the wildebeest and African buffalo2, and of the relative sizes of young giraffe. The early samples in 1926–1933, were obtained from photographs taken by Martin Johnson. These photos reside in the Martin and Osa Johnson Safari Museum, Chanute, Kansas. Unfortunately, the 1965–1973 photographs of buffalo herds have now all been lost or destroyed. More

The nature of the slug movement data collected in our field experiment (i.e. position on or beneath the soil surface observed at discrete moments of time) makes it possible to analyse the slug locomotory track in terms of the discrete-time random movement framework12,16,35,36. Within this framework, a curvilinear movement path is approximated by a broken line (see Fig. 2) and the movement of an individual slug is parameterized by the following frequency distributions:
1.
The distribution of the step sizes along the movement path (i.e. the distance between sequential pairs of recorded positions; Fig. 2) or the corresponding average speed

2.
The distribution of turning angle (the angle between the straight lines drawn between sequential pairs of recorded positions; Fig. 2).

Figure 2

A sketch of animal movement path and its discretization (adapted from36). (a) The original movement path is normally curvilinear. (b) Due to the limitations of the radio-tracking technique, position of the animal is only known at certain discrete moments of time; correspondingly, the curve is approximated by a broken line. (c) The movement path as a broken line is fully described by the sequence of the step sizes (lengths) along the path, i.e. the distances travelled between any two sequential recorded positions, and the sequence of the corresponding turning angles.

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Once all the information is available, it is possible to calculate the mean squared displacement as a function of time12,37. Additionally, in case the movement consists of alternating periods of active movement and immobility (periods with no recorded displacement resulting from feeding or inactivity, hereafter referred to as“resting time”), one should also consider the distribution of the corresponding periods.
Speed, squared displacements and the straightness index
It is apparent from the data that slug movement is intermittent, with periods of locomotion interspersed between periods in which they remain motionless. Tables 1 and 2 show, for the sparse and dense releases respectively, the number of ‘active’ time intervals when the slugs were moving. Periods during which slugs were motionless are marked by the zeros in Tables 1 and 2, but all these individuals resumed their movement during the following hours, confirming that they were alive throughout the assessment period. We therefore retain the zeros in the data for the subsequent analysis.
Table 1 Slug mean speed (averaged over the whole movement path), the mean SSD (see Eqs. (3) and (5), respectively) and the straightness index in the case of sparse release for each of 17 slugs used in the experiment. Here the straightness index is calculated using Eq. (4) where the values of the step size are immediately available from our field data.
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Table 2 Slug mean speed (averaged over the whole movement path), the mean SSD (see Eqs. (3) and (5), respectively) and the straightness index in the case of dense release for each of 11 slugs used in the experiment. Here the straightness index is calculated using Eq. (4) where the values of the step size are immediately available from our field data.
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The baseline discrete-time framework considers animal position at equidistant moments of time. However, in the field experiment (as described in the previous section), time taken to locate slugs at each assessment resulted in the time interval varying between measurements (sparse release treatment: 27–87 mins; dense release treatment: 20–103 mins). The step size, i.e. the displacement during one time interval, depends in part on the duration of that interval, hence risking bias in the results. We address this issue by scaling the step size by the duration of the corresponding time interval, i.e. by considering the average speed during the step:

$$begin{aligned} v_k(i)=, & {} frac{|Delta {mathbf{r}|_k(i)}}{Delta {t}_k(i)}, quad i=1,2,ldots ,N, end{aligned}$$
(1)

where

$$begin{aligned} |Delta {mathbf{r}|_k(i)}=, & {} |mathbf{r}_k(t_i)-mathbf{r}_k(t_{i-1})|, end{aligned}$$
(2)

is the displacement of the kth slug during the ith time interval, i.e. the distance between the two sequential positions in the field. Here N is the total number of steps made by the given slug during the full period of the experiment (in our field data, for all slugs (N=10)).
For each individual slug, we then calculate the mean speed over all steps along the movement path:

$$begin{aligned} _k=, & {} frac{1}{N} sum ^{N}_{i=1} v_k(i). end{aligned}$$
(3)

The results for the sparse and dense releases are shown in Tables 1 and 2, respectively; see also Fig. 3a.
The mean speed of slug movement, although being an important factor for slug dispersal, does not provide enough information about the rate at which the slug increases its linear distance from the point of release, because it does not provide information on the frequency of turning or the turning angle. In order to take that into account, we calculate the straightness index35, i.e. the ratio of the total displacement (distance between the point of release and the final position at the end of the experiment) to the total distance travelled along the path:

$$begin{aligned} s_k= & {} |mathbf{r}_k(t_N)-mathbf{r}_k(t_0)|/left( sum ^{N}_{i=1}|Delta {mathbf{r}}|_k(i) right) , end{aligned}$$
(4)

where (t_0) is the time of slug release and (t_N) is the time of the final observation. The actual distance travelled is approximated by the length of the corresponding broken line (see the dark solid line in Fig. 2).
Figure 3

(a) Slug mean spead and (b) slug mean SSD, black diamonds for the sparse release and red circles for the dense release.

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The straightness index quantifies the amount of turning (a combination of the frequency and angles of turns) along the whole movement path, i.e. over the whole observation time, but it says nothing about the rate of turning on the shorter time scale of a single ‘step’ along the movement path. To account for this, along with the mean speed we calculate the mean scaled squared displacement (SSD):

$$begin{aligned} langle sigma ^2 rangle _k=, & {} frac{1}{N} sum ^{N}_{i=1} sigma ^2_k(i) qquad text{ where }qquad sigma ^2_k(i)~=~frac{|Delta {mathbf{r}|^2_k(i)}}{Delta {t}_k(i)}, end{aligned}$$
(5)

see Tables 1 and 2 and Fig. 3b. For the same value of mean speed, a larger value of the SSD corresponds to a straighter movement on the timescale of a single step, with a smaller turning rate.
An immediate observation from visual analysis of the data shown in Fig. 3 is that both slug speed and the SSD are smaller in the case of dense release than in the sparse release. Therefore, a preliminary conclusion can be drawn that average slug movement is slower in the dense release compared to the sparse release treatment.
Turning angles
Figure 4

Frequency distribution of the turning angle in the case of (a) sparse and (b) dense releases of slugs. In calculating the turning angle, the periods of no movement were disregarded. The red curve shows the best-fitting of the data with the exponential function; see details in the text.

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We now proceed to analyse the distribution of turning angles. The histogram of different values of the angle is shown in Fig. 4. Let us consider first the case of sparse release (see Fig. 4a). We readily observe that the distribution is roughly symmetrical and has a clear maximum at (theta _T=0). The latter indicates that, on this timescale, slug movement is better described as the CRW than the standard diffusion1,16. Indeed, the standard diffusion (also known as the simple random walk) assumes that there is no bias in the movement direction, in particular there is no correlation in the movement direction in the intervals before and after the recorded position, which means that the turning angle is uniformly distributed over the whole circle. On the contrary, in the case where a correlation between the movement directions exists (hence resulting in the CRW), the distribution of the turning angle becomes hump-shaped. This is in agreement with the results of previous studies on animal movement (in particular, invertebrates12,38) as well as a general theoretical argument13.
In order to provide a more quantitative insight, we look for a functional description of the turning angle distribution using several distributions that are commonly used in movement ecology. The results are shown in Table 3. We establish that the turning angle data are best described by the exponential distribution. Somewhat unexpectedly, it outperforms the Von Mises distribution, although the latter is often regarded as a benchmark and its use has some theoretical justification1. However, the exponential distribution of the turning angle has previously been observed in movement data on some other species, e.g. on swimming invertebrates39.
Table 3 The (r^2) values for the turning angle movement data (in case of sparsely released slugs) described by different standard frequency distributions. The corresponding data are shown in Fig. 4a.
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The distribution of turning angle obtained in the case of dense release exhibit different features; see Fig. 4b. However, in this case, the distribution is not symmetric and has a clear bias towards positive values: the mean turning angle corresponding to the data shown in Fig. 4b is (langle theta _T rangle = 0.772approx pi /4). Since the slugs used in the dense release are from the same cohort as those used in the sparse release, we consider this bias as an effect of the slug density: the movement pattern of an individual slug is affected by the presence of con-specifics. We discuss possible specific mechanisms for the responsiveness to this factor in the Discussion.
An attempt to describe the turning angle data from the dense release by a symmetric distribution returns low values of (r^2) (see Suppl. Appendix A.1). However, the accuracy of data fitting comparable with the sparse release can be achieved by using an asymmetric distribution, i.e. where the corresponding function has different parameters for the positive and negative values of the angle. The results are shown in Table 4.
Table 4 The (r^2) values for the turning angle movement data (in case of densely released slugs) described by asymmetric frequency distributions. In calculating the turning angle, the periods of no movement were disregarded; the corresponding data are shown in Fig. 4b.
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The turning angle data shown in Fig. 4 were obtained using all active steps along the movement paths. However, since periods of slug movement alternate with periods of resting, it may raise the question of the relevance of the turning angle at the locations where slugs remained motionless for some time. In order to check the robustness of our results, we now repeat the analysis to calculate the turning angle differently by omitting the segments adjoined with the rest position. The results are shown in Fig. 5. In this case, a reliable fit may not be possible due to there being insufficient data. However, a visual inspection of the corresponding histograms suggests that the main properties of the turning angle distribution agree with those observed above for the bigger data set. Namely, in both cases the distribution has a clear maximum at (theta _T=0) (this is seen particularly well in the case of sparse release). In the case of sparse release the distribution is approximately symmetric, while in the case of dense release there is a clear bias towards positive values. We therefore conclude that the properties of the turning angle distribution are robust with regard to the details of its definition.
Figure 5

Frequency distribution of the turning angle in case of (a) sparse release, (b) dense release. The turning angle is only calculated for consecutive movements, i.e. if a slug does not move during a time step then its previous angle of movement is not used.

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Movement and resting times
Figure 6

Distribution of the proportion of the total time spent in movement in case of (a) sparse release and (b) dense release. The red curve shows the best-fit of the data with the normal distribution; see details in the text.

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Our field data shows that, while foraging, slugs do not move continuously but alternate periods of movement and rest; see the second column in Tables 1 and 2. Such behaviour is typical of many animal species38,40. In this section, we analyse the proportion of time that slugs spend moving, in particular to reveal the differences, if any, between the sparse and dense release.
Figure 6 shows the corresponding data where for the convenience of analysis the slugs are renumbered in a hierarchical order, so that slug 1 spends the highest proportion of time moving, slug 2 has the second highest, etc. We readily observe that the sparse release slugs tend to move more frequently than those from the dense release treatment: slugs that move for more than half of the total observation time constitute about 50% of the group in the case of sparse release but less than 30% in the case of dense release.
Figure 7

Distribution of the movement frequencies in case of (a) sparse release and (b) dense release.

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In order to make a more quantitative insight, we endeavour to describe the data using several standard distributions; see Tables 5 and 6. We find that the normal distribution performs better than others both in sparse and dense release treatments. Importantly, however, the parameters of the distribution are significantly different between the two cases; in particular, the standard deviation appears to be approximately twice as large in the case of sparse release. Arguably, it confirms the above conclusion that slugs move more frequently or for longer in the case of sparse release. Slugs released as a group tend to spend considerably more time at rest compared to the slugs released individually.
Table 5 The (r^2) values for the proportion of movement time described by different standard frequency distributions in the case of sparse release.
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To avoid a possible bias due to the different group size (17 slugs in the sparse release and 11 in the dense release), we now rearrange the data in terms of the proportion of the group that moves with a given frequency. The results are shown in Fig. 7. Although the amount of data in this case does not allow us to describe them using a particular function, the two cases clearly exhibit distributions with different properties. In particular, the average movement frequency is 0.467 for the sparse release and 0.264 for the dense release, and the corresponding variances are 0.090 and 0.065, respectively.
Table 6 The (r^2) values for the proportion of movement time described by different standard frequency distributions in the case of dense release.
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To further quantify the differences, Fig. 8 shows the number of slugs moving in each observation interval. Once again, we observe that the graph exhibits essentially different properties between the two releases. In particular, over the first interval, the majority of slugs (14 out of 17) move in the case of sparse release but none of the slugs move in the case of dense release. In the second half of the observation time (intervals 6–10) on average about 50% of slugs (8 out of 17) move in the case of sparse release but only about 25% of slugs (2–3 out of 11) move in the case of dense release.
Based on the differences between the two releases, we conclude that the presence of con-specifics is the factor that affects the distribution of slug movement time. Thus, along with the results of the previous sections, it suggests that slug movement is density dependent.
Figure 8

The number of moving slugs at each observation moment in case of (a) sparse release and (b) dense release.

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Definitions of terms
GPP is defined here as ‘the sum of gross carbon fixation (carboxylation minus photorespiration) by autotrophic carbon-fixing tissues per unit area and time54. GPP is expressed as mass of organic carbon produced per unit area and time, over at least one year. NPP consists of all organic carbon that is fixed, but not respired over a given time period54:

$${mathrm{NPP}} = {mathrm{GPP}}-R_{mathrm{a}} = {Delta}B + L + F + H + O = {mathrm{BP}} + O$$
(3)

with all terms expressed in unit of mass of carbon per unit area and time. Ra is autotrophic respiration (composed of growth and maintenance respiration components); ΔB is the annual change in standing biomass carbon; litter production (roots, leaves and woody debris) is L; fruit production is F; the loss to herbivores is H, which was not accounted here because of the very limited number of observations available. BP is biomass production4. Symbol O represents occult, carbon flows, i.e. all other allocations of assimilated carbon, including changes in the nonstructural carbohydrate pool, root exudates, carbon subsidies to symbiotic fungi (mycorrhizae) or bacteria (e.g. nitrogen fixers), and BVOCs emissions (Supplementary Fig. 1). These ‘occult’ components are often ignored or unaccounted when estimating NPP, hence this bias is necessarily propagated into the Ra estimate when Ra is calculated as the difference between GPP and NPP55.
Estimation methods
We grouped the ‘methods’ into four categories:

biometric: direct tree stock measurements, or proxy data together with biomass expansion factors, allometric equations and the stock change as a BP component. If not otherwise stated, we assumed that the values included both above- and below-ground plant parts (n = 13 for GPP; n = 200 for NPP or BP).

micrometeorological: micrometeorological flux measurements using the eddy-covariance technique to measure CO2 flux and partitioning methods to estimate ecosystem respiration and GPP (n = 98 for GPP; n = 4 for NPP or BP).

model: model applications ranging from single mathematical equations (for canopy photosynthesis and whole-tree respiration) to more complex mechanistic process-based models to estimate GPP and Ra, with NPP as the net difference between them (n = 53 for GPP; n = 24 for NPP or BP).

scaling: upscaling of chamber-based measurements of assimilation and respiration (GPP and Ra) fluxes at the organ scale, or the entire stand (n = 73 for GPP; n = 9 for NPP or BP).

The difference between ‘scaling’ and ‘modelling’ lies in the data used. In the case of ‘scaling’ the data were derived from measurements at the site. ‘Model’ means that a dynamic process-based model was used, but with parameters calibrated and optimized at the site, based on either biometric or micrometeorological measurements.
Data selection
The data were obtained from more than 300 peer-reviewed articles (see also ref. 5), adding, merging and extending published works worldwide on CUE or BPE4,9,11,23,25,56,57. Data were extracted from the text, Tables or directly from Figures using the Unix software g3data (version 1.5.2, Jonas Frantz). In most studies, NPP, BP and GPP were estimated for the tree stand only. However, GPP estimated from CO2 flux by micrometeorological methods applies to the entire stand including ground vegetation. We therefore included only those micrometeorological studies where the forest stand was the dominant primary producer. The database contains 244 records (197 for BPE and 47 for CUE) from >100 forest sites (including planted, managed, recently burned, N-fertilized, irrigated and artificially CO2-fertilized forests; Supplementary Information, Supplementary Fig. 3 and online Materials; https://doi.org/10.5281/zenodo.3953478), representing 89 different tree species. Globally, 170 records out of the total data are from temperate sites, 51 from boreal, and 23 for tropical sites, corresponding to 79 deciduous broad-leaf (DBF), 14 evergreen broad-leaf (EBF), 132 evergreen needle-leaf (ENF) and 19 mixed-forests records (MX). The majority of the data (∼93%) cover the time-span from 1995 to 2015. We assume that when productivity data came from biometric measurements the reported NPP would have to be considered as BP because ‘occult’, nonstructural and secondary carbon compounds (e.g. BVOCs or exudates) are not included. In some cases, multiple datasets from the same site were included, covering different years or published by different authors. We considered only those values where either NPP (or BP) and GPP referred to the same year. From studies where data were available from more than 1 year, mean values across years were calculated. When the same reference for data was found in different papers or collected in different databases, where possible, we used data from the original source. When different authors described the same values for the same site, one single reference (and value) was used (in principle the oldest one). By using only commonly available environmental drivers to analyse the spatial variability in CUE and BPE, we were able to include almost all of the data that we found in the literature. We examined as potential predictors site-level effects of: average stand age (n = 204; range from 5 to ∼500 years), mean annual temperature (MAT; n = 230; range −6.5 to 27.1 °C) and total annual precipitation (TAP; n = 232; range from ∼125 to ∼3500 mm yr−1), method of determination (n = 237), geographic location (latitude and longitude; n = 241, 64°07′N to −42°52′S and 155°70′W to −173°28′E), elevation (n = 217; 5–2800 m, above sea level), leaf area index (LAI, n = 117; range from 0.4 to 13 m2 m−2), treatment (e.g.: ambient or artificially increased atmospheric CO2 concentration; n = 34), disturbance type (e.g.: fire n = 6; management n = 55), and the International Geosphere-Biosphere Programme (IGBP) vegetation classification and biomes (n = 244), as reported in the published articles (online Materials). The methods by which GPP, NPP, BP (and Ra) were determined were included as random effects in a number of possible mixed-effects linear regression models (Supplementary Table 4).
We excluded from statistical analysis all data where GPP and NPP were determined based on assumptions (e.g. data obtained using fixed fractions of NPP or Ra of GPP). In just one case GPP was estimated as the sum of upscaled Ra and NPP58; however, this study was excluded from the statistical analysis. NPP or Ra estimates obtained by process-based models (n = 23) were also not included in the statistical analysis. No information was available on prior natural disturbance events (biotic and abiotic, e.g. insect herbivore and pathogen outbreaks, and drought) that could in principle modify production efficiency, apart from fire. The occurrence of fire was reported by only a few studies59,60,61. These data were included in the database but fire, as an explanatory factor, was not considered due to the small number of samples in which it was reported (n = 6).
Data uncertainty
Uncertainties of GPP, NPP and BP data were all computed following the method based on expert judgment as described in Luyssaert et al.55. First, ‘gross’ uncertainty in GPP (gC m−2 yr−1) was calculated as 500 + 7.1 × (70−|lat|) gC m−2 yr−1 and gross uncertainties in NPP and BP (gC m−2 yr−1) were calculated as 350 + 2.9 × (70−|lat|). The absolute value of uncertainty thus decreases linearly with increasing latitude for GPP and for NPP and BP, because we assumed that the uncertainty is relative to the magnitude of the flux, which also decreases with increasing |lat|. Subsequently, as in Luyssaert et al.55, uncertainty was further reduced considering the methodology used to obtain each variable, by a method-specific factor (from 0 to 1, final uncertainty (δ) = gross uncertainty × method-specific factor). Luyssaert et al.55 reported for GPP-Micromet a method-specific factor of 0.3 (i.e. gross uncertainty is reduced by 70% for micrometeorological measurements); and for GPP-Model, 0.6. GPP-Scaling and GPP-Biometric were not explicitly considered in ref. 55 for GPP. We we used values of 0.8 and 0.3, respectively. For BP-Biometric and NPP-Micromet we used a reduction factor of 0.3; for NPP-Model, 0.6; and for NPP-Scaling (as obtained from chamber-based Ra measurements), 0.8. When GPP and/or NPP or BP methods were not known (n = 7), a factor of 1 (i.e. no reduction of uncertainty for methods used, hence maximum uncertainty) was used. The absolute uncertainties on CUE (δCUE) and BPE (δBPE) were considered as the weighted means62 by error propagation of each single variable (δNPP or δBP and δGPP) as follows:

$$delta {mathrm{CUE}} = sqrt {left( {frac{{delta {mathrm{NPP}}}}{{{mathrm{GPP}}}}} right)^2 + left( {delta {mathrm{GPP}}frac{{{mathrm{NPP}}}}{{{mathrm{GPP}}^2}}} right)^2}$$
(4)

and similarly for δBPE, by substituting NPP with BP and CUE with BPE.
Data and model selection
The CUE and BPE data were combined into a single variable, as sites for which both types of estimates existed did not show any significant differences between these entities (Supplementary Fig. 2). CUE values based on modelling were excluded (in our database we do not have BPE data from modelling). Tests showed that the CUE value was systematically higher when GPP was estimated with micrometeorological methods, compared to values based on biometric or scaling methods. Only data with complete information on CUE, MAT, age, TAP, and latitude were used. Altogether, 142 observations were selected.
In order to use the most complete information possible, a full additive model was constructed first (Eq. (1)). The method used for estimation of GPP (GPPmeth) was specified as a random effect on the intercept, as visual inspection suggested that CUE values were smaller where ‘scaling’ was used to estimate GPP compared to cases where ‘micromet’ was used to estimate GPP.
In Eq. (1) the variable ‘age’ represents the development status of the vegetation, i.e. either average age of the canopy forming trees or the period since the last major disturbance. The other three parameters represent different aspects of the climate. The absolute latitude, |lat|, was chosen as a proxy of radiation climate, i.e. day length and the seasonality of daily radiation. The term ηZGPPMeth represents the random effect on the intercept due to the different methods of estimating GPP.
These variables were not independent (Supplementary Table 1). If the different driver variables contain information that is not included in any of the other driver variables, multiple linear regression is nonetheless able to separate the individual effects. If, on the contrary, two variables exert essentially the same effect on the response variable (CUE) this can be seen in an ANOVA based model comparison. These considerations led us to the selection procedure in which we started with the full model (Eq. (1)) and compared it with all possible reduced models (Supplementary Table 2). The result of this analysis is the model with the smallest number of parameters that does not significantly differ from the full model.
We also examined, whether there were any significant interactions of predictor variables. There were not.
We used the R function lmer from the R-package lme463 to fit the mixed and ordinary multiple linear models to the data. We checked for potential problems of multicollinearity using the variance inflation factor (VIF)64. All predictors had VIF  More

Temperature and pH
Figure 1 shows the temperature trend during the July, August and October PTBs. In the first 35 h, all the PTBs showed similar temperatures rising from 26 to 35 °C – 39 °C (Fig. 1). In the following hours, the temperature showed different trends according to the month. In July, the temperature was stable for the first four days (96 h) and then rose, reaching the max. temperature of 51 °C. In August, the temperature was stable for the first 55 h and then rose reaching the max. temperature of 61 °C. Finally, in October, after the first 35 h, the temperature rose immediately reaching 50 °C, and then was stable reaching the max. of 64.8 °C.
Figure 1

Temperature dynamic of herbs pile bath during PTB. Temperature was recorded for seven days from day 0 to d7 each hour (24 h = d1; 48 h = d2; 72 h = d3; 96 h = d4; 120 h = d5; 144 h = d6; and 168 h = d7) at 20 cm of depth in the middle of the pool bath. In yellow is the temperature trend for July, in red August and in blue October batch.

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The pH (Table 1), in the first two days, was in a range between 6.2 and 6.5 with the exception of October when pH sowed a mean value of 7.4. After d5, the pH increased significantly and stabilized in a range between 7.4 and 7.8.
Table 1 Microbiological counts (Log CFU g−1) and pH in the herbs samples in different days and month of the PTB.
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Microbial counts in herbs during PT process
The counts of viable total aerobic, mesophilic and thermophilic anaerobic bacteria, enterobacteria, yeasts and moulds in July, August and October at day 0, d2, d3, d5 and d7 are shown in Table 1. The plate counts showed no significant difference for depth of sampling (p value  > 0.05; data not shown). The aerobic bacteria were always high at day 0 (6.7, 7.7 and 9.1 Log CFU g−1 in July, August and October respectively). In July and August, they significantly rose until d7, reaching similar amounts (8.7 and 8.8 Log CFU g−1 respectively). The mesophilic and thermophilic lactic acid bacteria (LAB) were very low in July and August at day 0 when they were present in traces or not detected (Table 1). Mesophilic LAB rose from d2 to d7 with a similar trend to aerobic bacteria reaching 5.9 Log CFU g−1. By contrast, in October they showed different trend: as aerobic bacteria, mesophilic LAB counts were very high at day 0 and stable without significant differences until d3 and then significantly decreased until d7 reaching 4.9 Log CFU g−1. Counts of thermophilic LAB showed similar trends in all the three months: they rose until d7 reaching similar amount in July, August and October (5.2, 5.7 and 5.1 Log CFU g−1 respectively). Enterobacteria counts were lower in herbs at day 0 (3.8, 4.3 and 5.0 Log CFU g−1 in July, August and October respectively) and then significantly rose until d7 reaching 6.2, 5.7 and 6.7 Log CFU g−1 in July, August and October respectively. In July, yeasts and moulds in the first two days were not detected or present in traces, then reached their highest value at d3 and significantly decreased until d7. By contrast, their counts were very high in both August and October; in particular, moulds counts trends were similar: they significantly decreased until d7 to 3.2 and 6.4 Log CFU g−1 in August and October respectively.
Characteristics of the sequencing data
The DNA extracted from the 90 PTB samples had been all successfully amplified. After merging and quality trimming the raw data, 2,980,511 reads for bacteria and 1,227,092 reads for fungi remained for subsequent analysis (Table S1). After alignment, the remaining Operational Taxonomy Units (OTU) had been clustered at a 3% of distance.
Bacteria and fungi: alpha diversity
The number of OTUs and the Shannon diversity index were determined using QIIME2 at 97% similarity levels (Table 2), in order to analyse the bacterial and fungi community richness in samples obtained during the PT process. Regarding the sample position (5 and 40 cm depth), there was no significant difference in both observed OTUs number and Shannon diversity index for bacteria and fungi communities (p value  > 0.05). It is worth noting that the degree of bacterial diversity was significantly higher in July and August than in October samples, by contrast, the degree of fungal diversity was significantly higher in July and October than in August samples (Shannon diversity index in Table 2).
Table 2 Observed OTUs (Obs. OTUs) and Shannon diversity index (Shannon div. ind.) in the herbs at different depth, month and of day sampling of the PTB.
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The variation in number of OTUs and Shannon diversity index over time indicates highest microbial diversity at day 0 and d2, and a lower microbial diversity at d5 and d7.
Bacteria and fungi: beta diversity
The PCoA of UniFrac and Jaccard metric indicated clear clustering of both bacterial and fungi communities according to the different PTB days (Fig. 2a,b).
Figure 2

Principal coordinate analysis of Weighted UniFrac distances for bacterial community (a) and Bray–Curtis distances for fungi community (b) in PTB. The Time custom axis has been used to show the PCoA changes in the days. For interpretation of the symbols and colors the reader is referred to the legend.

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Bacterial and fungi communities were more phylogenetically dissimilar between successional days (day 0, d2, d3, d5 and d7) or months (July, August and October) than between position of sampling (5 and 40 cm). The bacterial Weighted UniFrac PCoA (Fig. 2a, total variation explained: 52.09%) and the fungal Jaccards PCoA (Fig. 2b, total variation explained: 32.83%) revealed a clearer picture of the similarities across different days. The PCoA plots emphasized the similarities of the bacterial and fungi communities in the PTB at d2 and d3 when compared with d5 and d7.
These results were supported by the PERMANOVA statistical analysis (Table 3). The differences between position of sampling (5 and 40 cm) were not significant both for bacteria and fungi communities as the p values were 0.19 for bacteria and 0.27 for fungi community respectively. The differences among months of sampling were significant comparing July and August with October for both bacteria and fungi communities as well as the differences among microbial communities through time. The pairwise comparison (Table 3) clearly showed two significantly different stages during the PTB after day 0: the first stage including d2 and d3 (1st stage), and the second stage including d5 and d7 (2nd stage). The time effect on microbial composition (pseudo-F value) was showing a growing trend with the proceeding of the sampling days (Table 3). The bacterial pseudo-F values were smaller and smaller with progression of the days; by contrast, fungi pseudo-F values were higher. This means that the bacteria became more similar and the fungi more different in the samples from the three piles studied as the process progressed.
Table 3 Permanova analysis (999 permutations) results for bacterial and fungi communities based on weighted unifrac and Jaccard distances respectively.
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Bacterial community structure
Eleven prokaryotic phyla were found in the 90 samples accounting for the total bacterial community. The predominant phylum across all bacterial communities was the Proteobacteria, accounting for 33%–83% of the OTUs in each time and month of the PTB (Fig. 3). The trend of Proteobacteria was similar in all the months with different amount of presence: at day 0 and d2 Proteobacteria abundance was between 61% and 85%; at d3, showed a slight decrease (between 58% and 72%) and reached the lower values at d5 and d7 (between 33% and 65%). Twenty-six bacterial phylotypes were found dominant across all samples, accounting for the 90% of the total bacterial community. Of these 26 phylotypes (in Fig. 4), 10 belonged to Proteobacteria. Erwinia was the most abundant genus in this phylum and reached the higher presence at d2 and d3. Other frequently sequenced genera included Acinetobacter, Pseudomonas, mainly found at day 0, and unclassified genera belonging to Xanthomonadaceae family.
Figure 3

Phylum composition (in mean relative abundance) of herbs samples as revealed by high-throughput sequencing analysis. The samples were collected in triplicate from the same pool, for five days (day 0, d2, d3, d5, and d7) at 5 and 40 cm of depth, in July, August (Aug) and October (Oct). For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.

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Figure 4

Bacterial taxa groups (genus level or above) composition, in mean relative abundance, of herb samples as revealed by high-throughput sequencing analysis. The samples have been collected in triplicate from the same pool, for five days (d0, d2, d3, d5, and d7) at 5 and 40 cm of depth, in July, August (Aug) and October (Oct). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).

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Of the Alphaproteobacteria, the genera Agrobacterium, Methylobacterium, Sphingomonas and unclassified genera of the family Beijerinckiaceae were the most abundant and dominant at day 0. All these phylotypes showed a lowering trend in time decreasing from day 0 to d7 with the only exceptions of the Beijerinckiaceae that were higher at d7 than at day 0.
Of the Betaproteobacteria, unclassified genera belonging to Alcaligenaceae and Oxalobacteraceae were the most abundant families. Their relative abundances were constant along the time and showed higher differences among the months than the sampling days (average values of relative abundance were 2.4%, 4.5% and 0.5% in July, August and October respectively).
Firmicutes accounted for 12%–38% of the OTUs from d2 to d7 of the PT process. At day 0, Firmicutes were present only in October’s samples at 7%, then increased at d2 and remained stable until the end of the process (Fig. 3). Overall, there were 10 Firmicutes in the 26 most abundant phylotypes found during the PTBs (Fig. 4). Most of these were thermophilic bacteria such as Bacillus, Thermoactinomycetaceae, Brevibacillus and Paenibacillus6. These themophilic phylotypes had never been detected at day 0, appeared at d2 and reached their higher values at d5 when their presence accounted for 29.9%, 19.4% and 8.5% in July, August and October respectively.
The Bacteroidetes constituted another dominant phylum detected in all the samples (Fig. 3). Bacteroidetes abundance at d0 was in the range of 1.4%–17.0%, decreased at d2, d3 and d5 to a range of 0.7%–8.1% and reached the highest values at d7 (between 8.1% and 21.2%). The most abundant genera belonging to this phylum were Flavobacterium and Sphingobacterium.
The abundance of Actinobacteria was 1.0%–3.3% at day 0 and increased until the end of the process reaching a maximum of 7.5–36.6% relative abundances respectively (Fig. 3). The most abundant phylotypes in the Actinobacteria phylum were Microbacteriaceae and Streptomyces (Fig. 4); in particular, Streptomyces was one of the genera dominating bacterial community biodiversity at d5 and d7.
Cyanobacteria were found at relative abundances higher than 1% only in July and August samples at day 0 and d2, with a maximum at day 0 (16.9% and 4.5% relative abundances in June and July samples respectively). After d2, Cyanobacteria decreased until the end of the process (Fig. 3). The relative abundance of Verrucomicrobia was 0.35%–2.8% at d0 and remained constant during the whole PTB process (Fig. 3). Chtoniobacteraceae was the most abundant bacterial family of the Verrucomicrobia phylum.
Further bacterial phyla had always been found at very low relative abundances (never higher than 1.0%, Fig. 3).
Fungal community structure
Before the PTB started, the fungal community in the herbs (day 0 in Fig. 5), was dominated by Mycosphaerellaceaes (Mycosphaerella, Ramularia and Zymoseptoria genera), representing the 21.5%, 21.4% and 15.0% of the total in July, August and October respectively, and Bulleribasidiaceaes (Vishniacozyma, and Dioszegia genera) representing the 22.3%, 32.4% and 23.4% of the total in July, August and October respectively. Other fungal taxonomic groups, mainly belonging to the Ascomycota phylum, were detected in lower relative abundance (lower than 10%). After two days (d2), the Aspergillaceae family was emerging, mainly constituted by the Aspergillus genus with traces of Penicillium in 13 out of the 90 samples. Aspergillaceae dramatically increased from day 0 (always less than 1%) to d2 in July and August trials (10.6% and 24.9% respectively), and after d3 they became the most dominant fungi (26.6% and 83.2% respectively). By October, Bullerobasidiaceae was always the dominant fungal family at d2 and d3. After five days (d5 in Fig. 5), Bulleribasidiaceaes (lower than 10.6%) and Mycosphaerellaceae (lower than 6.5%) relative abundances decreased sharply. Aspergillaceae kept their rising trend, remaining the dominant fungal family in July and August trials (47.9% and 56.6% respectively), but they represented only the 11.4% of the fungal relative abundance in October. Other thermophilic species emerged in July and August: the Trichocomaceae mainly constituted by Thermomyces lanuginosus whose relative abundance was never higher than 2.1% in the first three days and then suddenly increased to 32.8% and 23.2% in July and August respectively.
Figure 5

Fungi taxa groups (genus level or above) composition, in mean relative abundance, of herb samples as revealed by high-throughput sequencing analysis. The samples were collected in triplicate from the same pool, for five days (d0, d2, d3, d5, and d7) at 5 and 40 cm of depth, in July, August (Aug) and October (Oct). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).

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After seven days (d7 in Fig. 5), the fungal community was totally dominated by Aspergillaceae (46.6%, 69.2% and 35.9% in July, August and October respectively) and Thermomyces lanuginosus (44.2%, 23.3% and 21.6% in July, August and October respectively). None of the OTUs was predominant throughout all samples.
Volatiles organic compounds (VOCs) released during the PTBs
After raw GCxGC–MS data deconvolution and pre-processing, the three dataset (July, August and October) consisted of 722, 1105 and 815 volatiles respectively. As already reported by Narduzzi et al.7, the majority of the VOCs are not in common among the months. The identified volatiles through all the three months’ datasets were matched using their InchiKey, and produced a table consisting of 295 VOCs present in all the months (Table S2). As shown in the top part of the Fig. 6, there is a cluster of 34 compounds that are the most representative of all PTB samples because contributing to the 85% of the total VOCs mass emissions. In the heatmap Fig. 6, the samples from the same month clustered together. Moreover, within each month, the samples split in two different clusters according to the stages already identified in the microbial analysis. The first cluster is composed by the samples of d1, d2 and d3 (1st stage) and the second cluster by the samples of d4, d5, and d6 (2nd stage). Looking at the differences in the days within each batch, the d1, d2 and d3 samples were richer in aliphatic hydrocarbons (heneicosane, hexadecane, tetradecane and 3-methyltridecane), alpha-terpineol, and estragole. By contrast, the d4, d5 and d6 samples were richer in 1-methylnaphthalene, nonanal, 2-nonanone, 3-octanol, m-xylene, 2,6-dimethylheptadecane and 2-ethyl-hexanol.
Figure 6

Heatmap and hierarchical clustering based on the normalized quantities of the identified VOCs, for PTB herbs in the six days (d1, d2, d3, d4, d5, and d6) and three months (July, August and October) of sampling. The highest content is in red and the lowest in blue. The values have been UV scaled and clustered according the Ward algorithm. The list of the 34 compounds highlighted in the upper side represents the most abundant (core) VOCs found. In July, d6 is missing as the sample has not been collected.

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