Ecology

In natural ecosystems, the efficiency of energy transfer from resources to consumers determines the biomass structure of food webs. As a general rule, about 10% of the energy produced in one trophic level makes it up to the next1–3. Recent theory suggests this energy transfer could be further constrained if rising temperatures increase metabolic growth costs4, although experimental confirmation in whole ecosystems is lacking. We quantified nitrogen transfer efficiency (a proxy for overall energy transfer) in freshwater plankton in artificial ponds exposed to 7 years of experimental warming. We provide the first direct experimental evidence that, relative to ambient conditions, 4 °C of warming can decrease trophic transfer efficiency by up to 56%. In addition, both phytoplankton and zooplankton biomass were lower in the warmed ponds, indicating major shifts in energy uptake, transformation and transfer5,6. These new findings reconcile observed warming-driven changes in individual-level growth costs and carbon-use efficiency across diverse taxa4,7–10 with increases in the ratio of total respiration to gross primary production at the ecosystem level11–13. Our results imply that an increasing proportion of the carbon fixed by photosynthesis will be lost to the atmosphere as the planet warms, impairing energy flux through food chains, with negative implications for larger consumers and the functioning of entire ecosystems. More

Evolution of ACE2 in bats inhabiting urban or rural areas
We collected ACE2 orthologues from 46 bat species across the phylogeny (Fig. 1 and Supplementary Table 1). These species contained 28 species that roost or forage in urban areas near humans and 18 species more restricted to rural areas and hence likely to have minimal contact with humans (Supplementary Table 2). In total, we examined 46 species representing 11 bat families (Supplementary Table 3). After aligning the protein sequences of bat ACE2 orthologues, we examined 25 critical residues involved in the binding of the surface spike glycoprotein (S protein) of SARS-CoV-2 (ref. 9) (Extended Data Fig. 1). Genetic variations were observed in nearly all these 25 sites, which may have led to different abilities to support entry of SARS-CoV and SARS-CoV-2 (ref. 9). Furthermore, we detected at least 22 amino acid sites that are putatively under positive selection (Supplementary Table 4), which is indicative of heterogeneous selection pressure across sites. Notably, four of these positively selected sites are in the binding region of ACE2 to the SARS-CoV-2 S protein (Supplementary Table 4).
Fig. 1: Phylogenetic tree of 46 bat species in this study.

The labels of bat species in our experiments are indicated. Expression levels determined by western blot (Fig. 2a) are shown with asterisk symbols compared with human ACE2: the triple asterisk indicates high expression, the double asterisk indicates medium expression and the single asterisk indicates low but detectable expression. The ability of bat ACE2 to support SARS-CoV and SARS-CoV-2 pseudovirus entry is shown with different signs (Fig. 3a,b): infection data are presented as percentage mean values of bat ACE2 supporting infection compared with the infection supported by human ACE2. Infection efficiency 50% with a double plus sign. Bat phylogeny was taken from previous studies28,29,30.

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Interaction between bat ACE2 orthologues and SARS-CoV or SARS-CoV-2 receptor binding domain
Efficient binding between the S protein and the ACE2 receptor is essential for SARS-CoV and SARS-CoV-2 entry. This binding is mainly mediated by the interaction between the critical residues on the receptor-binding domain (RBD) and ACE2. To characterize the receptor function of ACE2 orthologues in a range of diverse bat species, we generated a stable cell library consisting of cell lines expressing the respective 46 bat ACE2 orthologues through lentiviral transduction of 293T cells lacking ACE2 expression10. All bat ACE2 orthologues were exogenously expressed at a comparable level after puromycin selection, as indicated by western blot and immunofluorescence assays detecting the C-terminal 3×FLAG-tag (Fig. 2a,b).
Fig. 2: Expression of bat ACE2 orthologues and their interaction with the SARS-CoV and SARS-CoV-2 RBD.

a, Western blot detected the expression levels of ACE2 orthologues on 293T stable cells by targeting the C-terminal 3×FLAG-tag. Glyceraldehyde 3-phosphate dehydrogenase was employed as a loading control. b, Visualization of the intracellular bat ACE2 expression level by immunofluorescence assay detecting the C-terminal 3×FLAG-tag. Scale bar, 100 μm. c,d, Assessment of the interaction between different ACE2 orthologues and SARS-CoV-RBD-hFc (c) or SARS-CoV-2-RBD-hFc (d) proteins. Species that do not support efficient binding are underlined. 293T cells stably expressing the different bat ACE2 orthologues were incubated with 5 μg ml−1 of the recombinant proteins at 37 °C for 1 h; binding efficiency was examined by Alexa Fluor 488 goat anti-human IgG via fluorescence assay. Scale bar, 200 μm.

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To analyse the interaction, we produced recombinant SARS-CoV or SARS-CoV-2 RBD human immunoglobulin G (IgG) Fc fusion proteins (RBD-hFc), previously reported to be sufficient to bind human ACE2 efficiently11,12. Protein binding efficiency was tested on the bat ACE2 cell library by means of immunofluorescence or flow cytometry targeting the human Fc. As expected, binding was almost undetectable on mock 293T cells but a strong binding signal was detected in the 293T cells expressing human ACE2 (Fig. 2c,d). Consistent with previous reports13,14, SARS-CoV-2 RBD showed higher binding to human ACE2 than SARS-CoV, which can also be observed on many bat ACE2 orthologues (Fig. 2c,d). Previous reports have shown that only a small fraction of ACE2 orthologues from tested mammalian species could not bind with SARS-CoV-2 S protein (n = 6 of 49 species7; n = 5 of 17 species15). However, our study revealed that many bat species (n = 32 and n = 28 of 46 species) do not support efficient binding with SARS-CoV-RBD and SARS-CoV-2-RBD, respectively (Fig. 2c,d). The overall profiles of bat ACE2 to bind to SARS-CoV and SARS-CoV-2 RBD are generally comparable; a few showed contrasting modes of binding preferences (Fig. 2c,d). For instance, Bat22 could bind to SARS-CoV but not SARS-CoV-2, whereas Bat14, 21 and 40 could bind to SARS-CoV-2 but not SARS-CoV (Fig. 2c,d). Flow cytometry analysis showed consistent results (Extended Data Fig. 2).
Overall, the RBD-hFc binding assays demonstrated that bat ACE2 orthologues showed different affinity and selectivity levels to SARS-CoV and SARS-CoV-2, indicating that the ACE2 receptors of many bat species may not support efficient SARS-CoV and SARS-CoV-2 infection.
Receptor function of bat ACE2 orthologues to support the entry of SARS-CoV and SARS-CoV-2 using pseudotyped and live viruses
To further evaluate the receptor function of different bat ACE2 orthologues, we employed a vesicular stomatitis virus (VSV)-based rhabdoviral pseudotyping system to mimic the coronavirus spike protein-mediated single-round entry15. SARS-CoV and SARS-CoV-2 pseudotypes were generated by assembling the coronavirus spike proteins and replication-deficient VSV with the VSV glycoprotein gene replaced with a fluorescence protein (VSV-dG-GFP) or a firefly luciferase (VSV-dG-Luc) reporter15. Both viruses showed minimal background infection on 293T cells, but efficient infection on 293T-human ACE2 cells (Extended Data Fig. 3). The susceptibility of the 293T cells expressing bat ACE2 orthologues was then examined with SARS-CoV and SARS-CoV-2 pseudotypes. The results showed that bat ACE2 orthologues have varying abilities to support coronavirus entry and different preferences for SARS-CoV and SARS-CoV-2. (Fig. 3a,b and Extended Data Fig. 4). Pseudotypes with green fluorescent protein (GFP) reporter showed similar results (Extended Data Fig. 5). Notably, we found that 24, 21 and 16 of the 46 bat species showed almost no entry for SARS-CoV, SARS-CoV-2 and both viruses, respectively (Figs. 1 and 3a,b and Supplementary Table 5), suggesting that these species are not likely to be potential hosts of either or both coronaviruses. The bat species showing no viral entry include those that occur in urban areas and those more restricted to rural areas (Fig. 1), suggesting that there is no correlation between proximity to humans and probability of being natural hosts of SARS-CoV or SARS-CoV-2. Although horseshoe bats were suggested as potential natural hosts of SARS-CoV and SARS-CoV-2 (refs. 1,2,3), only one of the three species examined (Rhinolophus sinicus) supported SARS-CoV entry; this species was suggested as the potential host of SARS-CoV3,16. None of these tested horseshoe bats showed entry for SARS-CoV-2 (Figs. 1 and 3). These results unambiguously indicate that ACE2 receptor usage is species-dependent.
Fig. 3: Characterization of bat ACE2 orthologues mediating entry of SARS-CoV and SARS-CoV-2 viruses.

a,b, Ability of bat ACE2 orthologues to support the entry of SARS-CoV and SARS-CoV-2 pseudovirus. 293T cells expressing bat ACE2 orthologues in a 96-well plate were infected with VSV-dG-Luc pseudotyped with SARS-CoV (a) and SARS-CoV-2 (b) spike proteins, respectively. Intracellular luciferase activity was determined at 20 h post-infection. RLU, relative light unit. c, 293T cells expressing bat ACE2 orthologues were inoculated with the SARS-CoV-2 live virus at an MOI = 0.01. N protein (red) in the infected cells was detected through immunofluorescence assay at 48 h post-infection. Scale bar, 200 μm. Samples expressing the indicated ACE2 orthologues that showed almost no entry for SARS-CoV-2 live virus are underlined. Data shown are representative results from 3 independent experiments and are presented as the mean ± s.d. (n = 3 for a and n = 2 for b).

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The SARS-CoV-2 S protein used in this study for pseudotyping contains a D614G mutation, which is currently a dominant variation17. The D614G mutation remarkably improved the in vitro infectivity of SARS-CoV-2 but may not significantly affect the receptor interaction since it is not in the RBD18. Indeed, we identified a very similar susceptibility profile using an original strain without D614G (Extended Data Fig. 4). We further demonstrated that the pseudotyped entry assay mimics the entry of live viruses through a SARS-CoV-2 infection assay (Fig. 3c). As expected, the profile of SARS-CoV-2 N protein expression is highly consistent with the results from the VSV-dG-based pseudotyped virus entry assay, except for some ACE2 that showed relatively higher infection efficiency (for example, Bat43–46) compared with the pseudovirus infection assay, which may be attributed to the different virus strains used (Fig. 3c). In addition, the live virus infection resulted in the phenotype of plaque formation, while the pseudotypes showed evenly distributed, single-round infection (Extended Data Fig. 5), which also partially explains why some bat ACE2 showed higher infection in the live virus infection assay.
When comparing the RBD-hFc binding and pseudotyped entry profiles, we found that binding and susceptibility are not always consistent, although the phenotypes were reproducible. For instance, some species (Bat12, 13, 14) were able to bind to SARS-CoV-2 RBD-hFc efficiently but could not support infection of the same virus, indicating that high binding affinity does not guarantee efficient viral entry (Figs. 2 and 3). In contrast, some species (Bat3–8) were defective or less efficient in SARS-CoV RBD-hFc binding but supported the entry of the same virus to some degree (Figs. 2 and 3). We hypothesize that such minimal binding may be sufficient for viral entry mediated by those ACE2 orthologues; alternatively, additional residues outside the traditional RBD region might be required for efficient interaction. These hypotheses should be tested in the future. Together, our results demonstrated dramatic variation of susceptibility to SARS-CoV and SARS-CoV-2 infection among bat species, suggesting that SARS-CoV and SARS-CoV-2 can selectively use some bat ACE2 as functional receptors for viral entry and many—if not most—bat ACE2 are not favoured by one or both viruses.
Evaluation of critical residues in bat ACE2 orthologues affecting viral binding and entry efficiency or specificity
We comprehensively analysed the relationship between critical RBD binding sites in bat ACE2 sequences and their ability to support SARS-CoV and SARS-CoV-2 RBD binding and viral entry. Several critical residues were identified that may play critical roles in the determination of species specificity (Extended Data Fig. 1). According to the sequence alignment, two species pairs (Bat33 and Bat34 and Bat38 and Bat40) were selected to demonstrate the role of critical residues in RBD binding and viral entry because they were phylogenetically close but showed contrasting phenotypes for supporting RBD binding and viral entry. Specifically, Bat34 and Bat38 do not support SARS-CoV and SARS-CoV-2 RBD binding and infection, while Bat33 supports efficient binding and infection of both viruses and Bat40 supports infection of both viruses and to a lesser degree SARS-RBD binding (Figs. 2 and 3). We compared their protein sequences and highlighted the residues that may affect RBD interaction. For example, substitutions I27K, N31G and K42E were observed when comparing Bat33 with Bat34, while Q24L, E30K, K35Q and G354N were present between Bat38 and Bat40 (Fig. 4a). We hypothesized that the discrepancy in binding and infection phenotype is determined by their differences in critical residues for RBD interaction. To test this hypothesis, we designed a residue swap mutagenesis assay to investigate the role of critical residues on RBD binding and virus entry (Fig. 4a). We generated four swap mutations and corresponding 293T stable cell lines to test whether these substitutions could achieve gain-of-function and loss-of-function. All bat ACE2 orthologues and related mutants were expressed at a comparable level after lentiviral transduction, as indicated by the immunofluorescence of the C-terminal 3×FLAG-tag (Fig. 4b). Recombinant SARS-CoV and SARS-CoV-2 RBD-hFc proteins were applied to the cells expressing different ACE2 and binding efficiency was evaluated by immunofluorescence (Fig. 4c) and flow cytometry assays (Fig. 4d). As expected, the swap of critical residues on the selected four bat ACE2 changed their receptor function to the opposite, except for Bat38 mutant, which remained unable to bind SARS-CoV RBD-hFc (Fig. 4c,d). GFP (Fig. 4e) and luciferase levels (Fig. 4f) from the pseudotyped virus entry assay and the N protein staining from the live SARS-CoV-2 infection assay (Fig. 4g) further confirmed our hypothesis at the viral entry level. Structure modelling of bat ACE2/SARS-CoV-2-RBD complexes showed that the substitutions of I27K and N31G between Bat33 and Bat34 lead to a reduced packing interaction and the substitution of K42E disrupts the hydrogen bond with Y449, which may be related to the difference of susceptibility between Bat33 and Bat34 (Fig. 4h,i and Extended Data Fig. 6). In comparison, the substitutions of Q24L and E30K between Bat38 and Bat40 destroyed the favourable hydrophilic interactions with N487 and K417, respectively (Extended Data Fig. 6).
Fig. 4: Evaluation of the critical binding sites determining the species-specific restriction of SARS-CoV and SARS-CoV-2 binding and entry.

a, Swap mutagenesis assay to investigate the role of critical residues on bat ACE2 orthologues for tropism determination. Residues involved in RBD (according to the structure between SARS2-RBD and human ACE2, Protein Data Bank 6M0J) interaction are shown in the table. Residues that changed in the mutagenesis assay are marked in red. b, The expression level of the bat ACE2 orthologues and related mutants in transduced 293T cells was determined by an immunofluorescence assay recognizing the 3×FLAG-tag. Scale bar, 200 μm. c,d, Binding efficiency of SARS2-RBD-hFc and SARS2-RBD-hFc on 293T cells expressing bat ACE2 and related mutants. Cells were incubated with 5 μg ml−1 of recombinant proteins at 37 °C for 1 h and then washed and incubated with a secondary antibody recognizing human Fc. Immunostaining (c) and flow cytometry (d) were conducted to show binding efficiency. Scale bar, 200 μm. e,f, Ability of the indicated ACE2 and related mutants to support the entry of coronavirus pseudotypes. The 293T cells expressing the indicated ACE2 and their mutants were infected with SARS-CoV and SARS-CoV-2 pseudotypes expressing GFP (e) and luciferase (f). Infection was analysed at 20 h post-infection. Scale bar, 200 μm. Data are presented as the mean with s.d. (n = 2). g, 293T cells infected by the SARS-CoV-2 live virus at an MOI = 0.01; the infection was examined at 48 h post-infection through N protein (red) immunostaining. Nuclei were stained with Hoechst 33342 (blue). Scale bar, 200 μm. h,i, Comparison of the interface between Bat33/SARS-CoV-2-RBD and Bat34/SARS-CoV-2-RBD. Bat33 and its complexed RBD are coloured cyan and gold, respectively (h); Bat34 and its complexed RBD are coloured wheat and green, respectively (i). The mutated residues in ACE2 and the corresponding residues in SARS-CoV-2-RBD are shown and labelled. The red dotted lines between residues indicate hydrogen or ionic bonds.

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In addition, two bat cell lines, the lung epithelial cell line Tb 1 Lu of Tadarida brasiliensis (Bat31) and the kidney epithelial cell line of Pteropus alecto (Bat2), were used to validate our findings derived from human HEK293T cells. Endogenous ACE2 expression was almost undetectable in these two cell lines, accounting for at least 1,000 folds lower than the susceptible Vero-E6 cells (Extended Data Fig. 7a). Therefore, these cells cannot support the entry of SARS-CoV and SARS-CoV-2. We successfully generated Tb 1 Lu stable cell lines expressing human ACE2 and bat ACE2 (Bat2, 3, 31, 32) since the transduction efficiency of Tb 1 Lu is much higher than that of PakiT03 cells (Extended Data Fig. 7b). As expected, Tu 1 Lu were susceptible to both SARS-CoV and SARS-CoV-2 when human ACE2 or some bat ACE2 orthologues (Bat2, 3 and 31) were expressed, yet remained non-susceptible when an ACE2 of a closely related species (Bat32) was expressed (Extended Data Fig. 7c–e). Furthermore, we conducted SARS-CoV and SARS-CoV-2 pseudovirus entry assays on the two bat cell lines transiently transfected with various bat ACE2 (Bat2, 3, 31, 32, 33, 34, 38, 40) and their mutants (mutant Bat33, 34, 38 and 40m). The results were consistent with those derived from human cells, further confirming that ACE2 is the main receptor for the species-specific entry of SARS-CoV and SARS-CoV-2 in these bat cells (Extended Data Fig. 7f,g). More

Natural soundscapes have always called to me. As an eco- and electro-acoustics researcher, with a background in sound engineering and electronic music composition, I have always tried to strike a balance between art and science in my work.
In 1998, when I first heard about the extinction crisis — more than 35,500 species of flora and fauna are endangered — the idea for the Fragments of Extinction project came to me very quickly. My vision was to build a collection of 24-hour-long ‘acoustic fragments’, recorded at the highest definition possible, capturing the sonic heritage of ancient, biodiverse, untouched tropical rainforests — before climate change damages them irreversibly.
In these forests, some species vocalize from the canopy, some from the ground and others from big tree trunks that act like sound diffusers. To capture a 3D acoustic portrait of the forest, we simultaneously record on 38 audio channels and microphones.
In this photograph, I am standing in the Sonosfera, a geodesic theatre in Pesaro, Italy, in which audiences can experience rainforest soundscapes captured in the Amazon, Africa and Borneo. Forty-five high-definition loudspeakers are positioned in an isolated, acoustically perfect space, realistically reproducing the ecosystems’ natural sounds.
For the first 15 minutes of the performance, the Sonosfera is completely dark. Sound helps listeners to ‘build’ the forest space around them — the position of every insect and amphibian; the birds and mammals moving through the canopy. My team then projects the spectrograms shown here to explain the sounds, and present data showing that these ecosystems are disappearing.
We have captured the deep infrasound calls of elephants and have recorded insects that sound exactly like violins or trumpets. Our ecosystem recordings are very different. But I don’t have a favourite — they’re a collection. More

Genome sequencing and assembly
We performed a de novo genome sequencing and assembly of CBB using a hybrid approach by combining 454-FLX and Illumina reads from female and male individuals. A total of 3.02 Gb of high-quality 454-FLX sequences and 26 Gb of Illumina sequences were obtained in this study (Table S1), which represent approximate 19 × and 160 × genome coverage respectively based on a previously estimated CBB genome size of 163Mb21. The genome hybrid assembly approach we used involved an initial pre-assembly of the 454FLX data with Newbler and the Illumina data with ABySS22, followed by merging of these two pre-assemblies into a single genome consensus with Metassembler23. Our final hybrid H. hampei CENICAFE_Hham1.1 (Hham1.1) genome assembly had a size of 162.57 Mb, comprising 8198 genome scaffolds (Table 1). This assembly represents an improvement in sequence contiguity, containing a 36.3-Kb contig-N50; 340.2-Kb scaffold-N50 and 4.9 Mb for the largest genome scaffold, compared with a previously published CBB genome assembly21, which resulted in contig and scaffold N50 of 10.5-Kb and 44.7-Kb respectively and largest genome scaffold of 440-Kb. The Hham1.1 genome assembly completeness was assessed using Benchmarking Universal Single-Copy Orthologs (BUSCO)24. BUSCO recovered 98.22% of the 1066 Arthropoda core gene set, from which 96.25% were complete genes and 2% were fragmented genes (Fig. S1). BUSCO results indicate that almost the entire genome of H. hampei was sequenced and de novo assembled in this study.
Table 1 Hypothenemus hampei genome assembly (CENICAFE_Hham1.1) statistics.
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Transcriptome assembly
Illumina RNA-seq data obtained from whole-body female and male adults were de novo assembled using rnaSPades25 and sequence redundancy reduced by CD-HIT26. The resulting transcript assembly was composed of 64,244 contigs (available at NCBI TSA accession: GIPB00000000.1). The average transcript length was 1103-bp, transcript N50 of 2145-bp and largest transcript of 26,019-bp. The transcript assembly completeness with BUSCO recovered 99.6% (98.97% completed and 0.65% fragmented genes) of the 1066 Arthropoda core gene set. (Fig. S1). Using TransDecoder27, we extracted 35,558 protein-encoding transcripts with full Open Reading Frames (ORFs), from which 33,378 (95%) were annotated against InterPro and NCBI NR proteins. As expected, top BLAST hits were against the Coleoptera species, including D. ponderosae (61%) Sitophilus orizae (22%), Anoplophora glabripennis (3%) and Tribolium castaneum (5.7%); whereas the remaining hits were against other insect species (14%).
Gene prediction and functional assignations
We identified 18,765 gene models encoding 20,801 proteins on the Hham1.1 genome assembly using BRAKER2 gene predictor and all available RNA-seq evidence for H. hampei at NCBI. The number of gene models found here for our Hham1.1 assembly is slightly smaller than the previous gene prediction (19,222) performed on the first published H. hampei genome draft21. Completeness of the Hham1.1 gene set using BUSCO recovered 97.2% (94.1% completed and 3.1% fragmented genes) of the Arthropoda core gene set (Fig. S1). BLASTP found 18,364 (88.3%) Hham1.1 predicted proteins similar (e-value  More

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National yield stability
We used the FAOSTAT database (http://www.fao.org/faostat, visited in September 2019) to obtain data on annual crop production (in tons) and area harvested (in hectares) from 1961 to 2010 for 138 crops in 91 populous nations. Following Renard and Tilman16, we accounted for differences among nations in data quality and excluded five nations, namely North Korea, Guinea, Kenya, Mozambique and Zambia, for which at least 20% of the data on area harvested or production were extrapolated by the FAO (see details in16). We calculated for each nation and each year the total annual caloric yield (millions of kcal ha-1). To do so, we first calculated the kcal production of each crop by multiplying the production of each crop by its commodity-specific kilocalorie conversion factor from the USDA Nutrient Database32. In doing so, we were able to compare the production of different crops. Then, we summed these kcal harvests across all crops and divided this value by the sum of harvested area for all crops. We calculated national yield stability (S) as the ratio of mean total annual caloric yield (µT) over its time-detrended standard deviation (σT) for fifty consecutive years (1961–2010). We accounted for a temporal trend of increasing total annual crop yield by implementing a loess regression between annual crop yield and years. σT corresponds to the standard deviation of the residuals of this regression. Finally, we compared this stability index (largely used in the biodiversity-ecological functioning research, e.g.14,16,17,18) with the resilience index used by Zampieri et al.22. Both indices were strongly correlated (r = 0.992), strengthening our findings.
Individual crop yield stability and yield asynchrony
For each country, we quantified the average stability of yields of individual crops as the mean of the inverse of the coefficient of variation of yield of each crop:

$$ {{left( {mathop sum limits_{i = 1}^{N} frac{{mu_{i} }}{{sigma_{i} }}} right)} mathord{left/ {vphantom {{left( {mathop sum limits_{i = 1}^{N} frac{{mu_{i} }}{{sigma_{i} }}} right)} N}} right. kern-nulldelimiterspace} N} $$
(1)

where (mu_{i}) is the temporal mean of crop’s annual kcal yield and (sigma_{i}) its time-detrended standard deviation. Time-detrended crop yield was computed through a loess regression between individual, annual crop yield and years.
We computed the asynchrony between crop yield fluctuations following the index developed by Loreau and De Mazancourt11:

$$ Phi = 1 – frac{{sigma^{2}_{T} }}{{left( {mathop sum nolimits_{i = 1}^{N} sigma_{i} } right)^{2} }} $$
(2)

where Φ is the asynchrony of crop species based on annual caloric yield (millions of kcal ha−1) with (sigma_{T}^{2}) the temporal variance of the time-detrended national yield and (sigma_{i}) the time-detrended standard deviation of each crop’s annual kcal yield. The value of asynchrony varies between zero (perfect synchrony) and one (perfect asynchronous temporal fluctuations).
To test whether yield fluctuations of the most abundant crops have a greater impact on the stability of national food production, we weighted the annual yield of each crop by the proportion of total harvested area occupied by that crop. Average stability of yields of individual crops and yield asynchrony were computed on both the non-weighted and abundance-weighted yields.
Crop diversity
For each country and year, we used both the total number of crop commodities (i.e. crop richness) and the Shannon information index (H′) to quantify crop diversity. H′ weights each crop in a nation by the proportion of total cropland it occupies (pi):

$$ H^{prime } = – mathop sum limits_{i = 1}^{N} left( {p_{i} lnleft[ {p_{i} } right]} right) $$
(3)

with N being the total number of crops grown in a country each year.
The exponential form of the Shannon diversity index gives the effective crop diversity that is the number of crops representing an equal share of harvested area24. In other words, the exponential of the Shannon diversity index weighs all species by their frequency, without favouring either common or rare species24. We averaged the annual effective diversity of crop across the fifty years studied to test the effect of crop diversity on national yield stability.
Agricultural inputs
We extracted the annual national application of nitrogen and the annual cropland area equipped for irrigation from the FAOSTAT database. Because Ireland, New Zealand and Netherlands use much of their fertilizers on pastures rather than croplands, we excluded these nations from our analysis. Similarly, we excluded Egypt because it has 100% of cropland equipped for irrigation. We calculated the annual rates of nitrogen application and irrigation per hectare by dividing their use by the total annual cropland area.
Climate variability
We used global gridded climatic data from the Climate Research Unit of the University of East Anglia33 to compute the year-to-year variability of growing season precipitation and temperature for each country, both strongly affecting the stability of national food production16. From these data, we derived annual precipitation and temperature for each grid cell in a country by taking the sum of monthly precipitation and the mean of monthly temperature values weighted by the proportion of cropland in each grid cell34. We then computed the year-to-year coefficient of variation of cropland-based temperature and precipitation for each country.
Statistical analysis
We used structural equation models (SEMs) to evaluate how irrigation, intensity of use of nitrogen fertilizers and crop diversity affected national yield stability through changes in the average stability of yields of individual crops and asynchrony of yields. SEMs represent a powerful way to disentangle complex mechanisms controlling crop diversity-stability relationships, as previously done in natural ecosystems (e.g.14,15,35,36). We set up two different structural equation models, one based on non-weighted indices of stability of individual crops and asynchrony, the other based on the same indices weighted by the proportion of total harvested area accounted for by each crop. We firstly considered the effects of agricultural inputs and crop diversity on the stability of national food production via the path of average yield stability. The second path quantified the indirect effects of agricultural inputs and crop diversity on national stability via their impacts on crop yield asynchrony. We also accounted for the direct effects of agricultural inputs and crop diversity on national yield stability. Finally, we controlled for the effects of climate variability on total, national yield stability, individual crop yield stability and yield asynchrony. SEMs were run with the lavaan R library37. We used the standardized estimates to compare the relative importance of the different paths. The model fit was evaluated using the Fisher C’score and its associated p values. Because the structural equation model assumes linear relationships between predictors and the dependent variable, we also plotted the relationships between total national yield stability and both asynchrony and average stability of individual crop yield to control for linearity (Fig. 2). Similarly, we investigated the relationships between crop diversity and asynchrony (Fig. 3), as well as between irrigation rate and the average stability of individual crop yield (Fig. 4). More