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Selection of surveys and extraction of dataWe selected published surveys that produced estimates of sperm whale population size or density (see Supplementary Information for methodology; surveys listed in Table 1). We extracted: the type of survey (ship, aerial; acoustic, visual), the years of data collection; the coordinates of the boundary of the study area; the estimates of g(0) and CV (g(0)) used to correct for availability bias, if given; and an estimate of sperm whale population or density in study area with CV. From these we calculated for each survey the survey area with waters greater than 1000 m deep (typical shallow depth limit of sperm whales3). When no value of g(0) was used (8 ship visual surveys) we corrected the population/density estimate using an assumed generic value of g(0) and recalculated the CV to include uncertainty in g(0) (as in Eq. 1 of8). Three ship visual surveys did calculate a single g(0) estimate: 0.62 (CV 0.35)32; 0.57 (CV 0.28)35; 0.61 (CV 0.25)37. These are consistent and suggest a generic g(0) = 0.60 (CV 0.29), also agreeing with g(0) = 0.60 estimated from pooled surveys in the California Current10.Global habitat of sperm whalesTo extrapolate sperm whale densities from surveyed study areas to the sperm whales’ global habitat, we created a one-degree latitude by one-degree longitude grid. We removed the following grid points as not being prime sperm whale habitat1,3,40: points on land or with central depths less than 1000 m; largely ice-covered points in the Beaufort Sea, and the waters north of Svalbard and Russia; the Black Sea and Red Sea both of which have shallow entrances that appear not to be traversable by sperm whales.Generally, food abundance is a good predictor of species distribution. However, this is not possible for sperm whales as we have no good measures of the abundance or distribution of most of their prey, deep-water squid57. Instead, oceanographic measures have been used to describe sperm whale distributions over various spatial scales with a moderate level of success13,14. We follow this approach. Measures that might predict sperm whale density were collected for each grid point, some at just the surface, others at the surface, 500 m depth, 1000 m depth or an average of the measures at the different depths (Supplementary Table S2). Water depth was the strongest predictor in Mediterranean encounters, when compared to slope and distance to shore13. Temperature and salinity have been used as predictors for the distribution of fish and larger marine animals, which could translate into prey availability and thus density for sperm whales58,59. Primary productivity and dissolved oxygen generally dictate the biomass of wildlife in an area, while nitrate and phosphate levels limit the amount of primary productivity in an area60. Eddy kinetic energy is a measure of the dynamism of physical oceanography which is becoming a commonly used predictor of cetacean habitat61. We did not use: latitude and longitude as these primarily describe the general geographic distribution of the study areas, and geographic aggregates of sperm whale catches62 as these proved to have no predictive power. The mean values of the 14 predictor measures were calculated over calendar months for each grid point, and then over the grid points in each study area.To obtain predictors of the sperm whale density at each grid point, we then made quadratic regressions of the density of sperm whales in each study area (i), d(i), on the mean values of the predictor measures, weighting each study area by its surface area. Because the surveys were conducted over different time periods, the densities were corrected based on the estimated trajectory of global sperm whale populations by multiplying d(i) by the ratio of the global population in 1993 over that in the mid-year of the survey (as in Fig. 4). Predictor variables were selected using forward stepwise selection based upon reduction in AIC.Sperm whale population sizeThe population of sperm whales globally, N, was then calculated as follows:$$N=sum_{k}dleft(kright)cdot aleft(kright),$$
(1)
where a{k} are the parameters of the regression; the summation is over k, the grid points; d(k) is the estimated sperm whale density at grid point k from the habitat suitability model; and a(k) is the area of the 1° cell centred on grid point k. Population estimates for other ocean areas (North Atlantic, North Pacific, Southern Hemisphere) were calculated similarly.The CVs of these population estimates were calculated following the methodology in8, (although there is an error in Eq. (3) of8 such that the squareroot symbol covers both the numerator and denominator rather than just the numerator). The error due to uncertain density estimates for the different surveys is:$$CVleft({D}_{T}right)=frac{sqrt{sum_{i}{left(CV({n}_{i})cdot {n}_{i}right)}^{2}}}{sum_{i}{n}_{i}}.$$
(2)
This is combined with the uncertainty in the extrapolation process (output from the linear models), CV(extrap.), to give an overall CV for the population estimate:$$CVleft(Nright)=sqrt{{CV({D}_{T})}^{2}+{CV(mathrm{extrap}.)}^{2}.}$$
(3)
Post-whaling trend in population sizeWe compiled a database of series of surveys producing population estimates of the same study area during the period 1978 (by which time most commercial sperm whaling had ceased) and 2022. Each series had to span at least 10 years, and all of the surveys in the series had to be comparable in terms of area covered throughout the time span. There also had to have been at least 3 surveys for a data set to be included.The data consisted of the survey area, A, the estimated population in area A in year y (for multi-year surveys, y would be the midpoint of the data collection years), nE(A,y), and the provided CV of that estimate, CV(nE(A,y)). The data series used for these analyses are summarized in Table 3.For each survey area, A, we calculated the trend in logarithmic population size, r(A), over time using weighted linear regression:$${text{Log}}left( {n_{E} left( {A,y} right)} right) , sim {text{ constant}}left( A right) , + rleft( A right) cdot y. left[ {{text{weight }} = { 1}/left( {{1} + {text{ CV}}left( {n_{E} left( {A,y} right)} right)} right)^{{2}} } right]$$
(4)
Table 3 also includes other published estimates of sperm whale population trends, from sighting rates or mark-recapture analyses of photoidentification data, with these estimates also having to span at least 10 years of data collection, and include data collected in three or more different years.Population trajectoryTo examine possible trajectories of the global sperm whale population following the start of commercial whaling in 1712, we used a variant of the theta-logistic, a population model that has been employed in other recent analyses of the population trajectories of large cetaceans45,63. The theta-logistic model is:$$nleft(y+1right)=nleft(yright)+rcdot nleft(yright)left(1-{left(frac{nleft(yright)}{nleft(1711right)}right)}^{theta }right)-fleft(yright)cdot cleft(yright).$$
(5)

Here, n(y) is the population of sperm whales in year y, r is the maximum potential rate of increase of a sperm whale population, and θ describes how the rate of increase varies with population size relative to its basal level before whaling in 1711, n(1711). The recorded catch in year y is c(y) and f(y) is a correction for bias in recorded catches.Whaling reduced the proportion of large breeding males64, likely disrupted the social cohesion of the females3, and may have had other lingering effects which reduced pregnancy or survival, and thus the rate of increase. Poaching has been found to reduce the reproductive output of African elephants, Loxodonta Africana, which have a similar social system to the sperm whales3, and this effect lingers well beyond the effective cessation of poaching46. There is some evidence for these effects of what we call “social disruption” on sperm whale population dynamics20,46,65. We added a term to the theta-logistic to account for such effects:$$nleft(y+1right)=nleft(yright)left[1+rcdot left(1-{left(frac{nleft(yright)}{nleft(1711right)}right)}^{theta }right)-qcdot frac{sum_{t=y-T}^{y}f(t)cdot c(t)}{nleft(y-Tright)}right]-f(y)cdot c(y).$$
(6)

Here, (frac{sum_{t=y-T}^{y}f(t)cdot c(t)}{nleft(y-Tright)}) is the proportion of the population killed over the last T years, and q is the reduction in the rate of increase when almost all the whales have been killed. This reduction is modelled to fall linearly as the proportion killed declines to zero.The global sperm whale population has some geographic structure18. Females appear to rarely move between ocean basins, and males seem to largely stay within one basin. Furthermore, sperm whaling was progressive, moving from ocean area to ocean area as numbers were depleted4. We model this by assuming K largely separate sperm whale subpopulations of equal size. Exploitation in 1712 starts in subpopulation 1 and moves to subpopulations 1 and 2 when the population 1 falls to α% of its initial value, and so on for the other ocean areas. The catch in each year in each area being exploited is pro-rated by the sizes of the different subpopulations being exploited. The population model for subpopulation k, which is one of the KE subpopulations being exploited in year y, is:$$nleft(k,y+1right)=nleft(k,yright)left[1+rcdot left(1-{left(frac{nleft(k,yright)}{nleft(k,1711right)}right)}^{theta }right)-qcdot frac{sum_{t=y-T}^{y}C(k,t)}{nleft(k,y-Tright)}right]-Cleft(k,yright),$$
(7)
where the estimated catch in year y in subpopulation k is given by: (Cleft(k,yright)=f(y)cdot c(y)cdot n(k,y)/sum_{{k}^{mathrm{^{prime}}}= More

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Dataset acquisitionPlant-frugivore network data were obtained through different online sources and publications (Supplementary Table 1). Only networks that met the following criteria were retrieved: (i) the network contains quantitative data (a measure of interaction frequency) from a location, pooling through time if necessary; (ii) the network includes avian frugivores. Importantly, we removed non-avian frugivores from our analyses because only 28 out of 196 raw networks (before data cleaning) sampled non-avian frugivores, and not removing non-avian frugivores would generate spurious apparent turnover between networks that did vs. did not sample those taxa. In addition, the removal of non-avian frugivores did not strongly decrease the number of frugivores in our dataset (Supplementary Fig. 20a) or the total number of links in the global network of frugivory (Supplementary Fig. 20b). Furthermore, non-avian frugivores, as well as their interactions, were not shared across ecoregions and biomes (Supplementary Fig. 21), so their inclusion would only strengthen the results we found (though as noted above, we believe that this would be spurious because they are not as well sampled); (iii) the network (after removal of non-avian frugivores) contains greater than two species in each trophic level. Because this size threshold was somewhat arbitrary, we used a sensitivity analysis to assess the effect of our network size threshold on the reported patterns (see Sensitivity analysis section in the Supplementary Methods and Supplementary Figs. 22–24); and (iv) network sampling was not taxonomically restricted, that is, sampling was not focused on a specific taxonomic group, such as a given plant or bird family. Note, however, that authors often select focal plants or frugivorous birds to be sampled, but this was not considered as a taxonomic restriction if plants and birds were not selected based on their taxonomy (e.g., focal plants were selected based on the availability of fruits at the time of sampling, or focal birds were selected based on previous studies of bird diet in the study site). The first source for network data was the Web of Life database42, which contains 33 georeferenced plant-frugivore networks from 28 published studies, of which 12 networks met our criteria.We also accessed the Scopus database on 04 May 2020 using the following keyword combination: (“plant-frugivore*” OR “plant-bird*” OR “frugivorous bird*” OR “avian frugivore*” OR “seed dispers*”) AND (“network*” OR “web*”) to search for papers that include data on avian frugivory networks. The search returned a total of 532 studies, from which 62 networks that met the above criteria were retrieved. We also contacted authors to obtain plant-frugivore networks that were not publicly available, which provided us a further 110 networks. The remaining networks (N = 12) were obtained by checking the database from a recently published study12. In total, 196 quantitative avian frugivory networks were used in our analyses.Generating the distance matrices to serve as predictor and response variablesEcoregion and biome distancesWe used the most up-to-date (2017) map of ecoregions and biomes3, which divides the globe into 846 terrestrial ecoregions nested within 14 biomes, to generate our ecoregion and biome distance matrices. Of these, 67 ecoregions and 11 biomes are represented in our dataset (Supplementary Figs. 1 and 2). We constructed two alternative versions of both the ecoregion and biome distance matrices. In the first, binary version, if two ecological networks were from localities within the same ecoregion/biome, a dissimilarity of zero was given to this pair of networks, whereas a dissimilarity of one was given to a pair of networks from distinct ecoregions/biomes (this is the same as calculating the Euclidean distance on a presence–absence matrix with networks in rows and ecoregion/biomes in columns).In the second, quantitative version, we estimated the pairwise environmental dissimilarity between our ecoregions and biomes using six environmental variables recently demonstrated to be relevant in predicting ecoregion distinctness, namely mean annual temperature, temperature seasonality, mean annual rainfall, rainfall seasonality, slope and human footprint38. We obtained climatic and elevation data from WorldClim 2.143 at a spatial resolution of 1-km2. We transformed the elevation raster into a slope raster using the terrain function from the raster package44 in R45. As a measure of human disturbance, we used human footprint—a metric that combines eight variables associated with human disturbances of the environment: the extent of built environments, crop land, pasture land, human population density, night-time lights, railways, roads and navigable waterways26. The human footprint raster was downloaded at a 1-km2 resolution26. Because human footprint data were not available for one of our ecoregions (Galápagos Islands xeric scrub), we estimated human footprint for this ecoregion by converting visually interpreted scores into the human footprint index. We did this by analyzing satellite images of the region and following a visual score criterion26. Given the previously demonstrated strong agreement between visual score and human footprint values26, we fitted a linear model using the visual score and human footprint data from 676 validation plots located within the Deserts and xeric shrublands biome – the biome in which the Galápagos Islands xeric scrub ecoregion is located – and estimated the human footprint values for our own visual scores using the predict function in R45.We used 1-km2 resolution rasters and the extract function from the raster package44 to calculate the mean value of each of our six environmental variables for each ecoregion in our dataset. Because biomes are considerably larger than ecoregions (which makes obtaining environmental data for biomes more computationally expensive) we used a coarser spatial resolution of 5-km2 for calculating the mean values of environmental variables for each biome. Since a 5-km2 resolution raster was not available for human footprint, we transformed the 1-km2 resolution raster into a 5-km2 raster using the resample function from the same package.To combine these six environmental variables into quantitative matrices of ecoregion and biome environmental dissimilarity, we ran a Principal Component Analysis (PCA) on our scaled multivariate data matrix (where rows are ecoregions or biomes and columns are environmental variables). From this PCA, we selected the scores of the four and three principal components, which represented 89.6% and 88.7% of the variance for ecoregions and biomes, respectively, and converted it into a distance matrix by calculating the Euclidean distance between pairs of ecoregions/biomes using the vegdist function from the vegan package46. Finally, we transformed the ecoregion or biome distance matrix into a N × N matrix where N is the number of local networks. In this matrix, cell values represent the pairwise environmental dissimilarity between the ecoregions/biomes where the networks are located. The main advantage of using this quantitative approach is that, instead of simply evaluating whether avian frugivory networks located in distinct ecoregions or biomes are different from each other in terms of network composition and structure (as in our binary approach), we were also able to determine whether the extent of network dissimilarity depended on how environmentally different the ecoregions or biomes are from one another.Local-scale human disturbance distanceTo generate our local human disturbance distance matrix, we extracted human footprint data at a 1-km2 spatial resolution26 and calculated the mean human footprint values within a 5-km buffer zone around each network site. For the networks located within the Galápagos Islands xeric scrub ecoregion (N = 4), we estimated the human footprint index using the same method described in the previous section for ecoregion- or biome-scale human footprint. We then calculated the pairwise Euclidean distance between human footprint values from our network sites. Thus, low cell values in the local human disturbance distance matrix indicate pairs of network sites with a similar level of human disturbance, while high values represent pairs of network sites with very different levels of human disturbance.Spatial distanceThe spatial distance matrix was generated using the Haversine (i.e., great circle) distance between all pairwise combinations of network coordinates. In this matrix, cell values represent the geographical distance between network sites.Elevational differenceWe calculated the Euclidean distance between pairwise elevation values (estimated as meters above sea level) of network sites to generate our elevational difference matrix. Elevation values were obtained from the original sources when available or using Google Earth47. In the elevational difference matrix, low cell values represent pairs of network sites within similar elevations, whereas high values represent pairs of network sites within very different elevations.Network sampling dissimilarityWe used the metadata retrieved from each of our 196 local networks to generate our network sampling dissimilarity matrices, which aim to control statistically for differences in network sampling. There are many ways in which sampling effort could be quantified, so we began by calculating a variety of metrics, then narrowed our options by assessing which of these was most related to network metrics. We divided the sampling metrics into two categories: time span-related metrics (i.e., sampling hours and months) and empirical metrics of sampling completeness (i.e., sampling completeness and sampling intensity), which aim to account for how complete network sampling was in terms of species interactions (Supplementary Table 2).We selected the quantitative sampling metrics to be included in our models based on (i) the fit of generalized linear models evaluating the relationship between number of sampling hours and sampling months of the study and network-level metrics (i.e., bird richness, plant richness and number of links), and (ii) how well time span-related metrics, sampling completeness and sampling intensity predicted the proportion of known interactions that were sampled in each local network (hereafter, ratio of interactions) for a subset of the data. This latter metric, defined as the ratio between the number of interactions in the local network and the number of known possible interactions in the region involving the species in the local network, captures raw sampling completeness. Therefore, ratio of interactions estimates, for a given set of species, the proportion of all their interactions known for a region that are found to occur among those same species in the local network. To calculate this metric, we needed high-resolution information on the possible interactions, so we used a subset of 14 networks sampled in Aotearoa New Zealand, since there is an extensive compilation of frugivory events recorded for this country48. After this process, we selected number of sampling hours, number of sampling months and sampling intensity for inclusion in our statistical models (Supplementary Figs. 7 and 8; Supplementary Table 2). We generated the corresponding distance matrices by calculating the Euclidean distance between metric values. Similarly, we generated a Euclidean distance matrix for differences in sampling year between pairs of networks, which aims to account for long-term changes in the environment, species composition and network sampling methods. We obtained the sampling year of our local networks from the original sources and calculated the mean sampling year value for those networks sampled across multiple years.Because sampling methods, such as sampling design, focus (i.e., focal taxa, which determines whether a zoocentric or phytocentric method was used), interaction frequency type (i.e., how interaction frequency was measured) and coverage (total or partial) might also affect the observed plant-frugivore interactions49, we combined these variables into a single distance matrix to estimate the overall differences in sampling methods between networks. Because most of these variables were categorical with multiple levels (Supplementary Table 3), we generated our method’s dissimilarity matrix by using a generalization of Gower’s distance method50, which allows the treatment of different types of variables when calculating distances. For this, we used the dist.ktab function from the ade4 package51. We ran a Principal Coordinates Analysis (PCoA) on this distance matrix, selected the first four axes, which explained 81.2% of the variation in method’s dissimilarity, and calculated the Euclidean distance between pairs of networks using the vegdist function from the vegan package46 in R45.Network dissimilarityWe generated three network dissimilarity matrices to be our response variables in the statistical models. In the first, cell values represent the pairwise dissimilarity in species composition between networks (beta diversity of species; βS)27. Second, we measured interaction dissimilarity (beta diversity of interactions; βWN), which represents the pairwise dissimilarity in the identity of interactions between networks27. Importantly, we did not include interaction rewiring (βOS) in our main analysis because this metric can only be calculated for networks that share interaction partners (i.e., it estimates whether shared species interact differently)27, which limited the number and the spatial distribution of networks available for analysis (but see the Rewiring analysis section for an analysis on the subset of our dataset for which this was possible). Metrics were calculated using the network_betadiversity function from the betalink package52 in R45.Finally, we calculated a third dissimilarity matrix to capture overall differences in network structure. We recognize that there are many potential metrics of network structure, and that many of these are strongly correlated with one another53,54,55,56. We therefore chose a range of metrics that captured the number of links, their relative weightings (including across trophic levels), and their arrangement among species, then combined these into a single distance matrix. Specifically, we quantified network structural dissimilarity using the following metrics: weighted connectance, weighted nestedness, interaction evenness, PDI and modularity.Weighted connectance represents the number of links relative to the number of possible links, weighted by the frequency of each interaction55, and is therefore a measure of network-level specialization (higher values of weighted connectance indicate lower specialization). Importantly, it has been suggested that connectance affects persistence in mutualistic systems54. We measured nestedness (i.e., the pattern in which specialist species interact with proper subsets of the species that generalist species interact with) using the weighted version of nestedness based on overlap and decreasing fill (wNODF)57. Notably, nested structures have been commonly reported in plant-frugivore networks33. Interaction evenness is Shannon’s evenness index applied for species interactions and represents how evenly distributed the interactions are in the network21,58. This metric has been previously demonstrated to decline with habitat modification as a consequence of some interactions being favored over others in high-disturbance environments21. PDI (Paired Difference Index) is a measure of species-level specialization on resources and a reliable indicator not only of specialization, but also of absolute generalism59. Thus, this metric contributes to understanding of the ecological processes that drive the prevalence of specialists or generalists in ecological networks59. In order to obtain a network-level PDI, we calculated the weighted mean PDI for each local network. Finally, we calculated modularity (i.e., the level of compartmentalization within networks) using the DIRTPLAwb+ algorithm60. Modularity estimates the extent to which species within modules interact more with each other than with species from other modules61, and it has been demonstrated to affect the persistence and resilience of mutualistic networks54. All the selected network metrics are based on weighted (quantitative) interaction data, as these have been suggested to be less biased by sampling incompleteness62 and to better reflect environmental changes21. All network metrics were calculated using the bipartite package63 in R45.We ran a Principal Component Analysis (PCA) on our scaled multivariate data matrix (N × M where N is the number of local networks in our dataset and M is the number of network metrics), selected the scores of the three principal components, which represented 89.9% of the variance in network metrics, and converted it into a network structural dissimilarity matrix by calculating the Euclidean distance between networks. In this distance matrix, cell values represent differences in the overall architecture of networks (over all the network metrics calculated), and therefore provide a complementary approach for evaluating how species interaction patterns vary across large-scale environmental gradients.Statistical analysisWe employed a two-tailed statistical test that combines Generalized Additive Models (GAM)29 and Multiple Regression on distance Matrices (MRM)30 to evaluate the effect of each of our predictor distance matrices on our response matrix. With this approach, we were able to fit GAMs where the predictor and responsible variables are distance matrices, while accounting for the non-independence of distances from each local network by permuting the response matrix30. The main advantage of using GAMs is their flexibility in modeling non-linear relationships through smooth functions, which are represented by a sum of simpler, fixed basis functions that determine their complexity29. Using GAM-based MRM models allowed us to obtain F values for each of the smooth terms (i.e., smooth functions of the predictor variables in our model), and test statistical significance at the level of individual variables. The binary versions of ecoregion and biome distance matrices (with two levels, “same” or “distinct”) were treated as categorical variables in the models, and t values were used for determining statistical significance. We fitted GAMs with thin plate regression splines64 using the gam function from the mgcv package29 in R45. Smoothing parameters were estimated using restricted maximum likelihood (REML)29. Our GAM-based MRM models were calculated using a modified version of the MRM function from the ecodist package65, which allowed us to combine GAMs with the permutation approach from the original MRM function (see Code availability). All the models were performed with 1000 permutations (i.e., shuffling) of the response matrix.We explored the unique and shared contributions of our predictor variables to network dissimilarity using deviance partitioning analyses. These were performed by fitting reduced models (i.e., GAMs where one or more predictor variables of interest were removed) using the same smoothing parameters as in the full model and comparing the explained deviance. We fixed smoothing parameters for comparisons in this way because these parameters tend to vary substantially (to compensate) if one of two correlated predictors is dropped from a GAM.Assessing the influence of individual studies on the reported patternsBecause our dataset comprises 196 local frugivory networks obtained from 93 different studies, and some of these studies contained multiple networks, we needed to evaluate whether our results were strongly biased by individual studies. To do this, we followed the approach from a previous study66 and tested whether F values of smooth terms and t values of categorical variables (binary version of ecoregion and biome distances) changed significantly when jackknifing across studies. We did this by dropping one study from the dataset and re-fitting the models, and then repeating this same process for all the studies in our dataset.We found a number of consistent patterns within different subsets of the data (Supplementary Figs. 15 and 16); however, some of the patterns we observed appear to be driven by individual studies with multiple networks, and hence are less representative. For instance, the study with the greatest number of networks in our dataset (study ID = 76), which contains 35 plant-frugivore networks sampled across an elevation gradient in Mt. Kilimanjaro, Tanzania67, had an overall high influence on the results when compared with the other studies. By re-running our GAM-based MRM models after removing this study from our dataset, we found that the effect of biome boundaries on interaction dissimilarity is no longer significant, whereas the effects of ecoregion boundaries, human disturbance distance, spatial distance and elevational differences remained consistent with those from the full dataset (Supplementary Table 33). Nevertheless, all the results were qualitatively similar to those obtained for the entire dataset when using network structural dissimilarity as the response variable (Supplementary Table 34).Rewiring analysisInteraction rewiring (βOS) estimates the extent to which shared species interact differently27. Because this metric can only be calculated for networks that share species from both trophic levels, we selected a subset of network pairs that shared plants and frugivorous birds (N = 1314) to test whether interaction rewiring increases across large-scale environmental gradients. Importantly, since not all possible combinations of network pairs contained values of interaction rewiring (i.e., not all pairs of networks shared species), a pairwise distance matrix could not be generated for this metric. Thus, we were not able to use the same statistical approach used in our main analysis, which is based on distance matrices (see Statistical analysis section). Instead, we performed a Generalized Additive Mixed-effects Model (GAMM) using ecoregion, biome, human disturbance, spatial, elevational, and sampling-related distance metrics as fixed effects and network IDs as random effects (to account for the non-independence of distances) (Supplementary Table 35). We also performed a reduced model with only ecoregion and biome distance metrics as predictor variables (Supplementary Table 36). The binary version of ecoregion and biome distance metrics (with two levels, “same” or “distinct”) were used as categorical variables in both models. Interaction rewiring (βOS) was calculated using the network_betadiversity function from the betalink package52 in R45. Although it has been recently argued that this metric may overestimate the importance of rewiring for network dissimilarity68, our main focus was not the partitioning of network dissimilarity into species turnover and rewiring components, but rather simply detecting whether the sub-web of shared species interacted differently. In this case, βOS (as developed by ref. 27) is an adequate and useful metric68. We fitted our models using the gamm4 function from the gamm4 package69 in R45. Smoothing parameters were estimated using restricted maximum likelihood (REML)29.Reporting summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More

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