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Bigg’s killer whale photo-identification datasetThe dataset of this study includes photos of Bigg’s killer whale individuals accumulated over a period of 8 years (2011–2018), from the coastal waters of southeastern Alaska down to central California15. None of these animals were directly approached explicitly for this study. All photo-identification data was collected under federally authorized research licenses or from beyond mandated minimum viewing distances.Supplementary Figure S1 visualizes a series of example images of this dataset. Each image contains one or more individuals. In addition to the identification name of the individual(s), further metadata such as photographer, GPS-coordinates, date, and time are provided. Every identification label is an alphanumeric sequence based on the animals’ ecotype (T—Transient), order of original documentation (e.g. T109), and order of birth (e.g. T109A2—the second offspring of the first offspring of T109)15.A parsing procedure was designed to verify, analyze, and prepare the image data, guaranteeing adequate preparation for subsequent machine (deep) learning methods. Results of the entire data parsing procedure are presented in Fig. 2 and Supplementary Table S1. Figure 2 visualizes the number of identified individuals, together with the total amount of occurrences in descending order, considering (1) all images, and (2) only photos including a single label. General statistics with respect to the entire dataset are reported in the caption of Fig. 2. Supplementary Table S1 illustrates the 10 most commonly occurring individuals across all 8 years of data, considering all images including single and multiple labels, compared to photos only containing a single label.The dataset exhibits a substantial class imbalance, as evidenced by the exponential decline in frequencies per killer whale individual (see Fig. 2). Especially for real-world datasets, such unbalanced data partitioning is a common and well-known phenomenon, also referred to as long-tailed data distribution79. Such long-tailed data distributions are divided into two sections79: (1) the Head region—representing the most commonly identified killer whale individuals, and (2) the Long-Tail region—visualizing a significantly larger number of killer whale individuals, however, with considerably less occurrences. For the purpose of this pilot study, the top-100 most commonly occurring killer whale individuals were selected for supervised classification and as boundary between the head and long-tail area (see Fig. 2). The defined boundary of the top-100 killer whales (head region) represents approximately 1/4 (100 out of 367) of the individuals, however, covering about 2/3 (55,305 out of 86,789) of the entire dataset of single-labeled images.Figure 2Bigg’s killer whale image long-tailed data distribution (2011–2018), summing up a total of 121,095 identification images, with 86,789 containing single labels, as well as 34,306 photos including multiple labels, resulting in 367 identified individuals (average number of images per individual (approx)456, standard deviation (approx)442). The two colored graphs visualize the number of identification images per whale in descending order w.r.t. all images, including single and multiple labels (purple curve) and those only containing a single label (green curve). Furthermore, an exemplary data point is visualized for both curves, presenting the number of identification images in relation to a selected number of whales, here for the top-100, clearly describing the exponential decline. Moreover, the number of animals at which the total amount of identification images is More

Selection-switch experimentThe dataset used for this article is previously published14, but we include a brief summary for completeness: Natural seawater was collected and used to inoculate microcosms in a 2 × 2 factorial crossover design with 3 replicates conducted for 50 days, which were sampled 18 times during the experiment. Half of the microcosms were given high (H) resource supply, whereas the other half were given low (L) resource supply. The factor of resource supply level was constant throughout the experiment. The other factor was the selection regime, which meant that the microcosms were either given continuous supply of nutrients (favouring K-selection, and hence the designation K) or being pulse-fed with nutrients after diluting the contents of the microcosms with growth medium (favouring r-selection, designated R). The active selection regime was switched at the experimental halfway point (between days 28 and 29), yielding two selection groups designated as RK and KR.DNA was extracted from the collected samples, and the V3-V4 region of the bacterial 16S-rRNA gene was amplified with PCR using broad-coverage primers and the index sequences were ligated. The amplicon library was pooled and sequenced with two runs on an Illumina MiSeq machine. The reads are available at the European Nucleotide Archive with accession number ERS7182426-ERS7182513.The USEARCH pipeline47 (v11) was used to remove low-quality reads and cluster the reads into OTUs at 97% similarity level. Finally, the taxonomy of the OTUs was determined by the Sintax classifier using data from the RPD training set (v.16) where the confidence threshold was set to 80%.Quantification of bacterial densityFor each sample, the bacterial density was quantified using flow cytometry (BC Accuri C6)14. In brief, the bacterial communities were diluted in 0.1x TE buffer, mixed with 2x SYBR Green II RNA gel stain (ThermoFisher Scientific) and incubated in the dark at room temperature for 15 minutes. Then, each sample was measured for 2.5 minutes at 35 μL min−1 with an FL1-H (533/30 nm) threshold of 3000. We gated the bacterial population as those events with an FL1-A ( > 10^4) and FSC-A (< 10^5). The raw flow cytometry data files are available at https://doi.org/10.6084/m9.figshare.15104409.Alignment and phylogentic treeThe selection-switch dataset was acquired directly from the authors14. This dataset consists of a total of 206 samples. Two of these samples were taken from the communities from which the reactors were inoculated, whereas the other samples were taken from the microcosms with 17 time points x 4 regimes x 3 replicates. We discarded the inoculum samples for further analysis. The OTU reference sequences were aligned with SINA version 1.6.148 using the SILVA Release 138 NR 99 SSU dataset49. Using this aligment, the phylogentic tree was constructed by neighbour-joining using MEGA X50 with default parameters.Filtering and preprocessingThe mean number of reads per sample was 63,460 with standard deviation 31,411. For our analysis, we wanted to estimate the abundance of each OTU as accurately as possible and therefore skipped any correction for unequal sequencing depth. Read counts for each OTU in each sample were divided by the total number of reads for the sample, generating relative abundances. Thereafter, all OTUs having a maximum abundance (across all samples) below a certain threshold, were removed. Three levels of filtering thresholds (as count proportions) were applied: High level at ( 5cdot 10^{-3} ), medium level at ( 1cdot 10^{-3} ) and low level at ( 5cdot 10^{-4}). The purpose of the filtering was to remove rare OTUs in order to avoid noise and spurious correlations11. For obtaining estimates of absolute abundances, the relative abundances were scaled by the estimate of total bacterial cell density for each sample. The phyloseq package (version 1.36.0)51 and the R programming language (version 4.1.1)52 facilitated this procedure. In addition, we wrote an R-package named micInt (version 0.18.0, available at https://github.com/AlmaasLab/micInt) to facilitate and provide a pipeline for the analysis.Similarity measures and addition of noiseFor this study, we used two similarity measures, the Pearson correlation and the Spearman correlation. A similarity measure, as referred to in this article, can be thought of as a function (f: mathbb {R}^ntimes mathbb {R}^n rightarrow D) where ( D = [-1,1] ). In this regard, (fleft( {mathbf {x}},{mathbf {y}}right) ) is the similarity of two abundance vectors ( {mathbf {x}} ) and ({mathbf {y}}) belonging to different OTUs, where (fleft( {mathbf {x}},{mathbf {y}}right) = 1) indicates perfect correlation, (fleft( {mathbf {x}},{mathbf {y}}right) = 0) indicates no correlation and (fleft( {mathbf {x}},{mathbf {y}}right) = -1) indicates perfect negative correlation. Noise was added to distort patterns of double zeros, which otherwise could result in spurious correlations. Given two vectors ( {mathbf {x}} ) and ( {mathbf {y}} ) of abundances, normally distributed noise was added to each of the abundance vectors, and the similarity measure has invoked thereafter: Given a similarity measure f, the similarity between the abundance vectors after adding noise is given by:$$begin{aligned} f^*left( {mathbf {x}},{mathbf {y}}right) =fleft( {mathbf {x}} +varvec{varepsilon _x},{mathbf {y}}+varvec{varepsilon _y }right) , end{aligned}$$ (1) where (varvec{varepsilon _x}) and ( varvec{varepsilon _y} ) are random vector where all components are independent and normally distributed with mean zero and variance ( gamma ^2 ). The level of noise ( gamma ) was determined by the smallest non-zero relative abundance ( x_{mathrm {min}} ) in the dataset and a fixed constant s called the magnitude factor, such that ( gamma = scdot x_{mathrm {min}}). For no noise, ( s=0 ), for low noise ( s=1 ), for middle noise ( s=10 ) and for high noise ( s=100 ).Network creationSignificance of the pairwise OTU associations were determined by the ReBoot procedure introduced by Faust et al.22 and shares the underlying algorithm used in the CoNet Cytoscape package53. This approach accepts a dataset of microbial abundances and a similarity measure, and evaluates for each pair of OTUs in the dataset the null hypothesis ( H_0 ): “The association between the OTUs is caused by chance”. By bootstrapping over the samples, the similarity score of each pair of OTUs is estimated, forming a bootstrap distribution. By randomly permuting the pairwise abundances of OTUs and finding the pairwise similarity scores, a bootstrap distribution is formed. The bootstrap and permutation distribution are then compared with a two-sided Z-test (based on the normal distribution) to evaluate whether the difference is statistically significant. For this, the z-value, p-value and q-value (calculated by the Benjamini-Hochberg-Yekutieli procedure54) are provided for each pair of OTUs in the dataset. Our ReBoot approach is based on the R-package ccrepe (version 1.28.0)55, but is integrated into the micInt package with the following major changes: The original ReBoot uses renormalization of the permuted abundances to keep the sum-to-constant constraint. Whereas this is reasonable to do with relative abundances, our modified version enables turning this feature off when we analyse data with absolute abundances. Optimizations have been made to memory use and CPU consumption to enable analyses of large datasets. In contrast to the usual ReBoot procedure, networks generated by the different similarity measures are not merged by p-value, but kept as they are. For our analysis the number of bootstrap and permutation iterations was set to 1000. All OTUs being absent in more than ( ncdot 10^{-frac{4}{n}} ) samples, where n is the total number of samples, were excluded through the errthresh argument but still kept for renormalization (if turned on). The associations were made across all samples, even the ones belonging to a different selection group or resource supply.Dynamic PCoA visualizationAll samples in the dataset were used for PCoA ordination, where the Bray-Curtis distance metric between the samples was applied before creating the decomposition. After the ordination was computed, the samples were divided into four facets based on their combination of current selection regime and resource supply. Finally, all samples belonging to the same microcosm were connected by a line in chronological order and the line was given a separate style based on the resource supply and coloured to visually distinguish it from the two other replicate microcosm within the same facet.Permutational multivariate analysis of varianceSequential PERmutational Multivariate Analysis of VAriance (PERMANOVA) of the samples was conducted on the absolute abundances, where only the samples from day 28 and 50 were included. These sample points correspond to time just before the experimental selection-regime crossover and a point at the end of the experiment. These days were selected because they were the most likely to capture the composition of stable communities in contrast to transient ones. The procedure was carried out by the function adonis from the R package vegan (version 2.5-7) with ( 10^6 ) permutations. The dependent data given to the function was the matrix of one minus the Spearman correlation of the samples (in order to resample dissimilarity), while the independent variables were the selection group (first variable) and the current selection regime (second variable).Network visualizationThe networks were plotted by the R package igraph (version 1.2.6)56. Network modules were found by the walktrap25 algorithm implemented in igraph with the setting steps=20, including the positive edges only. Later, the negative edges were added and the networks plotted with the community labelling.The time dynamics of the networks were visualised by taking the former network and adjusting the node colour and size, as well as the edge colour. For this, a certain combination of selection group (i.e RK) and resource supply (i.e H) was chosen. Further, let (x_{i,j,k} ) be the abundance of OTU k at sampling day i in microcosm j. As there are three replicates, we have that ( j= 1,2,3). If the underlying network was created by Pearson correlation, we denote the day mean ( x_{i,.,k} ) as the average over the replicates, this is:$$begin{aligned} x_{i,.,k}= frac{x_{i,1,k}+x_{i,2,k}+x_{i,3,k}}{3}. end{aligned}$$ (2) The time series mean of OTU k, (x_{.,.,k} ) is the mean of these daily means over all sampling days,$$begin{aligned} x_{.,.,k} = frac{sum _{i=1}^{N}x_{i,.,k}}{N}, end{aligned}$$ (3) where N denotes the number of sampling days. Furthermore, we have the associated standard deviation (sigma _k) as given by:$$begin{aligned} sigma _k =sqrt{ frac{1}{N}sum _{i=1}^{N}left( x_{i,.,k}-x_{.,.,k}right) ^2}. end{aligned}$$ (4) The z-value of the abundance of OTU k at day i is then:$$begin{aligned} z_{i,k} = frac{x_{i,.,k}-x_{.,.,k}}{sigma _k}. end{aligned}$$ (5) This value is used in the mapping of the node sizes and colours. The node for OTU k at sampling day i has the size ( a+bcdot left| z_{i,k}right| ), where a and b are constants. Furthermore, the same node is coloured: Black if ( z_{i,k} < -1 ). This indicates that the OTU that day had a lower abundance than the average. Grey if (-1 le z_{i,k} le 1 ). This indicates that the OTU that day had about the same abundance as the average. Orange if ( z_{i,k} > 1 ). This indicates that the OTU that day had a higher abundance than the average.

Furthermore, the edge colour are dependent on the product of the two participating nodes. Hence, the edge between OTU k and OTU l at day i will have the colour:

Red if ( z_{i,k}cdot z_{i,l} < -0.3 ). This shows a contribution to a negative interaction. Gray if (-0.3 le z_{i,k}cdot z_{i,l} le 0.3 ). This shows no major contribution of neither a positive nor negative interaction. Blue if (z_{i,k}cdot z_{i,l} > 0.3 ). This shows a contribution to a positive interaction.

Our approach is motivated by the fact that the Pearson correlation ( rho _{k,l} ) of the day means of OTU k and OTU l is given by:$$begin{aligned} rho _{k,l} = frac{1}{N} sum _{i=1}^{N} z_{i,k}cdot z_{i,l}. end{aligned}$$
(6)
For the Spearman correlation, the visualization is based on the rank of each of the OTU abundance values in a sample. Hence, instead of using the raw abundances ( x_{i,j,k} ) in the calculation of the day mean, the ranks ( r_{i,j,k} ) are used instead, and all subsequent calculations and mappings are the same. In a scenario when there is only one replicate, the quantity ( rho _{k,l} ) would then be the Spearman correlation of the abundances of OTU k and OTU l. More

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I study snakes in Brazil’s Ribeira Valley, an area where snake bites are very common. I focus mainly on the venomous lancehead (Bothrops jararaca), which is responsible for most of the 26,000 recorded snake bites in Brazil each year. In this photo, however, I’m holding a juvenile red-tailed boa (Boa constrictor).After my undergraduate biology degree at the Federal University of São Carlos, I spent two years at the Butantan Institute in São Paulo, studying snakes that live in São Paulo’s rivers and urban parks. I then did a master’s degree at São Paulo State University, researching the reproductive biology of the bushmaster (Lachesis muta) — one of the largest venomous snakes in the Americas and one of the few snakes that show a form of parental care. It lays its eggs in underground burrows and remains curled around them for long periods of time to keep them warm and protected.When I was 12 years old, I visited the Acqua Mundo aquarium on the coast of São Paulo and fell in love with a beautiful, giant, albino ball python (Python regius). Brazil has more than 400 snake species. At first, I just thought that snakes were pretty, but as I learnt about and worked with them, I became curious about how their environment influences their movement and activities.I’m now planning to attach accelerometers to snakes. These small data loggers can monitor fine-scale body movements and postures. Because many of the snakes are venomous, it is dangerous to work with them. But we learn to respect them and understand their defence behaviours, and two people always work together when handling them.One goal of my project is to learn more about interactions with humans, aiming to inform policies to mitigate snake bites. The biggest threat to snakes is habitat loss, which has been made worse by Brazil’s current environment policies, which encourage the clearing of land for farming.

Nature 600, 352 (2021)
doi: https://doi.org/10.1038/d41586-021-03629-6

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Estimating native plant species’ distributionsWe used the newly developed species database, GreenMaps, to estimate native plant species’ distributions59. GreenMaps includes global distribution maps for ~230,000 vascular plant species. Maps were generated using species distribution models – the statistical estimation of species geographic distributions based on only some known occurrences and environmental conditions – derived from carefully curated species occurrence records. Occurrence records were obtained from a variety of sources, including herbarium specimens, primary literature, personal observation, and online data repositories including the Global Biodiversity Information Facility60,61,62, and Integrated Digitized Biocollections (https://www.idigbio.org/). These records were thoroughly cleaned to reconcile names to follow currently accepted taxonomies [e.g., World Flora Online (www.worldfloraonline.org)], and to remove duplicates and records with doubtful or imprecise localities. Two stringent spatial filters were employed to restrict species’ distributions to their known native ranges (i.e., realized niches) and to prevent erroneous records and predictions in areas that contain suitable habitat but are unoccupied by the species (i.e., fundamental niche). First, we applied the spatial constraint, APGfamilyGeo, which are expert drawn occurrence polygons (“expert maps”) of plant family distributions63,64 (see Data availability) to restrict species to within these distributions. Second, we applied GeoEigenvectors, which are orthogonal variables representing spatial relationships among cells in a grid, encompassing the geometry of the study region at various scales65. For the latter, we generated a pairwise geographical connectivity matrix among grid cells to establish a truncation distance for the eigenvector-based spatial filtering, returning a total of 150 spatial filters. These filters were then resampled to the same resolution as the input environmental variables, and were included with the bioclimatic variables in the species distribution modeling. Bioclimatic variables were derived from WorldClim66 for a total of 19 variables (Supplementary Table 1). Species distribution models (SDMs) were fitted using four different algorithms: generalized linear models (GLM), generalized boosted models (GBM), maximum entropy (MaxEnt), and random forests (RF) with a binomial error distribution (with logit link). Model settings were chosen to yield intermediately complex response surfaces. Model performance was evaluated using area under the receiver operating curve (AUC) and true skill statistic (TSS) scores. AUC scores range from 0 to 1 and should be maximized whereas TSS scores range from −1 to 1. Prior to model building, all predictor variables were standardized. Univariate variable importance for each predictor was assessed in a 5-fold spatial block cross-validation design. The ensemble predictions from species distribution models were derived using un-weighted ensemble means. Predictive model performance was assessed using a 5-fold spatial block cross-validation. We generated a total of 230,000 range maps, representing species within 382 families at a resolution of 50 × 50 km which was also resampled to 100 × 100 km. To our knowledge, this makes it the largest and only global assessment of geographic distributions for plants at the species-level. Our approach of modeling species distributions follows the guidelines of ODMAP (Overview, Data, Model, Assessment, Prediction), a comprehensive framework of best practices for reporting species distribution models67 (see Supplementary Material 1). These maps were stacked and converted to a community matrix for downstream analyses. We also provide a new R function, sdm, for performing the SDMs across four algorithms (random forest, generalized linear models, gradient boosted machines, and MaxEnt) tailored for SDMs of large datasets. The sdm function is included in our R package phyloregion68 along with improved documentation and vignettes to show practical application of this functionality under various modeling scenarios. The sdm function was designed with multiple checks such that any species that did not meet one or more checks were filtered out. A feature of novelty of the sdm function is the addition of an algorithm that allows a user to exclude records that occur within a certain distance to herbaria, museums or other infrastructure. By default, we used the most updated version of Index Herbariorum, a global directory of herbaria69, but a user has the option to specify their own infrastructure to exclude.We validated the output distribution maps against the Kew Plants of the World Online database (POWO; http://www.plantsoftheworldonline.org/), which includes native distribution maps for all plants of the world within major biogeographically defined areas recognized by the Biodiversity Information Standards (also known as the Taxonomic Databases Working Group (TDWG))70. Although the Kew’s distributions of native species are largely based on state/province level such that if a species was observed in any location within a state the whole state is marked as its distribution range, our GreenMaps approach only used the Kew distributions to restrict modeled species distributions within such biogeographic areas. See ref. 59 for full description of the workflow. The range map rasters were converted to a community matrix using the function raster2comm in our new R package phyloregion68 for downstream analysis.Estimating non-native plant species’ distributionsWe used the Global Naturalized Alien Flora (GloNAF) database version 1.271,72 to compile a checklist of non-native species, including documented records of alien plants that have dispersed into new regions largely by humans, and which have become successfully naturalized73,74. The dataset includes non-native species distributions within TDWG regions. We generated species’ distributions for these species using the GreenMaps approach59 described above, but removing the spatial filters APGfamilyGeo and GeoEigenvectors. The non-native species ranges were modeled using occurrences that fell outside the boundaries of the native range of each species as determined by Plants of the World Online (POWO). Specifically, we used the following R code to subset occurrences falling outside of POWO as follows:$$y , < -!x[!complete.cases(sp::over(x,powo)),]$$ (1) where x is a data frame of occurrence of a species, and powo a shapefile of the native range of the species. We then used the output y to model the distribution of non-native species using the sdm function in the R package phyloregion68. We validated our non-native species distribution models against the GloNAF dataset by overlaying grid cells of non-native species predictions within GloNAF’s TDWG levels, and selecting only those projected occurrences that fell within the naturalized range indicated by GloNAF. Such approach allowed us to capture the precise distribution of the non-native species within a state/province as opposed to broadly scoring them present or absent in a state/province as did GloNAF. From our dataset of non-native species, we also identified ‘superinvasives’, here defined as non-native species with 1.5× the interquartile range above the third quartile of their invaded range size within a TDWG region.Recently extinct and threatened plant speciesWe compiled information on recent plant extinctions and conservation status of each mapped species. Our dataset of recent extinctions comes from a dataset that includes 1065 plant species that have become extinct since Linnaeus’ Species Plantarum75, derived from a comprehensive literature review and assessments of the International Union for Conservation of Nature (IUCN) Red List of Threatened Species26,76. We also explored alternative scenarios of increasing future extinction intensity, considering future losses of currently extant native species, some of which are not currently recognized as of global concern (data from ref. 27). For the latter analysis, we compiled information on the conservation status of each species and apply the term ‘extinction’ loosely, which included both native species lost from a region as well as native species that may still be present in some part or all of their native ranges, but they are unlikely to remain so in the near future if current trends continue (see ref. 27). This dataset comes from machine-learning predictions of conservation status for over 150,000 land plant species27 defined as the probability of each species as belonging to a Red List non-Least Concern category (i.e., likely of being at risk on some level) based on geographic, environmental, and morphological trait data, variables that are key in predicting conservation risk27. For our purposes here, we assumed that Least Concern species were not at risk of extinction; although we recognize that a substantial proportion of these species may in fact be endangered27,77. Within this framework, extinction risk is defined using the expected probability of extinction over 100 years of each taxon78, scaled as follows: Least Concern = 0.001, Near Threatened and Conservation Dependent = 0.01, Vulnerable = 0.1, Endangered = 0.67, and Critically Endangered = 0.999. We used these statistical projections to estimate future extinction scenarios because they can be fit to over 150,000 land plant species, whereas formal IUCN Red List assessments are currently available for only 33,573 plant species (March 15, 2020).The final dataset used for our analysis included 205,456 native species, 1065 recently extinct species, extinction projections for 150,000 species, and 10,138 naturalized species.Phylogenetic dataWe applied the dated phylogeny for seed plants of the world from ref. 79, which includes 353,185 terminal taxa. The ref. 79 phylogeny was assembled using a hierarchical clustering analysis of DNA sequence data of major seed plant clades and was resolved using data from the Open Tree of Life project. This represents one of the most comprehensive phylogenies of vascular plants at a global scale and includes all species in our analysis. It also provides divergence time estimates to facilitate downstream analytics.Data analysisWe quantified changes in alpha and beta diversity between the Holocene (native species’ assemblages in each region before widespread migration by humans as initiated by the Columbian Exchange circa 149216) and Anthropocene (non-native naturalizations, and recent past and projected plant extinctions)26 epochs across 100 × 100 km grid cells within major biogeographically defined areas recognized by the Biodiversity Information Standards (also known as the Taxonomic Databases Working Group (TDWG))70. These TDWG geographic regions correspond to continents, countries, states and provinces. We then explored differences in biotic homogenization under varying future scenarios of extinction including naturalizations only, ‘no superinvasives’, ‘best case’ ‘business as usual’, ‘increased extinction’ and ‘worst case’. Our definition of best case refers to recent plant extinctions and naturalizations, and assumes no future extinctions, business as usual assumes loss of Critically Endangered (CR) species, increased extinction assumes loss of Critically Endangered (CR) and Endangered (EN) species, and the worst case scenario assumes loss of all threatened species. Because biodiversity patterns are scale dependent, varying along spatial grains and geographic extents80,81, we repeated all analyses at spatial grid resolution of 50 × 50 km.Temporal changes in α-diversity across plant communitiesFor each grid cell, temporal and spatial change in α-diversity was quantified as the difference in species (or phylogenetic) diversity between the Anthropocene (j) and Holocene (i) periods (see above) expressed as:$$varDelta alpha =(alpha j-alpha i)/alpha i$$ (2) Negative Δα values imply that alpha diversity has decreased and positive values indicate increased alpha diversity. Species α-diversity was calculated as the total count of species in each grid cell. Phylogenetic α-diversity was computed as the sum of the phylogenetic branch lengths connecting species from the tip to the root of a dated phylogenetic tree in each grid cell82. We also assessed changes in phylogenetic (α) diversity standardized for species richness by calculating standard effects sizes of phylogenetic diversity in communities by shuffling the tips in the phylogeny based on 1000 randomizations. For each iteration of the randomization, the analysis was regenerated using the same set of spatial conditions, but using the randomized version of the tree after which the z-score for each index value was calculated (observed - expected)/sqrt (variance). Temporal changes in α-diversity was assessed at the spatial grain resolution of 50 and 100 km to account for the effects of scale.Temporal changes in compositional turnover across florasWithin TDWG geographic regions, we generated pairwise distance matrices of phylogenetic β-diversity (βphylo)83 and species β-diversity (βtax) between all pairs of grid cells, and compared Holocene and Anthropocene epochs. We used Simpson’s index for quantifying compositional turnover because it is insensitive to differences in total diversity among sites84,85. The phylogenetic equivalent, βphylo, represents the proportion of shared phylogenetic branch lengths between cells, and ranges from 0 (species sets are identical and all branch lengths are shared) to 1 (species sets share no phylogenetic branches). We calculated change in compositional turnover (Δβ) as:$$varDelta beta =(beta j-beta i)/beta i$$ (3) where j is the Anthropocene species pool and i refers to the Holocene species composition. Negative Δβ values imply that taxonomic/phylogenetic similarity has increased (i.e., biotic homogenization) and positive values indicate biotic differentiation. To assess sensitivity to our choice of diversity index, we re-ran all analyses using Sorensen and Jaccard dissimilarity indices. All (phylogenetic) β-diversity metrics were calculated using our new R package phyloregion68.Effect of superinvasive speciesTo determine the extent to which a small number of superinvasive non-native species may be driving patterns of homogenization, we re-ran the main analyses described above, but excluded non-native species with the widest ranges within biomes, i.e., species that are more than 1.5× the interquartile range above the third quartile of (invaded) range sizes (i.e., statistical outliers) within TDWG regions. Our definition of range size corresponds to the number of grid cells occupied by a species.Phylogenetic structure of naturalizationsWe evaluated whether naturalized species were more likely to have become naturalized in recipient communities in the absence of close relatives—Darwin’s naturalization hypothesis—by comparing the mean phylogenetic distance between each non-native species and its nearest phylogenetic neighbor in the recipient flora. Larger mean phylogenetic distances indicate that non-native species tend to be less closely related to the native flora. We first ran each analysis on a set of 100 trees. Significance was assessed by comparing the distribution of observed phylogenetic distances to a null model shuffling non-native status randomly on the tips of the phylogeny (1000 replicates) as implemented in the R package phyloregion68.Drivers of change in composition across florasTo relate change in alpha and beta diversity to possible external drivers, we obtained three sets of variables for each site: (i) ecological: mean annual precipitation (MAP), mean annual temperature (MAT), and elevation; (ii) evolutionary: range size (as proxy for dispersal potential, defined as the average range size across species within a grid cell); and (iii) anthropogenic: wilderness index (inverse of human footprint index). MAP, MAT, and elevation were obtained from the WorldClim database66; the geographic range of each species was calculated as the number of cells a species occupied. The Wilderness Index was obtained from ref. 86, and describes the degree to which a place is remote from and undisturbed by the influences of modern society86. These variables were converted to Behrmann equal-area projection using the function projectRaster in the R package raster87.We used a linear mixed effects (LME) model of temporal change in, separately, species (α) richness, phylogenetic (α) diversity, phylogenetic (α) diversity standardized for richness, β-diversity, and phylogenetic β-diversity between the Anthropocene and Holocene, against ecological, evolutionary and anthropogenic variables as predictors. We used level 3 regions as recognized by the Biodiversity Information Standards as a random effect, allowing us to account for idiosyncratic differences between regions. Changes in metrics of β-diversity were applied to grid cells by taking the average dissimilarity to other cells within a region as defined by the TDWG level 3 biomes, whereas changes in metrics of α diversity were applied directly to grid cells. We also included a spatial covariate of geographical coordinates as an additional predictor variable to account for spatial autocorrelation. Our model can be formulated as follows:$${triangle }_{i}=beta 0+beta 1,{{MAT}}_{i}+beta 2,{{MAP}}_{i}+beta 3,{{elevation}}_{i}+beta 4,{{range}{{{{{rm{_}}}}}}{_size}}_{i}+beta 5,{{wilderness}}_{i}+{e}_{i}$$ (4) where ∆i is the temporal diversity change (temporal changes in metrics of α or β diversity) between the Anthropocene and Holocene in grid cell i, β0 to β5 are fixed effect parameters, and ei is residual error. The LME model was fitted using the lme function in the nlme R package88.A vignette, with a worked example, data and R codes describing all the steps for the analyses, is also provided on Dryad (https://doi.org/10.5061/dryad.f4qrfj6st).Reporting summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More

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