Philippa Kaur

Our novel approach to bioacoustic source separation involves an end-to-end pipeline consisting of multiple discrete steps, including (1) synthesizing a dataset, (2) developing and training a separator network to disentangle the input mixture, and (3) constructing and training a classifier model to employ as a downstream evaluation task. This workflow requires few hyperparameter modifications to account for unique vocal behavior across different biological taxa but is otherwise general and makes no species-level assumptions about the spectrotemporal structure of the source calls. We develop a complete framework for bioacoustic source separation in a permutation-invariant mode using overlapping waveforms drawn from the same class of signals. We apply BioCPPNet to macaques, dolphins, and Egyptian fruit bats, and we consider two or three concurrent “speakers”. Note that we henceforth refer to non-human animal signalers as “speakers” for consistency with the human speech separation literature2. We address both the closed speaker regime in which the training and evaluation data subsets contain calls produced by individuals drawn from the same distribution as well the open speaker regime in which the model is tested on calls generated by individuals not present in the training dataset.Bioacoustic dataWe investigate a set of species with dissimilar vocal behaviors in terms of spectral and temporal properties. We apply BioCPPNet to a macaque coo call dataset47 consisting of 7285 coos produced by 8 unique individuals; a bottlenose dolphin signature whistle dataset26 comprised of 400 signature whistles generated by 20 individuals, of which we randomly select 8 for the purposes of this study; and an Egyptian fruit bat vocalization dataset48 containing a heterogeneous distribution of individuals, call types, and call contexts. In the case of the bat dataset, we extract the data (31399 calls) corresponding to the 15 most heavily represented individual bats, reserving 12 individuals (27586 calls) to address the closed speaker regime and the remaining 3 individuals (3813 calls) to evaluate model performance in the open speaker scenario.DatasetsThe mixture dataset is generated from a species-specific corpus of bioacoustic recordings containing signals annotated according to the known identity of the signaller. Motivated by WSJ0-2mix2, a preeminent reference dataset used for human single-channel acoustic source separation, we adopt a similar approach of constructing bioacoustic datasets by temporally overlapping and summing ground truth individual-specific signals to enable supervised training of our model. For macaques and dolphins, the mixture waveforms contain discrete source calls that overlap in the time domain, by design. For bats, mixtures are constructed by adding signal streams, each of which may exhibit one or more temporally separated sequential vocal elements. In all cases, the mixtures operate under the assumption that, without loss of generality, the constituent sources vary in the degree of spectral overlap due to differential spectrotemporal properties of sources, in accordance with the DUET principle (i.e, the mixtures contain approximately disjoint sources that rarely coincide in dominant frequency)19. The resultant dataset consists of an input array of the composite mixture waveforms, a target array containing the separated ground truth waveforms corresponding to the respective mixtures, and a class label array denoting the identities of the vocalizing animals responsible for generating the signals. In the case of macaques, we here consider closed speaker set mixtures of two and three simultaneous speakers, but our method is functionally not limited in the number of sources (N) it can handle. For dolphins, we consider the closed speaker regime with two overlapping calls, and for bats, we consider the closed and open speaker scenarios with two sources.We first extract the labeled waveforms either by truncating or zero-padding the waveforms to ensure that all the samples are of fixed duration. We select the number of frames either by computing the mean plus three-sigma of the durations of the calls contained in the corpus from which we draw the signals, by selecting the maximum duration of all calls, or by choosing a fixed value. For macaques, dolphins, and bats, we use 23156 frames (0.95s), 290680 frames (3.03s), and 250000 frames (1.0s), respectively. We then randomly select vocalizations from N different speakers drawn from the distribution of individuals used in the study (8 macaques, 8 dolphins, 12 bats for the closed speaker regime, 3 bats for the open speaker regime) and mix them additively, ensuring to randomly shift the overlaps to simulate a more plausible scenario and to provide for asynchronicity of start times, an important acoustic cue that has been suggested as a mechanism with which the animal brain can solve the CPP1. Despite higher computational and memory costs, we opt to use native sampling rates, since certain animal vocalizations may reach frequencies near the native Nyquist frequency. With this in mind, however, our method does provide for resampling when the vocalizations of the particular species of interest are amenable to downsampling. Explicitly, for the three species we consider including macaques, dolphins, and bats, we use sampling rates of 24414 Hz, 96 kHz, and 250 kHz, respectively. For the closed speaker regime, the training and evaluation subsets contain calls produced by the same distribution of individuals to ensure a closed speaker set. We segment the original nonoverlapping vocalizations into 80/20 training/validation subsets. We generate the mixture training waveforms using 80% of the calls, and we construct the mixture validation subset using the remaining 20% of calls held out from the training data. In the case of overlapping bat calls (for which the corpus of bioacoustic recordings contains (mathscr {O}(10text { hours})) of data as opposed to (mathscr {O}(10^{-1}text { hours})) for macaques and dolphins), we also address the open speaker source separation problem by constructing a further testing data subset of mixtures of calls of additional vocalizers not contained in the training distribution. For macaques, we construct a training data subset comprised of 12k samples and a validation subset with 3k samples, all of which contain calls drawn from 8 animals. For dolphins, we randomly select 8 individuals and construct training/validations subsets with 8k and 2k samples, respectively. For bats, we select 15 individuals, randomly reserving 12 for the closed speaker problem and the remaining 3 for the open speaker situation. We train the bat separator model on 24k mixtures. We evaluate performance in both the closed and open speaker scenarios using data subsets consisting of 6k mixtures containing unseen vocalizations produced by the appropriate distribution of individuals according to the regime under consideration. We repeat the bat training using a larger mixture dataset (denoted by +) containing 72k samples. We here report validation metrics to ensure that we are evaluating model performance on unseen mixtures of unseen calls in the closed speaker regime and on unseen mixtures of unseen calls of unseen individuals in the open speaker regime.For the downstream classification task, we extract vocalizations annotated according to the individual identity, and we segment the calls into an 80/20 training/testing split to ensure that we are evaluating model performance on unseen calls. For both the training and evaluation data subsets, we employ an augmentation scheme in which we apply random temporal shifts to call onsets to better reflect more plausible real-world scenarios.Classification modelsIn an effort to provide a more physically interpretable evaluation metric to supplement the commonly-implemented SI-SDR used in human speech separation studies, we develop CNN-based classifier models to label the individual identity of the separated vocalizations as a downstream task. This requires training classification networks to predict the speaker class label of the original unmixed waveforms. For each species we consider, we design and train custom simple and lightweight CNN-based architectures largely motivated by previous work24, tailored to accommodate the unique vocal behavior of the given species.The first layer in the model is an optional high pass filter constructed using a nontrainable 1D convolution (Conv1D) layer with frozen weights determined by a windowed sinc function49,50 to eliminate low-frequency background noise. We omit this computationally intensive layer for macaques and Egyptian fruit bats, but we implement a high pass filter for the dolphin dataset, selecting an arbitrary cutoff frequency of 4.7 kHz and transition bandwidth 0.08 to remove background without impinging on the region of support for dolphin whistles. After the optional filter is an encoder layer to compute on-the-fly feature extraction. We experimented with a fully learnable free Conv1D filterbank, a spectrogram, and a log-magnitude spectrogram and observed optimal performance using a non-decibel (dB)-scaled STFT layer computed with a nfft window width, a hop window shift, and a Hann window where nfft and hop are species-dependent variables. For macaques, we select nfft=1024 and hop=64 corresponding to temporal scales on the order of 40ms and frequency resolutions on the order of 20 Hz. We choose nfft=1024 and hop=256 for dolphins and nfft=2048 and hop=512 for bats, corresponding to temporal resolutions of ~ 10 ms and ~ 8 ms and frequency resolutions of ~ 90 Hz and ~ 120 Hz, respectively.Following the built-in feature engineering, the architecture includes 4 convolutional blocks, which consist of two sequential 2D convolution (Conv2D) layers with leaky ReLU activation and a max pooling layer with pool size 4. Next is a dense fully connected layer with leaky ReLU activation followed by another linear layer with log softmax activation to output the V log probabilities (i.e. confidences) where V is the number of individual vocalizers used in the study (8, 8, 12 for macaques, dolphins, and bats, respectively). We also include dropout regularization with p=0.25 for the macaque classifier and p=0.5 for the dolphin and bat classifiers to address potential overfitting. With these architectures, the macaque, dolphin, and bat classifier models have 230k, 279k, and 247k trainable parameters, respectively.For all species, we minimize the negative log-likelihood objective loss function using the Adam optimizer51 with learning rate lr = 3e−4. For macaques, dolphins, and bats, respectively, we train for 100, 50, and 100 epochs with batch sizes 32, 8, and 8. We serialize the model after each epoch and select the top-performing models. We opt not to carry out hyperparameter optimization since the classification task is of secondary importance and is used solely as a downstream task.Figure 1(a) Schematic overview of the BioCPPNet pipeline. Source vocalization waveforms are overlapped in time and mixed additively. BioCPPNet operates on the mixture waveform, yielding predictions for the separated waveforms, which are compared to the source ground truths, up to a permutation. The estimated waveforms are classified by the identity classification model24 (ID) to compute the downstream classification accuracy metric. (b) Block diagram of the BioCPPNet architecture. The input mixture waveform is transformed to a learnable or handcrafted representation (Rep), which then passes through a 2-dimensional U-Net52 composed of a contracting encoder path and an expanding decoder path with skip connnections. The encoder path consists of sequential downsampling convolutional blocks, each of which is constructed using two convolutional layers (Conv2D) with leaky ReLU activation and batch normalization (BatchNorm) followed by a max pooling. The decoder path employs upsampling convolutional blocks, consisting of an upsampling and skip connection concatenation followed again by the Conv2D layers with leaky ReLU and BatchNorm. The U-Net predicts masks (Mask 0 and Mask 1), the number of which is determined by the number of sources (N), that are multiplicatively applied to the original mixture representation. The predicted time-frequency representations of the separated waveforms are inverted with learnable or handcrafted inverse transforms (iRep) to output raw waveforms. All schematic diagrams were created using Affinity Designer (version 1.8.1) https://affinity.serif.com/en-us/designer/.Full size imageSeparation modelsBioCPPNet (Fig. 1) is a lightweight and modular architecture with a modifiable representation encoder, a 2D U-Net core, and an inverse transform decoder, which acts directly on raw audio via on-the-fly learnable or handcrafted transforms. The structure of the network is designed to provide for extensive experimentation, optimization, and enhancement across a range of species with variable vocal behavior. We construct and train a separation model for each species and each number N of sources contained in the input mixture.Figure 2Schematic diagram demonstrating the application of BioCPPNet to dolphin signature whistles using handcrafted STFT-based encoders and decoders. The source waveforms produced by N speakers of unique identity (e.g. T. truncatus 0 and T. truncatus 1) are overlapped in time, summed, and transformed to time-frequency space using an STFT layer, resulting in the mixture time-frequency representation (Mixture TFR). The U-Net predicts masks (Mask 0 and Mask 1) that are applied to the mixture representation. The separated spectrogram estimations (TFR 0 and TFR 1) are inverted using an iSTFT layer to yield the model’s predictions for the separated raw waveforms, which are compared to the ground truth waveforms and classified according to predicted identity using the classification model.Full size imageModel architectureAs with the classifier model, the network’s encoder consists of a feature engineering block, the initial layer of which is an optional high pass filter. This is followed by the representation transform, which includes several options including the Conv1D free encoder, the STFT filterbank, and the log-magnitude (dB) STFT filterbank. We choose the same kernel size (nfft) and stride (hop) parameters defined in the classifier model. Sequentially following the feature extraction encoder is a 2D U-Net core. This architecture consists of B (4 for macaques, 3 for dolphins, and 4 for bats) downsampling convolutional blocks, a middle convolutional block, and B upsampling convolutional blocks. The downsampling blocks consist of two 2D convolutional layers with filter number that increases with model depth with leaky ReLU activation followed by a max pooling with pool size 2, 6, and 3 for macaques, dolphins, and bats. The middle block contains two 2D convolutional layers with leaky ReLU activation. The upsampling blocks include an upsampling using the bilinear algorithm and a scale factor corresponding to the pool size used during downsampling, followed by skip connections in which the corresponding levels of the contracting and expanding paths are concatenated before passing through two 2D convolutional layers with leaky ReLU activation. All convolutional layers in the downsampling, middle, and upsampling blocks include batch normalization after the activation function to stabilize and expedite training and to promote regularization. Though our default implementation is phase-unaware, we also offer the option for a parallel U-Net pathway working directly on phase information, which has been shown to improve performance in other applications53,54,55. The final layer in the U-Net core is a 2D convolutional layer with N channels, which are then split prior to entering the inverse transform decoder. For the inverse transform, we again provide numerous choices including a free filterbank decoder based on a 1D convolutional transpose (ConvTranspose1D) layer, an iSTFT layer, an iSTFT layer accepting dB-scaled inputs, and a multi-head convolutional neural network (MCNN) for fast spectrogram inversion56. In detail, the U-Net returns N masks that are then multiplied by the original encoded representation of the mixture waveform. The separated representations are then passed into the inverse transform layer in order to yield the raw waveforms corresponding to the model’s predictions for the separated vocalizations. We initialize all trainable weights using the Xavier uniform initialization. In the case of macaques, we experiment across all combinations of representation encoders and inverse transform decoders, and we find optimal performance using the handcrafted non-dB STFT/iSTFT layers operating in the time-frequency domain. Since the model with the fully learnable Conv1D-based encoder/decoder uniquely operates in the time domain, we report evaluation metrics for this model, as well. For dolphins and bats, we here report metrics using exclusively the non-dB STFT/iSTFT technique.BioCPPNet (Fig. 1) is designed as a lightweight fully convolutional model in order to efficiently process large amounts of bioacoustic data sampled at high sampling rates while simultaneously minimizing computational costs and limitations and the likelihood of overfitting. For the macaque separators, the networks consist of 1.2M parameters (for the STFT, iSTFT combination), 2.5M parameters (for the STFT, iSTFT combination with parallel phase pathway), or 2.8M parameters (for the Conv1D free filterbanks). For the dolphin separator (Fig. 2), the model has 304k parameters, while the bat separator model has 1.2M parameters. This is to be contrasted with the comparatively heavyweight default implementations of models commonly used in human speech separation problems, such as Conv-TasNet3, which has 5.1M parameters; DPTNet4 with 2.7M parameters; or Wavesplit5 with 29M parameters. Regardless of the lower complexity of BioCPPNet, the model achieves comparable performance or even outperforms reference human speech separator models while still being lightweight enough to train on a single NVIDIA P100 GPU.Model training objectiveThe model training objective aims to optimize the reconstruction of separated waveforms from the aggregated composite input signal. We adopt a permutation-invariant training (PIT)57 scheme in which the model’s predicted outputs are compared with the ground truth sources by searching over the space of permutations of source orderings. This fundamental property of our training objective reflects that the order of estimations and their corresponding labels from a mixture waveform is not expressly germane to the task of acoustic source separation, i.e. separation is a set prediction problem independent of speaker identity ordering5.Source separation involves training a separator model f to reconstruct the source single-channel waveforms given a mixture (x=sum _{i=1}^N s^i) of N sources, where each source signal (s^i) for (i in [1, N]) is a real-valued continuous vector with fixed length T, i.e., (s^i in mathbb {R}^{1 times T}). The model outputs the predicted waveforms ({hat{s}^i}_{i=1}^N) where (forall i, hat{s}^i = f^i(x)), and a loss function is evaluated by comparing the predictions to the ground truth sources ({s^i}_{i=1}^N) up to a permutation. Explicitly, we consider a permutation-invariant objective function5,$$begin{aligned} mathscr {L}(hat{s}, s) = min _{sigma in S_N} frac{1}{N} sum _{i=1}^N ell (hat{s}^{sigma (i)}, s^i) qquad text {where} forall i, hat{s}^i = f^i(x) end{aligned}$$Here, (ell (cdot , cdot )) represents the loss function computed on an (output, target) pair, (sigma) indicates a permutation, and (S_N) is the space of permutations. In certain scenarios, we include the L2 regularization term,$$begin{aligned} mathscr {L} mapsto mathscr {L} + lambda sum _{j=1}^P beta _j^2 end{aligned}$$where (beta _j) represent the model parameters, P denotes the model complexity, and (lambda) is a hyperparameter empirically selected to minimize overfitting (i.e. enhance convergence of training and evaluation losses and metrics).For the single-channel loss function (ell), we consider a linear combination of several loss terms that compute the error in estimated waveform reconstructions ({hat{s}^i}_{i=1}^N) relative to the ground truth waveforms ({s^i}_{i=1}^N).

L1 Loss $$begin{aligned} |hat{s}^{sigma (i)} – s^{i}| end{aligned}$$ This represents the absolute error on raw time domain waveforms.

STFT L1 Loss $$begin{aligned} |text {STFT}(hat{s}^{sigma (i)}) – text {STFT}(s^{i})| end{aligned}$$ This term functions to minimize absolute error on time-frequency space representations. Empirically, the inclusion of this contribution enhances the reconstruction of signal harmonicity.

Spectral Convergence Loss $$begin{aligned} ||text {STFT}(hat{s}^{sigma (i)}) – text {STFT}(s^{i})||_F / ||text {STFT}(s^{i})||_F end{aligned}$$ where (||cdot ||_F) denotes the Frobenius norm over time and frequency. This term emphasizes high-magnitude spectral components56.

We also experimented with additional terms including L1 loss on log-magnitude spectrograms to address spectral valleys and negative SI-SDR (nSI-SDR), but the inclusion of these contributions did not yield empirical improvements in results.For macaques, we modify the training algorithm according to the representation transform and inverse transform built into the model. For the model with the fully learnable Conv1D encoder and decoder, we train using the AdamW58 optimizer with a learning rate 3e-4 and batch size 16 for 100 epochs. In order to stabilize training and avoid local minima when using handcrafted STFT and iSTFT filterbanks, we initially begin training the models for 3 epochs with batch size 16 using stochastic gradient descent (SGD) with Nesterov momentum 0.6 and learning rate 1e-3 before switching to the AdamW optimizer until reaching 100 epochs.For dolphins, we provide the model with the original mixture as input, but we use high pass-filtered source waveforms as the target, which means the separation model must additionally learn to denoise the input. We again initialize training with 3 epochs and batch size 8 using SGD with Nesterov momentum 0.6 and learning rate 1e-3 before switching to the AdamW optimizer with learning rate 3e-4 for the remaining 97 epochs. We use a similar training scheme for bats, initially training with SGD for 3 epochs before employing the optimizer switcher callback to switch to AdamW and to complete 100 epochs.Model evaluation metricsWe consider the reconstruction performance by computing evaluation metrics using an expression given by5,$$begin{aligned} mathscr {M}(hat{s}, s) = max _{sigma in S_N} frac{1}{N} sum _{i=1}^N m(hat{s}^{sigma (i)}, s^i) qquad text {where} forall i, hat{s}^i = f^i(x) end{aligned}$$where (m(cdot , cdot )) is the single-channel evaluation metric computed on permutations of (output, target) pairs.Specifically, we implement two evaluation metrics to assess reconstruction quality, including (1) SI-SDR and (2) downstream classification accuracy. We consider the signal-to-distortion ratio (SDR)2, defined as the negative log squared error normalized by reference signal energy5. However, as is commonly implemented in the human speech separation literature, we instead compute the scale-invariant SDR (SI-SDR), which disregards prediction scale by searching over gains5,40. Explicitly, SI-SDR((hat{s}, s) = -10log _{10}(|hat{s} – s|^2) + 10log _{10}(|alpha s|^2)) for optimal scaling factor (alpha = hat{s}^Ts / |s|^2).Additionally, to provide a physically interpretable metric, we evaluate the performance of the trained classifier models in labeling separated waveforms according to the predicted identity of the vocalizer. This metric assumes that the classification accuracy on a downstream task reflects the fidelity of the estimated signal relative to the ground truth source and thus serves as a proxy for reconstruction quality. More

Phylogenetic analysisFor both the mycobiont and photobiont molecular phylogenies from multi-locus sequence data (nrITS, mtSSU and RPB1 for the mycobiont (140 samples) and nrITS, psbJ-L and COX2 for the photobiont (139 samples) were inferred (Supplementary Figs. S1 and S3 online). Additionally, phylogenies based solely on the marker nrITS were calculated (Supplementary Figs. S2 and S4 online), to include samples where the additional markers were not available. Both analyses include only accessions from the study sites (Fig. 1; Table 1). The phylogenies based on the multi-locus data were congruent to the clades of the phylogenies based on the marker nrITS. Thus, in the following, the focus will be only on the latter.MycobiontThe final data matrix for the phylogeny based on the marker nrITS comprised 306 single sequences with a length of 550 bp. It included sequences of the families Lecanoraceae and Lecideaceae. The phylogenetic tree was midpoint rooted and shows a total of 19 strongly supported clades on species level, assigned to five genera. The backbone is not supported and therefore the topology will not be discussed. All genera are clearly assigned to their family level and are strongly supported. Only Lecanora physciella forms an extra clade as sister to the families Lecideaceae and Lecanoraeae, which is not the case at the multimarker phylogeny. L. physciella has still an uncertain status, because of morphological similarities to both sister families6. The clade of the genus Lecidea revealed seven species (L. andersonii, L. polypycnidophora, L. UCR1, L. sp. 5, L. lapicida, L. cancriformis and L. sp. 6), Lecanora five species (L. physciella, L. sp. 2, L. fuscobrunnea, L. cf. mons-nivis, L. sp. 3), Carbonea three species (C. sp. URm1, C. vorticosa, C. sp. 2), and Lecidella three species (L. greenii, L. siplei, L. sp. nov2). The samples allocated to the genus Rhizoplaca were monospecific (R. macleanii). The taxonomical assignment of the obtained sequences were based on the studies of Ruprecht et al.48 and Wagner et al.10.PhotobiontThe final data matrix for the phylogeny based on the marker nrITS comprised 281 single sequences with a length of 584 bp. The phylogenetic tree was midpoint rooted and shows six strongly supported clades, assigned to seven different OTU levels67, using the concept of Muggia et al.51 and Ruprecht et al.48. All of the OTUs belong to the genus Trebouxia (clades A, I, S), comprising Tr_A02, Tr_A04a, Tr_I01, Tr_I17, Tr_S02, Tr_S15 and Tr_S18. Photobiont sequences taken from Perez-Ortega et al.50, which were labelled only with numbers, were renamed to assign them to the appropriate OTUs48.Analysis of spatial distributionIn general, the most common mycobionts species were Lecidea cancriformis (94 of the 306 samples), Rhizoplaca macleanii (51 samples) and Lecidella greenii (37 samples), followed by Carbonea sp. 2 (13 samples), C. vorticosa (11 samples), Lecidea polypycnidophora (10 samples) and Lecidella siplei (10 samples; see Supplementary Fig. S5 online). Nine mycobiont species were found exclusively in area 5 (MDV, 78°S): Carbonea vorticosa, Lecanora cf. mons-nivis, L. sp. 2, Lecidea lapicida, L. polypycnidophora, L. sp. 5, L. sp. 6, L. UCR1 and Rhizoplaca macleanii. On the other hand, only Lecidea cancriformis was found in all the six areas; Lecanora fuscobrunnea was present in all the areas with the exception of area 2.The most common photobiont OTUs were Tr_A02 (165 of the 281 samples) and Tr_S02 (59 samples), both of them occurring in all the six different areas, followed by Tr_S18 (32 samples), Tr_S15 (10 samples, confined to area 5) and Tr_I01 (10 samples). However, of the 149 photobiont accessions of area 5, 134 (89.93%) were assigned to Tr_A02. This percentage is much higher than in the other areas (area 1: 44.44%, area 2: 69.23%, area 3: 21.74%, area 4a: 7.69%, area 4b: 6.67%), even if those samples with mycobionts occurring exclusively in area 5 (see above) were excluded (76.56% of the 64 remaining samples are assigned to Tr_A02).The alpha, beta and gamma diversity values are given in Table 2. For the mycobionts, the alpha diversity of the communities was the highest in area 5 (8.93, which results in nine species) and the lowest in area 4b (two species, 1.88). In contrast, for the photobionts, the lowest alpha diversity value was found in area 5 (two OTUs, 1.50) and the highest in area 4a (four OTUs, 4.06). Thus, referring to this, area 5 plays a remarkable role: compared to the other areas, it shows the highest diversity of mycobiont species on the one hand and the lowest diversity of photobiont OTUs on the other hand.Table 2 Number of lichen samples, number of identified mycobiont species and photobiont OTUs, as well as alpha, beta and gamma diversity values of mycobiont species/photobiont OTUs for the different areas.Full size tableThe beta diversity values (diversity of local assemblages) for mycobiont species and photobiont OTUs are quite similar (1.69 and 1.64, respectively). This is in contrast to gamma diversity values: the overall diversity for the different areas within the whole region is much higher for the mycobionts (ten species, 9.92) than for the photobionts (three OTUs, 3.35).For mycobionts, the overall sample coverage equals to 0.993. That means that the probability for an individual of the community to belong to a sampled species is 99.3%, or, from another point of view, the probability for an individual of the whole community to belong to a species that has not been sampled is 0.7%. The sample coverage is highest for area 4b (1.000) and lowest for area 2 (0.771). Sample coverage values of the other areas are in between (area 1: 0.895, area 3: 0.931, area 4a: 0.939, area 5: 0.981). The rarefaction/extrapolation curves for the mycobiont species (see Supplementary Fig. S6a) suggest that for any sample size up to the specified level of sample coverage of 0.95, alpha diversity within area 4b is significantly lower than alpha diversity within any other area, and alpha diversity within area 5 is significantly greater than that of area 4a and 4b (based on 95% confidence intervals).For photobionts, the overall sample coverage as well as the sample coverages of area 1, area 2, area 3, area 4b as well as area 5 is equal 1.000. Only the sample coverage of area 4a (0.951) differs. The rarefaction/extrapolation curves for the photobiont OTUs (see Supplementary Fig. S6b) suggest that for any sample size up to the specified level of sample coverage of 0.95, alpha diversity within area 1 is significantly lower than alpha diversity of area 3 and 4a and significantly greater than that of area 5. Alpha diversity of area 5 is significantly lower than that of area 1, area 3 and area 4a.Influence of environmental factors (elevation, precipitation and temperature)First, the proportion of the OTU Tr_A02 samples was significantly correlated to BIO10 means of the areas (R = 0.87, p = 0.022; see Supplementary Fig. S7 online): the higher the temperature mean values of the warmest quarter of an area, the higher the proportion of samples containing photobionts that are assigned to Tr_A02.The alpha diversity values of mycobiont species significantly positively correlated with BIO10 (R = 0.88, p = 0.021; see Supplementary Fig. S8 online): the higher the temperature mean values of the warmest quarter, the higher the mycobiont diversity within this particular area.Furthermore, the differences in mycobiont species community composition were significantly related to BIO10 (constrained principal coordinate analysis: F = 14.7137, p = 0.001, see Supplementary Fig. S9 online), BIO12 (F = 2.7535, p = 0.012), elevation (F = 2.5108, p = 0.025) and the geographic separation of the samples (Mantel statistic r = 0.1288, p = 0.0002).The differences in community composition of photobiont OTUs were related significantly to BIO10 (constrained principal coordinate analysis: F = 48.5952, p = 0.001, see Supplementary Fig. S10 online), BIO12 (F = 4.4848, p = 0.008), elevation (F = 6.8608, p = 0.002), and physical distance (Mantel statistic r = 0.4472, p = 0.0001).Haplotype analysisHaplotype networks were computed for the mycobiont species and photobiont OTUs with h ≥ 2 and at least one haplotype with n ≥ 3 (Carbonea sp. 2, Lecanora fuscobrunnea, Lecidea cancriformis, Lecidella greenii, L. siplei, L. sp. nov2 and Rhizoplaca macleanii, as well as Tr_A02, Tr_I01 and Tr_S02), in both cases based on nrITS sequence data (Figs. 2, 3). The samples of Carbonea vorticosa (11) were all assigned to a single haplotype, which was also true for Lecidea polypycnidophora (10 samples), Tr_S15 (10 samples) and Tr_S18 (32 samples). Figure 3b, c illustrate the subdivision of Tr_I0151 into Tr_I01j35,48 and Tr_I01k (in this study), and the subdivision of Tr_S02 into Tr_S0235, and Tr_S02b and Tr_S02c48.Figure 2Haplotype networks of mycobiont species with h ≥ 2 and at least one haplotype with n ≥ 3, showing the spatial distribution within the different areas, based on nrITS data. (a) Carbonea sp. 2, (b) Lecanora fuscobrunnea, (c) Lecidea cancriformis, (d) Lecidella greenii, (e) Lecidella siplei, (f) Lecidella sp. nov2, (g) Rhizoplaca macleanii. Roman numerals at the center of the pie charts refer to the haplotype IDs; the italic numbers next to the pie charts give the total number of samples per haplotype. The circle sizes reflect relative frequency within the species; the frequencies were clustered in ten (e.g. the circles of all haplotypes making up between 20 and 30% have the same size). Note: only complete sequences were included.Full size imageFigure 3Haplotype networks of photobiont OTUs with h ≥ 2 and at least one haplotype with n ≥ 3, showing the spatial distribution within the different areas, based on nrITS data. (a) Tr_A02, (b) Tr_I01, (c) Tr_S02. Roman numerals at the center of the pie charts refer to the haplotype IDs; the italic numbers next to the pie charts give the total number of samples per haplotype. The circle sizes reflect relative frequency within the species; the frequencies were clustered in ten (e.g. the circles of all haplotypes making up between 20 and 30% have the same size). Note: only complete sequences were included.Full size imageThe haplotype networks include pie charts showing the occurrence of the different haplotypes within the different areas. All haplotypes of Rhizoplaca macleanii are restricted to area 5, as well as Lecidella greenii mainly to area 5 and areas 1 and 4a, and Lecidella sp. 2 to areas 2 and 3. However, all other species do not suggest a spatial pattern with different haplotypes being specific for different areas. Moreover, the distribution turned out to be rather unspecific, with a great part of the haplotypes found in multiple areas. For the sake of completeness, additionally, haplotype networks based on multi-locus sequence data were computed for the most abundant mycobiont species and photobiont OTU with multi-locus data available (Lecidea cancriformis and Tr_S02). Not surprisingly, those networks show a greater number of different haplotypes, but they also do not allow conclusions concerning spatial patterns of area specific haplotypes (see Supplementary Fig. S11 online).Diversity and specificity indices of mycobiont species and photobiont OTUsThe diversity and specificity indices for the different mycobiont species and photobiont OTUs are given in Supplementary Table S8 online.For the sample locations of mycobiont species with n ≥ 10, BIO10 was strongly correlated to the specificity indices NRI (net relatedness index) and significantly correlated to PSR (phylogenetic species richness) and 1 – J′ (Pielou evenness index). BIO12 was significantly correlated to NRI, PSR and 1 – J′. Figure 4 illustrates these correlations: the higher the BIO10 and BIO12 mean values, the higher was the NRI (phylogenetic clustering of the photobiont symbiotic partners), the lower was the PSR (increased phylogenetically relatedness of photobiont symbiotic partners) and the higher was 1 – J′ (less numerically evenness of the photobiont symbiotic partners). Thus, for the mean values of the sample locations of a mycobiont species, a comparatively high temperature of the warmest quarter and high annual precipitation occurs with associated photobionts that are phylogenetically clustered and closer related to each other. The lowest values of NRI and the highest values of PSR were developed by Lecidea cancriformis and Lecanora fuscobrunnea, which also showed the lowest BIO10 and BIO12 mean values at their sample sites. On the contrary, the highest values of NRI and PSR were developed by Rhizoplaca macleanii, which also had the highest BIO10 and BIO12 means.Figure 4Correlation plots. Specificity indices NRI (net relatedness index), PSR (phylogenetic species richness and 1 – J′ (Pielou evenness index) against mean values of BIO10 (mean temperature of warmest quarter) and BIO12 (annual precipitation) for mycobiont species with n ≥ 10.Full size imageFor the sample locations of photobiont OTUs with n ≥ 10, elevation significantly negatively correlated with h (number of haplotypes) and Hd (haplotype diversity): the higher the mean elevation of sample sites, the lower the number of haplotypes and the lower the probability that two randomly chosen haplotypes are different (Fig. 5). The highest values of h and Hd were shown by Tr_A02, Tr_I01 and Tr_S02, which occurred at sample sites with comparatively low elevations. In contrast, Tr_S15 and Tr_S18 occurred at very high elevations and showed very low values of h and Hd.Figure 5Correlation plots. Diversity indices h (number of haplotypes) and Hd (haplotype diversity) against mean elevation of sample sites for photobiont OTUs with n ≥ 10.Full size imageAnalysis of mycobiont–photobiont associationsBipartite networks were calculated for all associations between mycobiont species (lower level) and the respective photobiont OTUs (higher level) for all areas (Fig. 6). The H2′ value (overall level of complementary specialization of all interacting species) was highest in area 2 (0.921), indicating a network with mostly specialized interactions: within this network, with the exception of Lecidea andersonii, the mycobiont species are associated exclusively with one single photobiont OTU. The second highest H2′ value was developed by area 4b (0.710); in contrast, area 4a showed the lowest H2′ value (0.260), with the most abundant mycobiont species Lecidea cancriformis showing associations with five different photobiont OTUs. The H2′ values of area 1, area 3 and area 5 indicate medium specification.Figure 6Bipartite networks showing the associations between mycobiont species and photobiont OTUs for the different areas. Rectangles represent species/OTUs, and the width is proportional to the number of samples. Associated species/OTUs are linked by lines whose width is proportional to the number of associations.Full size imageIn addition, the bipartite networks illustrate the different occurrence of mycobiont species and photobiont OTUs within the different areas: For example, in area 1 (and area 2), five (seven) different mycobiont species are associated with only three different photobiont OTUs. In contrast, in area 4b, only two different mycobiont species are associated with four different photobiont OTUs. In area 5, the number of associated photobiont OTUs is also four, but those four OTUs are associated with 16 different mycobiont species.The network matrix giving all the associations between the mycobiont species and photobiont OTUs is presented in Supplementary Table S9 online. 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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