Philippa Kaur

Human gut microbiome data and preprocessing
The publicly available data that we re-analyzed here were generated by David et al.32 accessible on the European Nucleotide Archive (ENA) under the accession number ERP006059, and by Hsiao et al.31 on the NCBI Short Read Archive (SRA) under the accession number PRJEB6358. The downloaded reads were trimmed with V-xtractor version 2.146 a HMM scan based method of isolating variable regions from 16S rRNA sequences) to ensure the amplicon sequences could be aligned across consistent fractions of the 16S rRNA variable regions. Trimmed reads were then clustered into OTUs using usearch v9.2.6447 with a minimum cluster size of two. Representative sequences from each OTU were classified using mothur v1.36.148 and the RDP reference 16S rRNA sequences v1649.
Prochlorococcus data
Data from Malstrom et al.33 was obtained from the Biological and Chemical Oceanography Data Management Office (https://www.bco-dmo.org), accession number 3381.
Mapper
Conceptually, the Mapper algorithm accepts as input a matrix of distances or dissimilarities between data, and aims to represent the shape of the distribution of data points in high-dimensional phase space as an undirected graph. In this graph, vertices represent neighborhoods of phase space spanned by subsets of adjacent data points, and edges represent connectivity between neighborhoods. In brief, it does this by dividing the data into overlapping subsets that are similar according to the output of at least one filter function that assigns a scalar value to each data point, performing local clustering on each subset, and representing the result as an undirected graph, where each vertex represents a local cluster of data points, and edges between vertices represent at least one shared data point between clusters.
Distance matrix
We interpreted microbiome relative abundances to be probability distributions, and thus used the square root of the Jensen-Shannon divergence as a metric50. However, it is important to note that any other metric can be used in place of the Jensen-Shannon distance, such as the Aitchison distance51, calculated from centered10 or isometric12 log-transformed relative abundances.
Filter functions and binning
For the filter functions used by Mapper to bin data points, we performed principal coordinate analysis (PCoA, also known as classical multidimensional scaling) in two dimensions on the pairwise distance matrix, and used the ranked values of principal coordinates (PCo) 1 and 2 as the first and second filter values for Mapper, following Rizvi et al.28. PCo ranks are an appropriate filter for our purposes, as it assigns similar filter values to points that are relatively close together in the original phase space. We wish to note that while PCoA leads to loss of information, the following local clustering step is performed using subsets of distances from the original distance matrix, and is thus not affected. The data points were then binned by overlapping intervals of the two ranked principal coordinates. For hyperparameters specifying these bins and their overlaps, see Table 1.
Table 1 Hyperparameters used to generate the Mapper representation of each data set.
Full size table

Local clustering
The algorithm first performs hierarchical clustering from all pairwise distances between data points within a bin of filter values. Then, it creates a histogram of branch lengths using a predefined number of bins, and uses the first empty bin in the histogram as a cutoff value, separating the hierarchical tree into single-linkage clusters. The algorithm thus finds a separation of length scales within each neighborhood of phase space represented by a bin of the filter values. We used the default number of histogram bins, 10, for each data set (Table 1).
Creating the undirected Mapper graph
The final output is produced by representing each local cluster of data points as a vertex, and drawing an edge between each pair of vertices that share at least one data point. When plotting, the size of each vertex represents the number of data points therein. Layout and visualization of the Mapper graph may be performed with any graph layout algorithm; we used the Fruchterman-Reingold force-directed layout algorithm52. It is important to note that the visualized shape of the Mapper graph depends on the algorithm used, and may not be deterministic. When performing a Mapper analysis, one should rely on the connectivity of the graph rather than the overall shape.
Selection of hyperparameters
The Mapper algorithm is relatively new, and there are currently no standard protocols to optimize the values of the hyperparameters. For our purposes, it was important that the algorithm achieved a sufficiently high resolution in partitioning data, but also adequately represented connections between regions of phase space. We thus used the following heuristic to set the number of intervals and percent overlap for each data set.
1.
The largest vertex in the resultant Mapper graph should represent no more than ≈10% of the total number of data points in the set;

2.
the number of connected components representing only one data point should be minimized.

We acknowledge that a heuristic determination of appropriate hyperparameter values leaves much to be desired; as such, we recommend future in-depth theoretical explorations of how the Mapper output depends on the choice of hyperparameters.
Density estimation
We estimated the inverse density for each vertex by calculating the k-nearest neighbors (kNN) distance53 for each constituent data point i.
We first define the k-neighborhood N(k)i of a point i, to be the set of k nearest neighbors of i, choosing k equal to 10% of the number of samples in each data set, rounded to the nearest integer. Then the kNN distance of point i is defined as:

$${rm{kNN}}(i,k)=frac{{sum }_{jin N{(k)}_{i}}{d}_{ij}}{k}$$
(1)

where dij is the distance between points i and j.
For a vertex V representing n points, we define its inverse density as

$${D}_{{rm{inv}}}(V)=frac{{sum }_{iin V}{rm{kNN}}(i,k)}{{n}^{2}}$$
(2)

The n2 term in the denominator compensates for the differing sizes of vertices. Finally, we invert the inverse density to obtain the estimated density:

$$D(V)=frac{1}{{D}_{{rm{inv}}}}$$
(3)

State assignment
We then defined states as topological features of the density surrounding local maxima of D. We designated each vertex with higher D than its neighbors to be a local maximum of the potential. Connected vertices tied for maximum D were each assigned to be a local maximum. To approximate a gradient, we converted the undirected Mapper graph to a directed graph, with each edge pointing from the vertex with lower D to the one with higher D. For each non-maximum vertex, we found the graph distance dg to each local maximum constrained by edge direction. We defined the state Bx of a maximum Vx as the set of vertices V with uniquely shortest graph distance to Vx:

$$Vin {B}_{x},{rm{if}},{d}_{g}(V,{V}_{x}), More

The aim of this study was to evaluate the kinetic of daily soil ingestion by growing bulls at tether-grazing when they received a very high sward and a large grazing area in which they stay during 11 days (no stake moving).
Use of herbage resource
The average sward height was 17.6 ± 0.3 cm (mean ± s.e.m.) along the 11 days of measurements from D2 to D12. Nevertheless, pregrazing sward height (at D2) was quite high with 49.2 ± 0.9 cm and significantly higher from those on D3 to D12 (14.4 ± 0.1 cm; P  More

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NEWS AND VIEWS
14 October 2020

An analysis of satellite images has pinpointed individual tree canopies over a large area of West Africa. The data suggest that it will soon be possible, with certain limitations, to map the location and size of every tree worldwide.

Niall P. Hanan &

Niall P. Hanan is with the Jornada Basin Long-Term Ecological Research Program, Department of Plant and Environmental Sciences, New Mexico State University, Las Cruces, New Mexico 88003, USA.
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Julius Y. Anchang

Julius Y. Anchang is in the Department of Plant and Environmental Sciences, New Mexico State University, Las Cruces, New Mexico 88003, USA.
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Terrestrial ecosystems are defined in large part by their woody plants. Grasslands, shrublands, savannahs, woodlands and forests represent a series of gradations in tree and shrub density, from ecosystems with low-density, low-stature woody plants to those with taller trees and overlapping canopies. Accurate information on the woody-vegetation structure of ecosystems is, therefore, fundamental to our understanding of global-scale ecology, biogeography and the biogeochemical cycles of carbon, water and other nutrients. Writing in Nature, Brandt et al.1 report their analysis of a massive database of high-resolution satellite images covering more than 1.3 million square kilometres of the western Sahara and Sahel regions of West Africa. The authors mapped the location and size of more than 1.8 billion individual tree canopies; never before have trees been mapped at this level of detail across such a large area.

The spatial resolution of most satellite data is relatively coarse, with individual image pixels generally corresponding to areas on the ground that are larger than 100 square metres, and often larger than one square kilometre. This limitation has forced researchers in the field of Earth observation to focus on measuring bulk properties, such as the proportion of a landscape covered by tree canopies when viewed from above (a measurement known as canopy cover).
However, during the past two decades, a variety of commercial satellites have begun to collect data at a higher spatial resolution, capable of capturing ground objects measuring one square metre or less. This resolution improvement places the field of terrestrial remote sensing on the threshold of a fundamental leap forward: from focusing on aggregate landscape-scale measurements to having the potential to map the location and canopy size of every tree over large regional or global scales. This revolution in observational capabilities will undoubtedly drive fundamental changes in how we think about, monitor, model and manage global terrestrial ecosystems.
Brandt et al. provide a striking demonstration of this transformation in terrestrial remote sensing. The authors analysed more than 11,000 images, at a spatial resolution of 0.5 m, to identify individual trees and shrubs with canopy diameters of 2 m or more. The authors completed this giant task using artificial intelligence — exploiting a computational approach that involves what are called fully convolutional neural networks. This deep-learning method is designed to recognize objects (in this case, tree canopies) on the basis of their characteristic shapes and colours within a larger image. Convolutional networks rely on the availability of training data, which in this case consisted of satellite images in which the visible outlines of tree and shrub canopies were manually traced. Through training using these samples, the computer learnt how to identify individual tree canopies with high precision in other images. The result is a wall-to-wall mapping of all trees larger than 2 m in diameter across the whole of southern Mauritania, Senegal and southwestern Mali.

A previous estimate2 of the total number of trees on a global scale was obtained using field data from approximately 430,000 forest plots around the world. The authors of that study used statistical regression models to estimate tree density between the field sites, on the basis of vegetation type and climate. Their analysis suggested that there are approximately three trillion trees globally. However, this approach to tree-density estimation has inherent errors and uncertainties, particularly for drylands, for which relatively few field measurements are available to calibrate the models.
A comparison (Fig. 1) of that earlier result with Brandt and colleagues’ findings in the western Sahel, for example, shows that the previous study tended to underestimate the number of trees in the drier regions (areas with annual rainfall of less than 600 millimetres). Moreover, the previous estimates provided no information on the location and size of individual trees within each square kilometre, whereas Brandt and colleagues provide detailed information on the location and size of every individual canopy. The improvement provided in the latest study can also be seen in the much higher level of detail it gives for the wetter regions (those with annual rainfall greater than 600 mm), and shows local spatial variability in trees that is presumably associated with contrasting soil types, water availability, land use and land-use history.

Figure 1 | Large-scale tree mapping. Accurate information about tree distribution provides useful ecological insights, but such data are difficult to obtain for large areas of land. a, A previous study2 estimating global tree density per hectare relied on data from field plots — samples of these data are shown for western Africa. The inset box in a is in a dry region (with an average annual rainfall of less than 600 millimetres per year), and corresponds to b. Dotted lines indicate the boundaries of average rainfall in millimetres per year. c, d, Brandt et al.1 report the detection of individual tree canopies across western Africa, obtained using an artificial-intelligence approach to analyse high-resolution satellite images. The authors found a higher tree density in dry regions of Africa than did the earlier study. For example, Brandt and colleagues’ analysis of the area corresponding to the inset box in a produced the tree density per hectare shown in c. They identified the size and location of individual tree canopies (green), as shown in d for an area corresponding to the inset box in c. Tree information at this level of detail was not available in the earlier study. (Images made using data from refs 1 and 2.) (Springer Nature remains neutral with regard to jurisdictional claims in published maps.)

There are, of course, caveats and limitations to Brandt and colleagues’ work and the potential for scaling up their approach to a global analysis. Successful canopy detection declined drastically below a canopy diameter of 2 m, owing to constraints imposed by the spatial resolution of the imagery, and consistent with earlier work3. Although we can expect further improvements in the spatial resolution of satellite images, it becomes pertinent to ask what minimum canopy size is needed to characterize woody-plant communities in various regions. For global tree-canopy mapping, if we assume that the computational and storage challenges associated with large data volumes can be overcome, the biggest roadblock would lie in developing efficient approaches for automated classification and delineation of canopies. Brandt and colleagues’ deep-learning method required an input of approximately 90,000 manually digitized training points. This approach becomes untenable for work on a global scale, and more-automated (unsupervised) methods for extracting information from satellite imagery would be necessary4.

A related problem is the ability to distinguish between what might look like one large canopy and adjacent, overlapping canopies of different individual trees. To improve canopy separation, Brandt et al. used a weighting scheme in training their convolutional neural network, but still resorted to a ‘canopy clump’ class to describe aggregated canopy areas of more than 200 m2, suggesting that the separation approach was not always effective. For application in wetter regions, where overlapping canopies in woodlands and forests are common, canopy delineation and separation methods will need refinement and automation to be feasible at global scales.
Yet more challenging is the identification of tree species. Although feasible, on the basis of canopy colour, shape and texture5, it will be particularly tricky at regional and global scales and across biodiverse ecosystems. The mapping of individual tree canopies by species will probably remain at the top of the Earth-observation research community’s wish list for some time6.
In the years ahead, remote sensing will undoubtedly provide unprecedented detail about vegetation structure as data from a range of sources — including light detection and ranging (lidar), radar and high-resolution visible and near-infrared sensors — become more readily available7. Satellite-derived high-resolution data on tree canopy size and density could contribute to the inventory and management of forests and woodland, deforestation monitoring, and assessment of the carbon sequestered in biomass, timber, fuel wood and tree crops. The ability to map the size and location of individual tree canopies using such satellite data will complement information available from other instruments that provide data for tree height, vertical canopy profiles and above-ground wood biomass. Continuing research will be needed to develop more-efficient canopy-classification algorithms. In the meantime, Brandt and colleagues have clearly demonstrated the potential for future global mapping of tree canopies at submetre scales.

doi: 10.1038/d41586-020-02830-3

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Brandt, M. et al. Nature https://doi.org/10.1038/s41586-020-2824-5 (2020).

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Draper, F. C. et al. Trends Ecol. Evol. https://doi.org/10.1016/j.tree.2020.08.003 (2020).

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National Academies of Sciences, Engineering, and Medicine. Thriving on Our Changing Planet: A Decadal Strategy for Earth Observation from Space (Natl Academies Press, 2018).

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