Project() launches a 'Shiny' application for the visualization and evaluation of tree spaces.

Project()

## Input tab

The input tab allows for the upload of sets of phylogenetic trees from file. Trees at the start or end of a file can be excluded, and the number of trees can be brought down to a manageable number by uniformly subsampling every _n_th tree. Samples of c. 100 trees can be analysed in seconds; analysis of larger samples will take longer, particularly with slower methods (e.g. quartet distances; Kruskal-1 MDS; large minimum spanning trees).

Different batches can be plotted with different colours / symbols.

If each tree is associated with a property -- for example, the data or method used to generate it, or its stratigraphic congruence -- a list of properties for each tree, with one entry per line/row, can be uploaded along with the trees. Points in tree space can then be styled according to the corresponding property.

If trees are subsampled (using the 'Sample every' slider), then the values in the tree properties file can also be subsampled accordingly. Unfortunately there is not yet support for multiple point property files; one file will be applied to all trees, in the sequence that they were added to memory.

## Analysis tab

Select from a suite of distance methods: clustering information and phylogenetic information are quick and satisfactory; quartet is slow but gives slightly better projections; path is very fast but may not reflect evolutionary signal very well; and Robinson--Foulds should probably never be used for analysis; it is included for comparison purposes.

Principle components projections should suffice for most purposes; Sammon and Kruskal projections are slower and seldom differ by much, in character or quality, but may emphasize outliers more.

Partitioning around medoids or minimax-linkage hierarchical clustering will typically find a close-to-optimal clustering where one exists; select additional methods for a more exhaustive search. To avoid redundant calculation, clusterings are only updated when 'recalculate clustering' is clicked, or the 'maximum cluster number' slider is modified; clustering solutions using more than this many clusters are not considered Clusterings with silhouette coefficients < 0.25 are unlikely to represent genuine structure and are not reported or depicted.

## Display tab

Up to 15 dimensions can be depicted; the quality of a projection -- that is, the faithfulness of projected distances to true tree-to-tree distances -- is quantified by the product of the Trustworthiness and Continuity metrics, which should exceed 0.9 (at least).

An interactive 3D plot can be explored by dragging the mouse and scrolling, but do be careful to check that three dimensions are enough to depict your data accurately.

The minimum spanning tree is the shortest possible line selecting the chosen subsample of trees; if it takes a convoluted zig-zagging route, then the projection is doing a poor job of reflecting true tree to tree distances.

Convex hulls are the smallest polygons enclosing all points in each cluster; they are handy for spotting clusters, but their area does not correspond to a genuine quantity, so should not be interpreted.

Tree numbers correspond to the sequence of trees in their original input file, before subsampling.

Each tree is denoted by a point, whose symbol can be styled according to cluster membership or according to the file that contains the tree, with each click of 'Add to existing' on the input tab constituting a new batch with a new symbol.

Points can be coloured according to a category -- the cluster or batch to which they belong, or custom data provided in the Point Property File on the input tab -- or continuously, either by the sequence in which they were added to memory, or according to custom data.

## Exporting tree spaces

A projection can be saved to PDF or as a PNG bitmap at the size selected.

## References

A list of references employed when constructing the tree space is populated according to the methods used; it would be appropriate to cite and briefly discuss these studies in any publication using figures generated using this application. The application itself can be cited using Smith (2020, 2021) below.

## References

Smith MR (2020). “Information theoretic Generalized Robinson-Foulds metrics for comparing phylogenetic trees.” Bioinformatics, 36(20), 5007--5013. doi: 10.1093/bioinformatics/btaa614 , https://doi.org/10.1093/bioinformatics/btaa614.

Smith MR (2021). “The importance of methodology when analysing landscapes of phylogenetic trees.” Forthcoming.

Other tree space functions: ProjectionQuality(), SpectralClustering(), median.multiPhylo()