In a survery of existing tree vizualisation and manipulation programs we screened over 40 programs (for extensive lists of such programs, e.g. see 56). In Table 1, we compare Dendroscope to a selection of tree viewing programs which are either widely used or have exceptional features: ATV 7, HyperTree 8, MEGA 9, PHYLIP's 10 drawtree/drawgram, SplitsTree4 11, TreeView 12, TreeJuxtaposer 3 and TreeDyn 13. Of the existing programs, only TreeJuxtaposer and PHYLIP's drawtree and drawgram can handle very large trees. PHYLIP's drawtree and drawgram are non-interactive and so are of limited use. TreeJuxtaposer is currently the viewer of choice for large trees. SplitsTree4 and TreeJuxtaposer provide different mechanisms for comparing two or more trees. TreeDyn provides useful features such as scriptability, interoperability with tree databases and especially the possibility to display and manipulate many trees in parallel. Its drawbacks are the limit to trees of only moderate size and the complex user interface.

The system requirements of existing viewers vary: some work only with particular versions of Unix/Linux or MacOS, or they need additional software to be installed. However, all viewers listed in Table 1 run on Linux/Unix, MacOS and Windows, except MEGA, which runs only on Windows.

Our objective was to build a tree viewer that is able to handle a tree as large as the current version of the NCBI taxonomy. On a standard laptop, Dendroscope performs well on this tree in all rectangular and slanted views. Circular and radial view are less suitable for very large data sets. Figure 1 shows a screenshot of the NCBI taxonomic tree loaded in Dendroscope showing Homo sapiens and the Hominidae. Figure 2 demonstrates some of the views provided by the program.

Since we want to represent very large trees, we need to be able to focus on the crucial parts of the representation to speed up calculations. To this end, we use bounding boxes: to each subtree, we assign a box containing the subtree. The tree is drawn from the root down, and each subtree is drawn only if its bounding box is in the visible region or at least intersects with it. In addition, we compare the height of the bounding box to the number of edges it contains; if we find too many edges in a too small a box, we draw the box as an opaque single element instead of drawing each edge separately. When we want to identify the element (edge or node) at a selected position, we also make use of the bounding boxes: The tree is searched from the root down, leaving out all subtrees whose bounding boxes do not contain the selected position. This reduces the search time from O MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGacaGaaiaabeqaaeqabiWaaaGcbaWenfgDOvwBHrxAJfwnHbqeg0uy0HwzTfgDPnwy1aaceaGae8NdX=eaaa@3763@(n) to O MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGacaGaaiaabeqaaeqabiWaaaGcbaWenfgDOvwBHrxAJfwnHbqeg0uy0HwzTfgDPnwy1aaceaGae8NdX=eaaa@3763@(log(n)).

We supply two different magnifiers to let the user easily access inner nodes and taxa: a horizontal magnifier band for rectangular and slanted views, and a circular one for radial tree views. In both cases, a point with distance d to the center of the magnifier is mapped to a point with distance f(d)=D/2⋅dd+D/12 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGacaGaaiaabeqaaeqabiWaaaGcbaGaemOzayMaeiikaGIaemizaqMaeiykaKIaeyypa0JaemiraqKaei4la8IaeGOmaiJaeyyXICDcfa4aaSaaaeaacqWGKbazaeaacqWGKbazcqGHRaWkcqWGebarcqGGVaWlcqaIXaqmcqaIYaGmaaaaaa@3E5F@ from the center, where D denotes the diameter or height of the magnifier, as appropriate.

To estimate the number of displayable taxa for each viewer (see Table 1), we applied the viewer to a list of trees containing increasingly large numbers of taxa: 1 k, 2 k, 5 k, 10 k, 20 k, 50 k, 100 k, 200 k, 334 k, 668 k, 1002 k, 1336 k and 2004 k. In Table 1, we report the maximal size of dataset that could be opened by the viewer, and then loaded and browsed in a reasonable amount of time (less than 90 seconds to open and an interaction response time of less than 15 seconds) on a standard workstation.