Quantitative visualizations of hierarchically organized data in a geographic context

Abstract

Here we introduce a novel quantitative technique for visualizing hierarchically organized data in a geographic context. In contrast to existing techniques, our visualization emphasizes the hierarchical relationships in the data by depicting them in a standard tree format that takes advantage of many fundamental perceptual properties. Our technique allows users to define a geographic axis and visualize how well a tree correlates with the ordering of geographical locations along this axis. This is accomplished by finding the ordering of leaf nodes, subject to the constraints of the tree topology, which minimizes the number of crossings that occur between lines that connect leaf nodes to their associated geographic locations. In this optimal layout, any crossings that occur between these lines indicate discordance between the topology of the tree and the user defined geographic axis. We have developed a branch-and-bound algorithm that allows optimal leaf orderings to be determined quickly enough to support interactive exploration of different geographic axes even for large multifurcating hierarchies. The quantitative nature of our visualization has allowed us to specify a permutation test for determining if the relationship between a tree topology and a geographic axis is statistically significant. In this paper, the utility of our visualization is demonstrated on biological data sets, but our method is applicable to any hierarchical data where geographic structure may be of interest.

Shaping species with ephemeral boundaries: the distribution and genetic structure of desert tortoise (Gopherus morafkai) in the Sonoran Desert region

“…We used Gengis 2.1.1 (Parks et al ., ) to visualize mtDNA sequence distributions and to test for geographical association of haplotypes. Gengis performed a Monte Carlo permutation test to determine if the fit of ordered leaf‐nodes at geographical locations from the tree topology was significantly greater than expected by chance alone (Parks & Beiko, ). We used Ntsyspc (2.02 h, Applied Biostatistics Inc., Port Jefferson, NY, USA) to perform Mantel tests to assess correlation between F ST values from the STRs and geographical distances among populations.…”

GenGIS: A geospatial information system for genomic data

“…Fewer crossings imply a better fit between geography and phylogeny, so the best fit of a given tree to a geographic axis must be found, which requires a crossing minimization algorithm. To determine the optimal tree layout, GenGIS uses a branch-and-bound algorithm (Land and Doig 1960) to determine the ordering of leaves and internal nodes of a tree that minimizes the number of crossings (Parks and Beiko 2009). The idea of a linear geographic axis can be generalized to a multisegment line of arbitrary complexity, allowing the specification of piecewise, nonlinear geographic hypotheses (Supplemental Fig.…”

“…1B). Coupled with the axis layout functions is a statistical test, based on randomization of leaf nodes, that determines whether the fit of tree leaves to geography is significantly better than random (Parks and Beiko 2009). Branches of a tree can also be colored in accordance with the coloring of different environmental types: A given branch will be assigned a consistent color if all children of a given branch are associated with the same environment type, or a default color if its children cover multiple environments.…”

GenGIS 2: Geospatial analysis of traditional and genetic biodiversity, with new gradient algorithms and an extensible plugin framework

“…Within GenGIS, potential migration routes or the influence of geography on community similarity can be explored by proposing linear or non-linear geographic axes, and visualizing the goodness of fit between a tree topology and the ordering of sample sites along the specified axis (Parks and Beiko 2009). The first version of GenGIS required the user to draw geographic axes by hand, allowing the testing of specific hypotheses but making it difficult to explicitly test all possible axes.…”

“…We previously proposed a branch-and-bound algorithm which allows the globally optimal layout to be found for large, multifurcating trees (~1000 leaf nodes with an average node degree < 8) in interactive time, i.e. <100 ms (Parks and Beiko, 2009). …”