Data from: Characterizing and comparing phylogenies from their Laplacian spectrum

Lewitus E, Morlon H

Date Published: May 17, 2016



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Title Figure_S1
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Description Toy example illustrating the construction of the spectral density for a hypothetical phylogeny. Top: example phylogeny. Middle: computation of the MGL. Each non-diagonal element (i, j) in the MGL Λ is equal to the negative of the branch length between nodes i and j. Each diagonal element i is computed as the sum of branch lengths between node i and all other nodes j. Bottom: the spectral density is obtained by convolving the λ calculated from Λ with a smoothing function.
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Title Figure_S2
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Description Speciation values for diversification models. Birth-death trees were constructed according to one of six diversification models: increasing speciation, decreasing speciation, decreasing speciation below extinction; and constant speciation-extinction with (i) ancient mass-extinction (0.1 survival probability), (ii) recent mass-extinction (0.1 survival probability), or (iii) no mass-extinction. For all models, μ = 0.05.
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Title Figure_S3
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Description Interpreting spectral density profiles For trees simulated under a constant birth-death model (open circle), the principal λ for the MGL is a good predictor of species richness (a) and phylogenetic diversity (b); there is a significant positive relationship between skewness and the γ statistic (c) and no significant relationship between kurtosis and the Colless index (d). The principal λ for the nMGL shows no significant relationship with species richness (a, inset) and a significantly negative relationship with phylogenetic diversity (b, inset). Only significant slopes are shown.
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Title Figure_S4
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Description Principal components analysis of simulated trees using traditional summary statistics. (a) K-medoids and (b) hierarchical clustering on principal components derived from mean branch length, branch length standard deviation, ln species richness, ln phylogenetic diversity, the Colless index, and γ calculated for 600 trees simulated under different diversification models. Both hierarchical clustering (bootstrap probability > 0.95) and k-medoids clustering (P < 0.05) extract three clusters of trees. Shape and color correspond to cluster assignment.
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Title Figure_S5
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Description Clustering on principal components and spectral density profiles from the nMGL. (a) Hierarchical clustering on spectral density profiles and (b) k-medoids clustering on principal components are computed as in Figure 3, except based on the nMGL. In (A), hierarchical clustering on the spectral density profile identified six clusters of trees (bootstrap probability > 0.95), each corresponding to a distinct underlying diversification model, whose property in terms of speciation-extinction rate variation is summarized in the left column. In (b), only four significant clusters were identified (P < 0.05).
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Title Figure_S6
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Description Undersampling affects spectral density profiles. The spectral densities of 3 (out of 100) trees (solid line) simulated under (a) constant birth-death, (b) increasing speciation-rate, and (c) recent mass-extinction models and their jackknifed trees (dashed lines) at 90%, 80%, 70%, 60%, 50%, and 40% are plotted. As the tree moves further from complete, the density plot shifts left, as a result of a declining principal λ, and the shape of the spectral density becomes increasingly different from the original, notably by decreasing skewness. The mean and standard deviation of the Jensen-Shannon distance between each tree and its 100 jackknifed trees are shown in a barplot. The distance between trees increases linearly with incompleteness.
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Title Figure_S7
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Description The reliability of the eigengap heuristic versus MEDUSA in recovering shifts in speciation rate and diversification pattern in simulated trees. The absolute deviation of shifts recovered by the eigengap (red) and MEDUSA (blue) from the known number of shifts for trees with 0–10 shifts in (a) speciation rate and (b) diversification pattern. In (a), only when five or ten shifts were simulated, MEDUSA performed significantly better (T > 2, P < 0.05) than the eigengap. (a, Inset) The average deviation across all trees is slightly lower for MEDUSA (2.89) than for the eigengap heuristic (3.10), although this is not significant (T = 1.88, P > 0.05). In (b), the eigengap heuristic outperformed MEDUSA for all trees with > 2 shifts and (b, inset) overall (T = 10.44, P < 0.01). In (a) and (b), only eigengaps supported by BIC post-hoc analysis were computed in the means. Asterisks indicate a significantly lower deviation for MEDUSA (blue) or the eigengap heuristic (red).
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Title Figure_S8
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Description Spectral density profile summary statistics across viral strains and hosts. Boxplot of avian (red) and human (gold) strains calculated from standard (a) and normalized (b) MGLs. Grey bars indicate across-host means; asterisks denote significant differences at P < 0.05. (c) Mean differences between hosts across all strains calculated from standard graph Laplacians.
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Title Figure_S9
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Description The cluster assignments for strains by country of origin. Six clusters were found based on k-medoid clustering on the standard spectral density profiles of all strains (P < 0.05). The distribution across those clusters for strains sampled from 25 countries are shown for avian (a) and human (b) hosts. Four clusters were found using the normalized profiles (P < 0.05) and the distributions are shown for each country for avian (c) and human (d) hosts. Only countries with all seven strains sampled are represented.
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When using this data, please cite the original publication:

Lewitus E, Morlon H (2015) Characterizing and comparing phylogenies from their Laplacian spectrum. Systematic Biology 65(3): 495-507.

Additionally, please cite the Dryad data package:

Lewitus E, Morlon H (2015) Data from: Characterizing and comparing phylogenies from their Laplacian spectrum. Dryad Digital Repository.
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