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. 2018 Dec 19;9:3112. doi: 10.3389/fmicb.2018.03112

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Copyright © 2018 Xiao, Chen, Yu, Zhang and Chen.

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

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Local smoothing effects of the proposed smoothness penalty. The data was generated based on a simulated phylogenetic tree (p = 200,“rcoal” from R “ape” package). The correlation C(α) was calculated based on the pairwise patristic distances with α = 2. (A) The elements of inverse correlation matrix (Ω_ij) are plotted against pairwise patristic distances (d_ij). (B) The elements of Laplacian matrix (L_ij) are plotted against pairwise patristic distances (d_ij).