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With unrooted trees the computing time becomes (nearly) quadratic (i.e., proportional to the square of the number of taxa).In all cases, very large input trees (10,000 taxa) can easily be processed and transformed into time-scaled trees.*The 4 Elements that KEEP a woman in love with you…*The biggest mistake men make in dating and exactly how to AVOID it…When the input tree is unrooted, they can provide an estimate for the root position, thus representing a new, practical alternative to the standard rooting methods (e.g., midpoint).Our algorithms exploit the tree (recursive) structure of the problem at hand, and the close relationships between least-squares and linear algebra.We apply these algorithms on a large data set comprising 1194 strains of Influenza virus from the pdm09 H1N1 Human pandemic.
With rooted trees, the former is solved using linear algebra in linear computing time (i.e., proportional to the number of taxa), while the resolution of the latter, constrained setting, is based on an active-set method that runs in nearly linear time.These algorithms are implemented in the LSD software (least-squares dating), which can be downloaded from this web page, along with all our data sets and detailed results.An Online Appendix, providing additional algorithm descriptions, tables, and figures can be found in the Supplementary Material available on Dryad at Here, we present very fast dating algorithms, based on a Gaussian model closely related to the Langley–Fitch molecular-clock model.We show that this model is robust to uncorrelated violations of the molecular clock.
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