Dating site for biologists
In all cases, very large input trees (10,000 taxa) can easily be processed and transformed into time-scaled trees.
The LF method assumes a SMC with a constant substitution rate, and models the number of substitutions along each branch of the tree by a Poisson distribution.Most of these methods deal with time calibration points, where the dates of certain ancestral nodes in the tree are known, possibly with uncertainty (e.g., min–max values), and all of the tree tips are contemporaneous. (2012) method use smoothing and averaging techniques to accommodate for local rate variations.These methods input a rooted tree with time calibration points, and return a time-scaled, ultrametric tree. Xia and Yang's (2011) method assumes a SMC or two different local clocks, and achieves least-squares estimations under these assumptions.The estimates of the global substitution rate and of the internal node dates are then obtained by maximizing the likelihood of the input, rooted tree. In this article, we study a model analogous to LF's, but using a normal approximation that allows for a least-squares approach, and show that this model is robust to uncorrelated violations of the molecular clock.Using the tree (recursive) structure of the problem at hand, and the close relationships between least-squares and linear algebra, we propose very fast algorithms to estimate the substitution rate and the dates of all internal tree nodes.