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Figure 1 | BMC Bioinformatics

Figure 1

From: Constructing a meaningful evolutionary average at the phylogenetic center of mass

Figure 1

Reparameterizing Brownian motion on a two-taxon phylogeny. (a) Species A is the most recent common ancestor of species 1 and 2. Their respective divergence times are t1 and t2. (b) The observed data X1 and X2 are assumed to have evolved independently from the ancestral value X A according to lineage-specific Brownian motion processes ω1 and ω2. (c) Considering the species data to be fixed and the ancestral datum to be random, the lineage-specific Brownian motions can be combined into one process ω, essentially running up one branch and then down the other. The x- axis is a reparameterization of time in (b) such that X1 is the value of the process at time 0 while X2 is the value of the process at time t1 + t2. The value of the process at time t1 is the unknown quantity X A , whose distribution is determined by the behaviour of the Brownian bridge obtained by conditioning a Brownian motion on its endpoints. Four representative sample paths of the Brownian bridge ω(t) are shown; for each, the value of X A is ω(t1) as indicated by a solid black dot. The mean of the process at any fixed time t is given by the dashed line, which in the case of t = t1 corresponds to the mean of the distribution of X A .

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