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Table 1 Notation used in the paper

From: A polynomial time algorithm for calculating the probability of a ranked gene tree given a species tree

Symbol Meaning
T Species tree with real-valued divergence times
G Ranked gene tree (real-valued coalescence times not specified)
n The number of leaves of T and G
s i Speciation times, with s1 >> sn−1, let s0 =
τ i Intervals between speciation times, τ i = [s i ,si−1)
i The number of gene tree lineages at time s i
m i The number of coalescence events in interval τ i
G i , i The ranked gene tree observed from time 0 to time s i
g i The minimum number of gene tree lineages at time s i
y i,z Population z in interval τ i in beaded tree
u i Internal node (coalescence) with rank i in the gene tree, u1 is most ancient, un−1 is the most recent
k i,j,z The number of lineages available for coalescence in population yi,z just after the j th coalescence (considered forward in time) in interval τ i ; ki,0,z is the number of lineages “exiting” at time si−1
δ(y),δ(u) The set of leaves descended from a node of the species tree or gene tree, respectively
lca(u) For a node u of the gene tree, the node y of the species tree with largest rank such that δ(u) δ(y)
τ(y) For a node y with rank i on the species tree, we denote τ(y) = τ i (the interval immediately above y)
λ i,j The overall coalescence rate in interval τ i immediately preceding (backwards in time) the j th coalescence
H k Number of sequences of coalescences above the root of the species tree starting with k lineages
f i The joint density of coalescence times in interval τ i