Symbol | Meaning |
---|---|
| Species tree with real-valued divergence times |
| Ranked gene tree (real-valued coalescence times not specified) |
n | The number of leaves of and |
s i | Speciation times, with s1 >⋯> sn−1, let s0 = ∞ |
τ i | Intervals between speciation times, τ i = [s i ,si−1) |
ℓ i | The number of gene tree lineages at time s i |
m i | The number of coalescence events in interval τ 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 |