From: An improved approximate-Bayesian model-choice method for estimating shared evolutionary history
Symbol | Description |
---|---|
Y | Number of population pairs. |
n i | The number of genome copies sampled from population pair i, with n1,i sampled from population 1, and n2,i from population 2. |
k i | Number of loci sampled from population pair i. |
K | Total number of unique loci sampled. |
X i, j | Sequence alignment of locus j sampled from population pair i. |
| Population genetic summary statistics calculated from Xi, j. |
X | Vector containing the sequence alignments of each locus from each population pair: . |
S ∗ | Vector containing the summary statistics of each locus from each population pair: . |
B ε (S∗) | Multi-dimensional Euclidean space around the observed summary statistics, S∗. |
ε | Radius of B ε (S∗), i.e., the tolerance of the ABC estimation. |
G i, j | Gene tree of the sequences in Xi, j. |
G | Vector containing the gene trees of each locus from each population pair: . |
|τ| | Number of population divergence-time parameters shared among the Y population pairs. |
τ | Time of population divergence in 4N C generations. |
τ | Set of divergence-time parameters: {τ1,…,τ|τ|}. |
t i | The index of the divergence-time in τ to which population pair i is mapped. |
t | Vector of divergence-time indices: (t1,…,t Y ). |
T i | Time of divergence in 4N C generations between the populations of pair i. |
T | Vector of divergence times for each of the population pairs: (T1,…,T Y ). |
| Scaled time of divergence between the populations of pair i for locus j. |
| Vector containing the scaled divergence times of each locus from each population pair: . |
θD1,i,θD2,i | Mutation-rate-scaled effective population size of the 1st and 2nd descendent population, respectively, of pair i. |
θ A,i | Mutation-rate-scaled effective population size of the population ancestral to pair i. |
θ D1 ,θ D2 | Vectors (θD1,1,…,θD1,Y) and (θD2,1,…,θD2,Y), respectively. |
θ A | Vector containing the θ A parameters for each population pair: (θA,1,…,θA,Y). |
υ j | Mutation-rate multiplier of locus j. |
υ | Vector containing the locus-specific mutation-rate multipliers: (υ1,…,υ K ). |
α | The shape parameter of the gamma prior distribution on υ. |
ζD1,i,ζD2,i | θ-scaling parameters that determine the magnitude of the population bottleneck in the 1st and 2nd descendant population of pair i, |
respectively. The bottleneck in each descendant population begins immediately after divergence. | |
ζ D1 ,ζ D2 | Vectors (ζD1,1,…,ζD1,Y) and (ζD2,1,…,ζD2,Y), respectively. |
τ B,i | Proportion of time between present and T i when the bottleneck ends for the descendant populations of pair i. |
τ B | Vector containing the τ B parameters for each population pair: (τB,1,…,τB,Y). |
m i | Symmetric migration rate between the descendant populations of pair i. |
m | Vector containing the migration rates for each population pair: (m i ,…,m Y ). |
ρ i, j | θ-scaling constant provided by the investigator for locus j of pair i. This constant is required to scale θ for differences in ploidy among loci |
or differences in generation times among taxa. | |
ν i, j | θ-scaling constant provided by the investigator for locus j of pair i. This constant is required to scale θ for differences in mutation rates |
among loci or among taxa. | |
ρ | Vector of ploidy and/or generation-time scaling constants: |
ν | Vector of mutation-rate scaling constants: |
| Mean of divergence times across the Y population pairs. |
| Variance of divergence times across the Y population pairs. |
D T | Dispersion index of divergence times across the Y population pairs . |
n | Number of samples from the joint prior. |
Λ | Vector of parameter values drawn from the joint prior. |
S | Vector containing the summary statistics calculated from data simulated under parameter values drawn from the prior (Λ). |
Λ | Random sample of Λ1,…,Λ n drawn form the prior. |
| Summary statistic vectors S1,…,S n for each Λ1,…,Λ n drawn from the prior. |