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Table 1 Summary of the notation used throughout this work; modified from Oaks et al. [7]

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.
S i , j Population genetic summary statistics calculated from Xi, j.
X Vector containing the sequence alignments of each locus from each population pair: X 1 , 1 , , X Y , k Y .
S Vector containing the summary statistics of each locus from each population pair: S 1 , 1 , , S Y , k Y .
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: G 1 , 1 , , G Y , k Y .
|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 ).
T i , j 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: ( T 1 , 1 ,, T Y , k Y ).
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: ( ρ 1 , 1 ,, ρ Y , k Y )
ν Vector of mutation-rate scaling constants: ( ν 1 , 1 ,, ν Y , k Y )
T ̄ Mean of divergence times across the Y population pairs.
s T 2 Variance of divergence times across the Y population pairs.
D T Dispersion index of divergence times across the Y population pairs s T 2 / T ̄ .
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.