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 n_{1,i} sampled from population 1, and n_{2,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,\phantom{\rule{0.3em}{0ex}}j}^{\ast} | Population genetic summary statistics calculated from X_{i, j}. |
X | Vector containing the sequence alignments of each locus from each population pair: \left({X}_{1,1},\dots ,{X}_{Y}{,}_{{k}_{Y}}\right). |
S ^{∗} | Vector containing the summary statistics of each locus from each population pair: \left({\mathit{\text{S}}}_{1,1}^{\ast},\dots ,{\mathit{\text{S}}}_{Y,{k}_{Y}}^{\ast}\right). |
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 X_{i, j}. |
G | Vector containing the gene trees of each locus from each population pair: \left({G}_{1,1},\dots ,{G}_{Y,{k}_{Y}}\right). |
|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: {τ_{1},…,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: (t_{1},…,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: (T_{1},…,T_{ Y }). |
{\mathcal{T}}_{i,\phantom{\rule{0.3em}{0ex}}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: ({\mathcal{T}}_{1,1},\dots ,{\mathcal{T}}_{Y,{k}_{Y}}). |
θ_{D1,i},θ_{D2,i} | Mutation-rate-scaled effective population size of the 1^{st} and 2^{nd} 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 (θ_{D1,1},…,θ_{D1,Y}) and (θ_{D2,1},…,θ_{D2,Y}), respectively. |
θ _{ A } | Vector containing the θ_{ A } parameters for each population pair: (θ_{A,1},…,θ_{A,Y}). |
υ _{ j } | Mutation-rate multiplier of locus j. |
υ | Vector containing the locus-specific mutation-rate multipliers: (υ_{1},…,υ_{ K }). |
α | The shape parameter of the gamma prior distribution on υ. |
ζ_{D1,i},ζ_{D2,i} | θ-scaling parameters that determine the magnitude of the population bottleneck in the 1^{st} and 2^{nd} descendant population of pair i, |
respectively. The bottleneck in each descendant population begins immediately after divergence. | |
ζ_{ D1 },ζ_{ D2 } | Vectors (ζ_{D1,1},…,ζ_{D1,Y}) and (ζ_{D2,1},…,ζ_{D2,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: (τ_{B,1},…,τ_{B,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: ({\rho}_{1,\phantom{\rule{0.3em}{0ex}}1},\dots ,{\rho}_{\mathit{\text{Y}},{k}_{Y}}) |
ν | Vector of mutation-rate scaling constants: ({\nu}_{1,\phantom{\rule{0.3em}{0ex}}1},\dots ,{\nu}_{\mathit{\text{Y}},{k}_{Y}}) |
\stackrel{\u0304}{\mathit{\text{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 \left({s}_{T}^{2}/\stackrel{\u0304}{\mathit{\text{T}}}\right). |
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 Λ_{1},…,Λ_{ n } drawn form the prior. |
| Summary statistic vectors S_{1},…,S_{ n } for each Λ_{1},…,Λ_{ n } drawn from the prior. |