Parameterization of the Model¶
iTRAILS leverages the following population parameters in order to infer the underlying gene tree topologies and coalescent event timings (see Figure iTRAILS_params).
Population Size Parameters¶
N_AB: Effective size of the ancestral population between the two most closely related species.
N_ABC: Effective size of the ancestral population between the three species.
Time Parameters (generations)¶
T1: Assuming an ultrametric model, time from sample to coalescence of species A and B.
T2: Time between the coalescence of species A and B and the coalescence of AB ancestral with species C.
T3: Time between coalescence of species ABC and coalescence of ABC ancestral with outgroup species.
T_A: Time from sample of species A to coalescence with species B.
T_B: Time from sample of species B to coalescence with species A.
T_C: Time from sample of species C to coalescence with AB ancestral.
T_Upper: Time from the start of the last discretized time interval in ABC ancestral to coalescence with the outgroup.
T_Out: Time from sample of the outgroup to coalescence with ancestral ABC.
Other Parameters¶
Recombination rate (ρ): Number of recombinations per site per generation.
Mutation rate (μ): Number of mutations per site per generation.
Dependencies and Restrictions¶
Recombination rate (ρ) must always be defined either as a fixed parameter or as a parameter to optimize.
Mutation rate (μ) must always be defined as a fixed parameter.
T_Upper and T3: At least one of them must be defined (fixed or optimized). If only one is defined, the other is automatically calculated.
T_Out: Can be defined or omitted; if defined, it must be fixed. If omitted, it will be automatically calculated.
T_A, T_B, T_C, and T1 should be defined (fixed or optimized) in the following combinations. The non-defined parameters will take values as indicated in the table below.
Relationship Between T_A, T_B, T_C, and T1¶
Specified Parameters |
Used T_A |
Used T_B |
Used T_C |
|---|---|---|---|
T_A / T_B / T_C |
T_A |
T_B |
T_C |
T1 / T_A |
T_A |
T1 |
T1 + T2 |
T1 / T_B |
T1 |
T_B |
T1 + T2 |
T1 / T_C |
T1 |
T1 |
T_C |
T_A / T_B |
T_A |
T_B |
(T_A + T_B) / 2 + T2 |
T_A / T_C |
T_A |
(T_A + T_C - T2) / 2 |
T_C |
T_B / T_C |
(T_B + T_C - T2) / 2 |
T_B |
T_C |
T1 |
T1 |
T1 |
T1 + T2 |