Covarion.TuffleySteel98 — The Tuffley-Steel Covarion Model
Usage
Covarion.TuffleySteel98(submodel: CTMC<a>, r: Double, pi1: Double) → CTMC<a>
Arguments
A default beginning with ~ specifies a prior
distribution.
-
submodel: -
The base model
-
r: -
s01 + s10
-
Default:
~Gamma(2,1/4) -
pi1: -
Fraction of time spent in the ON state.
-
Default:
~Beta(2,2)
Description
The Tuffley-Steel covarion model splits every state into an ON and an OFF version, increasing the number of states by a factor of 2. Rates for the ON version are given by the rate matrix Q of the submodel, while rates for the OFF version are 0:
rate ( (ON , state1) -> (ON , state2) ) = Q(state1, state2)
rate ( (OFF, state1) -> (OFF, state2) ) = 0
Rates for switching between ON and OFF are given by the s01 and s10 parameters, and are independent of the submodel state.
rate ( (ON , state ) -> (OFF, state ) ) = s10
rate ( (OFF, state ) -> (ON , state ) ) = s01
Rates for changing the level (ON,OFF) and the state at the same time are 0.
We parameterize s01 and s10 by:
pi1 = s01/(s10 + s01)
r = s01 + s01,
where pi1 is the fraction of time spent in the ON state. The total rate of switching between states is:
rate = 2*r*pi1*(1-pi1)
The priors avoid placing too much mass on boundary conditions where this model reduces to a simpler model.
Examples
GTR +> ts98GTR +> ts98 +> ts98Citation
Tuffley, Chris; Steel, Mike (1998). Modeling the covarion hypothesis of nucleotide substitution. Mathematical Biosciences 147(1): 63--91. DOI: 10.1016/S0025-5564(97)00081-3