ParameterPriors

A description of the default priors on each parameter of the standard models in BEAUti

Introduction

The aim is to provide every parameter with a proper and reasonable prior. This document is to describe our choices and the rationale behind each.

Parameters

Substitution Models

Parameter	Description	Bounds	Default Prior	Editable in BEAUTi	Rationale/Comments
*.frequencies	base frequencies	0 <= \pi_i <= \sum pi_i = 1	Uniform / Dirichlet(1,...,1)	Y	Dirichlet(1,\ldots,1) is uniform over this hyperplane
*.kappa	HKY transition-transversion parameter	0,+Inf	Log-Normal(M=1,S=1.25)	Y	Gamma(1/a,a) for a large is relatively uninformative - biological kappa values are greater than 1, but not much greater than 10. This prior is moderately diffuse with a median of 2.718
*.kappa1	TN93 1st transition-transversion parameter	0,+Inf	Log-Normal(M=1,S=1.25)	Y	biological kappa values are greater than 1, but not much greater than 10. This prior is moderately diffuse with a median of 2.718
*.kappa2	TN93 2nd transition-transversion parameter	0,+Inf	Log-Normal(M=1,S=1.25)	Y	biological kappa values are greater than 1, but not much greater than 10. This prior is moderately diffuse with a median of 2.718
*.ac, *.at, *.cg, *.gt	GTR A-C, A-T, C-G, G-T substitution parameters	0,+Inf	Gamma(0.05,10)	Y	If the GTR parameters are scale to C-T (a transition) then these four transversions should have a prior with a mean below 1. This prior is diffuse with a mean of 0.5. _A quote from Marc:_For the GTR, I think a hierarchical prior could be a reasonable way to go. All rates, rate_i, draw IID from a common distribution (say, log-Normal) with an estimable mean and variance. If one type of transition is not observed, the rate will become the mean of the others. Hierarchical priors generally provide the most statistically efficient estimators.
*.ag	GTR A-G substitution parameter	0,+Inf	Gamma(0.05,20)	Y	If the GTR parameters are scaled to C-T (a transition) then the other transition should have a prior with a mean of 1. This prior is moderately diffuse with a mean of 1
hfrequencies	Binary Covarion frequencies of the hidden rates	0 <= \pi_i <= \sum \pi_i = 1	Uniform / Dirichlet(1,1)	Y
bcov.alpha	Binary Covarion rate of evolution in slow mode	0,1	Beta	Y	Beta(1,1) is uniform
bcov.s	Binary Covarion rate of flipping between slow and fast modes	0,+Inf	Gamma(0.05, 10)	Y	The covarion model is normalized by setting the fast rate to 1.0. If the switching rate is much faster than the fast rate, then the covarion aspect of the model is a bit pointless. I have no good feeling for this, but would suggest a diffuse prior with a mean below 1.

Site Models

Parameter	Description	Bounds	Default Prior	Editable in BEAUTi	Rationale/Comments
*.alpha	Gamma shape parameter	1E-8,+Inf	Gamma	Y	The lower bound is to prevent numerical issues with the quantiles for exceptionally low values
*.pInv	proportion of invariant sites parameter	0,1	Beta	Y	Beta(1,1) is uniform
*.mu	relative rate parameter	0,+Inf	Gamma	Y

Clock Models

Parameter	Description	Bounds	Default Prior	Editable in BEAUTi	Rationale/Comments
clock.rate	Strict clock substitution rate	0,+Inf	Gamma	Y
uced.mean	uncorrelated exponential relaxed clock mean	0,+Inf	Gamma	Y
ucld.mean	uncorrelated lognormal relaxed clock mean	0,+Inf	Gamma	Y
ucld.stdev	uncorrelated lognormal relaxed clock stdev	Exp(mean=0.333)	Gamma	Y
branchRates.var	autocorrelated lognormal relaxed clock rate variance	0,+Inf	Gamma	Y
branchRates.categories	relaxed clock branch rate categories	0,branches	integer	N
*.rates	random local clock rates	0,+Inf	Gamma	N
*. changes	random local clock rate change indicator	0,1	Integer	N
treeModel.rootRate	autocorrelated lognormal relaxed clock root rate	0,+Inf	Gamma	N
treeModel.nodeRates	autocorrelated lognormal relaxed clock non-root rates	0,+Inf	Uniform	N

Tree Models

Parameter	Description	Bounds	Default Prior	Editable in BEAUTi	Rationale/Comments
treeModel.rootHeight	root height of the tree	0,+Inf	Tree Prior	Y
treeModel.internalNodeHeights	internal node heights of the tree (except the root)	dynamic	Tree Prior	N

Tree Priors

Parameter	Description	Bounds	Default Prior	Editable in BEAUTi	Rationale/Comments
constant.popSize	coalescent population size parameter	0,+Inf	Jeffreys (1/x)	Y
exponential.popSize	coalescent population size parameter	0,+Inf	Jeffreys (1/x)	Y
exponential.growthRate	coalescent growth rate parameter	-Inf,+Inf		Y
exponential.doublingTime	coalescent doubling time parameter	0,+Inf		Y
logistic.popSize	coalescent population size parameter	0,+Inf	Jeffreys (1/x)	Y
logistic.growthRate	coalescent logistic growth rate parameter	0,+Inf
logistic.doublingTime	coalescent doubling time parameter	0,+Inf		Y
logistic.t50	logistic shape parameter	0,+Inf		Y
expansion.popSize	coalescent population size parameter	0,+Inf	Jeffreys (1/x)	Y
expansion.growthRate	coalescent logistic growth rate parameter	0,+Inf		Y
expansion.doublingTime	coalescent doubling time parameter	0,+Inf		Y
expansion.ancestralProportion	ancestral population proportion	0,1		Y
skyline.popSize	Bayesian Skyline population sizes	0,+Inf	Exponential Markov	Y
skyline.groupSize	Bayesian Skyline group sizes	1,node count	Integer	Y
skyride.logPopSize	GMRF Bayesian skyride population sizes	-Inf,+Inf	GMRF	N	skyride.logPopSize is log unit unlike other popSize
skyride.precision	GMRF Bayesian skyride precision	0,+Inf	Gamma	Y
demographic.popSize	Extended Bayesian Skyline population sizes	0,+Inf		N
demographic.indicators	Extended Bayesian Skyline population switch	1,node count	Integer	N
demographic.populationMean	Extended Bayesian Skyline population prior mean	0,+Inf	Jeffreys (1/x)	Y
demographic.populationSizeChanges	Average number of population change points	0,x	Poisson	Y
yule.birthRate	Yule speciation process birth rate	0,+Inf		Y
birthDeath.meanGrowthRate	Birth-Death speciation process rate	0,+Inf		Y
birthDeath.relativeDeath	Death/Birth speciation process relative death rate	0,+Inf		Y

Star BEAST

Parameter	Description	Bounds	Default Prior	Editable in BEAUTi	Rationale/Comments
species.popMean	Hype-prior on population sizes	0,+Inf	Jeffreys (1/x)	Y
species.yule.birthRate	Tree birth rate	0,+Inf	Jeffreys (1/x)	Y
species.birthDeath.meanGrowthRate	Tree mean growth rate (birth-death)	0,+Inf	Jeffreys (1/x)	Y
species.birthDeath.relativeDeathRate	Tree relative death rate (death/birth)	[0,1]	uniform on [0,1]	Y
speciesTree.splitPopSize	species tree population sizes	0,+Inf	Gamma(2, species.popMean) for internal, Gamma(4, species.popMean) for tips	N