## Definitions and units of the standard parameters and variables

Crucial to the interpretation of all BEAST parameters is an understanding of the units that the tree is measured in. The simplest situation occurs when no calibration information is available, either from knowledge of the rate of evolution of the gene region, or from knowledge of the age of any of the nodes in the tree. If this is the case the rate of evolution is set to 1.0 (via the clock.rate or ucld.mean parameters) and the branch lengths in the tree are then in substitutions per site. However if the rate of evolution is known in substitutions per site per unit time, then the genealogy will be expressed in the relevant time units. Likewise, if the age of one or more nodes (internal or external) are known then this will also provide the units for the rest of the branch lengths and the rate of evolution. With this in mind, the following table lists the parameters that can be generated by BEAUTi, their interpretation and units. clock.rate The rate of the strict molecular clock. The units of this parameter are in substitutions per site per unit time. If this parameter is fixed to 1.0 then the branch lengths in the tree will be in units of substitutions per site. However, if, for example, the tree is being calibrated by using fossil calibrations on internal nodes and those fossil dates are expressed in millions of years ago (Mya), then the clock.rate parameter will be an estimate of the evolutionary rate in units of substitutions per site per million years (Myr).

**constant.popSize**This is the coalescent parameter under the assumption of a constant population size. This parameter represents the product of effective population size (N_{e}) and the generation length in units of time (τ). Therefore, only if time is measured in generations is this parameter a direct estimate of N_{e}. Otherwise it is a composite parameter and N_{e}can be computed from this parameter by dividing it by generation length in the units of time that your calibrations (or clock.rate) are defined in. Finally, if clock.rate is set to 1.0 then`constant.popSize`is an estimate of N_{e}μ for haploid data such as mitochondrial sequences and 2N_{e}μ for diploid data, where μ is the substitution rate per site per generation.**exponential.growthRate**This is the coalescent parameter representing the rate of growth of the population assuming exponential growth. The population size at time t is determined by N(t)=N_{e}exp{-gt} where t is in the same units as the branch lengths and g is the`exponential.growthRate`parameter.**exponential.popSize**This is the parameter representing the modern day population size assuming exponential growth. Like constant.popSize, it is a composite parameter unless the time scale of the genealogy is in generations.**gtr.{ac,ag,at,cg,gt}**These five parameters are the relative rates of substitutions for A↔C, A↔G, A↔T, C↔G and G↔T in the general time-reversible model of nucleotide substitution (Rodriguez et al, 1990). In the default set up these parameters are relative to rC↔T = 1.0.**hky.kappa**This parameter is the transition/transversion ratio (κ) parameter of the HKY85 model of nucleotide substitution (Hasegawa et al, 1985)**siteModel.alpha**This parameter is the shape (α) parameter of the gamma distribution of rate heterogeneity among sites (Yang, 1994).**siteModel.pInv**This parameter is the proportion of invariant sites (pInv) and has a range between 0 and 1.**treeModel.rootHeight**This variable represents the total height of the tree (often known as the time to the most recent common ancestor of all the taxa, tMRCA). The units of this variable are the same as the units for the branch lengths in the tree and will depend on the calibration information for the rate and/or dates of calibration nodes.**ucld.mean**This is the mean rate under the uncorrelated log-normal relaxed molecular clock (in real space). Under default BEAUTi options for the uncorrelated log-normal relaxed clock this parameter has the same units as`clock.rate`.**ucld.stdev**This is the standard deviation (σ) of the uncorrelated log-normal relaxed clock (in log-space). If this parameter is 0 there is no variation in rates among branches. If this parameter is greater than 1 then the standard deviation in branch rates (in real space) is greater than the mean rate.**yule.birthRate**This parameter is the rate of lineage birth in the Yule model of speciation. If clock.rate is 1.0 then this parameter estimates the number of lineages born from a parent lineage per substitution per site. If the tree is instead measure in, for example, years, then this parameter would be the number of new lineages born from a single parent lineage per year.