SIMMAP | morphology priors

Morphology Priors

As a prelude to this help document I recommend that you read Schultz and Churchill (1999) [link to journal] which is an excellent description of dealing with priors in morphological (standard) data analyses. In addition, since SIMMAP uses this approach, you should cite the authors.

SIMMAP uses one or two priors, depending on the number of states that exists for a character, when analyzing morphological or standard data types. For the rest of this document I will refer to characters as "standard" and this should be interpreted as including both, discrete morphological traits (e.g., polygamy vs. monogamy) and standard coded traits (e.g., forest vs. savannah). The two priors are: (1) a bias prior on two-state characters, and (2) an overall evolutionary rate prior. Each of these are dealt with below. First, I will discuss the overall rate prior, then deal with the bias prior for two-state characters.

Overall Rate Prior

SIMMAP uses a gamma prior on the overall substitution rate of a character. This method is similar to that suggested by Yang (1994) [link to journal] for molecular data but both parameters of the Γ (gamma) distribution can be defined. The definition of both parameters allows the distribution to have a mean that is not centered on a value of one. The basic approach is that the overall rate of standard characters are unknown (although the relative evolutionary divergences may be known using molecular divergence), that uncertainty can be satisfactorily accommodated by using a Bayesian prior. The Γ distribution is made discrete using k categories. α and β are the parameters of the Γ distribution. The expected value and standard deviation of the Γ prior is displayed dynamically as the parameter values are changed. You can select to break the distribution into 10, 20, 30, 40, 50, 60, and 70 categories.

What is the algorithm used by SIMMAP in applying a gamma rate prior?

Re-scale the branch lengths of the tree in memory such that the overall length of the tree (sum of all branch lengths) is one (you can select to NOT re-scale the branch lengths - see below).
The posterior probability of each gamma (Γ) category, defined by the prior, is calculated and a stochastic draw is made from this distribution.
The rate value, for the sampled category, is used as multiplier of the branch lengths on the un-scaled or re-scaled tree.

The use of rescaling and placing a prior on the tree allows the user to explore the effects of a range of rates on the character histories while maintaining the branch length proportionality. A variety of different gamma (Γ) priors are shown below to give a feel for the different shapes that the gamma can adopt, the expectation of the distribution, and the allowable values under the prior distribution.

Two-state Bais Parameter Prior

SIMMAP places a symmetrical Beta prior for morphological state frequencies of two-state characters (called the bias parameter and denoted by π). The Beta distribution is made discrete using k categories. α is the parameter of the Beta distribution. As α gets large the distribution becomes a narrow peak around 0.5 (see α=100.0 below). Therefore, if you wish to have equal prior probabilities for each state this value should be large. Alternatively, if you want an uninformative prior a Beta α parameter of 1 results in equal prior probabilities. You can select to break the distribution into 5, 7, 9, 11, 13, and 15 categories.

What is the algorithm used by SIMMAP in applying a beta bias prior?

The posterior probability of each beta category, defined by the prior, is calculated and a stochastic draw is made from this distribution.
The bias value, for the sampled category, is used.

Setting Morphological Priors

SIMMAP offers the option of using prior distributions or fixed (point) values. To set values describing the priors (or to turn the priors off) select Set Morphology Priors... [

9] item in the Models menu. This action opens the Morphology Priors window shown below.

If the character is a two-state character the user can select to use one of the following prior options by selecting one of the following radio buttons:

Bias parameter prior distribution
- You can set the α parameter describing the shape of the distribution and the number of categories, k, used to make the distribution discrete.
Fixed prior on bias parameter
- You can select to fix the bias parameter value by entering the π(0) value (the π(1) value is set such that π(0) + π(1) = 1.0).
Equal prior on bias parameter
- This allows users to set the bias parameter to be exactly 0.5 representing an equal probability.

To set the overall gamma rate prior the user can select to use one of the following prior options by selecting one of the following radio buttons:

Rate parameter prior distribution
- You can set the α and β parameter describing the shape of the gamma (γ) distribution and the number of categories, k, used to make the distribution discrete.
Fixed prior on rate parameter
- You can select to fix the overall rate, T (rate), be entering the desired rate.
No prior on rate parameter
- This allows users to to not apply a rate multiplier and use the branch lengths, un-scaled, as the rate. This option is only useful if the branch lengths represent the true rate of evolution for the character being mapped.

By default SIMMAP rescales morphological tree to a total length of one. When applying a prior distribution on the overall rate this should be selected. If the No prior on rate parameter option has been selected this should be de-activated to allow the branch lengths to directly represent the evolutionary rate.


	Help Documentation Current document


	Page Last Updated: 6 August 2008