Choice of the a priori discordance parameter α

α=0 corresponds to the a priori assumption that there is no discordance among gene tree topologies, i.e. that all loci must have the same topology.
α=infinity corresponds to the a priori assumption that gene trees are completely independent, as in a consensus approach.

Prior probability that two genes share the same topology

The prior probability that two randomly sampled genes share the same tree is approximately p=1/(α+1) .
The exact value of this probability depends on the total number T of a priori possible topologies:
p=(1+α/T)/(α+1) .

Prior distribution on the number of distinct trees

You can visualize this distribution using R as follows.
1. Download this file: prior_standalone.r,
2. Open an R session in the same directory where the file is located or change R's working directory to where the file is located,
3. 'Source' the file with: source("prior_standalone.r") , but adapt the file name if you changed it,
4. Get the graph using a command of this form: priorPlot(ntax=8,ngenes=106,alpha=2,las=1,lwd=3)
and replace 8 by the desired number of taxa (ntax), etc.

The webform below has some issues from time to time...

Number of genes Number of taxa Alpha
(positive integer; example 10000) (positive integer; example 8) (positive number; example 1)

(This may take a few moments. Some browsers require you to reload the page.)