Lambda

# lambda [-l values | -s | -r start:step:end] [-t lambda structure]

In CAFE terms, lambda represents the rate of change of evolution in a tree. Λ values may be specified in one of four ways:

1. A single value, shared by the entire tree
2. Multiple values, with different values applied to different branches of the tree
3. A range of values for which CAFE will calculate the likelihood
4. No value, in which case CAFE will calculate an appropriate value

-l lambda values: This option allows the user to specify the value(s) of λ. If more than one λ is specified, then the -t option must also be used. λ values are specified in the order 1 2 3... which correspond to the integers specified in the -t option. λ values should be separated by spaces.

Note

1. The product of λ and the depth of the tree structure should not exceed one (i.e., λ × t < 1 must be true; where t is the time from tips to the root). See the Known Limitations section for details as to how to diagnose this problem.
2. CAFE will use the last λ value(s) estimated (or user-specified) to compute ancestral gene family sizes and to run Monte Carlo simulations.

-s: CAFE will search using an optimization algorithm to find the value(s) of λ that maximize the log likelihood of the data for all families. CAFE starts with an intermediate value and then searches iteratively for the best value for λ (or set of λ values if used in conjunction with the -t option). Subsequent analyses will automatically use the results from the lambda search.

-r start:step:end: Returns the likelihood scores for λ values in the user specified range (start:step:end). For example, to see the score distribution with a lambda between 0.003 and 0.005, the range would be 0.003:0.001:0.005. In case of more than one lambda, ranges are separated by a space.

-t lambda structure: To investigate whether different parts of the tree are evolving at different rates, the user may specify which branches of the tree will take the same or different λ values. Input the same NEWICK tree structure as in the tree command, but exclude branch lengths and substitute integer values from 1 up to n or taxon names (where n = the total number of branches on the tree; matching integer values indicate that these branches will take the same value of λ). Default: all branches have the same value for λ. Here is an example of a lambda structure:

(((1,1)1,(2,2)2)2,2)

This λ structure corresponds to the tree example above, and specifies λ = 1 for the Human, Chimp, and Ape branches, and λ =2 for the remaining branches.

Note

CAFE will not always converge to a single optimum with models that contain many parameters. See the Known limitations section below for details on assessing this problem.