These functions are internally used for the likelihood computations in
`pml`

or `optim.pml`

.

## Usage

```
lli(data, tree = NULL, ...)
edQt(Q = c(1, 1, 1, 1, 1, 1), bf = c(0.25, 0.25, 0.25, 0.25))
pml.free()
pml.init(data, k = 1L)
pml.fit(tree, data, bf = rep(1/length(levels), length(levels)), shape = 1,
k = 1, Q = rep(1, length(levels) * (length(levels) - 1)/2),
levels = attr(data, "levels"), inv = 0, rate = 1, g = NULL,
w = NULL, eig = NULL, INV = NULL, ll.0 = NULL, llMix = NULL,
wMix = 0, ..., site = FALSE, ASC = FALSE, site.rate = "gamma")
```

## Arguments

- data
An alignment, object of class

`phyDat`

.- tree
A phylogenetic

`tree`

, object of class`phylo`

.- ...
Further arguments passed to or from other methods.

- Q
A vector containing the lower triangular part of the rate matrix.

- bf
Base frequencies.

- k
Number of intervals of the discrete gamma distribution.

- shape
Shape parameter of the gamma distribution.

- levels
The alphabet used e.g. c("a", "c", "g", "t") for DNA

- inv
Proportion of invariable sites.

- rate
Rate.

- g
vector of quantiles (default is NULL)

- w
vector of probabilities (default is NULL)

- eig
Eigenvalue decomposition of Q

- INV
Sparse representation of invariant sites

- ll.0
default is NULL

- llMix
default is NULL

- wMix
default is NULL

- site
return the log-likelihood or vector of sitewise likelihood values

- ASC
ascertainment bias correction (ASC), allows to estimate models like Lewis' Mkv.

- site.rate
Indicates what type of gamma distribution to use. Options are "gamma" approach of Yang 1994 (default), "gamma_quadrature" after the Laguerre quadrature approach of Felsenstein 2001 and "freerate".

## Details

These functions are exported to be used in different packages so far only in
the package coalescentMCMC, but are not intended for end user. Most of the
functions call C code and are far less forgiving if the import is not what
they expect than `pml`

.

## References

Felsenstein, J. (1981) Evolutionary trees from DNA sequences: a
maximum likelihood approach. *Journal of Molecular Evolution*,
**17**, 368--376.

## Author

Klaus Schliep klaus.schliep@gmail.com