calc_prob_forward_onebranch_dense: Dense matrix exponentiation forward on a branch, with...
In BioGeoBEARS: BioGeography with Bayesian (and Likelihood) Evolutionary Analysis in R Scripts

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Take input probabilities, and get the probabilities at the end of a branch using matrix exponentiation.

1 2	calc_prob_forward_onebranch_dense(relprobs_branch_bottom, branch_length, Qmat)

`relprobs_branch_bottom`	The relative probability of each state at the base of the branch (should sum to 1).
`branch_length`	The length of the branch.
`Qmat`	A Q transition matrix in square (dense) format

The calc_loglike_sp function calculates most transition probabilities internally via rexpokit. These are then stored and can be used again when an uppass is being done for ancestral state estimates. However, if there is a root branch below the lowest fork, the uppass needs to calculate the forward probabilities.

actual_probs_after_forward_exponentiation The probabilities of each state at the top of the branch.

Go BEARS!

Nicholas J. Matzke matzke@berkeley.edu

http://phylo.wikidot.com/matzke-2013-international-biogeography-society-poster http://www.bioinf.org/molsys/data/idiots.pdf

Matzke_2012_IBS

FosterIdiots

expokit_dgpadm_Qmat2, expokit_dgpadm_Qmat, rexpokit

# Make a square instantaneous rate matrix (Q matrix)
# This matrix is taken from Peter Foster's (2001) "The Idiot's Guide
# to the Zen of Likelihood in a Nutshell in Seven Days for Dummies,
# Unleashed" at:
# \url{http://www.bioinf.org/molsys/data/idiots.pdf}
#
# The Q matrix includes the stationary base freqencies, which Pmat
# converges to as t becomes large.
Qmat = matrix(c(-1.218, 0.504, 0.336, 0.378, 0.126, -0.882, 0.252, 0.504, 0.168,
0.504, -1.05, 0.378, 0.126, 0.672, 0.252, -1.05), nrow=4, byrow=TRUE)

relprobs_branch_bottom = c(0.25, 0.25, 0.25, 0.25)

# Make a series of t values
branch_length = 0.1

calc_prob_forward_onebranch_dense(relprobs_branch_bottom, branch_length, Qmat)
calc_prob_forward_onebranch_dense(relprobs_branch_bottom, branch_length=0.5, Qmat)
calc_prob_forward_onebranch_dense(relprobs_branch_bottom, branch_length=1, Qmat)
calc_prob_forward_onebranch_dense(relprobs_branch_bottom, branch_length=2, Qmat)
calc_prob_forward_onebranch_dense(relprobs_branch_bottom, branch_length=10, Qmat)
calc_prob_forward_onebranch_dense(relprobs_branch_bottom, branch_length=20, Qmat)