Converting between birth rate, death rate (speciation and extinction) and r (diversification rate) and epsilon (relative death rate)

birthdeath_example

# Example converting between 
# birth rate, death rate (speciation and extinction) 
# and 
# r (diversification rate) and epsilon (relative death rate)

library(ape)
library(BioGeoBEARS)

# Load the Psychotria tree
trfn = np(paste(addslash(extdata_dir), "Psychotria_5.2.newick", sep=""))
tr = read.tree(trfn)

# Estimate the rates (this is a simple method in APE, 
#   see geiger for more sophisticated options)
# birthrate means: speciation rate
# deathrate means: extinction rate
#
# Note: the lineage extinction rate is a different thing
#       from the "e" in DEC, which is a range of range
#       contration
#
birthdeath_results = birthdeath(tr)
birthdeath_results

diversification_rate = birthdeath_results$para["b-d"]
relative_extinction_rate = birthdeath_results$para["d/b"]

birthrate = diversification_rate / (1-relative_extinction_rate)
deathrate = relative_extinction_rate * birthrate
birthrate
deathrate