etienne {untb} | R Documentation |
Function etienne()
returns the probability of a given dataset
given theta
and m
according to the Etienne's sampling
formula. Function optimal.params()
returns the maximum likelihood
estimates for theta
and m
using numerical optimization
etienne(theta, m, D, log.kda = NULL, give.log = TRUE, give.like = TRUE) optimal.params(D, log.kda = NULL, start = NULL, give = FALSE, ...)
theta |
Fundamental biodiversity parameter |
m |
Immigration probability |
D |
Dataset; a count object |
log.kda |
The KDA as defined in equation A11 of Etienne 2005. See details section |
give.log |
Boolean, with default TRUE meaning to return
the logarithm of the value |
give.like |
Boolean, with default TRUE meaning to return
the likelihood and FALSE meaning to return the probability |
start |
In function optimal.params() , the start point for
the optimization routine (theta,m). |
give |
In function optimal.params() , Boolean, with
TRUE meaning to return all output of the optimization
routine, and default FALSE meaning to return just the point
estimate |
... |
In function optimal.params() , further arguments
passed to optim() |
Function etienne()
is just Etienne's formula 6:
omitted...see PDF
where log K(D,A) is given by function logkda()
(qv). It
might be useful to know the (trivial) identity for the Pochhammer symbol
[written (z)_n] documented in theta.prob.Rd
. For
convenience, Etienne's Function optimal.params()
uses
optim()
to return the maximum likelihood estimate for
theta and m.
Compare function optimal.theta()
, which is restricted to no
dispersal limitation, ie m=1.
Argument log.kda
is optional: this is the K(D,A) as defined
in equation A11 of Etienne 2005; it is computationally expensive to
calculate. If it is supplied, the functions documented here will not
have to calculate it from scratch: this can save a considerable amount
of time
Robin K. S. Hankin
R. S. Etienne 2005. “A new sampling formula for biodiversity”. Ecology letters, 8:253-260
data(butterflies) ## Not run: optimal.params(butterflies) #takes too long without PARI/GP #Now the one from Etienne 2005, supplementary online info: zoo <- count(c(pigs=1, dogs=1, cats=2, frogs=3, bats=5, slugs=8)) l <- logkda.R(zoo, use.brob=TRUE) # Use logkda() if pari/gp is available optimal.params(zoo, log.kda=l) #compare his answer of 7.047958 and 0.22635923.