| 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.