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, 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 the reference |
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 K(D,A) is given by function logkda
(qv). It might be
useful to know the (trivial) identity for the Pochhammer symbol
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=1x
Robin K. S. Hankin
R. S. Etienne 2005. “A new sampling formula for biodiversity”. Ecology letters, 8:253-260
data(butterflies) optimal.params(butterflies) #Now the one from Etienne 2005, supplementary online info: zoo <- count(c(pigs=1, dogs=1, cats=2, frogs=3, bats=5, slugs=8)) optimal.params(zoo) #compare his answer of 7.0479586 and 0.22635923.