etienne {untb}R Documentation

Etienne's sampling formula

Description

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

Usage

etienne(theta, m, D, log.kda = NULL, give.log = TRUE, give.like = TRUE)
optimal.params(D, start = NULL, give = FALSE, ...) 

Arguments

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()

Details

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

Author(s)

Robin K. S. Hankin

References

R. S. Etienne 2005. “A new sampling formula for biodiversity”. Ecology letters, 8:253-260

See Also

logkda,optimal.theta

Examples

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.


[Package untb version 1.2-5 Index]