Description Usage Arguments Details Author(s) References See Also Examples

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

1 2 |

`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 |

`give.like` |
Boolean, with default |

`start` |
In function |

`give` |
In function |

`...` |
In function |

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

1 2 3 4 5 6 7 8 9 | ```
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.
``` |

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