Function etienne() is just Etienne's formula 6:
$$P[D|\theta,m,J]=
\frac{J!}{\prod_{i=1}^Sn_i\prod_{j=1}^J{\Phi_j}!}
\frac{\theta^S}{(\theta)_J}\times
\sum_{A=S}^J\left(K(D,A)
\frac{(\theta)_J}{(\theta)_A}
\frac{I^A}{(I)_J}
\right)$$
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