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