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 $K(D,A)$ 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 $m=1$.
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 saves a considerable amount of
time.