How to calculate a community similarity index not supported by vegan

Hi,
I have to  calculate similarity in community composition(in a community
matrix) as the probability of randomly drawing two individuals of the  same
species  at  each  pair  of  sampling  points.
The details as follows:
For two plots, the probability F can be calculated as F =sum (fi1*fi2), where
fij is the relative  abundance  of  species  i at  site  j,  and  the sum is
over all species at both sites.
I did not find any functions in library vegan and ecodist to calculate this
index. Can anyone help on this?

Dear Qi Li,

I am not quite sure I understand correctly what you want to achieve, but it
looks to me like you want to have a crossproduct of a matrix standardized to
unit row sums. With more words: (1) you want to standardize your data so
that your rows have unit sum so that species are expressed as relative
abundances, and (2) then you want to have a sum of products of these
relativized values for each pair of sites.

There are many ways of doing this (if this was what you wanted to do). In
vegan you can use decostand() for the first task, and designdist() for the
second:

designdist(decostand(dune, "tot"), "J", terms="quadratic")

This will give similarities, but vegan and all standard R functions expect
dissimilarities. So you may consider asking for probabilities of randomly
drawing individuals of *different* species, or

designdist(decostand(dune, "tot"), "1-J", "quadratic")

There are many other ways of doing this, though, as method = "J" with terms
= "quadratic" in designdist() is just a crossproduct (or tcrossprod()).

I am not sure if this was what you wanted to have, but you can see if you
can define your method with designdist() which allows you design your sweet
own dissimilarity indices.

Cheers, Jari Oksanen