  Many species of plants are found in regions to which they are alien and their
global distribution has been found to exhibit several remarkable
patterns,characterised by exponential functions of the kind that could arise
through versions of MacArthur's broken stick. We show here that these various
patterns are all quantitatively reproduced by a simple algorithm, in terms of a
single parameter- a single stick to be broken. This algorithm admits a
biological interpretation in terms of niche structures fluctuating with time
and productivity; with sites and species highly idiosyncratic. Technically,
this is an application of statistical mechanics to ecology quite different from
the familiar application to species abundance distributions.
