On random splitting of the interval

We study the colonizing process of space by some populations which can be verbally described as follows: suppose a first incoming species occupies a random fraction of the available unit space. The forthcoming species takes an independent random fraction of the remaining space. There are n species and so there is a fraction of space occupied by no species. This model constitutes an approximation to the celebrated GEM interval partition. Essentially using moments, we study some statistical features of the induced partition structure of space.