3.4. Indexes of aggregation

   1. Coefficient of dispersion: [eqcd.gif]

   2. Mean crowding [eqmcr1.gif] (Lloyd 1967) is equal to the mean number of
   "neighbors" in the same quad:
   Sample No. No. of individuals
   (N) No. of neighbors
   (N-1) N(N-1)
   1 5 4 20
   2 3 2 6
   3 0 -1 0
   4 1 0 0
   5 7 6 42
   Total 16 - 68

   It means that the mean number of "neighbors" is [eqmcr1.gif] = 4.25.

   Note: mean crowding has biological sense only if the size of each quad
   corresponds to "interaction distance" among individuals.

   Consider probability distribution p(i) = the proportion of samples with i
   individuals. Then:

                                     [eqmcr2.gif]

   For a random (poisson) distribution, CD=1, and thus, [eqmcr1.gif] = m.

   3. Lloyd (1967) suggested a "patchiness" index: [eqmcr1.gif] /m, which is 1 for a
   random distribution, > 1 for aggregated distributions, and