# The “inside cell” ratio

Let $$C_s = \{c _1 , c_2 , …d_n \}$$ be the
set of cells at scale $$s$$ where the occurrences of a node X where found. The $$C _{s−1} = \{d_ 1 , d_ 2 , …d _k \}$$ is
the corresponding set of cells at an upper scale (ancestor of $$s$$) where the occurrences of a node X where found.

Note that the ratio:
$$r_s = \frac{\#C_{s-1}}{\#C_s}$$

gives us an indicator of how the occurrences are dispersed in the space.

If $$r_s$$ is low means that the
spatial distribution is constrained in a region as small as the unit area of the upper scale while if $$r_s$$ is close to 1 it tells us that the occurrences are as spatially distributed as the cells in the upper scale.
The method can be applied recursively to the sucessive scales to obtain a list of ratios $$r_1 , r_2 , ..r_s ,..$$ that can be fitted in model to estimate geographic extensions.