Fig. 1

Patterns of population density as a function of cell size. Occupancy is the average proportion of sub-cells occupied when a cell is subdivided into 16 smaller units. In each case the width refers to the sub-cell size, not the mother-cell size. For each population the solid curve is the outcome of 1000 simulations obtained by locating the grid in slightly different positions relative to the population. The black line is the average. The thin broken line is the occupancy of the equivalent fractal model while the rising broken curve is the occupancy of the equivalent Poisson distribution