Fig. 1.

The ‘sphere of influence’ model (adapted from Stubbs et al. [2009]). A simple analogy can be drawn between this model and a gumball machine. Imagine a spherical gumball machine completely filled with balls. An imaginary line is drawn between the centre of the gumball machine and the centre of each and every ball. All individual distances are added up and then divided by the total number of balls to give an average distance. The reasoning behind this model is the same except that it assumes all the balls are infinitely small. A straightforward mathematical function is performed by integration to sum up the infinite number of imaginary lines. In the end, an average distance from the centre of the sphere is calculated.