Mammalian herbivores require drinking water to differing degrees (e.g., Western 1975). The congregation of these animals around focal points on rangeland from where they acquire this supplementary water results in a concentration of environmental impacts (Andrew 1988). The subsequent land modification is considered by some to be localised degradation (Perkins & Thomas 1993b) or desertification (e.g., Dean et al. 1995), and is especially noticeable in arid and semiarid landscapes. The affected area has been termed a piosphere (Lange 1969). Gradient sampling strategies have been used to quantify the piosphere effect (e.g., Tolsma et al. 1987), revealing remarkable consistency in their mathematical characterisation (Graetz & Ludwig 1978).
Source: Derry (2004)
Derry (2004) actually contains several examples of applying the SimSAGS modelling software to piosphere studies, exploring what combination of factors is most important in generating the piosphere pattern, how it is maintained and how it influences animal foraging efficiency and ultimately animal survival.
These introductory sections contain more details about piosphere ecology and efforts to mathematically model the piosphere effect
It is possible to fit a series of such curves to a sequence of your simulation output from the Piosphere Plot to show the generation of a piosphere, for example
and also from your grid file output to show the focus of animal activity if they are dependent on the water source, for example
Of course there are more advanced analyses possible, e.g., multiple regressions of piosphere extent against animal and plant factors. More advanced examples are also given in Derry (2004).