Fig 9. Schematic plot of how nonlinear individual resistance functions r averaged over different water levels of the common stomach w might yield a linear average resistance function.

Suppose individual CS wasps have sigmoid resistance functions (black solid line). Suppose half of the CS wasps are empty (r(0) = 0) and the remaining half are half-full ((r(0.5) = 0.5). The average resistance of the whole common stomach lies on the secant line (grey dashed line) joining (0, 0) and (0.5, 0.5); the average water level is w = 0.25, and the average resistance is r = 0.25. This means that a linear average resistance function does not imply linear individual resistance functions. Thus, the result that σ = 0 holds for the common stomach as a whole but does not necessarily hold for individual CS wasps.