Cristina Armas, Ramón Ordiales, and Francisco I. Pugnaire. 2004. Measuring plant interactions: a new comparative index. Ecology 85:2682–2686.

Sensitivity is defined as the response of a function to small changes in a variable. In a non-vectorial function, sensitivity can be defined as its first derivative and allows to compare the sensitivity of two points of the same function. The sensitivity of two functions can be compared by standardization, which is made in several steps. We take a reference value, calculate the sensitivity of the function near this point and standardize the result respect to this point. The sensitivity of the two functions then can be compared as they have the same range.

The four indices could be expressed as in Table C1:

Standardization of these indices around a point "x" is done as follows:

The definition of symmetry in our manuscript can be expressed as f(u)= -f(1/u) where u is the independent variable. When there is facilitation and x are >1 and we use the terms _F and x_F; conversely, when there is competition and x <1, and we use _C and x_C as 1/ and 1/x respectively. All terms range from 0⁺ to +.

The above equations can be expressed as follows (in terms of _F, x_F and _C, x_C)

Sensitivity is calculated by testing the function index variation when changes around x

We only allowed for a maximum deviation of _F and _C of an order of magnitude from the pivotal point (i.e., small changes around x). Replacing  = x-1, the standardized sensitivity is expressed as