As it is know local sensitivity analysis attempt to quantify the local impact of input factors on the model, through partial derivatives: a derivative of the outputs accordingly to the inputs, when the last ones are slightly perturbed. Many methods are used to estimates this derivatives: Direct method, Green Function Method, etc.
However, the input-output relationship is generally assumed to be linear (from Saltelli textbooks on the subject). Why it is assumed to be linear in a local neighborhood, even the whole system may not be linear. I guess it may have a relation with Taylor expansion expression. I am trying to understand the real reason behind this assumption. Thank you.