Comparative sensitivity analysis of stable stage structures and reproductive values

New formulas for deriving the sensitivities of stable stage structures and reproductive values to changes in vital rates are presented. They enable comparison of the sensities to changes of different elements in the projection matrix; in other words, comparison of partial derivatives of the eigenvectors. These kinds of sensitivities can be used in applied problems such as an analysis of the effect of harvesting on the population structure. However, in this paper, we examine the application of the sensitivities in a more general ecological context. We investigate why the stable stage structure of the mustard aphid,Lipaphis erysimi, changes very little in the temperature interval 10–30°C. The sensitivities of the stable stage structure at 15°C and 25°C were derived. The character of the sensitivites were the same in both temperatures although the stage structure was more sensitive to changes at 15°C than at 25°C. The sensitivity analysis also revealed that the temperature variation results in changes in fecundity and developmental rate that have a counteractive effect on the population structure.