A consistent equation for ecological sensitivity in matrix population analysis

Matrix population analysis is now accepted widely as an important tool in ecological studies, as reaffirmed in the excellent recent TREE review by Benton and Grant 1 . The controversy over whether elasticity or sensitivity is a better measure of the effect of a change in one vital rate on a population’s growth rate, has been largely settled by accepting that each measure provides an accurate answer to a different question 2 , 3 . Nevertheless, Benton and Grant’s reaffirmation inadvertently perpetuates a commonly used, but inconsistent, equation for sensitivity. Specifically, Benton and Grant – as well as previous authors 2 , 3 – assert that the sensitivity matrix is invariably equal to the outer product of the dominant left and right eigenvectors of the population projection matrix (Box 1). Unfortunately, in general, this equation is not consistent with the life cycle graph that generates the projection matrix: it sometimes implies flows along nonexistent arcs.