Scaling in sensitivity analysis

Population matrix models allow sets of demographic parameters to be summarized by a single value λ, the finite rate of population increase. The consequences of change in individual demographic parameters are naturally measured by the corresponding changes in λ; sensitivity analyses compare demographic parameters on the basis of these changes. These comparisons are complicated by issues of scale. Elasticity analysis attempts to deal with issues of scale by comparing the effects of proportional changes in demographic parameters, but leads to inconsistencies in evaluating demographic rates. We discuss this and other problems of scaling in sensitivity analysis, and suggest a simple criterion for choosing appropriate scales. We apply our suggestions to data for the killer whale, Orcinus orca.