Elasticities: A review of methods and model limitations

Elasticity is a perturbation measure in matrix projection models that quant ifies the proportional change in population growth rate as a function of a proportional change in a demographic transition (growth, survival, reproduc tion, etc.). Elasticities thus indicate the relative "importance" of life c ycle transitions for population growth and maintenance. In this paper. we d iscuss the applications of elasticity analysis, and its extension, loop ana lysis, in life history studies and conservation, Elasticity can be interpre ted as the relative contribution of a demographic parameter to population g rowth rate. Loop analysis reveals the underlying pathway structure of the l ife cycle graph. The different kinds of results of the two analyses in stud ies of life histories are emphasized. Because elasticities quantify the rel ative importance of life cycle transitions to population growth rate, it is generally inferred that management should focus on the transitions with th e largest elasticities. Such predictions based on elasticities seem robust, but we do identify three situations where problems may arise. The mathemat ical properties and biological constraints that underlie these pitfalls are explained. Examples illustrate the additional information that needs to be taken into account for a sensible use of elasticities in population manage ment. We conclude by indicating topics that are in need of research.