Elasticities: A Review of Methods and Model Limitations

Elasticity is a perturbation measure in matrix projection models that quantifies the proportional change in population growth rate as a function of a proportional change in a demographic transition (growth, survival, reproduction, etc.). Elasticities thus indicate the relative ''importance'' of life cycle transitions for population growth and maintenance. In this paper, we discuss the applications of elasticity analysis, and its extension, loop analysis, in life history studies and conservation. Elasticity can be interpreted as the relative contribution of a demographic parameter to population growth rate. Loop analysis reveals the underlying pathway structure of the life cycle graph. The different kinds of results of the two analyses in studies of life histories are emphasized. Because elasticities quantify the relative importance of life cycle transitions to population growth rate, it is generally inferred that management should focus on the transitions with the largest elasticities. Such predictions based on elasticities seem robust, but we do identify three situations where problems may arise. The mathematical 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 management. We conclude by indicating topics that are in need of research.