Elasticities : a review of methods and model limitations

• Elasticity is a perturbation measure in matrix projection models that quantifiesthe proportional change in population growth rate as a function of a proportionalchange in a demographic transition (growth, survival, reproduction, etc.). Elasticities thusindicate 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 therelative contribution of a demographic parameter to population growth rate. Loop analysisreveals the underlying pathway structure of the life cycle graph. The different kinds ofresults of the two analyses in studies of life histories are emphasized. Because elasticitiesquantify the relative importance of life cycle transitions to population growth rate, it isgenerally inferred that management should focus on the transitions with the largest elasticities.Such predictions based on elasticities seem robust, but we do identify three situationswhere problems may arise. The mathematical properties and biological constraints thatunderlie these pitfalls are explained. Examples illustrate the additional information thatneeds 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.

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