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

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

Elasticities: A Review of Methods and Model Limitations

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Pre-dispersal seed predation in Primula veris: among-population variation in damage intensity and selection on flower number

The geographic mosaic theory of co-evolution states that evolution of interactions is driven by geographical variation in interactions between species. We investigated whether the intensity of pre-dispersal seed predation differed among nine Primula veris populations over 5 years, and whether such differences lead to geographical variation in selection on flower number. Seed predation intensity differed significantly among years and populations, and it increased with canopy closure and decreased with the density of the field layer vegetation. Individuals in open habitats also produced the highest number of flowers. Moreover, the phenotypic selection on flower number differed among years and populations. In populations of closed habitats, with high seed predation pressure, the increased number of flowers was often correlated with an increased number of damaged capsules. However, an increased flower number did not result in fewer intact fruits due to seed predation in any population