Elasticities and the Link between Demographic and Evolutionary Dynamics

Multivariate selection models and demographic matrix projections are closely related. The subtle differences among the parameters of both approaches (sensitivities, elasticities, selection differentials, and gradients) can be confusing. I suggest a hierarchical framework for analysis using elasticity path diagrams, "elastograms." The framework combines selection analysis for the links between phenotypic traits (morphology, behavior) and fitness components (vital rates) with matrix analysis for the relationship between fitness components and population growth rate/fitness. Elasticities are often used to quantify the impact of a transition rate in the projection matrix on the population growth rate (λ ). Elasticities for underlying fitness components such as fecundity and survival rates can be derived from their connection with the transition matrix entries. Yet other traits may affect λ due to a functional relationship with one or more components of fitness; for instance, the timing of flowering of a plant may affect its seed yield. Elasticities can also be used to quantify the effects of such traits: they can be interpreted as selection gradients for traits expressed on a proportional (mean-standardized) scale. "Evolvabilities" (additive genetic variation in mean-standardized traits), rather than the heritabilities of traits, are needed to predict expected selection responses from the elasticities. Elasticities quantify the direct effect of a focal trait on λ . Integrated elasticities measure the impact of a trait through both its direct and indirect effects. This requires knowledge of the correlations among traits. Matrix projections and selection analysis (through multiple regression or path analysis) can be merged into an elasticity path diagram that summarizes the hierarchical relationships among traits and fitness. Such diagrams facilitate the identification of those traits that have the highest impact on the life cycle of the study organism and can be a tool to define the targets of management practices, as well as an aid in comparative life history research.