Elasticity is proportional change in population growth rate
resulting from a small change in a vital rate. Elasticities are
usually calculated for long-run population growth rates: dominant
eigenvalue of the projection matrix in a deterministic environment
or stochastic growth rate in the presence of environmental
variation. We derive elasticities of yearly growth rates, which
are time dependent, in varying environments. This is called
real-time elasticity. We show that moving averages of real-time
elasticities converge to long-run stochastic elasticity, thus
making a connection between short-term and long-term selection.
When there is no environmental variation real-time elasticities
reduce to transient elasticities. Our results explain why
transient elasticities differ from asymptotic ones and how this
difference depends on the demography of the species. We describe
applications of our results in life-history evolution and
conservation biology.
