How do unit or proportional changes in vital rates affect populations in th
e short term? We present a new extension to standard methods of matrix mode
l analysis that allows us to answer this question for the first time. By us
ing the sensitivities of all the eigenvalues/vectors, rather than just the
leading eigenvalue/vector pair, we can predict the consequences of unit or
proportional changes in vital rates to population size and structure at any
arbitrary time, not just when populations have neared their stable distrib
ution. These extensions are particularly important in studying populations
subject to frequent disturbance, where stable growth rare and stable distri
bution do not provide sufficient information about the effects of changes i
n the vital rates; managed populations in which short-term goals are define
d; and the adequacy of the underlying matrix model for either short- or lon
g-term understanding. We use analysis of empirical data on the cactus Coryp
hantha robbinsorum to demonstrate this approach and show that short-term pr
edictions can differ substantially from those based on standard, asymptotic
, analysis.