Plants in seasonal environments exhibit phenological patterns in growth, survival, development, and reproduction. These phenological patterns are an example of multiple time scales (one seasonal and intra-annual, the other inter-annual) in population growth. The goal of demographic analysis is to incorporate these multiple time scales and extract their consequences. The problem is particularly challenging in annual or short-lived plants, but also applies in long-lived perennials. The methods appropriate to these analyses include periodic matrix population models, matrix calculus, and extensions of loop analysis.
**Results/Conclusions **Application of these methods yields new results on population growth rate, net reproductive rate, life expectancy, and sensitivity analysis in deterministic and stochastic environments. These results make it possible to evaluate the contribution of alternate life history events (on the phenological time scale) to population growth (on the inter-annual time scale), and thus have applications to conservation and evolutionary demography.