We characterize the dynamics of age-structured density-dependent populations with yearly reproduction. In contrast to prior studies focusing primarily on behavior near the stability boundary, we describe the dynamics over the full range of linear and nonlinear behavior. We describe model dynamics in terms that have direct biological interpretations. We illustrate the use of our approach by examining the dynamics of Dungeness crab (Cancer magister) in detail. Model dynamics are found to be very sensitive to changes in life-history parameters. Small changes in vital rates can cause population density to suddenly jump from low to high variability or vice versa. Nonmonotonic switching between chaotic and nonchaotic dynamics is also observed. The period (or dominant timescale) of cyclic behavior is loosely related to values of vital rates, typically increasing with adult survivorship, but can remain constant while vital rates change. Model dynamics are also found to be sensitive to environmental perturbations. For example, model dynamics may be chaotic or nonchaotic for fixed parameter values with environmental perturbations switching model dynamics between these distinct behaviors (i.e., the dynamics are nonstationary). These findings illustrate one possible explanation for the variety of dynamic behavior in Dungeness crab populations (and other natural populations) and temporal (or spatial) shifts in behavior.