The design of most agricultural systems ignores the possibility that cropping system characteristics may affect weed population dynamics by altering key demographic rates of weeds. We examined legume green manure and tillage timing effects upon giant foxtail (Setaria faberi) demography with prospective and retrospective perturbation analyses of a periodic matrix population model. Demographic data were collected for S. faberi grown in a wheat–corn–soybean crop sequence in the central USA in 2000 and 2001, with either a wheat sole-crop (W) or wheat/red clover crop mixture (R) in the wheat phase. Wheat phase residues were incorporated either in fall (FT) or spring (ST) to form four cropping system treatments: FT/W, FT/R, ST/W, and ST/R. Demographic rates estimated from the field data included seed survival from October to March and March to October, seedling recruitment, plant survival, fecundity, and seed predation. The variable efficacy of postemergence weed control was modeled by varying the proportion of seedlings surviving to reproductive maturity from 0.025 to 0.20. Deterministic simulations indicated that there was both interannual and management-induced variation in S. faberi population growth rate. Stochastic population growth rate depended upon an interaction between legume green manure and tillage-timing effects, such that stochastic population growth rate was lowest for fall-tilled wheat and red clover, greater for fall-tilled wheat, and greatest for both spring-tilled management regimes. Within the fall-tilled regime, the cropping system (wheat vs. wheat plus clover) had a greater influence on relative rates of stochastic population growth as plant survival increased. However, plant survival did not affect the stochastic population growth rates in the spring-tilled treatments. Elasticity analysis suggested that seed survival through the winter, fecundity, and the proportion of seeds escaping predation were important driving variables for this system. Retrospective perturbation analysis supported these results but also indicated that fecundity and predation levels varied more in response to changing management treatments than winter seed survival, leading to their having a greater influence on differences in population growth among the four management treatments. Perturbation analyses of matrix population models will aid the development of integrated weed-management systems by elucidating cropping-system effects upon weed demography.