Understanding and predicting population spread rates is an important problem in basic and applied ecology. In this article, we link estimates of invasion wave speeds to species traits and environmental conditions. We present detailed field studies of wind dispersal and compare nonparametric (i.e., data-based) and mechanistic (fluid dynamics model-based) dispersal kernel and spread rate estimates for two important invasive weeds, Carduus nutans and Carduus acanthoides. A high-effort trapping design revealed highly leptokurtic dispersal distributions, with seeds caught up to 96 m from the source, far further than mean dispersal distances (approx. 2 m). Nonparametric wave speed estimates are highly sensitive to sampling effort. Mechanistic estimates are insensitive to sampling because they are obtained from independent data and more useful because they are based on the dispersal mechanism. Over a wide range of realistic conditions, mechanistic spread rate estimates were most sensitive to high winds and low seed settling velocities. The combination of integrodifference equations and mechanistic dispersal models is a powerful tool for estimating invasion spread rates and for linking these estimates to characteristics of the species and the environment.