Successful invasion may depend of the capacity of a species to adjust genetically to a spatially varying environment. This research modeled a species invasion by examining the interaction between a quantitative genetic trait and population density. It assumed: (1) a quantitative genetic trait describes the adaptation of an individual to its local ecological conditions; (2) populations far from the local optimum grow more slowly than those near the optimum; and (3) the evolution of a trait depends on local population density, because differences in local population densities cause asymmetrical gene flow. This genetics-density interaction determined the propagation speed of populations. Numerical simulations showed that populations spread by advancing as two synchronic traveling waves, one for population density and one for trait adaptation. The form of the density wave was a step front that advances homogenizing populations at their carrying capacity; the adaptation wave was a curve with finite slope that homogenizes populations at full adaptation. The largest speed of population expansion, for a dimensionless analysis, corresponded to an almost homogeneous spatial environment when this model approached an ecological description such as the Fisher-Skellam's model. A large genetic response also favored faster speeds. Evolutionary speeds, in a natural scale, showed a wide range of rates that were also slower compared to models that only consider demographics. This evolutionary speed increased with high heritability, strong stabilizing selection, and high intrinsic growth rate. It decreased for steeper environmental gradients. Also indicated was an optimal dispersal rate over which evolutionary speed declined. This is expected because dispersal moves individuals further, but homogenizes populations genetically, making them maladapted. The evolutionary speed was compared to observed data. Furthermore, a moderate increase in the speed of expansion was predicted for ecological changes related to global warming.

Corresponding Editor: A. Caballero