Biotic invasions provide a natural experiment in evolution: when invasive species colonize new ranges, they may evolve new clines in traits in response to environmental gradients. Yet it is not clear how rapidly such patterns can evolve and whether they are consistent between regions. We compare four populations of the invasive cabbage white butterfly (Pieris rapae) from North America and Japan, independently colonized by P. rapae 150 years ago and 300 years ago, respectively. On each continent, we employed a northern and southern population to compare the effects of latitude on body mass, development rate and immune function. For each population, we used a split-sibling family design in which siblings were reared at either warm (26.7°C) or cool (20°C) temperatures to determine reaction norms for each trait. Latitudinal patterns in development time were similar between the two continents. In contrast, there were strong geographical differences in reaction norms for body size, but no consistent effects of latitude; there were no detectable effects of latitude or continent on immune function. These results imply that some life history traits respond consistently to selection along climatic gradients, whereas other traits may respond to local environmental factors, or not at all.