It has been widely suggested that invasion success along broad environmental gradients may be partially due to phenotypic plasticity, but rapid evolution could also be a relevant factor for invasions. Seed and fruit traits can be relevant for plant invasiveness since they are related to dispersal, germination, and fitness. Some seed traits vary along environmental gradients and can be heritable, with the potential to evolve by means of natural selection. Utilizing cross-latitude and reciprocal-transplant experiments, we evaluated the adaptive value of seed thickness as assessed by survival and biomass accumulation in plants. In addition, thickness of a seed and Endosperm to Seed Coat Proportion (ESCP) in a second generation ( ) was measured to evaluate the heritability of this seed trait. On the other hand, we characterized the genetic variability of the sampled individuals with amplified fragment length polymorphism (AFLP) markers, analyzing its spatial distribution and population structure. Overall, thickness of seed coat (plus wall achene) decreases with latitude, indicating that individuals of from northern populations have a thicker seed coat than those from southern populations. Germination increased with greater addition of water and seeds from southern localities germinated significantly more than those from the north. Additionally, reciprocal transplants showed significant differences in survival percentage and biomass accumulation among individuals from different localities and moreover, the high correlation between maternal plants and their offspring can be suggesting a high grade of heritability of this trait. Although genetic differentiation was found when was considered all populations, there was no significant differentiation when only was compared the northernmost populations which inhabit in the driest climate conditions. Our results suggest that climatic conditions could affect both, the ESCP and the genetic variability in the invasive , suggesting that this seed trait could be indicative of adaptive selection. Thus, colonization along broad geographical gradients in many cases may be the result -in part- for the presence of functional traits as shown in invasive plant species with rapid adaptive capacity.