An analytical model consisting of adult plants and two types of seeds (unripe and mature) is considered and successfully tested using experimental data available for some invasive weeds (Echium plantagineum, Cytisus scoparius, Carduus nutans andCarduus acanthoides) from their native and exotic ranges. The model accounts for probability distribution functions (pdfs) for times of germination, growth, death and dispersal on two dimensions, so the general life-cycle of individuals is considered with high level of description. Our work provides for the first time, for a model containing all that life-cycle information, explicit relationship conditions for the invasive success and expressions for the speed of invasive fronts, which can be useful tools for invasions assessment. The expressions derived allow us to prove that the different phenotypes showed by the weeds in their native (exotic) ranges can explain their corresponding non-invasive (invasive) behavior.