It is an ongoing issue to better understand colonization process, adaptation potential to new environments, and invasiveness of a species. The sub Antarctic Kerguelen Islands are a perfect model to model population dynamics in an invasion context, because it represents a simplified case of invasion by brown trout (Salmo trutta L.), a facultative anadromous fish. Introduced in the 1950s, and thanks to its dispersive and adaptive capacities, the brown trout provides a unique study model for understanding the causes and mechanisms underlying biological invasions. Understanding dispersal mechanisms, through the study of life history traits related to migration (e.g. growth, age at migration) and their temporal evolution in shifting expansion range population, is the core of this thesis work. Through the study of scales collected in this unique framework, the life histories of nearly 5000 fish have been rebuilt. This work demonstrates the importance of the methodology to determine accurate estimates of individual life history traits. Modelling the evolution of freshwater growth, body size at age and age at first migration demonstrates that evolutionary processes are at work according to the time since colonization. In particular, the decrease in growth rate over time and the decrease in body size at age over time and space suggest that the dispersal capacity is decreasing in populations located at the margins. The evolution of the threshold size at first migration confirms this results, and illustrates the importance of phenotypic plasticity and local adaptation in the choice of migratory tactics. However, the approach taken in this manuscript focuses on the evolution of migration, and would benefit from the study of the joint evolution of traits involved in fitness (costs-benefits balance), such as reproduction, or growth at sea.