Birds arriving from spring migration have higher chances of securing a territory if they reach the breeding area before their companions. However, an early arrival may compromise their chances of surviving until reproduction begins. Here, we study how evolutionarily stable responses to these opposite constraints may shape patterns of arrival in a population of migratory birds, with the help of a simple evolutionary algorithm. We show that, initially, an increasing level of competition for breeding territories generates a massive peak of early arrivals. However, when the level of competition becomes very high, the temporal distribution of arrivals may take different shapes, depending on the modalities of competition. If individuals trying to usurp territories have relatively high chances of success, a second peak of arrival emerges at the very end of the arrival period. Birds arrive then in two successive waves. By contrast, if these chances are low, a single early peak of arrival is still present. Many individuals do however continuously arrive afterwards, at a regular and increasing tempo, until reproduction begins. The prior residence effect, that rules competition between resident birds and their challengers, is thus expected to influence the whole distribution of arrival dates on breeding grounds. This distribution will, in turn, affect the ability of the population to respond to changing environmental conditions.