An intrinsic property of invaders that determines many of the effects they produce in the areas they colonize is their great abundance. However, a lack of data generally hampers the exploration of the complex interactions of factors that regulate the abundance of most invasive populations. This lack of data generally hinders the understanding of the invasion process and, more specifically, interferes with the management of these populations. This paper uses hierarchical complex models to investigate how temperature, humidity, competitive interactions and resource availability affect the growth rates of naturalized populations of two invaders in the Brazilian Savanna: the African Drosophila simulans and Zaprionus indianus. We also assess how morphological (life-history) and demographic traits mediate these effects. Our results suggest that the population growth rates of both species depend on complex interactions between several of the studied variables but are regulated primarily by rapid and direct responses to resource availability. We found evidence that resources determine immediate oviposition rates, inducing a very rapid regulation of population sizes (in one generation, i.e., approximately 1 month). Our study also demonstrates a lower predictability for Z. indianus and we suggest that this finding is a result of the shorter evolutionary history of Z. indianus in the Brazilian Savanna. These results, valid for the system we have investigated, if validated by other studies, will help to increase the mechanistic understanding of invasions and may contribute to the development of effective management strategies to mitigate their effects on natural and agro-ecosystems.