The current study presents an agent-based model which simulates the innovation and competition among lexical items in cases of language contact. It is inspired by relatively recent historical cases in which the linguistic ecology and sociohistorical context are highly complex. Pidgin and creole genesis offers an opportunity to obtain linguistic facts, social dynamics, and historical demography in a highly segregated society. This provides a solid ground for researching the interaction of populations with different pre-existing language systems, and how different factors contribute to the genesis of the lexicon of a newly generated mixed language. We take into consideration the population dynamics and structures, as well as a distribution of word frequencies related to language use, in order to study how social factors may affect the developmental trajectory of languages. Focusing on the case of Sranan in Suriname, our study shows that it is possible to account for the composition of its core lexicon in relation to different social groups, contact patterns, and large population movements.