The evolution of the vocabulary of a language is characterized by two different random processes: abrupt lexical replacements, when a complete new word emerges to represent a given concept (which was at the basis of the Swadesh foundation of glottochronology in the 1950s), and gradual lexical modifications that progressively alter words over the centuries, considered here in detail for the first time. The main discriminant between these two processes is their impact on cognacy within a family of languages or dialects, since the former modifies the subsets of cognate terms and the latter does not. The automated cognate detection, which is here performed following a new approach inspired by graph theory, is a key preliminary step that allows us to later measure the effects of the slow modification process. We test our dual approach on the family of Malagasy dialects using a cladistic analysis, which provides strong evidence that lexical replacements and gradual lexical modifications are two random processes that separately drive the evolution of languages.