The causal correlations between human genetic variants and linguistic (typological) features could represent the mechanism required for gradual, accretionary models of language evolution. The causal link is mediated by the process of cultural transmission of language across generations in a population of genetically biased individuals. The particular case of Tone, ASPM and Microcephalin is discussed as an illustration. It is proposed that this type of genetically-influenced linguistic bias, coupled with a fundamental role for genetic and linguistic diversities, provides a better explanation for the evolution of language and linguistic universals.