It has recently been proposed (Dediu, D., Ladd, D.R., 2007. Linguistic tone is related to the population frequency of the adaptive haplogroups of two brain size genes, ASPM and Microcephalin. Proc Natl Acad Sci USA 104, 10944-10949) that genetically coded linguistic biases can influence the trajectory of language change. However, the nature of such biases and the conditions under which they can become manifest have remained vague. The present paper explores computationally two plausible types of linguistic acquisition biases in a population of agents implementing realistic genetic, linguistic and demographic processes. One type of bias represents an innate asymmetric initial state (Initial Expectation bias) while the other an innate asymmetric facility of acquisition (Rate of Learning bias). It was found that only the second type of bias produces detectable effects on language through cultural transmission across generations and that such effects are produced even by weak biases present at low frequencies in the population. This suggests that learning preference asymmetries, very small at the individual level and not very frequent at the population level, can bias the trajectory of language change through the process of cultural transmission.