The present dissertation is a study of language development in children. From a biological perspective, the development of language, as the development of any other organic systems, is an interaction between internal and external factors; specifically, between the child's internal knowledge of linguistic structures and the external linguistic experience he receives. Drawing insights from the study of biological evolution, we put forth a quantitative model of language acquisition that make this interaction precise, by embedding a theory of knowledge, the Universal Grammar, into a theory of learning from experience. In particular, we advance the idea that language acquisition should be modeled as a population of grammatical hypotheses, competing to match the external linguistic experiences, much like in a natural selection process. We present evidence -- conceptual, mathematical, and empirical, and from a number of independent areas of linguistic research, including the acquisition of syntax and morphophonology, and historical language change -- to demonstrate the model's correctness and utility.