Language acquisition maps linguistic experience, primary linguistic data (PLD), onto linguistic knowledge, a grammar. Classically, computational models of language acquisition assume a single target grammar and one PLD source, the central question being whether the target grammar can be acquired from the PLD. However, real-world learners confront populations with variation, i.e., multiple target grammars and PLDs. Removing this idealization has inspired a new class of population-based language acquisition models. This paper contrasts 2 such models. In the first, iterated learning (IL), each learner receives PLD from one target grammar but different learners can have different targets. In the second, social learning (SL), each learner receives PLD from possibly multiple targets, e.g., from 2 parents. We demonstrate that these 2 models have radically different evolutionary consequences. The IL model is dynamically deficient in 2 key respects. First, the IL model admits only linear dynamics and so cannot describe phase transitions, attested rapid changes in languages over time. Second, the IL model cannot properly describe the stability of languages over time. In contrast, the SL model leads to nonlinear dynamics, bifurcations, and possibly multiple equilibria and so suffices to model both the case of stable language populations, mixtures of more than 1 language, as well as rapid language change. The 2 models also make distinct, empirically testable predictions about language change. Using historical data, we show that the SL model more faithfully replicates the dynamics of the evolution of Middle English.
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