Bayesian nonparametric models have gained increasing attention due to their flexibility in modeling natural and social phenomena, demonstrating significant success in various applications. For instance, the well-known Dirichlet process and Poisson-Dirichlet process are widely used to model species distributions in population genetics. A key parameter in Bayesian nonparametric models is the concentration parameter, which represents the mutation rate in population genetics literature. Motivated by the question of what occurs when the mutation rate is large, we derive the asymptotic behavior of a rich class of Bayesian nonparametric priors, namely normalized random measures with independent increments, as the concentration parameter approaches infinity. In this talk, I will review the background of Bayesian nonparametrics and then present the asymptotic results, including the law of large numbers, the (functional) central limit theorem, and the Berry–Esseen theorem for normalized random measures with independent increments.