Increasingly, Large Language Models (LLMs) are used to simulate human behavior and social systems. However, despite rapidly growing scientific and commercial applications of LLMs along these lines, threats to the validity and robustness of such applications remain poorly understood and responses to these threats remain ad hoc. Replication strategies inspired by prior social science and statistical research offer insights into these challenges. This talk characterizes some key threats to LLM simulations of human behavior and explores two strategies---perturbation and iteration---to evaluate LLM simulations of human behavior in the context of social scientific replication.