Silicene, the single layer of silicon atoms arranged in a honeycomb lattice, has been synthesized in recent experiments and attracted significant attentions. Silicene is promising in future nanoelectronic devices due to its outstanding electronic properties. In experiments, however, different silicene superstructures coexist on Ag(111) substrate. For the device applications, homogenous silicene sheet with large scale and high quality is highly desired. Here, for the first time, we investigate both the temperature and the coverage effects on the thermal stability of epitaxial silicene on Ag(111) surface by ab initio molecular dynamics simulations. The relationship between the stability of various silicene superstructures and the growth conditions, including temperature and coverage of silicon atoms, is revealed by plotting the chemical potential phase diagram of silicene on Ag(111) surfaces at different temperatures. Our results are helpful for understanding the observed diversity of silicene phases on Ag(111) surfaces and provide some useful guidance for the synthesis of homogenous silicene phase in experiments. (C) 2017 Elsevier B.V. All rights reserved.