This well-written paper deals with discrete-time Lotka-Volterra models obtained by applying nonstandard finite difference (NSFD) schemes to the continuous-time counterpart of the model. The NSFD schemes are noncanonical symplectic numerical methods proposed previously by the author [J. Difference Equ. Appl. 12, No.~9, 937--948 (2006; Zbl 1119.65075)]. The local dynamics of three classes of discrete-time models are analyzed and compared with the dynamics of the continuous model. For each discrete-time model with appropriately chosen parameters, it is shown that independently of the stepsize, the same stability criteria hold as those for the continuous-time model. In other words, the discrete-time models are dynamically consistent with the original continuous-time system with respect to the stability properties of the equilibria. With a special parameter setting, two of the three discrete-time models also preserve the positivity and the boundedness of solutions and the monotonicity of the system. Finally, the NSFD schemes are compared with the well-known Euler's method for which the local stability is consistent with the continuous model only with some restriction on the stepsize.