N-body orbital evolution of the GJ 581 system using initial orbital parameters from the median NS stable sample to represent the system’s dynamical behavior for the first 2000 yr of evolution. The top panels show the evolution of planetary semi-major axes on the left and mutual orbital period ratios are shown on the right. The bottom panels show the evolution of planetary eccentricities on the left, along with the evolution of the mutual apsidal alignment angles. No secular or MMR dynamical architecture was observed for GJ 581.