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In this paper, we study the validity and limitations of the additive white Gaussian noise (AWGN) model in quasi-linear, long-haul, return-to-zero, direct-detection optical fiber communications systems. Our approach is to compare bit-error ratios (BERs) computed using the additive white Gaussian noise method to those obtained using standard and multicanonical Monte Carlo (MMC) simulations and to a noise-linearization method, referred to as the noise covariance matrix (NCM) method. We show that the AWGN method provides a very good approximation to the actual system BER for power levels and dispersion profiles that are used in typical modern-day quasi-linear systems. For example, the BER obtained using the AWGN method is within a factor of 4 of the actual system BER computed using MMC simulations for a realistic 10 Gb/s, 6000 km system based on dispersion-shifted fiber in which the peak signal power at the transmitter is 1 mW and the absolute residual dispersion at the receiver is less than 200 ps/nm. However, when the peak power is increased to about 4 mW, or the average map dispersion is zero and the absolute residual dispersion exceeds 200 ps/nm, the AWGN and NCM methods may simultaneously breakdown due to a combination of nonlinear signal-noise and noise-noise interactions during transmission. In addition, for a 5000 km system based on low-nonlinearity D + and D - fiber with an average map dispersion that is 4% of the dispersion variation within the map, and that operates at a peak power of 5 mW, we find that the BERs obtained using the AWGN and NCM methods are about 500 times smaller than the actual system BER computed using MMC simulations.