(A) Average weight change as a function of width (for the asymmetric window in Equation 14) for phase precession and phase locking (colored curves). The solid black line depicts the theoretical maximum for large (, Equation 8). The dashed curves show the analytical small-tau approximations (Equation 5). The dotted curve depicts the analytical approximation for the ’no theta’ case (Equation A2-46 in Appendix 2). The vertical dashed lines mark s and the value of , respectively. (B) The benefit of phase precession is largest for narrow learning windows, and it approaches 0 for wide windows. Simulations (gray line) and analytical result (black line, small-tau approximation from Equation 20) match well. (C) The signal-to-noise ratio (SNR; phase precession: blue, phase locking: red, no theta: cyan) takes into account that only the asymmetric part of the learning window is helpful for temporal-order learning. For large , all three coding scenarios induce the same SNR. The horizontal dashed black line depicts the analytical limit of the SNR for large and overlapping firing fields (, Equation A1-17 of Appendix 1). The dotted black line depicts the analytical expression for the ’no theta’ case (Equation A2-48 in Appendix 2, the curve could not be plotted for s due to numerical instabilities). Dots represent the SNR for experimentally observed learning windows. The learning windows were taken from ‘B&P’, Bi and Poo, 2001: their Figure 1, ‘F’, Froemke et al., 2005: their Figure 1D bottom, ‘W&W’, Wittenberg and Wang, 2006: their Figure 3, ‘P&G’, Pfister and Gerstner, 2006: their Table 4, ‘All to All’, ‘minimal model’, and ‘B’, Bittner et al., 2017: their Figure 3D. For ‘B&P’, ‘F’, and ‘B’, the position of the dots on the horizontal axis was estimated as the average time constants for positive and negative lobes of the learning windows. Wittenberg and Wang modeled their learning rule by a difference of Gaussians — we approximated the corresponding time constant as 30 ms. For the triplet rule by Pfister and Gerstner, we used the average of three time constants: the two pairwise-interaction time constants (as in Bi and Poo) and the triplet-potentiation time constant. Parameters for all plots: s, Hz, s, , , . Colored/gray curves and dots are obtained from stochastic simulations; see Materials and methods for details.