Gordon-Riley criterion, equation 2. τmax is the maximum doubling time (= ln [2]/k), in minutes, that can allow establishment, plotted as a function of Vmax at a given value of Vmin. Curves are for λ = 60 h−1 and Vmin = 1, 5, 10, 20, and 50 ml (from bottom to top). Doubling times shown below each line allow establishment under the given conditions.