Figure 2. Horizontal transmission facilitates the fixation of altruism-inducing microbes.

Using condition (1) we calculate the minimal b/c value that allows the fixation of microbe α for different values of the cost c (subfigures a, b, c, with c=0.01, c=0.05 and c=0.2, respectively), T_α , T_β and vertical transmission VT. For all c and VT values, the critical b/c value decreases with increasing horizontal transmission, even when T_α<T_β and vertical transmission is imperfect (VT<1). When the horizontal transmission probabilities are equal T_α=T_β=T (green solid lines), the condition for the spread of altruism becomes , for any VT>0 (see Methods for details). Thus, the line depends only on T and is identical in all three subplots. However, the altruism-inducing bacteria spreads more slowly when VT<1 (Supplementary Note 1, Rate of α's spread as a function of vertical transmission). As c increases (from a to c), the fitness effect of interaction on vertical transmission increases, diminishing the relative effect of imbalance between the horizontal transmission rates. The effect of imperfect vertical transmission (VT<1), is opposite, diminishing the effect of fitness differences on vertical transmission, thus giving more weight to imbalance between the horizontal transmission rates (compare red and blue solid lines to dashed lines). Presented are b, c parameters within the range of the prisoner's dilemma (namely, b>c). All curves have an asymptote at T_α=0, namely altruism cannot evolve without horizontal transmission. Similarly, altruism cannot evolve in such a fully mixed population when it is encoded in the host's genome (see Methods).