Fig. 4.

Microbiome composition is only heritable when vertical transmission dominates horizontal transmission. (A) Horizontally acquired cells eventually dominate over vertically acquired cells. The densities of the total population and of vertically and horizontally acquired cells were calculated analytically (SI Appendix, Eqs. S7 and S8) and are shown for the case $T_{vert}=2T_{horiz}$. (B) Frequency of vertically transmitted cells decreases over time in a nonlinear way. The frequency of vertically inherited cells was calculated analytically (SI Appendix, Eq. S8) and is shown for 4 different ratios of vertical to horizontal transmission. Microbiome composition is heritable (i.e., dominated by vertically transmitted cells) for long periods when vertical transmission dominates (dark blue) and for short periods when horizontal transmission dominates (light blue). (C) Heritability timescale ${\tau }_{her}$ is short when vertical transmission $T_{vert}$ is weak compared with horizontal transmission $T_{horiz}$. The heritability timescale ${\tau }_{her}$ is defined as the time after birth at which the frequency of vertically acquired cells reaches 0.5 and was calculated numerically (SI Appendix, Eq. S8).