Fig. 5

Persistence of lineage taxa in hosts. A microbial taxon is initially present in hosts \(x_1(0)>0\), but not in the pool of colonizers, \(p_1 = 0\). A The frequency within a host decreases through time. For some conditions, Eq. (8), there is a period of increase. If the taxon is transmitted to offspring before the gain is lost, this might persist in the host population (although extinction within the parent occurs sooner). C Low immigration (\(m \rightarrow 0\)) and fast occupation of available space (\(\alpha _0 \rightarrow 0\)) allow increase and prolong the time before extinction, Eq. (8). Large initial available space (\(x_i + o_i \rightarrow 0\)) and lineage taxon fractions (\(x_1 / (x_1+o_1) \rightarrow 1\)) also prolong this time. B After the increase stops (\(x^*_1\)), the average time to extinction is shorter for large immigration (\(m \rightarrow 1\)) and a smaller fraction of the taxon. (D) At the host population level, lines indicate the death probability after which most hosts lose the lineage taxon (\(\tau _{0.5}\)), Eq. (9). The early increase shown in (A) only occurs within the darkened area. The distribution of microbes inherited, Fig. 1B and Eq. (4), affects the initial load and fraction of lineage taxa in offspring. Asymmetric inheritance in low microbial loads might preserve lineage taxa as well as symmetric inheritance in high loads. We set \(N = 10^5\). Each point corresponds to \(10^4\) simulated hosts