Fig. 5

Each gray circle represents a population of transferable genes that resides within a microbial host population. The white circle represents a naïve microbial population, one that has not yet acquired the transferable gene. An ancestral population (A) with character state \(\left({y}_{i},{z}_{i}\right)\) can contribute to a descendant metapopulation by avoiding gene loss (by persistence, P) or by colonizing naïve microbial populations by HGT (by multiplication, M). A population generated by persistence inherits its indispensability and connectivity from its ancestor subject to change due to gene-host coevolution, \(\left({y}_{i}+\Delta {y}_{i} ,{z}_{i}+\Delta {z}_{i}\right)\). The character state of a population generated by multiplication is \(\left(0,{z}_{i}\right)\). In this case indispensability is set to \(y=0\) because dependencies accumulated by the ancestral host population are assumed to be absent in the naïve microbial population. The connectivity of T remains \({z}_{i}\) due to the simplifying assumption that gene-host coevolution does not occur until the transferable gene has been fixed following HGT