Table 1.

Summary of the Persistence Conditions and their Validity

Critical HGT rate	Validity	Regime
h*PP = d – r	s = 0	Neutral regime
h*PP ≈ d – r + s d/(d – r)	s ≪ d – r	Loss-driven regime
h*PP = f(r,s,d) = de	s ∼ d	Mixed regime
h*PP ≈ s + d s/(r + s)	s ≫ d – r	Selection-driven regime

Parasites can persist in a population if their HGT rate is larger than the critical value reported in the table, h > $h_{\text{PP}}^{*}$. Other designations: d, loss (or deletion) rate; r proliferation (duplication) rate, s fitness cost, d_e effective loss bias. See supplementary fig. S1 in the Supplementary Material online for a comparison of these approximations and the exact numerical results.