A conjugative plasmid spreads through a well-mixed bacterial population when a plasmid-bearing cell (a donor, orange) forms a mating-pair contact with a plasmid-free recipient (blue). If transfer succeeds, the recipient becomes a transconjugant (purple) — genetically a recipient, but now itself infectious. This is the classic Levin–Stewart–Rice mass-action model of conjugative plasmid transmission:
dD/dt = ψ_D·D·(1 − N/K)
dR/dt = ψ_R·R·(1 − N/K) − γ·R·(D+T)
dT/dt = ψ_T·T·(1 − N/K) + γ·R·(D+T) − τ·T
ψ_X = ψ_max for R (no plasmid)
ψ_X = ψ_max·(1 − s) for D, T (plasmid carriage cost)
N = D + R + T
This simulator runs the individual-based version of that same model: every cell drifts through the culture volume, and a recipient within contact range of a plasmid carrier converts with probability 1 − e−γ·contacts·dt each tick — the discrete analogue of the mass-action term γ·R·(D+T). Cells divide logistically toward a carrying capacity K, with plasmid carriers paying the fitness cost s as slower growth, and a transconjugant can spontaneously lose the plasmid at rate τ (segregational instability), reverting to a recipient.
- Conjugation rate γ — probability weight per nearby donor/transconjugant contact per hour; higher γ lets the plasmid invade faster even against a fitness cost.
- Fitness cost s — fractional growth-rate penalty plasmid carriers pay; above a threshold set by γ and τ, the plasmid cannot persist and prevalence collapses toward zero.
- Segregational loss τ — rate at which a transconjugant's daughter cell fails to inherit the plasmid at division, converting back to a recipient.
- Initial donor fraction — donor share of the starting population (applies on Reset).
Real-world relevance: this exact dynamic drives the spread of antibiotic-resistance plasmids through hospital and gut microbiota, and is the standard framework (Levin, Stewart & Rice, 1979; Simonsen, 1991) used to estimate conjugation rate constants from culture data.