To persist a plasmid relies on being passed on to a daughter cell, but this does not always occur. Plasmids with post-segregational killing (PSK) systems kill a daughter cell if it has not been passed on. By killing the host, it also kills competing plasmids in the same host, something competing plasmids without a similar system cannot do. Accordingly, plasmids with PSK systems can displace other plasmids. In nature, plasmids with and without PSK systems coexist and prior theory has suggested this is expected to be very rare or unstable, such that one or the other type of plasmid eventually takes over. Here, we show that if there is spatial structure and plasmids confer benefits to hosts, coexistence of plasmids occurs broadly. Often plasmids confer benefits (even ones with a PSK system) and bacteria are often spatially structured. So, our results may be generally applicable.

The data was collected by running two different models that tested PSK+ and PSK- plasmids ability to coexist in an environement. The two models are split between a single strain model and a specialization model. There are two ways each model was run one for numerical analysis and another for the parameter walks. The numerical analysis was conducted using the ode() function and ’lsoda’ method in Scientific Python (vers. 0.19.0). The ’lsoda’ method was used because both the single-strain model and specialization model are numerically ’stiff’. Parameters for ’lsoda’ were set to their default values, except for runs that characterized all outcomes of the model (both coexistence and exclusion); here, numerical tolerance parameters atol and was lowered to 10−9. The default tolerance values (which are both equal to 10−5) were used for runs that specifically sought coexistence of PSK+ and PSK- plasmids. These larger tolerances may miss some points of coexistence, but allow for faster numerical simulation, which was necessary given that a large number of parameter sets needed to be studied to find points of coexistence. In all cases, numerical solutions were checked that they successfully completed the full time interval, which in our case was 10⁹ time steps. Numerical analysis also used the numpy library (vers. 1.12.1) and the Python environment was vers. 3.6.1. Python scripts of the numerical systems are provided as further Supplementary Materials, as well as Juypter Notebooks that allow for the examination of single parameter sets.

The parameter walks consisted of starting at a point of coexistence and running the simulations again with parameters randomly perturbed from their initial value. In particular, the parameter walk was either unbiased or biased. For an unbiased walk, a parameter was perturbed uniformly to up to 10% above or 10% below its current value. For a biased walk, a parameter was uniformly perturbed 1% above and 10% below, or 10% above and 1% below its current value. If a random perturbation of a parameter resulted in a new coexistence point, that set of parameters was taken as the current set and perturbed again.

Python as well as Jyupter notebooks.