DOI: 10.5061/dryad.sf7m0cgb1
title: Spatial structure and benefits to hosts allow plasmids with and without post-segregational killing (PSK) systems to coexist

description: 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.
description: 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 10<sup>9</sup> 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.
description: Python as well as Jyupter notebooks.