Spatial structure and benefits to hosts allow plasmids with and without post-segregational killing (PSK) systems to coexist

The code for the numerical analysis and parametric walks for both the single strain and specialization model for the paper "Spatial structure and benefits to hosts allow plasmids with and without post-segregational killing (PSK) systems to coexist "

Programs Need: Python, Jyupter notebooks and WinZip (to unzip the package).

The Data files: The Data files are in .OUT meaning they can be overwritten if the code is run again, so if one wishes to examine the outputs, copy them into another folder or create a second copy of this folder to investigae

Numerical Analysis

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.

Parameteric Walks 

To assess whether points of coexistence of PSK- and PSK+ are mutationally connected, we took one point of coexistence for each of the single-strain and specialization models and subjected them to a parameter walk. A parameter walk consist 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 parameter resulted in a new coexistence point, that set of parameters was taken as the current set and perturbed again.