## On the Meaning and Estimation of Plasmid Transfer
Rates for Surface-Associated and Well-Mixed Bacterial Populations

*Xue Zhong, Jason Droesch, Randal Fox, Eva M. Top, Stephen M. Krone*
**Abstract**

While conjugative plasmid transfer is key to the ability of bacteria to
rapidly adapt to new environments, there is no agreement on a single
quantitative measure of the rate of plasmid transfer. Some studies derive
estimates of transfer rates from mass-action differential equation models
of plasmid population biology. The often-used 'endpoint method' is such
an example. Others report measures of plasmid transfer efficiency that
simply represent ratios of plasmid-bearing and plasmid-free cell densities
and do not correspond to parameters in any mathematical model. Unfortunately,
these quantities do not measure the same thing-sometimes differing by orders
of magnitude - and their use is often clouded by a lack of specificity.
Moreover, they do not distinguish between bulk transfer rates that are only
relevant in well-mixed populations and the 'intrinsic' rates between
individual cells. This leads to problems for surface-associated populations,
which are not well-mixed but spatially structured. We used simulations of a
spatially explicit mathematical model to evaluate the effectiveness of these
various plasmid transfer efficiency measures when they are applied to
surface-associated populations. The simulation results, supported by some
experimental findings, showed that these measures can be affected by initial
cell densities, donor-to-recipient ratios and initial cell cluster size, and
are therefore flawed as universal measures of plasmid transfer efficiency. The
simulations also allowed us to formulate some guiding principles on when these
estimates are appropriate for spatially structured populations and how to
interpret the results. While we focus on plasmid transfer, the general
lessons of this study should apply to any measures of horizontal spread
(e.g., infection rates in epidemiol-ogy) that are based on simple mass-action
models (e.g., SIR models in epidemiology) but applied to spatial settings.