Using the Price equation to analyze multi-level selection on the reproductive policing mechanism of bacterial plasmids

The replication control system of non-conjugative bacterial plasmids constitutes a simple and elegant example of a reproductive policing mechanism that moderates competition in the intra-cellular replication pool and establishes a mutually beneficial partnership among plasmids within a bacterial host and between plasmids and their hosts. The emergence of these partnerships is a product of the conflict between the evolutionary interests of hosts, who seek to maximize their growth rates within the population, and plasmids, who seek to maximize their growth rates within hosts. We employ a multi-scale computational model describing the growth, division and death of hosts, as well as the independent replication of plasmids within hosts, in order to investigate the implications of this conflict for the evolution of the plasmid replication parameters. We apply the multi-level form of the Price equation in order to quantify and elucidate the various selective pressures that drive the evolution of plasmid replication control. Our analysis shows how the evolution of the constituent components of the plasmid replication control system are shaped by selection acting at the level of hosts and the level of plasmids. In addition, we calculate finer-grained selective pressures that are attributed to atomic plasmid-related events (such as intra-cellular replication and plasmid loss due to host death) and demonstrate their special role at the early stages of the evolution of policing. Our approach constitutes a novel application of the Price equation for discerning and discussing the synergies between the levels of selection given the availability of a mechanistic model for the generation of the systems dynamics. We show how the Price equation, particularly in its multi-level form, can provide significant insight by quantifying the relative importance of the various selective forces that shape the evolution of policing in bacterial plasmids.