Virulent phages can expose their bacterial hosts to devastating epidemics, in principle leading to a complete elimination of their hosts. Although experiments indeed confirm large reduction of susceptible bacteria, there are no reports of complete extinctions. We here address this phenomenon from the perspective of spatial organization of bacteria and how this can influence the final survival of them. By modeling the transient dynamics of bacteria and phages when they are introduced into an environment with finite resources, we quantify how time-delayed lysis, the spatial separation of initial bacterial positions, and the self-protection of bacteria growing in spherical colonies favor bacterial survival. This suggests that spatial structures on the millimeter and sub-millimeter scale plays an important role in maintaining microbial diversity.
Author summaryFor virulent phage that invade a bacterial population, the mass-action kinetics predict extinction for a wide range of infection parameters. This is not found in experiments, where sensitive bacteria repeatedly are seen to survive the first epidemics of phage attack. To explain the transient survival of infected bacterial populations we develop a combination of local mass-action kinetics with lattice models. This model includes May 13, 2019 1/24 population dynamics, a latency time between phage infection and cell lysis, spatial separation with percolation of phages as well as colony level protection on the sub-millimeter scale. Our model is validated against recently published data on infected Escherichia Coli colonies. Introduction 1 Naturally occurring bacteria live in spatially structured habitats: in the soil [1, 2], in our 2 guts [3, 4], and in food products [5]. The spatial heterogeneity is in part generated by 3 the diversity of the microbial world [6], in part by clusters of food sources, and in part 4 caused by the fact that bacterial division leaves the offspring close to their "mother" 5 and thereby often form microcolonies [7-9]. The spatial heterogeneity may in turn 6 amplify itself through propagation of host specific phages, if these percolate devastating 7 infections through the parts of space with most homogeneous distribution of their 8 hosts [10]. 9 Traditionally, phage-bacteria ecosystems are modeled by generalized versions of the 10 classical Lotka-Volterra equations [11-20]. In its simplest form, such mass-action 11 equations predict sustained oscillations which becomes damped when one takes into 12 account resource limitations. In contrast to the oscillating lynx-hare systems from 13 macroscopic ecology [21], the microbial ecology experiments appear much more damped. 14 However, with realistic parameters for phage infections [22] and realistic bacterial 15 starting populations, the Lotka-Volterra type equations predict that an invading phage 16 typically cause a collapse of the bacterial population to less than one bacterium, i.e. 17 extinction. This is clearly not seen in microbial experiments. Rather, after an initial 18 collapse to a m...