The primary results presented here are from numerical simulations of the model described above, supported by steady-state analysis (given in Appendix Appendix B: Steady-state analysis) where appropriate. This section first addresses the diversifying effect of phage on the bacterial population, which underpins subsequent examination of the evolvability benefits conferred on bacteria by coevolving phage, and their sensitivity to model parameters. Full sensitivity analysis of model parameters is given in Appendix Appendix C: Sensitivity analysis.
Bacterial diversity from density-dependent phage predation
To illustrate the negative frequency-dependent selection pressure imposed on bacteria by density-dependent phage predation, simulations were performed in which bacteria evolved on a smooth single-peak adaptive landscape. Figure 2 shows timeseries of resource concentration, total bacteria and phage density, and the density distribution of bacteria and phage in genotype space, together with fields showing bacteria/phage fitness landscapes over time, for an exemplar case study simulation. The simulation was initialised with a single bacterial host and perfect-match infectious phage (with genotype h
init
=v
init
=0.2) and run for a duration of T=20×106min. Simulation parameters are given in Table 1.
The striking overall feature of this scenario is that there is rapid diversification of bacteria and correlated diversification of phage, corresponding to a pattern of frequency-dependent coevolution (Figure 2C). Consistent with ‘kill-the-winner’ ecological dynamics [20, 21], specialised phage limit host density, preventing competitive exclusion and maintaining diversity, with resources partitioned between multiple strains. Phage predation selects for bacterial mutants with reduced susceptibility to infection by current dominant phage types. This creates diversifying selection on bacteria that leads to branching of the population into distinct clusters (hereafter strains) separated in genetic space by intervening regions in which mutants are susceptible to multiple phage strains and thus maladaptive. Host diversification selects for phage mutants that maintain infectivity by increasing genetic similarity to dominant bacterial strains. Phage therefore diversify to track their evolving hosts. Overall, bacterial populations act as attractors for phage in genetic space, while phage populations act as repellors for bacteria; the balance between these forces leads to the genetic dispersal of strains.
Diversification is ultimately limited by resource competition. As hosts diversify, the total host density increases substantially, with associated draw-down of resource concentrations (Figures 2A&2B). Without adaptation, the population density of a single bacterial host strain infected by perfect-match phage will tend to a lysis-limited steady state density that is significantly below the potential resource-limited carrying capacity of the system (Appendix Appendix B: Steady-state analysis). However, resource partitioning allows multiple bacterial strains to coexist and collectively draw down resource to limiting levels (Appendix Appendix B: Steady-state analysis). The value of R∗plotted in Figure 2A shows the resource concentration at which the fastest-growing (highest δ) bacterial strain would become resource-limited in the absence of phage (calculated using the method given in Appendix Appendix B: Steady-state analysis). Observed resource concentrations do not reach this theoretical minimum level, since the diverse community includes many strains with slower growth rates (and hence higher limiting concentrations) and most strains are phage-limited. However, total bacterial productivity is still ultimately limited by resource supply, when the slowest-growing (lowest δ) strain in the community (which does not reach sufficient density to support associated phage) reaches a resource-limited steady state. Strain diversity at steady-state depends on system parameters and is positively related to resource supply (Appendix Appendix B: Steady-state analysis).
Figures 2D and 2G show the fitness landscapes for bacteria and phage over time, found by calculating the growth rates of hypothetical genotypes in the current biotic and resource environment at each timepoint (see Appendix Appendix A: Supplementary Methods). Fitness landscapes for both bacteria and phage are highly dynamic, changing as a function of resource levels and the biotic environment. The overall selection pressure imposed on bacteria (visualised by gradients in the net rate of density change, , Figure 2D) is determined by contributions from growth phenotype δ(selected via resource competition, Figure 2E) and resistance phenotype ĥ (selected via lysis, Figure 2F). The phage fitness landscape (visualised by gradients in the net rate of density change, , Figure 2G) reflects the density distribution of bacteria, with positive growth only possible for phage genotypes with abundant hosts.
Within the evolutionary dynamics, three qualitatively different phases can be distinguished. Early in the simulation, bacteria can both increase growth rate and escape phage by adapting towards the fastest-growing phenotype (arbitrarily positioned at h=0.5, Figure 2H). This synergy drives rapid adaptation of bacteria, tracked by rapid adaptation of phage. When bacteria reach the optimal growth phenotype, they can only escape phage by adapting downhill in terms of growth rate (Figure 2E). This creates an evolutionary trade-off that allows diversification and coexistence of multiple strains. During this phase, repeated host divergence and phage counter-adaptation are observed, so that diversity of both phage and bacteria strains increases. Finally, as the system approaches steady state, there are no significant fitness gradients to drive adaptation of either bacteria or phage (i.e. and for all genotypes) and the genotype distributions are relatively constant over time (Figures 2D&2G).
The rate of bacterial adaptation (rate of change of genotype frequencies) is proportional to the deviation from a perfect linear correlation between growth and lysis across the bacterial community; the form of Equation 2 means that genotype density only changes when there is an imbalance between growth and lysis rates. This can be seen in Figure 2I, which shows the correlation between lysis and growth rates for all bacterial strains forming >1% of total density, observed during three time intervals at the beginning, middle, and end of the simulation. Imbalances can occur when mutation adds new bacteria/phage strains (e.g. if a novel bacterial strain arises with reduced susceptibility to current phage) but are reduced over time by ecological dynamics. Correlations increase over time, until at steady state, variation in growth rates is tightly correlated with variation in lysis rates, such that no net variation in fitness (net density change) is observed. In general, strong positive correlations are universally observed, showing that faster-growing host phenotypes experience greater levels of lysis; this highlights an ecological trade-off that allows multiple bacterial strains to coexist. Coexisting strains have varying growth rates, but any selective benefit from increased growth rate is balanced by a cost from increased lysis, resulting in kill-the-winner dynamics [20, 21].
Two evolvability benefits to hosts of specialised phage
Having established the diversifying effect of specialist phage on host bacteria, the impact of diversification on bacterial evolution was explored. Figure 3 shows evolutionary dynamics for paired case study simulations of bacterial evolution with and without coevolving phage. Simulations are initialised with h
init
=v
init
=0.2 in each case; the only parameter difference is the initial density of phage (set to V
init
=0 for the no-phage case). Two forms of adaptive landscape were used to demonstrate two distinct evolvability benefits to hosts of diversification driven by coevolving phage. In the absence of phage, bacteria are selected by resource competition to maximise growth rate and thus increase fitness by local hillclimbing. Thus populations tend to become tightly converged on the nearest peak in the adaptive landscape. This leaves them unable to cross fitness valleys and on landscapes with multiple peaks they can become trapped on suboptimal local maxima. However, when forced to diversify by coevolving phage, it was found that: (i) standing diversity facilitates adaptation in dynamic environments, and (ii) local trade-offs between resistance and growth allow populations to adapt across fitness valleys.
Standing diversity facilitates adaptation in dynamic environments
The first scenario that was explored was bacteria evolving in a dynamic environment, using an adaptive landscape in which a second peak that sequentially increases in height was introduced alongside a static initial peak. Figure 3A visualises this dynamic landscape by colour-coding the landscape profile used at different timepoints (see Appendix Appendix A: Supplementary Methods). On the dynamic landscape, bacteria evolving alone and coevolving with phage quickly adapt to the initial peak. When evolving alone, the bacterial population is tightly converged on the initial peak, with a small amount of diversity provided by mutation-selection balance. When coevolving with phage, bacteria diversify to form a set of distinct strains distributed symmetrically around the peak.
The standing diversity produced and maintained by specialist phage can facilitate more rapid opportunistic adaptation to novel environments. As the second peak is introduced, a fitness valley is formed that separates the initial static peak from the new dynamic peak. As the relative height of the new peak is sequentially increased over time, eventually it reaches a stage where one of slowest-growing strains of the bacterial community is within mutation range of the lower slopes of the new peak. This strain then adapts rapidly towards the new peak, driven by synergistic selection pressures for increasing growth rate and reducing phage predation. A new diverse community then forms around the second peak, ultimately displacing the community around the initial peak due to resource competition. In contrast, the bacterial population evolving alone is unable to access the second peak until the fitness valley is completely removed, remaining trapped at the initial peak even when it becomes sub-optimal.
It is important to note that this is a benefit of diversity per se and is not unique to diversity created by phage; alternative mechanisms that preserve diversity might achieve a similar benefit. However, one particular advantage of phage-produced diversity is that it is maintained at steady-state by kill-the-winner ecological dynamics, whereas some other diversity-producing mechanisms (e.g., environmental change) might offer only transient diversity increases.
Local trade-offs between resistance and growth allow populations to adapt across fitness valleys
The next scenario was bacterial evolution on a rugged adaptive landscape, with multiple local peaks separated by fitness valleys on a slope of globally increasing growth rate (Figure 3B). As in the single-peak landscape example shown in Figure 2, the fitness benefit of escaping phage can counterbalance the fitness cost of moving downhill in terms of growth rate, allowing valleys to be traversed. On the multiple-peak landscape, bacteria diversify to form a fitness-neutral distribution in which most strains experience negligible selective gradients and do not adapt significantly once they arise. The only significant positive gradients are observed at the leading (uphill) edges of the strain distribution and this is where most adaptation (in the sense of a coherent subpopulation shifting its genetic composition) is observed, with the initial strain adapting steadily towards higher growth rates while new strains sequentially branch off. As the bacteria community climbs the landscape, slow-growing strains are lost at the trailing edge due to resource competition. As growth rates increase, more strains can enter the population (since higher growth rates enable growth at progressively lower resource concentrations) and bacterial strain diversity rises.
The proximate mechanism by which fitness valleys are crossed in this case study is a trade-off between local resistance and growth rate that allows host strains to adapt downhill in terms of growth rate. Effectively, the host population is pursued across the valley by coevolving phage; at each stage, the transient benefit of escaping phage outweighs the cost of reduced growth rate. The population always follows positive local gradients in the net rate of density change. While crossing a valley, this implies decreasing growth rates, compensated by the decreased lysis rates that result from reduced susceptibility to dominant phage. This mechanism is a dynamic (non-steady-state) effect of ecological trade-offs, and is distinct from the intrinsic benefit of steady-state diversity that is identified above.
Controls on host diversification and evolvability
The ability to respond to a changed environment depends on the diversity of bacterial genotypes at steady state, which is determined by the balance between resource competition and phage predation; bacteria minimise dispersal away from the optimal growth phenotype, within the constraint of reducing phage infection (Appendix Appendix B: Steady-state analysis). Figure 4 shows the sensitivity of community-wide bacterial genotype variation with respect to resource supply (R0), the slope of the adaptive landscape (manipulated using δ
min
), and the host specificity (s) of phage. Variation was measured from coevolutionary simulations on smooth single-peak landscape (e.g. Figure 2H) using ensembles of simulation runs to account for stochastic effects. Simulations were initialised with a single bacterial genotype and matched phage genotype at the optimal growth phenotype (h
init
=v
init
=0.5) and run for T=5×106min. Variation was measured as the total range of genotypes (h
max
−h
min
) in the final bacterial community for which the corresponding strain density represented >1% of the total community. The range of host genotypes at steady state is positively related to resource supply R0; more strains can be supported with greater available resource. Since the separation between strains is held roughly constant, adding more strains implies greater overall variation. Genotype range is negatively related to the gradient of the landscape. Thus for a fixed maximum growth rate δ
max
it is positively related to the minimum growth rate δ
min
, which controls the cost of diversifying away from the optimal growth phenotype. Host genotype range is negatively related to the specificity s of the phage, i.e. negatively related to the rate of decline in infection rate with genetic dissimilarity.
To quantify the ability of phage to drive bacteria across fitness valleys using local trade-offs, ensembles of simulations were performed on rugged-slope landscapes formed by adding a uniform-random noise signal to a smooth linear slope (see examples in Figure 5), measuring sensitivity of bacterial adaptation to specificity of phage (s) and the ruggedness of the landscape (manipulated by varying the size span of the moving-average smoothing window used to create the landscape; see Appendix Appendix A: Supplementary Methods). For each value of span, an ensemble of landscapes was generated. On each landscape, a simulation was then performed with bacteria evolving alone, followed by multiple coevolutionary simulations varying the specificity parameter s. All simulations were initialised with the same seed strains (h
init
=v
init
=0.2) and run for T=20×106min. Adaptation was measured by recording the maximum growth rate (highest δ) in the final bacterial community at the end of each simulation.
Figure 5 shows examples of the adaptive landscapes used and the frequency distribution of final maximum growth rates across each associated ensemble. For all levels of ruggedness (all values of span), bacteria evolving alone were able to achieve only a modest increase in maximum growth rate above the initial condition, typically becoming trapped at suboptimal local maxima. For almost all parameter combinations, the presence of coevolving phage offered a substantial improvement in adaptive performance, showing a significant shift towards a greater frequency of higher growth rates. For the smoother landscapes (higher span) the presence of phage often allowed the bacteria to reach the maximum possible growth rate. For the more rugged landscapes (lower span), the presence of phage increased the frequency of high growth rates, though instances still occurred when the population became trapped at suboptimal local peaks and performance was not significantly better than bacteria evolving alone. The most generalist phage (e.g. s={100,200}) offered little adaptive benefit on the most rugged landscapes, explained by the shallow gradient in lysis rates with increasing genetic distance relative to the steep local gradients in growth rate.
Overall, standing diversity (hence adaptive capacity in dynamic environments) is increased by generalist phage (that increase strain separation) and shallow growth rate gradients (that reduce the costs of diversifying away from the fastest-growing genotype). However, specialist phage offer the greatest evolvability benefit on rugged landscapes, since they can drive host populations across deeper fitness valleys.