Evolution of acuteness in pathogen metapopulations: conflicts between “classical” and invasion-persistence trade-offs

Abstract

Classical life-history theory predicts that acute, immunizing pathogens should maximize between-host transmission. When such pathogens induce violent epidemic outbreaks, however, a pathogen’s short-term advantage at invasion may come at the expense of its ability to persist in the population over the long term. Here, we seek to understand how the classical and invasion-persistence trade-offs interact to shape pathogen life-history evolution as a function of the size and structure of the host population. We develop an individual-based infection model at three distinct levels of organization: within an individual host, among hosts within a local population, and among local populations within a metapopulation. We find a continuum of evolutionarily stable pathogen strategies. At one end of the spectrum—in large well-mixed populations—pathogens evolve to greater acuteness to maximize between-host transmission: the classical trade-off theory applies in this regime. At the other end of the spectrum—when the host population is broken into many small patches—selection favors less acute pathogens, which persist longer within a patch and thereby achieve enhanced between-patch transmission: the invasion-persistence tradeoff dominates in this regime. Between these extremes, we explore the effects of the size and structure of the host population in determining pathogen strategy. In general, pathogen strategies respond to evolutionary pressures arising at both scales.

1 Introduction

Infectious diseases afford perhaps the best illustrations of how natural selection can exert conflicting pressures at different scales of biological organization. The pathogen strategy that maximizes between-host transmission (as measured by the basic reproductive ratio, R₀) is classically considered to be the most fit. When a trade-off between rate and duration of transmission exists at the level of the individual infected host, this optimum is associated with intermediate pathogen loads and transmission rates (May and Anderson, 1983; Ewald, 1993). In this case, overly “prudent” pathogens will tend to have low within-host abundance and consequently transmit inefficiently whilst overly aggressive pathogens, by multiplying rapidly within the host, will tend either to kill the host or to elicit early clearance by the host immune system, in either case abbreviating the infectious period.

This ‘classical’ trade-off theory nicely illustrates how the presence of a transmission bottleneck introduces complexity into pathogen life-history evolution (Coombs et al, 2007; Gilchrist and Coombs, 2006; Antia et al, 1994; Alizon and van Baalen, 2005; Levin and Pimentel, 1981). In comparison, free-living organisms represent a relatively simple case, in which, all else being equal, the strategy that maximizes the instantaneous rate of increase (r) is the most fit. In pathogens, however, the strategy that maximizes within-host population growth—and thus has the competitive advantage within the host—may yet be at a disadvantage overall relative to the strategy that maximizes host-to-host transmission. There is likewise the potential for conflicting selection pressures at higher scales of organization. The observation that acute immunizing infections such as measles were apparently unable to establish in humans until population aggregations of sufficient size and density arose (along with agriculture in the neolithic period; Black et al, 1974; Black, 1975; Mira et al, 2006), has recently led to the notion of an ‘invasion-persistence’ trade-off. Grenfell (2001) hypothesized that while acute immunizing infections have a competitive advantage early in an outbreak due to their ability to quickly invade a susceptible population, they may be disadvantaged late in the outbreak due to their greater tendency to go locally extinct in their deep post-epidemic troughs. Exploring this idea, King et al (2009) developed a model explicitly linking within-and between-host dynamics to show that, depending on the shape of transmission’s dose-response curve, the invasion-persistence trade-off has indeed the potential to influence life-history evolution through extinction-mediated group selection. Here we study this phenomenon in more detail, asking specifically which metapopulation conditions give rise to selection pressures discordant from those of the classical trade-off theory. Using a model that explicitly incorporates within-host dynamics, between-host transmission, and colonization and extinction at the metapopulation scale, we demonstrate that—depending on the configuration of the host metapopulation—pathogen life histories will evolve either to maximize between-host R₀ (if local populations are large) as predicted by the classical trade-off theory or adopt a more “prudent” strategy to increase the between-patch reproductive ratio, R_* (if local populations are small) according to the invasion-persistence trade-off. Thus, depending on circumstances, group selection in a metapopulation may override selection acting at the individual-host scale to shape the life-history traits of acute immunizing infections in a manner analogous to that in which ‘group’ selection at the individual-host scale can override within-host selection for greater virulence.

A number of theoretical studies have examined how the spatial structure of host populations affects pathogen evolution. When transmission is limited to local neighborhoods, Boots and Sasaki (1999) showed that ‘self shading’ behavior—wherein virulent pathogens quickly deplete their local neighborhoods of susceptible hosts—diminishes the chance of virulent strains spreading. Changes in the ratio of local to global contact rates, however, can allow virulence to spread or lead to evolutionary bi-stability of avirulent and virulent strains (Boots et al, 2004). In a similarly lattice-structured theoretical landscape, but allowing for waning of immunity, van Ballegooijen and Boerlijst (2004) studied evolution of self-organized spatial dynamics ranging from localized disease outbreaks to epidemics spreading in waves. Their model predicted evolution towards pathogen traits that maximized infection frequency (the number of times a host becomes infected), and not the maximization of R₀. Assuming a competition/persistence trade-off, Keeling (2000) showed analytically that competition between a locally fitter but more extinction-prone strain versus a less fit, less extinction-prone strain, can lead either to domination by one strain or the other or to coexistence, depending on the strength of local and global transmission. King et al (2009) showed that stylized yet biologically reasonable within-host mechanisms plausibly lead to selection for more acute pathogen life histories and, under some circumstances, to evolution that drives pathogens to the edge of their own extinction. At the edge of extinction, we speculated that further R₀-enhancing selection for acuteness could be countered by group selection because of frequent extinction of overly acute lineages. Beyond this speculation, however, King et al (2009) did not explore how local extinction and selection for rapid invasion would combine to shape life-history strategies in a metapopulation context. In such a context, the number and sizes of local populations and rates of dispersal among them should together influence the dominance of ‘invasion-persistence’ versus ‘classical’ trade-offs in pathogen evolution. Herein we use a three-tiered model to explore how these aspects of spatial structure modulate the interaction between these potentially conflicting trade-offs.

2 A three-tiered model

Our hierarchical approach has three submodels (Fig. 1). First, we consider how a pathogen trait shapes the time-varying within-host infection intensity and infection duration. We then translate infection intensity to transmission via a dose-response curve relating shedding rate to transmission rate; this determines the pattern of outbreaks within each local host population. Finally, we integrate from local to regional dynamics using an epidemiological metapopulation model. The deterministic models for within-host dynamics are detailed in the Section 2.1. In our earlier study (King et al, 2009), we used the McKendrick-von Foerster framework as a bridge between within-host dynamics to epidemiological dynamics. Here, to study evolution within the metapopulation, we implement instead a stochastic, individual-based model and simulate the progress of evolution explicitly. In this way, we allow both competition for susceptibles and extinction to shape pathogen evolution. The individual-based model is fully described in Section 2.2.

Fig. 1. Schematic representation of the three-tiered model.

We consider the selective forces acting on a specific pathogen trait, namely the within-host proliferation rate, r. Under the dynamics prescribed by the within-host model (Eq. 1), this trait determines the duration of an infection, ac, as well as pathogen load, P, over the infection’s course. The transmission model translates within-host pathogen load to between-host transmission (Eq. 2). The epidemiological model then describes the progress of epidemics across the metapopulation. Mutation, together with differential survival and reproduction among pathogens (Section 2.2), leads to natural selection on r.

2.1 Models of within-host and transmission dynamics

We use a phenomenological description of the pathogen-immunity interactions to model within-host dynamics. The model is that studied by Pilyugin and Antia (2000), simplified to incorporate a linear functional response of the immune effectors (see also King et al 2009). The pathogen load, P, and host immunity, X, are modeled as functions of the age of infection, a. Pathogen and host immunity interact in a predator-prey-like fashion according to:

$$\frac{dP}{da}=rP-kXP,\frac{dX}{da}=\alpha -dX+\gamma kXP,$$ (1)

where r is the pathogen intrinsic growth rate, k is the killing γ rate, measures proliferation of immune cells as a function of their encounter rate with pathogen, and α and d are background influx and death rates of immune cells, respectively. We assume that this system of differential equations is initiated with unit pathogen load in the absence of pre-existing specific immunity, i.e., P(0) = 1, X(0) = 0. There are two dynamical regimes in this system with stable equilibria at (i) P = 0, X = α/d when d/k < α/r, and (ii) $P=\frac{1}{\gamma }(d/k-\alpha /r)$, X = r/k when d/k > α/r (Pilyugin and Antia, 2000). En route to the second equilibrium, however, the parasite load, P, exhibits damped oscillations with transient excursions to biologically unrealistically low values. To remedy this, we assume a threshold parasite load, P_θ: when P first falls below the threshold, we interpret it as clearance. We set this clearance threshold to equal the inoculum size, i.e., P_θ = P(0) = 1. It follows that there is a strain-specific but always finite period of infection, a_c, defined by the conditions P(a_c) = 1, P(a) 1 for 0 < a < a_c. Since the within-host dynamics are deterministic, each infection of a given pathogen strain follows the same dynamics. The strain-specific pathogen growth rate, r, plays a key role in shaping these dynamics: high values of r lead to acute but short-lived infections whilst low r values result in mild but long-lasting infections (see Fig. 2 and King et al 2009).

Fig. 2. Transmission rate, duration of infection, and R₀ in the combined within-host and transmission models.

(A) The within-host proliferation parameter, r, controls both average transmission rate and infection infectious period. Infections become more acute as r increases. At the same time peak pathogen load increases. (B) Within-host dynamics filtered by the transmission dose-response curve leads to maximization of the basic reproduction ratio, R₀, for intermediate values of r.

The within-host pathogen model (Eq. 1) governs the infection intensity, P, within each infected host as a function of its infection age, a. We assume that the rate, β, at which an infected host transmits infection (the dose response curve) is a saturating function of P according to

$$\beta (r,a)=q_s(1-\text{exp}(-\frac{P(r,a)}{P*}\left)\right).$$ (2)

The parameters q_s and P* are given in Table 1. Fig. 2 shows how average transmission rate, infection duration, and R₀ depend on r under this model. We discuss the alternative of a linear dose response curve in the Discussion.

Table 1.

Synopsis of symbols.

Symbol	Parameter	Value
Within-host model:
r	parasite growth rate (‘strategy’)	3–60
r0	the R0 maximizing strategy
r*	the R* maximizing strategy
k	kill rate of the immune response	3.5
α	baseline production rate of immune response	1.0
d	death rate of immune response	0.5
γ	immune response recruitment rate	0.1
β(a)	age-specific transmission rate
Transmission model:
qs	transmissibility factor	100.0
P*	saturation constant	−0.01
Population model:
NP	number of patches	1–200
n	expected number of hosts in each patch	20–2000
m	migration rate	0.1
μ	host birth rate	0.1
χ	mutation rate (probability per transmission event)	0.01
σ	mutation size (standard deviation)	0.35
R0	the basic reproductive ratio
R*	the patch-level reproductive ratio

2.2 Model for population structure and evolutionary dynamics

Here, we use an individual-based approach that explicitly tracks each strain-specific infection. For simulations, we utilize a τ-leap algorithm (Higham, 2008), with a small and fixed timestep, Δt, in lieu of more expensive event-driven simulations.

We subdivide the host population into N_P patches. The population size, n_j, of patch j varies stochastically according to a logistic birth-death process. The per capita host birth rate is constant and equal to μ, whilst the per capita host mortality rate is density dependent, equal to μ n_j/n. Here, the parameter n is the expected patch size. Thus, in the interval Δt, each host in patch j faces a probability of death, 1 − e^{−μ (n_j/n) Δt}. The number of births in the same interval is negative-binomially distributed with size parameter nj and probability e^−μΔt. Newborns are all susceptible.

We assume that host migration is independent of infection status and that the population is globally connected so that migration is equally likely between all patches (at a constant rate m). Thus, the number of hosts that emigrate from patch j in a small time-interval Δt is binomially distributed with parameters n_j, p = 1 − e^−mΔt.

Transmission is assumed to occur exclusively within patches. Pathogen strains are characterized by their within-host growth rate r and infected hosts are differentiated by the pathogen strains they carry. We disallow coinfections. These assumptions ensure that the pathogen can evolve only in response to selection pressures at the between-host/within-patch and between-patch scales; unlike several recent studies (Coombs et al, 2007; Gilchrist and Coombs, 2006), there is no within-host competition in our model. We further assume perfect cross-immunity between strains and lifelong immunity. Transmission is assumed to scale in a frequency-dependent fashion (e.g., Bjørnstad et al, 2002; Ferrari et al, 2011). This makes transmission rate, β, comparable across differing metapopulation configurations. Within a patch, a host infected with strain r exactly a time units ago carries a pathogen load P(r, a) (Eqn. 1) and contributes β (r, a) to the total force of infection within that patch (Eqn. 2). Although the number of allowable strains is unbounded, the number of strains circulating at any time is finite. The strain specific force of infection for strain r in patch j in a metapopulation with N_P patches is:

$${\lambda }_{r,j}=\frac{1}{n_j}\sum _{\text{hosts}h\text{in patch}j\text{infected with strain}r}\beta (r,a_h),$$ (3)

where a_h is the age-of-infection in host h. Thus, if s_j is the number of susceptible individuals in patch j and the total force of infection in patch j is λ_j = Σ_r λ_r,j, then the vector of new strain-specific infections, Δi_j = (Δi_r,j), occurring in patch j over the small time interval Δt, is distributed according to

$$\Delta i_j~\text{multinomial}(s_j,p_j),$$ (4)

where p_j is a vector of probabilities, p_j = (p_r,j) and p_r,j = (1 − e^−λ_jΔt) λ_r,j/λ_j is the probability that a patch-j susceptible becomes infected with strain r. Thus, competition among strains for susceptibles within each patch is governed by both strain frequency and strain-specific transmission rate, since λ_r,j depends on both of these quantities.

In the model, the diversity of strains is reduced by competition and increased by mutation. During each transmission event, we assume that an offspring from a strain with r = r₁ will mutate to r = r₂ with probability χ. The value r₂ of the mutant is drawn from a normal distribution with mean r₁ and standard deviation σ.

One thousand replicate simulations were performed for each set of parameters. Each simulation run was initialized by infecting 1% of the hosts randomly across the metapopulation, each with a single strain with growth rate drawn from a uniform distribution on the interval (3, 10). Simulations were conducted in two phases. In the first phase, the simulation proceeded until transients died out. In the second phase, 1000 replicate simulations were performed with mutation, each beginning from the distribution of the extant strains at the end of the first phase. These simulations are run for 2000 time units, a sufficient amount of time to ensure that the strain distribution has stabilized. In all simulations, we use a time-step Δt = 0.01 time units.

2.3 Fitness measure, R₀

If we consider only a single patch (N_P = 1) and disallow mutation (χ = 0), the model reduces to a stochastic version of the model described in Section S1. In this setting, a pathogen with growth rate r, has a basic reproductive ratio,

$$R_0={\int }_0^{a_c}\beta (r,a)\text{exp}(-\mu a)da,$$ (5)

where β(r, a) is as defined in Eqn. 2. Numerical integration of Eqns. 1, 2, and 5 yields the dependence of the R₀ on r. Fig. 2B shows this dependence. R₀ reaches a maximum at an intermediate r = r₀; diminishing returns due to the saturating dose response curve reduce R₀ beyond this point (see King et al, 2009, for a detailed discussion).

2.4 Model for patch dynamics

To obtain some insight retrospectively into the scenario with many small patches, we can reason by analogy that the host patches are themselves similar to infected hosts and the migration of infected hosts comparable to the host-host transmission process. This leads to the following set of equations, which can be viewed as an approximation to the patch-to-patch transmission dynamics:

$$\frac{dSp}{dt}=f(\mu )R_P-\mathrm{\iota ̅}mn{S}_P\frac{I_P}{N_P}\frac{d{I}_P}{dt}=\mathrm{\iota ̅}mn{S}_P\frac{I_P}{N_P}-\frac{1}{\mathrm{\delta ̅}}{I}_P\frac{d{R}_P}{dt}=\frac{1}{\mathrm{\delta ̅}}{I}_P-f(\mu )R_P$$ (6)

where, S_P, I_P, R_P and N_P are number of susceptible, infected, recovered and total patches respectively; μ is the host birth rate; n is the local population size; m is the between patch migration rate; ι̅ is the average proportion of infected hosts in an infected patch; and δ̅ is the average duration of an epidemic. Susceptible patches become infected when infected hosts move from an infected patch to a susceptible patch. The rate at which this happens depends on the between-patch migration rate, m, the average number of infected hosts in an infected patch, given by the product of ι̅ and n, and the probability such patches exchange hosts, given by the product of S_P and I_P/N_P. An epidemic in a patch will last an average of δ̅ time units, at which point the patch becomes “recovered”, i.e., temporarily refractory to outbreaks. The rate f(μ) that recovered patches turn susceptible, is a function of the host turnover rate, μ. Following Ball et al (1997) and Ball and Neal (2002) we define the patch-level reproductive ratio, R_*, as the average number of new infected patches resulting from a single infected. For our patch-level model

$$R_{*}=\mathrm{\iota ̅}\mathrm{\delta ̅}mn.$$ (7)

Analytic expressions exist neither for ι̅ nor δ̅ but consistent deterministic and stochastic approximations can be computed for each, as shown in Section S2. Fig. 3 shows R_* as a function of r; importantly, the strategy that maximizes R₀ (r = r₀) is distinct from that which maximizes R_* (r = r_*).

Fig. 3.

R₀ and R_* have different optima. R0 (red curve) is maximized at r = r₀, whilst R_* (blue curve) is maximized for r = r_*. Here, R is calculated with patch size, n = 30, and migration rate, m = 0.1. The left-hand axis relates to the blue line; the right-hand, to the red.

3 Results

3.1 In a single patch, pathogens evolve to maximize R₀

When N_P = 1, hosts mix homogeneously within the population. Diversity of pathogen strains is maintained through mutation events and the strains that circulate compete against one another for susceptible hosts. In this case, we observe directional selection and slow convergence of the strain distribution to the evolutionarily stable strategy, r = r₀, the strategy maximizing R₀. Heightened in-host replication rates lead to shortened infectious periods but less-than-proportionally higher transmission rates due to the saturating dose-response curve. Note that the trade-off here is not, as in the classical theory (e.g., Levin and Pimentel, 1981), due to disease-induced mortality but rather because more rapid in-host growth leads to faster immune clearance. Fig. 4A shows the transient and steady state behavior of the model as the strain distribution settles around r = 16. Fig. 4B shows that this strategy coincides with the maximum R₀.

Fig. 4. An evolutionary trajectory.

Simulation results for a single patch model with 2000 hosts. The grayscale indicates the distribution of r(t) within the pathogen population; the dashed line plots the mean value of r(t). Pathogens evolve to a evolutionarily stable r = r₀, this is equal to the r that maximizes the net reproductive number R₀. Sample trajectories for multi-patch configurations are shown in the appendix.

3.2 In a metapopulation, conflicting selection pressures arise

When the host population is subdivided into smaller patches (N_P patches, each of mean size n), the R₀-maximizing r = r₀ is no longer optimal. As patch size decreases, acute lineages become increasingly prone to local extinction and as a result, the R₀-maximizing strains are selected against at the metapopulation level. Instead, more persistent strategies that increase between-patch spread are favored. Fig. 5 shows how the evolutionarily stable strategy (ESS) varies over a range of metapopulation configurations. When the regional population size is too small, the pathogen goes globally extinct (crosses). Above this global extinction threshold, the ESS depends on the both N_P and n and takes values between r = r₀ and r = r_*. Generally, when patches are large enough to support R₀-maximizing strains, the ESS approaches r = r₀ and when patches are small but numerous, the ESS approaches r = r_*. Transect B in Fig. 5 illustrates the effect of varying the metapopulation configuration while keeping the expected global host population size, nN_P, fixed. Transect C holds expected patch size fixed while varying the number of patches: the optimal strategy does not change, though the probability of global extinction declines as N_P increases. Transect D shows the effect of varying n while holding N_P fixed: optimal acuteness increases with the size of local patches. To summarize, both the number and size of patches determine the balance of the selection pressures arising at the two scales.

Fig. 5. Evolutionarily Stable Strategy (ESS) as a function of host population structure.

Panel A shows ESS r (mean r in the stable strain distribution, indicated by color) and survival fraction (chance of avoiding extinction by time 10000, indicated by symbol size), at various metapopulation configurations. Metapopulations are characterized by size of patch, n (vertical axis) and number of patches, N_P (horizontal axis). Black crosses indicate extinction in all of 1000 replicate runs by time 10000. The bottom panels show steady-state strain distributions along three different transects across metapopulation structure: (B) size and the number of patches vary, total regional population size remains constant at 2000; (C) number of patches varies, size of each patch remains constant at 100; (D) size of patches varies, number of patches remains constant. Metapopulations with many large patches were not explored due to computational infeasibility.

A sensitivity analysis of our results with respect to host demography (μ) and mobility (m) reveals, unsurprisingly, that increasing either parameter drives the ESS towards the within-patch optimum r = r₀. Increasing μ decreases local extinction rates, whilst making m larger tightens patch-to-patch coupling, effectively making the metapopulation more homogeneous (Fig. S2). We explored the effects of removing density-dependent host population regulation, thus allowing host populations to walk randomly. Under the resulting larger variation in local population sizes, more acute strains are favored in some regions of parameter space (cf. Fig. S4).

4 Discussion

In this study we have taken a “bottom-up” approach to understanding the evolution of acuteness in pathogens as a function of the size and structure of the populations of their hosts. Our model connects three distinct levels of organization: within an individual host, between hosts within a local population, and between local populations. We find that the structure of the host population is a critical determinant of the pathogen’s evolution. Specifically, in larger and more well-mixed host populations, a pathogen’s ESS shifts toward the strategy that maximizes between-host R₀; the classical trade-off theory applies in this regime. By contrast, in smaller, more patchy host populations, emergent metapopulation dynamics favor more persistent strategies; the invasion-persistence trade-off dominates in this regime. Between these extremes, the ESS reflects the balance of the conflicting pressures arising at the two scales.

Several authors have pointed out the shortcomings of R₀ as a measure of pathogen fitness in structured host populations. Ball et al (1997) and Ball and Neal (2002) derived a threshold quantity for pathogen invasion in the context of several meta-population models. We have retained their notation, R_*, for the patch-level reproductive ratio. Cross et al (2005, 2007) found that, when host populations are patchy, R_* gives a more accurate prediction of the invasion threshold than does R₀. Here, we have gone further to show that the ESS lies in general between the within-patch and between-patch optima and that patch size and number determine where on this continuum the evolutionarily stable acuteness falls.

The within-host model at the bottom of our three-level model hierarchy is only a caricature of infection dynamics, useful here inasmuch as it links a pathogen trait to the components of the pathogen’s fitness and makes plain the trade-off between transmission rate and persistence. We chose this model because it and closely related models have been well studied (e.g., Gilchrist and Sasaki, 2002; Ganusov and Antia, 2003; Alizon and van Baalen, 2005) and because it allows for direct connection with our earlier work (King et al, 2009). While our results are derived using a particular model, we expect that qualitatively similar conclusions would arise from other within host models as long as (i) between-host transmission rate increases with pathogen load and (ii) more aggressive pathogens elicit faster clearance. In particular, under such conditions, selection at the within-patch level will, to a point, favor acute strains whilst at the metapopulation level the dynamics of local extinction and recolonization will exert a balancing pressure.

As in our earlier work (King et al, 2009), the shape of the dose-response curve (relating within-host intensity of infection to between-host transmission) is an important determinant of the pathogen’s evolutionary trajectory. In this paper, we have focused on evolution under the assumption of a saturating curve because this affords the clearest illustration of the evolutionary tension between two well-defined maxima: that maximizing within-patch transmission vs. that maximizing between-patch spread. When the dose-response curve is non-saturating, in contrast, R₀ increases monotonically with r, i.e., r₀ is effectively infinite. Selection at the within-patch level is thus for ever-increasing acuteness, continually pushing the pathogen toward more extinction-prone strategies. As illustrated in Fig. 6, under the assumption of a linear dose-response, regional persistence is much more frail and global extinctions more frequent. The saturating dose-response diminishes the advantage of extreme acuteness and thus yields greater regional persistence (cf. Fig. 6C–D vs. Fig. 5A). Rand et al (1995) discussed a similar phenomenon.

Fig. 6. Evolution to the edge of extinction.

Top panels: Simulation results for a single-patch model (initialized with 2000 hosts) with a linear transmission dose-response curve, showing pathogen evolution through time. We construct the pathogen distribution at a given time, r(t), by observing the average r of the pathogen present at that time, t, in each of the 1000 simulations. In (A), shades of grey shows the pathogen densities, and the dashed line plots the average of the distribution r(t). The evolutionary trajectory shows pathogen evolution towards higher acuteness. More acute strains become more prone to extinction; extinction events are indicated with red crosses. Probability of extinction (proportion of simulations that result in extinction) increases as r grows, as shown in (B). (C, D) Simulation results for a multi-patch model (with 20 patches each with 100 hosts). The evolutionary trajectory to the edge of extinction, though for this configuration the edge is associated with lower acuteness.

Previous studies of pathogen evolution have shown that spatial structure may lead to evolutionary branching or bistability in pathogen traits (e.g., Boots et al, 2004). While this was not the focus of our study, we saw no such effects in the extensive numerical explorations we performed. This may be because we assumed global mixing, thus preventing localized ‘self shading’ behavior (Boots and Sasaki, 1999; Boots et al, 2004), disallowed super-infection (e.g., Boldin and Diekmann, 2008), or excluded pathogen-driven mortality (e.g., Morozov and Best, 2012). Interestingly, when we removed density-dependent host population regulation, thus allowing greater variation in size of patches, a greater diversity of strains were found to co-circulate in the metapopulation (Fig. S4). The role of extinction and hierarchical population structure in generating and maintaining polymorphism is an interesting area for future research (Svennungsen and Kisdi, 2009).

Our study was originally motivated by the diverse life histories exhibited by bacteria of the genus Bordetellae. Two acute strains, B. pertussis and B. parapertusis, have emerged in humans from the less acute and persistent B. bronchiseptica that infects a wide range of wild animals (Bjørnstad and Harvill, 2005). In our previous work (King et al, 2009), we speculated that this was an illustration of the operation of the invasion-persistence trade-off via an implicit appeal to metapopulation dynamics. Here, through a more careful consideration of the evolutionary metapopulation context, we have explored how extinction and recolonization dynamics lead to conflicting selection pressures at the local and metapopulation scales. In particular, we have shown how changing metapopulation structure can shift the balance between the ‘classical’ and invasion-persistence trade-offs and that this shifting balance remains a viable hypothesis for the emergence and maintenance of acute pathogens.