How infection-triggered pathobionts influence virulence evolution

Abstract

Host–pathogen interactions can be influenced by the host microbiota, as the microbiota can facilitate or prevent pathogen infections. In addition, members of the microbiota can become virulent. Such pathobionts can cause co-infections when a pathogen infection alters the host immune system and triggers dysbiosis. Here we performed a theoretical investigation of how pathobiont co-infections affect the evolution of pathogen virulence. We explored the possibility that the likelihood of pathobiont co-infection depends on the evolving virulence of the pathogen. We found that, in contrast to the expectation from classical theory, increased virulence is not always selected for. For an increasing likelihood of co-infection with increasing pathogen virulence, we found scenario-specific selection for either increased or decreased virulence. Evolutionary changes, however, in pathogen virulence do not always translate into similar changes in combined virulence of the pathogen and the pathobiont. Only in one of the scenarios where pathobiont co-infection is triggered above a specific virulence level we found a reduction in combined virulence. This was not the case when the probability of pathobiont co-infection linearly increased with pathogen virulence. Taken together, our study draws attention to the possibility that host–microbiota interactions can be both the driver and the target of pathogen evolution.

This article is part of the theme issue ‘Sculpting the microbiome: how host factors determine and respond to microbial colonization’.

1. Introduction

The gut microbiota of metazoans plays a significant role for host fitness via nutrition and maintaining metabolic homeostasis of the host [1,2]. It also influences interactions with pathogens by either facilitating or preventing pathogen infection [3,4]. In Anopheles mosquitoes for example, the microbiota reduces malaria infection but facilitates viral infections [5]. Also members of the gut microbiota can become virulent, such members are called pathobionts [6]. Pathobiont infection can be triggered by dysbiosis and dysbiosis can be elicited directly by pathogen infection in the gut, or indirectly by disrupting host homeostasis resulting in altered gut immunity. Here, we use a mathematical framework to study the evolution of pathogen virulence in the presence of pathobionts (figure 1).

Figure 1.

Schematic illustration of how the virulence of a pathogen can trigger pathobiont co-infections via changes in the host immune system and subsequent emergence of dysbiosis. In our analysis we focus on how pathobiont co-infections that are triggered in this way can influence the evolution pathogen virulence.

Before we delve into virulence evolution, we first discuss examples of how pathogens elicit dysbiosis releasing the breaks on pathobionts and opportunistic pathogens. In Anopheles stephensi, it has been demonstrated that a fungal infection of the haemocoel by Beauveria bassiana results in a downregulation of antimicrobial peptide expression in the host [7]. As a consequence, the gut microbiota is altered and Serratia marcescens, a member of the gut microbiota, starts to dominate and subsequently also contributes to an increased host mortality [7]. In the pacific oyster Crassotrea gigas, the complex Pacific oyster mortality syndrome (POMS) is also driven by one pathogen causing dybiosis [8]. In this case, infection by the OsHV-1 μVar virus results in a subsequent change in the bacterial microbiota: rare members of the gut microbiota such as Vibrio and Arcobacter start to proliferate and elevate host mortality. These bacteria can also colonize from the seawater and do not necessarily arise from the gut microbiota itself. In Drosophila, bacterial species such as Gluconbactor morbifer and Lactobacillus brevis are members of the bacterial gut microbiota that can become pathobionts [9]. A recent study in Drosophila melanogaster also reported that avirulent Acetobacter species upon infecting the haemocoel reduce host survival and lead to a bloating phenotype that is also observed in wild flies [10].

An open question is how the virulence of pathogens evolves when pathogen infections trigger subsequent infections of pathobionts, or more generally opportunistic pathogens. Here we define virulence as pathogen-induced host mortality [11]. In our case, we investigate a combined virulence, caused by a pathogen and a pathobiont. We focus on the virulence evolution of the pathogen in the context of the combined virulence. Our investigation is based on classical theory on virulence evolution for which a trade-off between virulence and transmission is central, even though the empirical support is limited [12–14]. The classical theory has been extended to account for multiple infections and their role in virulence evolution [15–17]. Here we consider that a pathogen infection can trigger a pathobiont infection, which we refer to as a pathobiont co-infection. More precisely such a type of infection would be a suprainfection in the recently proposed framework by Sofonea et al. [18]. Our main contribution to the already existing theoretical framework on multiple infections is to consider that triggering of a pathobiont co-infection depends on pathogen virulence.

In our theoretical investigation, we are specifically interested in whether predictions on pathogen evolution can be readily derived from classical theory of bipartite host–pathogen interactions—or whether it is useful to explicitly consider the dynamics of tripartite interactions between hosts, pathogens and pathobionts. We assume that pathogen triggering of a pathobiont infection results in increased host mortality. According to classical theory on bipartite interactions, this additional host death rate should select for increased virulence [14,19]. This prediction, however, is based on the assumption of a constant additional host death rate. This assumption only applies to pathobiont co-infections if triggering of a co-infection is independent of pathogen virulence. However, what if the probability of co-infection, and thus the additional host death rate, increases with the virulence of pathogens? In such a scenario with more complex tripartite interactions, the costs of pathogen virulence will increase, selecting against high virulence. In our study, we investigate the occurrence and consequences of such conflicting selection pressures.

2. Theoretical development

To develop a model of how pathobiont co-infections can affect pathogen virulence evolution, we initially considered different possibilities of how to approach this topic formally. During this process, we realized that the problem that we are interested in is mathematically equivalent to a previously published model on a different topic. In this previous study, Day et al. [20] investigated the influence of immunopathology on the evolution of pathogen virulence. In their model, these authors assumed that the host immune activation following an infection could lead to an increase in host mortality. Thus, the effect of immunopathology considered by Day et al. [20] is formally equivalent to the biologically distinct effects of pathobiont co-infections that we aimed to investigate here.

In our analysis, we build on the model of Dayet al. [20] while adapting the model and its analysis for our own purpose. First, we simplify the model by removing the possibility that the ability of the host to clear an infection could lead to additional host mortality—a possibility that is of importance in immunopathology but does not apply in the context of pathobiont co-infections. Second, we expand the description of how the models are analysed and change some steps and related interpretation in the analysis. We hope these changes will facilitate the understanding of the model analysis by non-specialists. Third, we extended the analysis of the model in order to derive testable predictions that are particularly useful for empirically testing the influence of pathobiont co-infections on pathogen virulence evolution.

3. General model without co-infections

As a starting point for our analysis, we investigate a baseline model that describes pathogen virulence evolution in the absence of pathobiont co-infections. We also use this model to provide some basic insights into how predictions regarding virulence evolution are derived. In the following section, we will then expand this model to investigate the expected effects of pathobiont co-infections.

Following Day et al. [20], the baseline of our model development and analysis is a simple model that has already served as a key resource for theoretical investigations of virulence evolution [12,21]. Despite some limitations [22], this simple approach is useful to gain some basic insights into the dynamics of pathogen virulence evolution. In our baseline model, the fitness of the pathogen is given by the baseline reproduction ratio ($R_0$), defined as:

$$R_0={\displaystyle \frac{N\cdot \beta (\alpha )}{\mu +c+\alpha },}$$ 3.1

where N is the host population size, $\mu$ is the background mortality of the host, c is the rate with which the host clears the infection, $\alpha$ is the pathogen virulence, i.e. the additional host death rate owing to the infection, and $\beta (\alpha )$ is the transmission rate of the pathogen, which is a function of its virulence. In agreement with the trade-off hypothesis of virulence evolution, we assume that the transmission rate increases with increasing virulence, and that this increase should show a decelerating pattern [12]. The term $1/(\mu +c+\alpha )$ quantifies the average duration of an infection. Thus, in this model, pathogen fitness is determined by the product between the average infection duration and the transmission rate per unit of time. The model assumes that all rates are constant throughout the infection. However, these rates can be also interpreted as average rates in more dynamic infections [20].

Without making specific assumptions regarding $\beta (\alpha )$, it is not possible to precisely predict the level of $\alpha$ that maximizes the fitness of the pathogen—and for example derive predictions of how changes in model parameters affect the evolution of virulence. Nevertheless, it is still possible to derive general predictions by calculating the selection gradient, which is achieved by differentiating equation (3.1) with respect to $\alpha$, giving:

$${\displaystyle \frac{\mathrm{d}{R}_0}{\mathrm{d}\alpha }={\displaystyle \frac{{\beta }^{\mathrm{\prime }}(\alpha )}{\mu +\alpha +c}-{\displaystyle \frac{\beta (\alpha )}{{(\mu +c+\alpha )}^2}.}}}$$ 3.2

The right-hand side of this equation quantifies for a given virulence level $\alpha$, the changes in pathogen fitness that occur owing to an increase in virulence. Here, the first term quantifies the change in fitness owing to a change in transmission rate, which relates to the benefits of virulence for the pathogen. Thus, this first term can be interpreted as the additional fitness benefits due to an increased transmission rate, that the pathogen received when increasing its virulence. By contrast, the second term quantifies the additional fitness cost of increased virulence, which is related to a decrease in infection duration.

Equation (3.2) can be simplified by dividing it by $R_0$ (equation (3.1)):

$${\displaystyle \frac{\mathrm{d}{R}_0/\mathrm{d}\alpha }{R_0}={\displaystyle \frac{{\beta }^{\mathrm{\prime }}(\alpha )}{\beta (\alpha )}-{\displaystyle \frac{1}{\mu +c+\alpha }.}}}$$ 3.3

Thus, after this normalization the additional cost and benefit terms can now be interpreted as additional relative costs and benefits of an increase in virulence. (Note that this simplification and subsequent interpretation of these terms differs from the approach taken by Day et al. [20]; also a similar result was already obtained by van Baalen & Sabelis [16], however, based on a different overall approach.) An inspection of equation (3.3) shows that the additional relative fitness benefits decrease with increasing transmission rates $\beta (\alpha )$. Furthermore, the additional fitness benefits are higher for a higher ${\beta }^{\mathrm{\prime }}(\alpha )$, which quantifies how strongly the transmission rate increases owing to an increase in virulence. The additional relative costs $1/(\mu +c+\alpha )$ equal the infection duration for a given virulence level of $\alpha$. If the assumptions of the trade-off hypothesis for virulence evolution are fulfilled, then increasing levels of virulence always lead to a decrease in both the additional benefits and costs (figure 2). Furthermore, increases in additional benefits and decreases in costs will increase the level of virulence and that maximizes pathogen fitness (figure 2).

Figure 2.

A hypothetical example illustrating the relationship between (a) a trade-off between virulence and transmission, (b) relative fitness benefits and costs of increased virulence (equation (3.3)), and (c) pathogen fitness ($R_0$, equation (3.1)). The vertical dotted and dash-dotted lines indicate the virulence levels that maximize pathogen fitness in two different scenarios. Note that these levels are reached when the additional costs equal the additional benefits, which implies that at this virulence level it is for the pathogen neither beneficial to increase nor decrease its virulence. Solid lines depict a baseline scenario in this illustration. Dashed lines depict changes in an alternative scenario with increased host background mortality. In this alternative scenario pathogen fitness is maximized at a higher virulence level, which is consistent with the prediction that increases in host background mortality lead to the evolution of increased pathogen virulence.

4. General model with co-infection effect on host mortality

In the following, we extend the above-described model by including the aggregated effects of co-infections by a pathobiont. In this context, we rely on some simplifying assumptions. First, we assume that in all host individuals the pathobiont is a member of the microbiota, and we do not explicitly model how hosts acquire pathobionts from other hosts or the environment. Second, we do not explicitly describe how the infection with the pathogen might trigger a pathobiont co-infection. Instead, we focus on the outcome that a co-infection can increase the death rate of the host—which in our model is a major determinant for the evolution of pathogen virulence (figure 2). Additionally, we assume that if co-infections occur then they do so very shortly after the onset of the pathogen infection and co-infections last at least as long as the pathogen infection, which is consistent with the above described example of fungal infections that trigger S. marcescens co-infections in mosquitoes [7].

In our extended model, we consider the possibility that the additional host death rate can depend on the virulence of the pathogen. Such an effect could arise if a more virulent pathogen increases the probability that a co-infection occurs, or if a more virulent pathogen triggers more severe co-infections than less virulent ones. We define $\delta (\alpha )$ as the additional host death rate owing to a co-infection, which results in:

$$R_0={\displaystyle \frac{N\cdot \beta (\alpha )}{\mu +\delta (\alpha )+\alpha +c},}$$ 4.1

with the corresponding normalized fitness gradient with respect to $\alpha$:

$${\displaystyle \frac{\mathrm{d}{R}_0/\mathrm{d}\alpha }{R_0}={\displaystyle \frac{{\beta }^{\mathrm{\prime }}(\alpha )}{\beta (\alpha )}-{\displaystyle \frac{{\delta }^{\mathrm{\prime }}(\alpha )+1}{\mu +c+\alpha +\delta (\alpha )}.}}}$$ 4.2

Based on equation (4.2), we can derive some general predictions on how the additional host death rate owing to a co-infection affects pathogen virulence evolution (figure 3). Specifically, in the following we will use a scenario without co-infection as a baseline (equation (3.1)) and assess how additional co-infections (equation (4.1)) influence the virulence evolution. In this context, we assess (i) how the virulence of the pathogen $\alpha$ evolves, and (ii) how changes in $\alpha$ affect the combined virulence $\alpha +\delta (\alpha )$, which captures the added host death rate due to the primary infection and the co-infection.

Figure 3.

Summary of the model predictions. Predictions concern the virulence evolution of the pathogen ($\alpha$) and the combined virulence of the pathogen and the co-infecting pathobiont ($\alpha +\delta (\alpha )$). Arrows indicate the predicted direction of evolution, and question marks indicate cases where it is not possible to derive a prediction for a consistent directional effect. (a–d) Predictions derived from the general model (equations (4.1,4.2)) for different assumptions of how the virulence of the pathogen affects the expected virulence of the co-infecting pathobiont, which is described by the function $\delta (\alpha )$. Note that $\delta (\alpha )$ could capture changes in the probability that a co-infection occurs. (a) $\delta (\alpha )$ is constant, i.e. independent of $\alpha$. (b) $\delta (\alpha )$ always increases with $\alpha$, with different line types indicating possibilities for different quantitative relationships. (c) $\delta (\alpha )$ always decreases with $\alpha$. (d) $\delta (\alpha )$ more complex functions of $\alpha$, e.g. which increase for some $\alpha$ levels and decrease for others. (e–g) Predictions derived from a model that specifically assumes that $\delta (\alpha )$ increases linearly with $\alpha$ (equation (5.1)), for different assumptions of how $\alpha$ relates to the transmission rate of the pathogen $\beta (\alpha )$. (e) $\beta (\alpha )$ is a polynomial function (equation (5.3)). (f) $\beta (\alpha )$ is a saturating function (equation (5.6)), with the saturation threshold indicated by the dashed line. (g) $\beta (\alpha )$ is a hump-shaped function (equation (5.9)). (h–i) Predictions derived from a model that specifically assumes that $\delta (\alpha )$ increases in a step-like manner with $\alpha$ (equation (5.2)), for different assumptions regarding at which level of $\alpha$ co-infections start occurring and how high the additional host mortality is. The dotted lines indicate the virulence that maximizes pathogen fitness in absence of co-infections. For more details, see figure 4.

Equation (4.2) shows that the additional host mortality owing to co-infections can affect the virulence evolution of the pathogen by modifying the added costs of increased virulence (i.e. the second term on the right-hand side). Specifically, there are two different ways in which co-infections influence these added costs. First, the additional host mortality owing to co-infections $\delta (\alpha )$ adds to the denominator and thus decreases the added costs. Accordingly, a higher additional host mortality $\delta (\alpha )$ favours the evolution of increased virulence $\alpha$ of the pathogen. Second, the derivative of the additional host mortality ${\delta }^{\mathrm{\prime }}(\alpha )$ adds to the numerator of the added costs. This derivative can in principle be positive, negative or zero, which generates different selection pressures on $\alpha$.

In the simplest case ${\delta }^{\mathrm{\prime }}(\alpha )$ is zero, which means that the effect of co-infections on host mortality is independent of the virulence of the pathogen (figure 3a). Such a situation could occur for example if co-infections are not triggered by pathogen infections or if they are triggered by the pathogen infection but this triggering occurs independently of the virulence of the pathogen. Thus, this scenario is equivalent to the well-known effect of increased host background mortality, which leads to the evolution of increased pathogen virulence (figure 2). Furthermore, in this scenario, also the combined virulence $\alpha +\delta (\alpha )$ increases.

The more interesting and probably most relevant scenario for our study is the case when the additional host mortality owing to co-infection increases with the pathogen virulence, i.e. when ${\delta }^{\mathrm{\prime }}(\alpha )$ is always positive (figure 3b). Such a scenario could occur if a higher virulence of the pathogen increases the probability and/or severity of co-infections. Unfortunately, in this scenario no general predictions can be derived for the pathogen virulence evolution. A positive ${\delta }^{\mathrm{\prime }}(\alpha )$ in the numerator increases the added costs, which conflicts with the added $\delta (\alpha )$ term in the denominator, which decreases the added costs of increased virulence. Accordingly, the pathogen virulence might evolve to higher or lower levels, and thus the combined virulence might also increase or decrease. In the next section below, we are investigating more specific functions of $\delta (\alpha )$, for which we are able to obtain clearer predictions.

In principle, it could be possible that the additional host mortality owing to co-infection decreases with the virulence of the pathogen, i.e. when ${\delta }^{\mathrm{\prime }}(\alpha )$ is always negative (figure 3c). Such a scenario could occur if a higher virulence of the pathogen decreases the probability and/or severity of co-infections. In this case, the effects of ${\delta }^{\mathrm{\prime }}(\alpha )$ and $\delta (\alpha )$ both decrease the added costs, which lead to the evolution of increased virulence of the pathogen, which also leads to an increased combined virulence. Furthermore, it is possible that $\delta (\alpha )$ is captured by a more complex function, e.g. which increases for some virulence levels and decreases for others (figure 3d). In this case, it is also not possible to derive general predictions based on equation (4.2). However, in the following we are not pursuing this possibility any further and instead focus on different scenarios of how $\delta (\alpha )$ might increase with increasing $\alpha$.

5. Specific models

In the following, we further investigate the case in which the additional host mortality owing to a co-infection $\delta (\alpha )$ can increase with increasing pathogen virulence $\alpha$. This case seems to be particularly relevant for pathobiont co-infections, but the above analysis of the general model could not provide any insights into expected evolution of pathogen virulence. Therefore, we now investigate more specific models that focus on two contrasting scenarios of how the additional host mortality owing to a co-infection $\delta (\alpha )$ can increase with increasing $\alpha$: (i) a linear increase:

$$\delta (\alpha )=d\alpha ,$$ 5.1

and (ii) a step-like increase, in which co-infections occur only above a certain threshold t of $\alpha$, which then leads to a constant additional increase in host mortality $d$:

$$\delta (\alpha )=\{\begin{array}{c}0\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{for}\hspace{0.17em}\hspace{0.17em}\alpha <t\hspace{0.17em}\\ d\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{for}\hspace{0.17em}\hspace{0.17em}\alpha \ge t\hspace{0.17em}\end{array}.$$ 5.2

(a) . Models with a linear increase in the additional host mortality owing to a co-infection δ(α)

The case of a linear increase was to some extent already analysed by Day et al. [20]. Specifically, to obtain predictions for virulence evolution, Day et al. [20] needed to also assume a specific functional relationship between the virulence of the pathogen $\alpha$ and the its transmission rate $\beta (\alpha ).$ Here, we first reiterate the analysis of Day et al. [20]. In two additional sub-scenarios, we then investigate two different functional relationships between the virulence of the pathogen $\alpha$ and its transmission rate $\beta (\alpha ).$ In this way, we aim to assess the robustness of the derived predictions.

In the first sub-scenario, we assume a polynomial function (figure 3e):

$$\beta (\alpha )=k{\alpha }^b,$$ 5.3

with $0<b<1,$ which leads to an evolved virulence of the pathogen:

$$\hat{\alpha }={\displaystyle \frac{b}{1-b}\hspace{0.17em}{\displaystyle \frac{\mu +c}{d+1},}}$$ 5.4

and a combined virulence:

$$\hat{\alpha }+\mathrm{d}\hat{\alpha }={\displaystyle \frac{b}{1-b}(\mu +c).}$$ 5.5

Equation (5.4) shows that in this sub-scenario, co-infections (which occur when $d>0$) lead to the evolution of lower pathogen virulence. However, equation (5.5) shows that the additional host mortality owing to co-infections exactly compensates this reduction and the combined virulence does not change due to the occurrence of co-infections (because the parameter d does not occur anymore on the right-hand side of equation (5.5).

In the second sub-scenario, we assume a function in which the transmission rate converges to a fix level k (figure 3f):

$$\beta (\alpha )={\displaystyle \frac{k\alpha }{b+\alpha },}$$ 5.6

which leads to an evolved virulence of the pathogen:

$$\hat{\alpha }=\sqrt{{\displaystyle \frac{b(\mu +c)}{d+1}}},$$ 5.7

and a combined virulence:

$$\hat{\alpha }+\mathrm{d}\hat{\alpha }=\sqrt{(d+1)b(\mu +c)}.$$ 5.8

Equation (5.7) shows that also in this sub-scenario co-infections lead to the evolution of lower pathogen virulence. However, in contrast to the previous sub-scenario the combined virulence increases as indicated by equation (5.8).

In the third sub-scenario, we assume a hump-shaped function in which the transmission rate initially increases and later decreases again (figure 3g):

$$\beta (\alpha )={\displaystyle \frac{k\alpha }{e^{b\alpha }},}$$ 5.9

which leads to an evolved virulence of the pathogen:

$$\hat{\alpha }={\displaystyle \frac{\sqrt{\mu +c}\sqrt{b\mu +4d+bc+4}-\sqrt{b}(\mu +c)}{2\sqrt{b}(d+1)},}$$ 5.10

and a combined virulence:

$$\hat{\alpha }+\mathrm{d}\hat{\alpha }={\displaystyle \frac{\sqrt{\mu +c}\sqrt{b\mu +4d+bc+4}-\sqrt{b}(\mu +c)}{2\sqrt{b}}.}$$ 5.11

Based on equation (5.10), it is not possible to derive a prediction regarding the direction of pathogen virulence evolution (because d appears in the numerator and denominator). Nevertheless, equation (5.11) shows that in this sub-scenario the combined virulence always increases.

Taken together in this section, we analysed three sub-scenarios with a linear increase in the additional host mortality owing to a co-infection $\delta (\alpha ).$ This analysis revealed some similar trends for the expected evolutionary dynamics, but the predicted evolutionary changes in virulence differed between the sub-scenarios. We therefore expect that the evolutionary dynamics triggered by pathobiont co-infections depend on the specifics of the direct host–pathogen interaction. Nevertheless, the robust general insight emerges that for a linear increase in $\delta (\alpha )$ the combined virulence is predicted to either remain unchanged or increase, but not to decrease (figure 3e–g).

(b) . Models with a step-like increase in the additional host mortality owing to a co-infection δ(α)

In this section, we aim to pursue the question of whether and how the expected evolutionary dynamics derived above for a linear increase in $\delta (\alpha )$ can change if there is a highly nonlinear increase in $\delta (\alpha )$. In their analysis, Day et al.[20] did not pursue this questions, which, however, seems to be particularly relevant in the context of pathobiont co-infections. For our purpose, we investigate here the extreme case of a step-like increase in $\delta (\alpha )$ (equation (5.2)).

In contrast to the above analysis of linear $\delta (\alpha )$ functions, here we are able to derive predictions without the need for considering specific assumptions for how pathogen virulence relates to the transmission rate. Such derivations are now possible because we can exploit the fact that the first part of the step-function ($\alpha <t$) corresponds to our baseline model because no pathobiont infections occur. In addition, the second part of the step function ($\alpha \ge t$) also corresponds to our baseline model—just with an elevated level of host background mortality. For this baseline model, it is already well known that an elevated background mortality results in (i) a higher optimal virulence (figure 2), and (ii) a reduced pathogen fitness across the whole range of possible virulence levels (equation (3.1); figure 3).

Based on this knowledge, it is possible to derive general predictions regarding the evolution of pathogen virulence. Specifically, these predictions are independent of the specific functional relationships regarding how pathogen virulence is related to the transmission rate of the pathogen and to the probability of pathobiont co-infection. However, also here we will consider three different sub-scenarios. These sub-scenarios are based on a comparison of the step-function in relation to the fitness of the pathogen in the absence of any co-infections (equation (3.1)). In this context, we assume that ${\hat{\alpha }}_0$ denotes the pathogen virulence that maximizes the fitness of the pathogen in the absence of any co-infections.

In the first sub-scenario, the threshold t of $\alpha$ at which co-infections start occurring is larger than ${\hat{\alpha }}_0$ (figure 4a,d). Accordingly, in case of co-infections pathogen fitness is reduced for all $\alpha \ge t$ (figure 4g). However, this reduction does not affect the level of $\alpha$ that maximizes the pathogen fitness. Importantly, in this sub-scenario all that matters is the threshold t of $\alpha$ at which co-infections start occurring. The additional mortality d that the host experiences owing to the co-infection has no influence on virulence evolution in this scenario. Accordingly, neither the pathogen virulence nor the combined virulence is expected to evolve.

Figure 4.

Illustration of how co-infections affect virulence evolution of the pathogen when the additional host mortality owing to a co-infection $\delta (\alpha )$ is a step-function (equation (5.2)). Each column refers to a different scenario. (a–c) Hypothetical fitness landscape for the pathogen virulence in absence of co-infections. (d–f) Functions of $\delta (\alpha )$ that differ (i) in the threshold t of $\alpha$ at which co-infections start occurring, and (ii) in the additional host mortality d. (g–i) Fitness landscapes for the pathogen virulence when effects of co-infections are accounted for. Dotted lines indicate the level of $\alpha$ that that maximizes the pathogen fitness in absence of co-infections, denoted here ${\hat{\alpha }}_0$. Dashed lines indicate the level of $\alpha$ that that maximizes the pathogen fitness in presence of co-infections, denoted here $\hat{\alpha }$. First column: co-infections occur only for $\alpha$>${\hat{\alpha }}_0$, which does not affect $\hat{\alpha }$. Note that in this case d has no influence on virulence evolution. Second column: co-infections start occurring for $\alpha \le {\hat{\alpha }}_0$ and particularly small levels of t and/or small levels of d, which results in an increase in $\hat{\alpha }$. This shift occurs because an additional constant amount of host mortality decreases the costs of increased pathogen virulence (equation (4.2), figure 2a). Third column: co-infections start occurring for $\alpha \le {\hat{\alpha }}_0$ and particularly large levels of t and/or large levels of d, which results in a decrease in $\hat{\alpha }$. This shift occurs because the additional host mortality owing to co-infections is so severe that the maximum fitness is now attained at a level of $\alpha$ just before the threshold$\hspace{0.17em}t$ at which co-infections start to occur. In this scenario, the pathogen maximizes its fitness by completely avoiding co-infections and the associated fitness costs.

In the second and third sub-scenario, the threshold t of $\alpha$ at which co-infections start occurring is smaller than or equal to ${\hat{\alpha }}_0$ (figure 4e,f). Under this condition, two contrasting outcomes can emerge depending on the specific values of the threshold t and the additional mortality d that the host experiences owing to the co-infection. If the levels of t and/or d are sufficiently small (figure 4e), then co-infections lead to an increased level of $\alpha$ that maximizes the pathogen fitness (figure 4h). This shift occurs because an additional constant amount of host mortality decreases the costs of increased pathogen virulence (equation (4.2); figure 2a). Additionally, the combined virulence should also increase because at the increased optimal level of pathogen virulence, pathobiont co-infections will always occur and further increase host mortality.

The third sub-scenario occurs if the levels of t and/or d are sufficiently large (figure 4f). In this case, co-infections lead to a decreased level of $\alpha$ that maximizes the pathogen fitness (figure 4i). This decrease occurs because the additional host mortality owing to co-infections is so severe that the maximum fitness is now attained at a level of $\alpha$ just before the threshold $\hspace{0.17em}t$. In this scenario, the pathogen maximizes its fitness by completely avoiding co-infections and the associated fitness costs. As a consequence, because in this sub-scenario no pathobiont infections are expected, pathobiont co-infections do not contribute to the combined virulence. Thus, the predicted decrease in pathogen virulence should also result in a decreased combined virulence.

Taken together in this section, we analysed three sub-scenarios with a step-like increase in the additional host mortality owing to a co-infection $\delta (\alpha )$. This analysis revealed that the predicted evolutionary changes in virulence strongly differed between the sub-scenarios (figure 3h–j). In contrast to a linear increase in $\delta (\alpha )$, for the step-like increase we could identify a sub-scenario in which pathogen evolution is expected to result lower pathogen virulence and also lower combined virulence. In this sub-scenario, the level of virulence at which the pathogen triggers the pathobiont co-infection (t) is below the optimal virulence without co-infection (${\hat{\alpha }}_0$) (figure 4f), and the costs of triggering the pathobiont co-infection (which are related to d) exceed the additional benefits of increased pathogen virulence (figure 4i). As a consequence, the presence of the pathobiont forces the pathogen to evolve a lower level of virulence that prevents pathobiont co-infection. Accordingly, the lower evolved pathogen virulence also implies a lower combined virulence.

6. Discussion

Here we performed a theoretical investigation of how pathobionts, members of the microbiota, affect the evolution of pathogen virulence and the resulting combined virulence of the pathobiont and the evolved pathogen. We explored the possibility that the likelihood of pathobiont co-infection, and its associated contributions to host death, could depend on the evolving virulence of the pathogen. We found that, in contrast to the expectation from classical theory in bipartite host–pathogen interactions, increased virulence is not always selected for. Instead the tripartite interactions between hosts, pathogens and pathobiont can lead to different evolutionary dynamics. In scenarios in which the likelihood of pathobiont co-infection increases with increasing pathogen virulence we found scenario-specific selection for either increased or decreased virulence. Evolutionary changes, however, in pathogen virulence do not always translate into similar changes in combined virulence. Only in one of the scenarios where pathobiont co-infection is triggered above a pathogen virulence threshold we found a reduction in combined virulence. This was not the case when the probability of pathobiont co-infection linearly increased with pathogen virulence.

We only found selection for decreased combined virulence in one scenario. In this scenario, the level of virulence at which the pathogen triggers the pathobiont co-infection is below the optimal virulence without co-infection, and the costs of triggering the pathobiont co-infection exceed the benefits of increased pathogen virulence (figure 4c,f). As a consequence, pathogen virulence evolves to lower levels, resulting in the avoidance of triggering pathobiont co-infection (figure 4i). Thereby the pathobiont, while present in the microbiota, does not contribute to overall virulence in infections with such a pathogen.

An important empirical challenge to test our predictions is to determine the virulence of the pathogen, its relation to pathobiont co-infection ($\delta (\alpha )$) and their combined virulence ($\alpha +\delta (\alpha )$) (figure 3). The studies on Anopheles infection by B. bassiana and its pathobiont S. marcescens provide a useful experimental approach to estimate the virulence of a pathogen, a pathobiont and their combination [7]. It should be possible to extend this approach to also determine the dependency of pathobiont co-infection on pathogen virulence with a suite of pathogen strains that differ in virulence. If an experimental system such as the one with the spore-forming pathogen B. bassiana is used however, this might require to adapt our model to spore formers (e.g. [23]). In spore formers, the costs of virulence can differ from other pathogens which could affect corresponding evolutionary dynamics (e.g. [24,25]).

Here we focused on how pathogen virulence evolves in the presence of a non-evolving pathobiont. However, our approach to consider that co-infections could depend on the virulence of the primary infection is also applicable to more general scenarios, e.g. when pathobionts coevolve alongside pathogens or when multiple pathogens coevolve. This extension is interesting as multiple infections are very prevalent [26]. Alizon et al. [27] made a clear distinction between combined virulence and the evolutionary outcome of multiple infections that also entails changes in transmission. The aspect we have modelled here is the situation if and when a co-infection occurs depending on the virulence of the primary pathogen. We are not aware of any empirical studies that explicitly tested such situations. A study by Lohr et al. [28] using the waterflea Daphnia and two of its pathogens, the protozoan Caullerya mesnili and the fungus Metschnikowia, investigated how sequential co-infection determines combined virulence and pathogen fitness, including a measure of co-infection probability. Such studies could be extended to explore the effect of strains of the same pathogen that differ in virulence. For example, in their study on fish parasites, Louhi et al. [29] combined six genotypes of a pathogenic flavobacterium and five genotypes of the parasitic worm Diplostomum. Thus, in study systems as used by Lohr et al. [28] and Louhi et al. [29], it seems feasible to quantify the relationship between the virulence of the primary pathogen and the probability of co-infection. Also, other study system such as Caenorhabditis elegans, where a number of pathobionts, especially in the context of impaired host immunity have been studied [30], should be well suited to test the predictions on virulence evolution derived from our model.

Theoretical models on virulence evolution of co-infecting pathogens emphasized the importance of interacting evolutionary and ecological dynamics [16,31,32]. Specifically, it has been pointed out that, while the evolution of pathogen virulence can depend on the frequency of co-infections, the reverse is also true: evolutionary changes in pathogen virulence can also affect the frequency of co-infections [16]. Here the relationship between pathogen virulence and the frequency of co-infections emerges from the effects of virulence on host population dynamics. In our model, we also considered different relationships between pathogen virulence and the frequency of co-infections. However, in our case these relationships emerge at the level of host individuals, based on altered within-host processes (figure 1)—instead of emerging at the population level based on altered host population dynamics. In future investigations it would be interesting to explore how the combination of both influences on co-infection frequencies, i.e. mediated by within-host processes and by host population dynamics, affects pathogen virulence evolution. Existing models already considered the possibility that pathogen evolution could alter the susceptibility of an infected host to subsequent co-infection, e.g. via the evolution of immunosuppression [33]. Such models could be extended to include the effect that we focused on in our study, i.e. that the evolution of pathogen virulence also modulates the susceptibility to co-infections.

In our study we considered how pathogens cause dysbiosis in the host gut microbiota, mediated by the host immune system. Importantly, the focus of our study reached beyond this relationship: we explored how this relationship can be modulated by pathogen evolution. Specifically, we studied how pathobiont infection resulting from dysbiosis affects pathogen fitness and consequently pathogen virulence evolution (figure 1). The picture that emerges is that evolutionary changes in pathogen virulence can change the dysbiotic effects of pathogen infections and the related negative effects of pathobiont co-infections (figure 3). Thus, our study draws attention to the possibility that host–microbiota interactions can be both the driver and the target of pathogen evolution.

Ethics

This work did not require ethical approval from a human subject or animal welfare committee.

Data accessibility

This article does not use any data.

Declaration of AI use

We have not used AI-assisted technologies in creating this article.

Authors' contributions

M.F.: conceptualization, formal analysis, writing—original draft, writing—review and editing; R.R.R.: funding acquisition, writing—original draft, writing—review and editing; J.R.: funding acquisition, writing—original draft, writing—review and editing.

All authors gave final approval for publication and agreed to be held accountable for the work performed therein.

Conflict of interest declaration

We declare we have no competing interests.

Funding

This work was supported by the Deutsche Forschungsgemeinschaft DFG for funding to J.R. (grant no. RO 2284/8-1) and a Mercator fellowship to R.R.R. as part of the Research Unit FOR 5026 ‘InsectInfect’.