PARASITE CO-TRANSMISSION AND THE EVOLUTIONARY EPIDEMIOLOGY OF VIRULENCE

Authors


Abstract

Hosts are often co-infected by several parasite genotypes of the same species or even by different species and this is known to affect virulence evolution. However, epidemiological models typically assume that only one of the co-infecting strains can be transmitted at the same time, which is often at odds with the observed biology. Here, I study the effect of co-transmission on virulence evolution in a case where parasites compete for host resources. For co-infections by strains of the same species, increased co-transmission selects for less virulent strains. This is because co-transmission aligns the interests of co-infecting strains, thus decreasing the selective pressure for increased within-host competitiveness. For co-infection caused by different parasite species, the evolutionary outcome depends on the respective virulence of the two parasite species. Finally, I investigate asymmetric scenarios, for example that of plant viruses that require “helper” molecules produced by viruses from another species to be transmitted. These results show that even if parasite strains compete for host resources, the prevalence of co-infections can be a poor predictor of virulence evolution.

Co-infection, that is simultaneous infection of the same host by different parasite strains or species, is a widespread phenomenon and is a major public health concern (Rigaud et al. 2010; Balmer and Tanner 2011). These co-infections are known to affect not just the epidemiology of infectious diseases (Telfer et al. 2010) but also their evolution (Read and Taylor 2001; Schmid-Hempel 2011).

Evolutionary epidemiology models show that if the within-host competitive ability of a strain is positively correlated with its virulence, which has been shown experimentally for rodent malaria (de Roode et al. 2005) and for Pasteuria ramosa in Daphnia (Ben-Ami et al. 2008), then the occurrence of co-infections should favor more virulent strains (van Baalen and Sabelis 1995; May and Nowak 1995; Choisy and de Roode 2010). For other relationships between competitive ability and virulence, for example if parasites produce public goods or if they exhibit spiteful interactions (Brown et al. 2002; Buckling and Brockhurst 2008), then more or less virulent strains can be selected depending on trade-offs and epidemiological feedbacks (Alizon and Lion 2011).

A common feature of all these studies is that they assume that only one of the co-infecting strains can be passed on to the new host upon a transmission event; an assumption that is sometimes at odds with the biology of the host–parasite interaction. In the case of HIV for instance, Keele et al. (2008) reported that more than 20 % of the 104 infections they considered seem to have been initiated by at least two founder strains. For hepatitis C virus (HCV), infections by multiple strains have also been detected (Bull et al. 2011). There is even indication that co-transmission of HIV and HCV might occur through needle transmission (Ridzon et al. 1997). More generally, transmission through blood-transfusion or needle sharing is likely to increase the risk of co-transmission (Bar et al. 2010).

A large body of evidence supporting co-transmission, that is simultaneous transmission of more than one parasite strain upon the same transmission event, can be found among vector-borne diseases. This makes sense because the transmission event can be dissected experimentally by focusing on the vector. In the case of human malaria, several genotypes of the same Plasmodium species or even from different Plasmodium species can infect the same mosquito (Taylor et al. 1997). More recent data on the genetic relatedness between co-infecting strains of Plasmodium falciparum in eight individuals seems to be more consistent with simultaneous infection by all the strains rather than sequential infections (Nkhoma et al. 2012). In the case of viruses, Vazeille et al. (2010) have shown that Aedes albopictus can be co-infected by dengue and chickungunya and are likely to transmit the two parasite species. Infection of mosquitoes by different strains of the same virus species also occurs and Craig et al. (2003) even isolated a mosquito infected by two dengue 2 “parental” genomes and their recombinant genome.

Co-transmission has been described and studied for a long time in plant viruses. In fact, for some of these viruses, co-transmission is likely to be a common phenomenon. In the Sequiviridae family for instance, species from the sequivirus genera require the presence of a “helper” molecule produced by viruses from the waikavirus genera (Pirone and Blanc 1996). Another striking example is that of umbraviruses, which, contrary to most viruses, do not produce a coat protein but use that of luteoviruses (Taliansky and Robinson 2003). Some experimental results have also been obtained using plant viruses. To disentangle the different steps of co-transmission, Ohnishi et al. (2011) designed a study, where whitefly vectors were given two successive acquisition feedings on tomato plants infected by two different strains of Tomato yellow leaf curl virus. After feeding on each singly infected plant, the vectors were then transferred to healthy tomato plants. They found that 75 % of the vectors transmitted the two viruses, whereas 25 % transmitted only one strain. This value was affected by the order of inoculation (the virus strain inoculated first tended to be more transmitted alone). Unfortunately, we are not aware of similar data being obtained from the field.

In spite of the significant occurrence of co-transmission for a wide variety of parasites, this process remains largely absent from epidemiological models. Here, I study how the probability of co-transmission of the different strains co-infecting a host affects the evolutionary epidemiology of parasite virulence, that is the disease-induced mortality of the host. This is done separately in the case of co-infections caused by two parasite strains of the same species or by two strains from different species because the two cases call for different epidemiological frameworks.

In both cases, I show that if parasites compete for host resources then increasing the probability of co-transmission tends to select for lower levels of virulence. This is because co-transmission, even though it increases the prevalence of co-infected hosts, also aligns the interests of the parasite strains, which lowers the selection for increased within-host competition. Interestingly, in the case of co-infections by different species, this result might not hold for all parameter values. Finally, I study the case of the helper and defector plant viruses discussed above. These results are analyzed in the light of kin selection theory, in particular with reference to “budding dispersal” (Pollock 1983; Goodnight 1992; Gardner and West 2006). I also discuss implications for public health policies, particularly the fact that monitoring the prevalence of co-infections can be a poor predictor for virulence evolution.

The Model

The evolutionary epidemiology approach used here is based on adaptive dynamics (Geritz et al. 1998; Dieckmann et al. 2002) and consists in studying the invasion fitness of a rare mutant strain that emerges in a host population already infected by a resident parasite strain (or by two resident strains in the case of co-infections by different species). The resident and its corresponding mutant strain are assumed to differ only slightly in one quantitative trait (their virulence). The invasion fitness is measured using the baseline reproductive ratio (or R0, Anderson and May 1991), which is obtained by computing the dominant eigenvalue of the Jacobian matrix of the system of equations capturing the dynamics of the mutant strain (Diekmann and Heesterbeek 2000; Otto and Day 2007). If the fitness of the mutant is greater than 0, the mutant invades and replaces the resident. By repeating these challenges, we can identify parasite trait values that are evolutionarily stable (ES), that is cannot be invaded by any mutant strain.

Below, I present the two epidemiological frameworks used in this study. In both cases, I only allow for co-infections by up to two strains to keep the analysis tractable. In the main text, I also assume that the host population has a constant density (normalized to 1). This implies that the input of new hosts is limited by other constrains than the parasite such that each host death is immediately compensated by the birth of a susceptible host. Earlier evolutionary epidemiology models also make this assumption, because it allows to model changes in the composition of the host population (in terms of the fraction of infected or susceptible hosts) without dealing with population size feedbacks (Choisy and de Roode 2010; Alizon and Lion 2011). I show in Appendix S2 that allowing the population size to vary does not affect the results qualitatively.

About parasite transmission

Before presenting the epidemiological frameworks, I describe the assumptions made regarding parasite transmission in further details. The transmission rates are the following: hosts singly infected by strain 1 have a transmission rate β1, hosts singly infected by strain 2 have a transmission rate β2, and co-infected hosts have a total transmission rate β1221 (where βij is the transmission rate of strain i in a host co-infected by strains i and j).

For co-infected hosts, the nature of the transmitted strain is either only strain 1 (with probability (1 −ε) β12/(β1221)), only strain 2 (with probability (1 −ε) β21/(β1221)), or both strains (with probability ε, which corresponds to the probability of co-transmission). Note that when co-transmission is impossible (ε= 0), we are back to the case studied in earlier models and the transmission rate of strain i in co-infected hosts is βij. Conversely, when co-transmission is always required (ε= 1), the transmission rate of a focal strain is as important for its transmission as the transmission rate of the other strain.

We also need to define how the co-infection affects the transmission rate of a strain, in other words what the relationship is between βij and βi. Here we consider two scenarios: either the different strains compete for host resources (and then βiji/2), or the two strains exploit distinct niches in the host in which case their transmission rates are unaffected by the presence of the competitor (βiji). As we will see below, the former scenario (host resources being equally shared) is difficult to avoid in the framework for co-infections by different strains of the same species (which makes sense biologically because the resident and the mutant strain are assumed to differ only slightly). For the other framework (co-infection by different species), both scenarios are studied.

Finally, I assume that there exists a transmission–virulence trade-off such that the transmission rate of strain i is proportional to the square root of the virulence of strain i:

image(1)

where b is a proportionality constant.

This assumption is made in many evolutionary epidemiology and it is one of the most parsimonious adaptive explanations as to why parasites harm their host (Anderson and May 1982; Ewald 1983; Alizon et al. 2009). The trade-off originates from the fact that parasites need to exploit their hosts to get transmitted but that increasing host exploitation also leads to an increase host mortality. This generates a positive relationship between the virulence and the transmission rate. If the relationship saturates, the parasite fitness at the epidemiological level (i.e., R0) is maximized for an intermediate level of virulence (van Baalen and Sabelis 1995). Such a saturating relationship has been shown empirically for instance for HIV in humans (Fraser et al. 2007) or for a protozoan parasite of monarch butterflies (de Roode et al. 2008).

In the context of multiple infections, one might be tempted to define a trade-off relationship for a co-infected host, with, for instance, an “overall transmission rate” that would be a function of the overall virulence. The conceptual problem with this is that the trade-off relationship depends on the host exploitation strategy of a parasite. It is because a parasite strain i uses a given amount of host resources (say Ri) for its transmission that virulence increases. In terms of virulence, we expect the deleterious effects of co-infecting strains to add up, especially if the two strains use the same type of host resources. However, the way these resources are converted into a transmission rate is likely not to be linear (which is consistent with equation (1)). Therefore, in a co-infection, there is no reason to expect that the sum of the transmission rates achieved by the two strains by using an amount of resources Rij and Rji, respectively, should be equal to the transmission rate that one strain would have achieved by using an amount of resources Rij+Rji. This is another illustration of the fact that in a co-infection the virulence depends on the density of all the co-infecting strains but the transmission rate of a strain depends only on its own density.

About overall virulence

We define a parasite strain i by its virulence (αi), which is here assumed to be the increase in host mortality it causes when infecting a host in a single infection. Importantly, because the parasite is not transmitted vertically, virulence needs to correspond to a decrease in the survival component of host fitness otherwise it does not affect the parasite’s R0 (Alizon et al. 2009).

A key step in the elaboration of co-infection models consists in defining the “overall-virulence,” that is the disease-induced mortality of co-infected hosts. The overall virulence can depend on the virulence of the two co-infecting strains and the link between these basically depends on the within-host interactions. For instance, if strains compete for host resources, the virulence is likely to be at least as high as the most virulent of two strains. If strains compete for a public goods they produce, then we can expect the overall virulence to be in between the virulence of the two strains. Finally, if there is spite between the two strains, the overall virulence can even be smaller than that of the two strains (for further details about the value of overall virulence and how it can affect evolutionary epidemiology of parasite virulence, see Buckling and Brockhurst 2008; Alizon 2008; Choisy and de Roode 2010; Alizon and Lion 2011).

As mentioned in Introduction, we assume that any interaction between co-infecting parasites can only originate from competition for host resources. As for the transmission rate, we can envisage two divergent scenarios: either the strains are competing for the exact same host resource, or they use completely different host resources. In the former scenario, it makes sense to assume that the overall virulence is the average of the virulence of the two strains (αij= (αij)/2). In the latter scenario however, an additive virulence (αijij) would make more sense because the deleterious effects on the host originate from different sources. Again, we can explore both scenarios when co-infections are caused by different parasite species but, for the case with co-infection by strains from the same species, the scenario with averaged virulence seems the only one to be biologically relevant.

Co-infection by two strains of the same species

We build upon the framework initially developed by van Baalen and Sabelis (1995), which is sketched in Figure 1A. The specificity of this setting is that it tracks hosts co-infected by the resident strain. The addition of this extra host class is necessary to remove the frequency-dependent advantage of the mutant strain and allow us to perform an unbiased invasion analysis (for further discussions on this point, see Alizon (2008) and Lipsitch et al. (2009)).

Figure 1.

Epidemiological model with co-infections by two strains of the same species (A) or by two different species (B). S, I and D stand for susceptible, infected and doubly infected hosts, respectively. The resident system is in black and the host classes linked to the mutant (on which the invasion analysis is performed) is in red. The subscript r and m stand for the resident or the mutant strain of the same species. In the two-species framework, there is one resident strain for each species (these are denoted 1 and 2) and one mutant strain of species 2 (denoted m). The dashed lines indicate co-transmission events.

In the case of infections caused by micro-parasites (i.e., viruses, bacteria and protozoa), the addition of the hosts doubly infected by the same strain has a technical motivation rather than a biological one. Indeed, if a host infected by a given strain is re-infected by the exact same strain, we do not expect to see a change in parasite load (and hence in virulence or transmission rate). We would thus expect hosts doubly infected by the same strain to behave similarly to singly infected hosts (the only difference being that they cannot be infected). This is why the scenario where parasite strains compete for the exact same resources in the host (αij= (αij)/2 and βiji/2) is the only one considered when infections are caused by strains from the same species. Note that this would not be the case if we were to consider infections caused by macroparasite because then the parasite load could increase upon re-infection by the same strain.

The equations capturing the dynamics of the resident system can be found in Appendix S1. If we assume that the total host population size is constant, the endemic equilibrium state (with the resident strain only) can be written as:

image

The notations are listed in Table 1. Note that increasing the co-transmission probability (ε) decreases the density of singly infected hosts at equilibrium and therefore increases the density of double infected hosts.

Table 1.  Notations used and default values. v indicates variables.
SymbolDescriptionDefault value
R 0 Basic reproduction number v
  Baseline mortality rate 0.1
Φ Host input rate v
S Density of susceptible hosts v
Ii Density of hosts singly infected by i v
Dij Density of hosts co-infected by i and j v
ε Probability of co-transmissionin [0, 1]
αi Virulence of a host infected by i v
αij Overall virulence of a host co-infected by i and j v
λi or ϕi Force of infection of strain i v
βi Transmission rate of i in single infection v
βij Transmission rate of strain i in a host co-infected by i and j v
b Proportionality constant for the trade-off relationship1
σS Scaling parameter for the sensitivity of susceptible hosts to infection 1
σI Scaling parameter for the sensitivity of infected hosts to co-infection1

As specified above, I conduct an invasion analysis and perturbate this resident state by adding a rare mutant strain (in red in Fig. 1A). The dynamics of the mutant strain (m) are governed by the following set of ODEs:

image(2a)
image(2b)
image(2c)

where inline image and λmm Imm1 D1m+ 2  βmm Dmm are the “force of infection” (Anderson and May 1991) of the resident and the mutant strain. As can be seen from equation (2a), co-transmission decreases the force of infection to move from the uninfected (S) to the singly infected (Im) class because some hosts move directly to a co-infected class (D1m or Dmm). Earlier studies neglected hosts infected twice by the mutant strain (eq. 2c) because they arose through second-order terms (if the mutant is very rare it is unlikely that the same host will be infected twice by the mutant). This is not the case here because this host class can be reached after only a single co-transmission event.

A final subtle underlying assumption has to do with what happens when a co-infected host encounters a singly infected host. According to our model, there is a probability ε that the doubly infected host passes on both its strains during the infection process. However, we only allow up to two strains per host. The simplifying assumption made to solve this issue is that the singly infected host only acquires the strain it does not already have. Overall we end up with the forces of infections (the term inline image in eq. (2b)) because the terms with and without co-transmission simplify.

We can calculate the dominant eigenvalue (denoted ρ) of the Jacobian matrix of system 2 (shown in Appendix S1). If ρ is strictly positive, it means that the mutant strain invades and replaces the resident (Diekmann and Heesterbeek 2000; Otto and Day 2007). By definition, an ES level of virulence (denoted α*) must satisfy the following conditions:

image(3a)
image(3b)

The first condition states that α* is an extremum value of the fitness function (ρ) and the second condition states that this extremum is a maximum. The ES level of virulence is a function of the probability of co-transmission (ε). Unfortunately the expressions are too complex to be written down here and I only show numerical results below.

Co-infection by different species

Studying co-infections by different species requires a different epidemiological framework because the presence of two species calls for two resident strains (one for each species). I here use the framework introduced by Choisy and de Roode (2010). In this setting, each of the two resident strains can be challenged by a mutant. For simplicity, co-infections are assumed to only occur between different species, that is that a mutant strain of species 1 cannot co-infect a host with the resident strain of species 1. Again, I modify Choisy and De Roode’s model by allowing for co-transmission of different species such that a host can switch directly from the uninfected class (S) to the class “co-infected by two parasite species” (D12), as shown in Figure 1B.

The analysis is done in the following way. We start from the equilibrium state in the population with two resident species (1 and 2). Equilibrium densities are denoted inline image, inline image, inline image, and inline image. We then assume that a mutant strain of species 1 emerges. This new mutant strain (denoted m) can only be found in two types of hosts: Im and Dm2 (because co-infection between two strains of the same species are not allowed). Assuming that the mutant is rare so that its emergence does not affect the equilibrium state, the invasion fitness of the mutant depends on the following equations:

image(4a)
image(4b)

where inline image and ϕmm Imm2 Dm2 are the forces of infection of the resident strain of species 2 and of the mutant strain of species 1. Again, the probability of co-transmission decreases the force of infection to go from the S class to the Im class. The invasion fitness of a rare mutant is calculated as explained above using the dominant eigenvalue of the Jacobian matrix of equation system 4 (Appendix S1).

An additional technical problem with this framework is that the resident equilibrium (inline image) cannot be found analytically and it is necessary to resort to numerical simulations in which first the value of ε is set, then the value of α1 is set, and then invasion analyses are performed to find the ES value of α2 (denoted inline image) given the other two variables. This is repeated for all values of ε and α1. In the end, this method yields the ES level of virulence of species 2 as a function of the probability of co-transmission (ε) and of the virulence of the other strain (α1).

If the system is symmetric, the results are identical when we derive the ES virulence of species 1 (inline image) as a function of the probability of co-transmission (ε) and of the virulence of the other species (α2). However, if there is asymmetry (e.g., in the transmission–virulence trade-off shapes), we need to repeat the same procedure but this time we replace species 1 by species 2 and investigate the invasion fitness of a rare mutant of species 2.

Once we can express the ESV of species 1 as a function of ε and α2 and the ESV of species 2 as a function of ε and α1, we can look for the coevolutionarily stable (coES) virulence, that is the virulence each species will achieve if they are allowed to coevolve (Choisy and de Roode 2010). This is done by plotting inline image as a function of α2 and inline image as a function of α1 on the same graph and looking for the intersection. If the system is symmetric, the two species have the same virulence α at the coESS, but if the system is asymmetric, each species has its own virulence at the coESS (inline image and inline image). Note that the coESS is a function of ε.

Contrary to the one-species framework, in the two-species framework there is no biological reason to make specific assumptions regarding the transmission rate from co-infected hosts and the overall virulence. I thus consider four scenarios. In scenario 1, I use the assumptions used in the one-species framework, that is that the two species compete for the exact same resource within the host (therefore, β121/2 and β212/2 and α12= (α12)/2). This allows me to compare the two frameworks. In scenario 2, I assume that the parasite species occupy completely different within-host niches so that their transmission rate are not affected by host sharing (i.e., β121 and β212) and the overall virulence is the sum of the virulence of the two species (α1212). In scenario 3, I use the assumptions of scenario 2 (additive overall virulence) but I also assume that the virulence of the two species is constrained by different transmission–virulence trade-off such that one of the two strains has a higher ES virulence in a system with single infections only. In this latter scenario, there is no symmetry anymore. This means that we need one set of ODEs to investigate the evolutionary dynamics of species 1 and another set of ODEs for species 2. The invasion dynamics of each species are then conducted separately.

Scenario 4 investigates co-infections by a helper and a defective strain, which are observed in several plant virus infections (see the Introduction). This scenario requires the modification of the expression of the forces of infection of the two-species framework. To have system 4 capture the dynamics of a mutant strain of the helper species (species 2 being the defective species), we need to set inline image and ϕmm Imm2 Dm2. To capture the dynamics of a mutant strain of the defective species (species 2 then being the helper species) we need to set inline image and ϕmm2 Dm2. In both cases, the density of singly infected hosts is removed from the expression of the force of infection of the defective species (both for a mutant or a resident strain). As in scenario 3, there is no symmetry and the evolutionary stable level of virulence of the helper species is likely to differ from the evolutionary stable level of virulence of the defective species.

Results

CO-INFECTIONS BY THE SAME SPECIES

Increasing the probability of co-transmission (ε) favors less-virulent strains (Figure 2A). In fact, when co-transmission is very likely, the evolutionarily stable level of virulence (ESV) is close to that expected in a system without co-infections (i.e., α*=μ).

Figure 2.

Evolutionary stable level of virulence (ESV) as a function of the probability of co-transmission (A) or as a function of the average multiplicity of infection in the host population (B). The dashed horizontal line indicates the ESV in a system with single infections only. In panel B, the average number of strains per host is increased either by increasing the probability of co-transmission (ε, in black) or by increasing the susceptibility of singly infected hosts (σI, in red). In both panels, the more co-transmissions, the more the ESV converges toward the level predicted for single infections. Parameter values are default (see Table 1).

In classical models, if parasites compete for host resources, increasing the prevalence of co-infection selects for more virulent strains (van Baalen and Sabelis 1995). This is because in co-infections the overall virulence depends on the strategy of the two strains but the transmission rate of a strain depends on its own strategy. Co-transmission counters this effect by tying together the fitnesses of the two co-infecting strains. If ε= 1, the two strains essentially behave as a single entity (they have the same virulence and the same transmission rate).

Increasing co-transmission also increases the average number of strains per host (i.e., the proportion of hosts that are co-infected). This number is usually expected to correlate with the selective pressure on virulence. This is shown by the red curve in Figure 2B, which was obtained by increasing the susceptibility of infected hosts to co-infections (parameter σI). Interestingly, if the increase in the prevalence of co-infections is due to an increase in co-transmission (parameter ε), then it can lead to a decrease in virulence (the black curve in Figure 2B). This result thus questions the use of co-infection prevalence as an indicator of the selective pressure on virulence.

CO-INFECTIONS BY DIFFERENT SPECIES

Scenario 1:Species using the same host niche

With co-infections caused by different parasite species, the results are slightly more complex because the ESV of species 2 (inline image) depends not only on the probability of co-transmission (ε) but also on the virulence of the other species (α1).

In Figure 3A, the ESV of species 2 (inline image) depends α1 in a non monotonic way. For any value of ε, increasing α1 (i.e., moving vertically from the bottom toward the top of the contour plot) first favors more virulent strains of species 2. This increase is due to the fact that species 2 needs to match species 1’s competitiveness at the within-host level, which requires an increase in virulence. However, when the virulence of species 1 becomes too high (α1 > rsim 0.3), increasing α1 selects for less virulent strains in species 2. This seemingly counter-intuitive result can only be understood by embracing the whole epidemiological dynamics. By being extremely virulent, species 1 is logically very competitive at the within-host level but it also “burns out” its host very rapidly. Therefore, in single infections, species 1 produces much less secondary infections than a less-virulent strain that would exploit host resources more efficiently. In a way, the virulence of species 2 decreases because it adapts to exploit singly infected hosts more efficiently rather than trying to compete at the within-host level.

Figure 3.

(A) ESV of species 2 (inline image) as a function of the probability of co-transmission (ε) and of the virulence of the second species (α1) with scenario 1 (species exploit the same host niche). (B) Same as panel A but for scenario 2 (species exploit different host niches). The dashed line indicates the ESV with single infections only. The thick black curve indicates the value of the coESV. In panel A, the dots indicate the areas where the system is not defined. Parameter values are default.

If we consider the effect of the probability of co-transmission (ε) on the ESV of species 2, we find results consistent with that found in the one-species model: increasing the probability of co-transmission (i.e., moving horizontally from left to right in Figure 3A) selects for less virulent strains in species 2 (inline image). However, if the virulence of the resident strain of the other species is very high (α1 > rsim 0.4), the pattern shifts and increasing ε leads to higher values of inline image. To understand this pattern, recall that for highly virulent species 1 strain, the evolutionarily stable strategy (ESS) of species 2 is to focus on the competition at the epidemiological level (through the exploitation of singly infected hosts) and sacrifice its competitiveness at the within-host level. This strategy is no longer an option when ε increases because co-infections are overrepresented in the population. As a consequence, species 2 cannot avoid adapting at the within-host level, whence the increase in virulence.

In the two-species framework, we can also determine the coevolutionarily stable virulence (coESV), that is the ESV that will be reached by each parasite species if they are allowed to coevolve. In this scenario we do not make specific assumptions regarding each species so the system is symmetric and the coESV is the same for the two species. This coESV is shown with a black thick curve in Figure 3A. As in the one-species framework, increasing the probability of co-transmission (ε) decreases the coES virulence. Interestingly, the coESV converges toward the ESV found with single infections only (the dashed line) as ε increases. This is because the co-infecting strains essentially behave as one entity (see also Appendix S1 for an analytical resolution of the case where ε= 1).

Finally, it is important to point out that the nonmonotonic behaviors only occur here if one of the species is extremely virulent to the host. This is more likely to occur if species 1 arrived in the system through migration recently and is not yet adapted to its new environment. If the two species are allowed to coevolve, observing such mismatches between the species (given that their virulence evolution is governed by the same trade-off relationship) is less likely.

Scenario 2: Species using different host niches

The two-species framework is heavier to analyze that the one-species framework but it also allows us to investigates scenarios where the two co-infecting strains differ. The contour plot in Figure 3B shows the ESV of species 2 (inline image) as a function of ε and α1 in a case where the species exploit different host resources and where the overall virulence is assumed to be the sum of the virulence of the two co-infecting strains.

As in the previous scenario, we find the relationship between inline image and α1 is nonmonotonic for any value of ε. The interpretation is the same as above: at first, species 2 should try to compete with species 1 but at some point it becomes more adaptive to sacrifice within-host competitivity to increase between-host competitivity (by evolving toward a virulence closer to the ESV in single infections).

The main difference with Figure 3A is that there is now also a nonmonotonic relationship between inline image and ε. This pattern is less intuitive to explain because it interacts with the virulence of the other species (α1). When α1≲ 0.3 (i.e., when species 1 is not too maladapted in single infections), increasing co-transmission selects for less virulent strains of species 2. This is consistent with what we found in the model with one species, that is that the interests of the two parasite strains (here species) become aligned and there is no point in competing at the within-host level through increased virulence. If species 1 has a high virulence (the upper part of the Figure 3B), increasing co-transmission selects for higher values of inline image. Again this is because the more ε increases, the more avoiding competition at the within-host level becomes impossible. The pattern that differs from scenario 1 is that if ε increases even further, we again see a decrease in inline image. This is because the interests of the two species become so aligned that species 2 actually evolves toward lower levels of virulence to compensate for the maladaptation of species 1. In other words, co-transmission selects for cooperative behavior between parasite of different species.

The coESV (black thick line in Figure 3B) decreases as a function of the probability of co-transmission (ε). Interestingly, in this scenario the existence of co-infections can lead to the evolution of a virulence lower than the ESV in single infections (the dashed line) if the value of ε is high enough. This is due to the conjecture of two factors: first the two species have increasingly tied fitness and second the overall virulence is the sum of the virulence of the two strains.

Scenario 3: Species with different trade-offs

I now extend scenario 2 by assuming that the two species exploit their hosts differently so that their transmission–virulence trade-off relationships differ. For species 1, I use the default relationship (inline image) but for species 2 I assume that inline image. The ESV of species 1 in single infections only is still equal to μ (the host base-line death rate) but that of species 2 is equal μ/2. I will thus refer to species 1 as the “virulent” species in the following.

We now need two contour plots (one for each species) because the system is not symmetric anymore. In both cases (Figure 4A and B), we see the nonmonotonic pattern already in response to variations in virulence of the other species. Furthermore, if the other species has a low virulence (approximately lower than 0.2), then the trends are similar for the two species: increasing the probability of co-transmission decreases the ESV. For both species, we also observe the nonmonotonic effect in terms of ε described above: at first the ESV increases with ε but when ε becomes large the ESV decreases. One difference with our earlier results is that for the less-virulent species (species 2, Fig. 4A) this nonmonotonous effect occurs for intermediate virulence values of the other species, whereas for the virulent species (species 1, Fig. 4B) it only occurs if the other species has a high virulence. Another difference between the two species is that, for the virulent species, the highest level of virulence is observed for low values of ε, whereas for the less-virulent species they are observed for ε≈ 1.

Figure 4.

(A) ESV of the less-virulent species (inline image) as a function of the probability of co-transmission (ε) and of the virulence of the “virulent” species (α1), (B) ESV of the virulent species (inline image) as a function of the probability of co-transmission (ε) and of the virulence of the “less-virulent” species (α2) and (C) coESV for the virulent species (in red) and the virulent species (in black). The dotted lined in panel C indicate the ESV with single infections only for each species. Parameter values are default.

When we consider the virulence of each species at the coESS, we find that, as expected, they both decrease as a function of ε (Figure 4C). An interesting pattern occurs when the probability of co-transmission becomes extremely high: the ES virulence of the “virulent” species drops below that of the “less-virulent” species. The reason for this is that when ε is close to 1, the transmission of a species depends as much on its own transmission rate than on that of the other species. Because the “virulent” species faces an even more saturating trade-off than the “less-virulent” species and because their interests are largely aligned, it is more advantageous for the “virulent” strain to virtually stop exploiting the host and rely on the performance of the “less-virulent” strain.

Scenario 4: Helper versus defective species

We now consider the scenario where species 1 can only be transmitted from a co-infected host because it requires molecules produced by species 2. This is often observed among plant viruses. Note that obligate co-infections is not the same as obligate co-transmission because in the former there still is a probability 1 −ε that only one parasite is transmitted. However, as shown in Figure S1, the defective species can only persist in the system if there is some co-transmission (ε > rsim 0.3 with our parameter values).

We are again in an asymmetric case. Therefore, to find the coES virulences, we first need to plot the ESV of the helper species (inline image) as a function of the virulence of the defective species (the plain lines in Fig. 5) and then the ESV of the defective species (inline image) as a function of the virulence of the helper species (the dotted lines in Fig. 5). The coES virulences are found at the intersection between the two lines.

Figure 5.

Evolutionary dynamics of the helper species (plain lines) and the defective species (dotted lines) for low co-transmission (ε= 0.35 in black), medium co-transmission (ε= 0.5 in red) and high co-transmission (ε= 0.9 in blue). coESV are at the intersection between plain and dashed lines from the same color. The gray curve goes through the coESV for increasing values of ε. The gray dot indicates the coESV when the two species always co-transmit.

For the lowest sustainable co-transmission probability, the coES virulence of both species is close from the ESV found without co-infections (inline image). When the probability of co-transmission increases (the gray thick curve in Fig. 5), we observe a pronounced decrease in the coESV of the defective species and a slight increase in the coESV of the helper species. In fact, for a range of values of ε the coESV of the helper species is greater than its ESV in single infections. When the probability of co-transmission increases even more, the coES virulence of both species decreases and converges toward the unique equilibrium observed when co-transmission is obligatory (ε= 1), which is inline image (see Appendix S1 for further details).

Note that in this example we assumed that the two parasite species only differ from their ability to be infectious in singly infected hosts (for instance, the transmission–virulence trade-off relationships are the same for the two species), but this is sufficient to generate an asymmetry in the coESV observed for each species when they are allowed to coevolve.

Discussion

Co-transmission, which is defined here as the infection of a host by more than one parasite strain or species during the same transmission event, has been shown to occur for many parasites species. The probability of co-transmission modifies the epidemiology of the parasite and can therefore be expected to have important consequences for virulence evolution.

If co-infections are caused by different strains from the same species, I show that increased probabilities of co-transmission favor less-virulent strains. If co-infections are caused by strains from different species, this needs not be the case and, depending on the virulence of species 1, increasing the probability of transmission can select for higher or lower levels of virulence in species 2. The coevolutionary stable level of virulence, which is reached if the two species are allowed to coevolve for a long time (and if the co-transmission rates are the same for the two species) always decreases as a function of co-transmission. This is due to the assumption that co-infecting strains only interact in a host through competition for host resources (e.g., red blood cells for Plasmodium or CD4+ T-cells for HIV). It is known that parasites can exhibit a wide range of interactions, such as production of public goods or spite (Mideo 2009), and the exact type of within-host interaction is very likely to determine virulence evolution. However, a significant advantage of focusing on competition for host resources is that the predicted evolutionary outcome in this case is clear whereas in the case of public-goods producing parasites, for instance, the direction of virulence evolution strongly depends on epidemiological feedback (Alizon and Lion 2011). As the goal of this study is to investigate the effect of co-transmission on virulence evolution, it is simpler to study the deviations from robust predictions.

One of the consequences of co-transmission is that it leads to increased prevalence of co-infections in the host population. Such increases have long been expected to correlate with selection for higher levels of virulence (van Baalen and Sabelis 1995). More recently, it has already been argued that within-host interactions should be considered before looking at the average number of strains per host. Indeed, if parasites produce public goods within a host, a lower relatedness between co-infecting parasites favors less-virulent strains (Brown et al. 2002; Buckling and Brockhurst 2008). Here, I show that even if parasite competes for host resources, the number of strains per host can be a poor predictor of the direction of virulence evolution because the way parasites are transmitted matters. In other words, a high prevalence of co-infections can select for more virulent strains if this increase is due to an increased sensitivity of singly infected hosts to co-infection, or it can select for less-virulent strains if the high prevalence is due to increased co-transmission.

I also consider asymmetric scenarios, for example co-infection by helper versus defector viruses, as observed in several plant virus species. The asymmetry in the system (the fact that one of the virus species is not infectious in single infections) can generate asymmetry in terms of evolutionary stable levels of virulence. In particular, I show that, at first, increasing the probability of co-transmission selects for more virulent strains in the helper parasite species. Increasing this probability of co-transmission even further selects for lower virulence in both the helper and the defective species. As expected, the system converges toward a symmetric coESS where the two virus species have the same virulence (this is because the two species are assumed to differ only in their ability to be infectious in single infections or not). Note that, with our assumptions, the defective species is always less-virulent than the helper species.

This study underlines the importance of distinguishing between co-infections by different strains of the same species or by different strains of different species. Each requires a specific framework and, even with the same biological assumptions regarding parasite transmission from co-infected hosts and overall virulence, the two-species framework leads to more complex dynamics than the one-species framework because the ESV of a species depends on the virulence of the other species. Note that the two-species framework is less rigid in terms of biological assumptions. For instance, one can assume that the two species have different transmission–virulence trade-offs. I show that this can lead to counter-intuitive results, such as the virulence of the “virulent” species becoming lower than that of the “less-virulent” species for high co-transmission probabilities.

I focused on horizontally transmitted parasites but similar questions occur for vertically transmitted parasites. Co-transmission is a key aspect of co-infections between such parasites and several studies have considered the evolution of strategies to fight or enforce co-transmission (Vautrin and Vavre 2009). I also made assumptions concerning the shape of the transmission–virulence trade-off curve. However, this should not affect the results qualitatively because the sole role of the trade-off relationship here is to generate an intermediate ESV and this will be achieved for any saturating trade-off curve (van Baalen and Sabelis 1995). The exact shape of the relationship would be much more critical if parasites were to compete for public goods they produce in the host (Alizon and Lion 2011).

These result can be analyzed in the light of earlier results on the evolution of cooperation. In particular, one of the mechanisms that explains how cooperation can evolve between unrelated individuals is repeated interaction, because it generates a link between the fitness of the two individuals (what Sachs et al. 2004, call the “partner fidelity feedback”). In our case, if there is a high probability of co-transmission, two parasites that are “trapped” in the same host are likely to be co-transmitted several times and thus interact repeatedly. Still in our case, a cooperative strategy for a parasite consists in not competing too much against co-infecting strains, that is in having a host exploitation strategy close from the ESS in single infections. Note that this result can also be analyzed in terms of kin selection because the co-transmission de facto increases the probability that two parasites sampled from the same host are identical by descent (see Lion et al. 2011, for further details on the interchangeability of different methods to study the evolution of cooperation).

There is also an interesting parallel to make between this host–parasite system and “budding dispersal” (Pollock 1983; Goodnight 1992; Gardner and West 2006). Kin selection approaches predict that if individuals are allowed to disperse from a patch as a small group rather than individually, which allows to preserve a high degree of relatedness among individuals, this leads to a decrease in the level of competition among kin that typically occurs when there is local (individual) dispersal. As a consequence, the ability of cooperators to invade increases with the size of the group that disperses. Here, I obtain a similar outcome with the difference that the level of cooperation of a strain is inversely proportional to its virulence (as in Frank 1996).

In this analysis, the whole range of values for the probability of co-transmission was explored. This probability can be high for co-infections by difference species and several plant viruses have long be known to only co-transmit (see e.g. Pirone and Blanc 1996). Recent studies suggests that this probability could be high, even for strains of the same species. First, Ohnishi et al. (2011) found that two strains of the Tomato yellow leaf curl virus infecting the same whitefly tend to co-transmit most of the time when infecting new hosts (even if this could be an effect of the experimental conditions). Second, relatedness of co-infecting strain of P. falciparum is high suggesting an infection by the same mosquito (Nkhoma et al. 2012). Third, Karvonen et al. (2012) showed that infection was more successful when a fish host is challenged by mixed genotypes of trematode parasite. Their interpretation is that co-exposure compromises the immune system.

This study shows that knowing how species interact within a host it not sufficient to predict the effect of multiple infections on virulence evolution and that it is necessary to understand the details of the transmission process. Furthermore, there is a clear lack of data on co-transmission even though this process could prove to be essential to understand the link between multiple infections and virulence evolution.


Associate Editor: S. West

ACKNOWLEDGMENTS

I thank S. Blanc, L. Lambrechts, S. Lion, F. Luciani, and F. Renaud for discussion, M. Hartfield for comments on the manuscript and two reviewers for their careful reading and their suggestions. I am funded by the CNRS and the IRD and by an ATIP-Avenir grant from CNRS and INSERM.

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