Coinfecting parasites can modify fluctuating selection dynamics in host–parasite coevolution

Abstract Genetically specific interactions between hosts and parasites can lead to coevolutionary fluctuations in their genotype frequencies over time. Such fluctuating selection dynamics are, however, expected to occur only under specific circumstances (e.g., high fitness costs of infection to the hosts). The outcomes of host–parasite interactions are typically affected by environmental/ecological factors, which could modify coevolutionary dynamics. For instance, individual hosts are often infected with more than one parasite species and interactions between them can alter host and parasite performance. We examined the potential effects of coinfections by genetically specific (i.e., coevolving) and nonspecific (i.e., generalist) parasite species on fluctuating selection dynamics using numerical simulations. We modeled coevolution (a) when hosts are exposed to a single parasite species that must genetically match the host to infect, (b) when hosts are also exposed to a generalist parasite that increases fitness costs to the hosts, and (c) when coinfecting parasites compete for the shared host resources. Our results show that coinfections can enhance fluctuating selection dynamics when they increase fitness costs to the hosts. Under resource competition, coinfections can either enhance or suppress fluctuating selection dynamics, depending on the characteristics (i.e., fecundity, fitness costs induced to the hosts) of the interacting parasites.

Furthermore, ecological factors can alter genetic specificity in determining parasite infection success (Sadd, 2011;Zouache et al., 2014), which could affect the ability of parasites to induce frequency-dependent selection on their hosts. Therefore, ecological factors contributing to and creating variation in the outcome of host-parasite interactions could be important in determining the potential for fluctuating selection dynamics in host-parasite coevolution.
Importantly, these effects could modify selection between hosts and parasites, depending on the composition of the coinfecting parasite community.
Earlier, in a related field of parasite-mediated selection for sex, coinfections by multiple parasite species have been suggested to be important, as the combined effect of coinfecting parasites could reduce host fitness enough for sexual reproduction to be favored by selection (Hamilton, Axelrod, & Tanese, 1990). The same could enhance fluctuating selection dynamics if several parasite species, each having only a weak negative impact on host fitness, track the host genotypes in a frequency-dependent manner. Many parasites, however, do not show strict genetic specificity to their hosts, but can infect different host genotypes and even species (reviewed in Schmid-Hempel, 2011). Nonetheless, such generalist parasites could alter the performance of hosts and their genetically specific parasites through the above-mentioned interaction mechanisms and this way contribute to fluctuating selection dynamics.
Here, we formally examined if and how coinfections by a genetically nonspecific generalist parasite could contribute to fluctuating selection dynamics between a host and its genetically specific parasite using numerical simulations. We modeled host population dynamics and parasite epidemiology under three different scenarios: (a) when hosts coevolve with a single parasite species that must genetically match the host to infect, (b) when hosts are also exposed to a genetically nonspecific parasite species that increases fitness costs to the hosts in coinfections (coinfection does not alter parasite performance compared with single infections), and (c) when coinfecting parasites compete for the shared host resources (coinfection does not increase host fitness costs compared with the mean of single infections). We focused on these two coinfection scenarios because of their contrasting effects on host and parasite fitness, as well as their likely commonness in nature (e.g., some parasites use the same and some different host resources). Our model shows that the presence of coinfecting parasites can strongly impact fluctuating selection dynamics. Coinfections can enhance fluctuating selection dynamics when they increase fitness costs to the hosts. Under resource competition, coinfections can either enhance or suppress fluctuating selection dynamics, depending on the characteristics (i.e., fecundity, fitness costs induced to the hosts) of the interacting parasites.

| MODEL
Our simulation is based on the epidemiological model by Lively (2010b), which incorporates two ecologically relevant aspects that are likely to be important. First, it considers host fitness to be density-dependent. Second, it does not define the probability of infection as simply a function of the frequency of the matching parasite genotype, but considers the numerical feedbacks from the parasite population. This is important because epidemiological dynamics can influence host-parasite coevolution (e.g., Gokhale, Papkou, Traulsen, & Schulenburg, 2013;MacPherson & Otto, 2018). The model by Lively (2010b) assumes discrete generations (one generation per time step) in which the resistance of sexually reproducing individuals to infection is determined by two loci each having three alleles (giving nine genotypes). We used similar discrete time steps, but because our model is not connected to the question of sexual/ asexual reproduction we simplified the original model by assuming that hosts reproduce clonally. We did not reduce the number of host genotypes from nine to two, although only two are commonly used in other theoretical studies (e.g., Gokhale et al., 2013;MacPherson & Otto, 2018;Song, Gokhale, Papkou, Schulenburg, & Traulsen, 2015).
We chose to use nine host genotypes to increase the ecological relevance of the model (see Dybdahl & Lively, 1998;Jokela et al., 2009;Little & Ebert, 1999) and because the pilot runs of the simulation indicated an increased role of stochasticity in determining host population dynamics when only two genotypes were used.
To examine the potential role of interactions between coinfecting parasites on fluctuating selection dynamics, our model assumed that hosts can be exposed to two different horizontally transmitted parasite species. Parasite species A is genetically specific: Each genotype is only able to infect one of the host clones (i.e., a matching allele model [see Agrawal & Lively, 2002] that reflects self-nonself recognition in invertebrates [Frank, 1993;Luijckx, Fienberg, Duneau, & Ebert, 2013]). All host clones are, however, exposed to all parasite genotypes, but parasites that do not match the host are eliminated by host defenses. On the other hand, parasite species B is genetically nonspecific and able to infect all host genotypes. We chose these two parasite types because genetic specificity in determining the outcome of a host-parasite interaction (here parasite A) is required for fluctuating selection dynamics, but many parasite species do not show strict genetic specificity (here parasite B) being able to infect a broad range of different host genotypes and even different host species (reviewed in Schmid-Hempel, 2011). Therefore, owing to the commonness of coinfections in nature, these parasite types are likely to often interact.
We examined fluctuating selection dynamics under two different scenarios of interactions between the parasite species. In the first scenario, we assumed that in coinfections, parasites use different host resources, but exploit hosts with the same efficiency as in single infections. Therefore, coinfections increase fitness costs to the hosts. We chose this increase to be multiplicative rather than additive. Multiplicative increase in fitness costs is possible, for example, if one parasite species reduces the host's ability to detect resources and the other parasite reduces the efficiency of resource use after detection. Additive effects of coinfections on host fitness are also likely in nature. These interaction types are, however, conceptually similar. Our choice to use multiplicative effects is based on their stronger impacts on hosts, which makes it easier to evaluate whether interactions that reduce host fitness could potentially alter fluctuating selection dynamics. In this scenario, coinfections did not affect parasite performance.
In the second scenario, we assumed that coinfecting parasites compete for the shared host resources. For simplicity, we did not consider variation in parasite within-host growth rate. Furthermore, we did not specifically model possible priority effects in resource use in sequential coinfections (e.g., Clay, Dhir, Rudolf, & Duffy, 2019;Hoverman, Hoye, & Johnson, 2013). This was because we conducted modeling at the population level. Thus, we assumed that, on average, each coinfecting species has access to 50% of the available host resources. We also assumed that each species uses these resources with the same efficiency as the resources available in single infections. Therefore, reduced availability of host resources for each parasite species in coinfections reduces parasite fecundity to one half of their reproductive output in single infections. Consequently, the fitness cost of coinfection to the hosts was equal to the mean of the costs experienced in single infections. Host fitness was density-dependent following the formulation by Maynard Smith and Slatkin (1973): and for uninfected hosts and hosts infected with parasite A and parasite B (single infections), respectively. In these equations, b U is the reproductive output of uninfected hosts when competition is absent, b I(A) is the reproductive output of hosts infected with parasite A when competition is absent, b I(B) is the reproductive output of hosts infected with parasite B when competition is absent, a is a parameter that scales the effect of the total host density on host reproductive output, and N is the total host population density. Note that the effects of infections and host population density on host reproductive output can arise from both differences in host fecundity and survival. Here, we used the same a for uninfected and infected individuals, hence infection reduced host fecundity, but it did not make infected individuals more sensitive to competition. When defined this way, the cost of infection to the hosts induced by parasites A (C A ) and B (C B ) become (1) and for all host densities, and the population dynamics are stable for all values of b (Doebeli & de Jong, 1999;Lively, 2010b where β A is the number of parasite propagules produced by each singly infected host, β AB is the number of parasite A propagules produced by each coinfected host (scenario 1: β AB = β A ; scenario 2: is the density of hosts of genotype i that are infected with parasite A only, G iI(AB) is the density of coinfected hosts of genotype i, and Nʹ is the total host population density at time point t + 1. The term (β A G iI(A) + β AB-G iI(AB) )/Nʹ gives the Poisson mean number of exposures per host. The number of produced parasite propagules (i.e., the numerator in the equation) is divided by the total host population density in the next generation because host individuals are exposed to all parasite genotypes but only those that genetically match the host lead to infections.
The exponential term gives the probability of not being exposed by a In the second phase of each simulation run, the host population was invaded by nine individuals (one per clone) infected with the genetically nonspecific parasite species B. In scenario one, this parasite used different host resources than parasite A, which increased the costs of infection to the hosts. In scenario two, parasites competed for the shared host resources (the fitness cost of (3b)  when C B = 0.9). This way we could examine the effects of coinfecting parasites that have different frequencies in the host population.
We chose the levels of fitness costs induced to the hosts to cover a broad range of parasites with different potential to control for host population density. If infecting the host population alone, a

| Epidemiological and fluctuating selection dynamics in one host-one parasite interaction
The examined parameter space over different levels of parasite fecundity and host fitness costs showed separation into regions with distinct epidemiological and coevolutionary features ( Figure 1).
When parasite fecundity β A was nine (i.e., equal to the number of host clones) or lower, parasites did not spread in the host population (the completely white region 1 in Figure 1a), they did not control for the host population density (Figure 1b,c), and did not lead to fluctuations in host clone frequencies (Figures 1d and 2a). The inability of the parasite to spread in the host population was most likely because when, on average, 8/9 of the parasite propagules die when contacting nonmatching host genotypes the basic reproductive number of the parasite is less than one (Lively, 2010a).
When parasite fecundity was higher than the number of host clones in the population, the parasites spread. The subsequent effects on the host population dynamics, however, depended on the level of fitness costs of infection to the host (Figure 1). When the costs were low to moderate, increasing parasite fecundity rapidly led to high infection prevalence (dark blue region 2 in Figure 1a) and infections kept the host population density constantly at a reduced level (Figure 1b,c). Under these conditions, host clone frequencies did not fluctuate over time (Figures 1d and 2b). The above dynamics, however, changed when the fitness costs of infection increased, unless parasite fecundity was very high. When the parasite reduced host fitness, for example, by 80% and parasite fecundity was 20

F I G U R E 2
Examples of the dynamics of host clone frequencies (nine clones) in individual runs of the simulation representing regions of parameter space with different epidemiological and/or coevolutionary dynamics (numbers 1-4 in Figure 1a). (a) Parasite-induced fitness costs to the hosts (C A ) and parasite fecundity (β A ) are 0.5 and 5, respectively (region 1 in Figure 1a), (b) C A and β A are 0.5 and 20, respectively (region 2 in Figure 1a), (c) C A and β A are 0.8 and 20, respectively (region 3 in Figure 1a), (d) C A and β A are 0.9 and 20, respectively (region 4 in Figure 1a)   required for fluctuating selection dynamics when parasite fecundity increased (Figure 1d).
When the fitness costs of infection were even higher than above (e.g., 90% reduction in host fitness) and parasite fecundity was 20 (or any other values in the almost white region 4 in Figure 1a), the coevolutionary dynamics changed again (Figures 1d and 2d). Now, alterations in host clone frequencies were detected periodically, but these reflected extinction and recolonization dynamics of host clones, rather than fluctuating selection dynamics (see generations 1900-1940 in Figure 2d). This was because highly harmful parasites drove the host clones quickly to extinction. These clones recovered only after the immigration of new individuals into the population.
However, those clones were pushed back to extinction quickly after the parasite invaded the population owing to the immigration of an infected host individual. Furthermore, clone frequencies were stable when parasites were extinct (see generations 1940-1990 in Figure 2d).

| Fluctuating selection dynamics in one hosttwo parasites interactions
The above coevolutionary dynamics were affected by the presence of the coinfecting genetically nonspecific parasite species (Figures 4   and 5). When the parasites used different host resources, thus increasing the fitness costs of infection to the hosts (scenario 1), coinfections enhanced fluctuating selection dynamics (Figure 4). This effect was, however, clearly detected only when the genetically nonspecific parasite species was highly harmful to its hosts (see Figure 4 for C B being equal to or higher than 0.7). Furthermore, the effect got stronger with the increasing fecundity and thus the prevalence were low to moderate ( Figure 5). This is likely to be because such a coinfecting species would frequently interact with the genetically specific parasite but not limit fluctuations in densities of host clones as it would not strongly reduce host population size. However, when the fecundity of the coinfecting genetically nonspecific parasite species was high (β B = 2.6; i.e., it was common in the host population) coinfections suppressed fluctuating selection dynamics ( Figure 5) as even maximal reduction in host fitness induced by the genetically specific parasite could not lead to fluctuating selection dynamics.

| D ISCUSS I ON
Individual hosts are often infected with multiple parasite species and genotypes that interact (reviewed in Holmes & Price, 1986;Read & Taylor, 2001). These interactions are expected to be important for key evolutionary processes in host-parasite interactions including selection for higher virulence (reviewed in Alizon, de Roode, & Michalakis, 2013) and the maintenance of genetic polymorphism in parasite traits (reviewed in Seppälä & Jokela, 2016). Additionally, increased fitness costs to the hosts owing to multiple infections have been proposed to strengthen parasite-mediated selection for sex (Hamilton et al., 1990). In this study, we expanded the investigation on evolutionary consequences of coinfections to their potential role in host-parasite coevolutionary dynamics. We formally examined if and how fluctuating selection dynamics between coevolving host and parasite populations could be modified by the presence of another parasite species that does not track its hosts in a genetically specific manner but (a) increases fitness costs of infection to the hosts or (b) competes for the shared host resources with the coevolving parasite. We found that interactions that increase fitness costs to the hosts can enhance fluctuating selection dynamics.
However, resource competition among parasites can both enhance and suppress coevolution, depending on the characteristics (i.e., fecundity, harmfulness to the hosts) of the interacting parasites.
Our results on fluctuating selection dynamics in a single hostsingle parasite interaction are in line with earlier findings suggesting that coevolutionary fluctuations are likely to take place only with certain combinations of parasite fecundity and fitness costs of infection to the hosts (see e.g., Lively, 2010b;May & Anderson, 1983).
Specifically, fluctuating selection dynamics required high costs of infection to the hosts (C A > 0.6, depending on parasite fecundity) that induce strong parasite-mediated selection. However, very high costs led to host population dynamics that were mainly driven by temporal extinctions of the host and parasite genotypes. The requirement for "sufficiently high" costs of infection could limit the occurrence of fluctuating selection dynamics in natural systems.
This is because many host species may not be frequently exposed to parasites that are harmful enough. The above-mentioned idea of Hamilton et al. (1990) that suggests that simultaneous infections with multiple parasite species, each having a weak negative impact on their hosts, could lead to a total reduction in host fitness that is high enough to favor sexual reproduction could also hold for fluctuating selection dynamics. This would be the case when several mildly harmful parasite species simultaneously track the host genotypes in a frequency-dependent manner.
Many parasites, however, do not show strict genetic specificity to their hosts. Although such parasites cannot induce frequency-dependent selection on their hosts, they could still contribute to fluctuating selection dynamics by being part of the coinfecting parasite community. This is because coinfecting parasites often interact (e.g., Adams et al., 1989;Bashey et al., 2012;Patrick, 1991).
Our study suggests that such interactions can be highly import- In scenario one, the presence of the coinfecting parasite species and the increased fitness costs to the hosts in coinfections should lead to stronger control of the host population density by the parasites compared with the single host-single parasite interaction.
Therefore, lower host densities that reduce the transmission potential of the genetically specific parasite can be expected. This would prevent a parasite that is not highly harmful to its hosts from spreading to a high and constant prevalence in the host population but instead inducing fluctuating selection dynamics (see the mechanism in Figure 3). Similarly, in scenario two, the presence of the coinfecting parasite that reduces the reproductive output of the genetically specific species would prevent it from driving host clones to extinction even if it was highly harmful to its hosts. However, the observed increase in the range of levels of fitness costs to the hosts induced by the genetically specific parasite leading to fluctuating selection dynamics would not be expected if only the mean changes in fitness costs to the hosts and parasite fecundity in coinfections contributed to epidemiological and coevolutionary dynamics. Thus, variation in both host and parasite performance when coinfections take place (i.e., some host individuals are infected with one and some with two parasite species) is likely to be important.
Because our results on the effects of coinfections on epidemiological and coevolutionary dynamics are likely to be explained by their impact on the ability of the genetically specific parasite to spread in the host population and to drive host clones to extinction also other ecological/environmental factors that modify host and parasite performance could have conceptually similar effects.
For instance, resource availability and ambient temperature are well known to induce within-population variation in host and parasite traits (see Brown et al., 2000;Guinnee & Moore, 2004;Krist et al., 2004;Paull & Johnson, 2011;Seppälä et al., 2008). To our knowledge, however, the potential effects of such factors on fluctuating selection dynamics have not been examined. Thus, our model gives the first insights on how ecological/environmental factors may affect fluctuating selection dynamics when host and parasite performance in the two coevolving populations is affected by external factors. The effects of other factors than coinfections should, however, be modeled separately. This is because changes in factors such as resource availability and ambient temperature are likely to follow different spatial and temporal dynamics than the epidemiology of coinfecting parasites that we modeled in this study.
Although the role of ecological/environmental factors on fluctuating selection dynamics in host-parasite interactions has not been examined before this study, earlier theoretical work has considered the combined effects of epidemiological and coevolutionary dynamics in host and parasite populations (e.g., Gokhale et al., 2013;MacPherson & Otto, 2018). Those studies suggest epidemiological dynamics to suppress coevolutionary cycles. However, our study, as well as the model by Lively (2010b) that was used as a basis for our simulation, both demonstrate fluctuating selection dynamics although they allow epidemiological dynamics. Additionally, most theoretical studies on host-parasite coevolution, including ours, assume host and parasite populations to be completely mixed and thus the encounters between the interacting partners to be random. Certain host and parasite types may, however, be clustered spatially, which could modify infection dynamics. For example, the aggregation of hosts into family groups can suppress coevolutionary fluctuations (Greenspoon & Mideo, 2017). Thus, also other deviations from random encounters such as vertical transmission could be important. Therefore, we argue that future studies should not only examine the possible effects of new factors on host-parasite coevolution but also their combined effects. We find it especially relevant to investigate how factors that can enhance fluctuating selection dynamics (e.g., certain coinfections) interact with factors that are known to suppress it (e.g., epidemiology, parasite transmission among relatives).

ACK N OWLED G M ENTS
We are grateful to A. F. Read for helpful discussions and anonymous reviewers for commenting on the manuscript. The Genetic Diversity Centre (GDC), ETH Zurich, provided the computing hardware. The study was funded by the Emil Aaltonen Foundation and the Swiss National Science Foundation (grant 31003A 169531) to OS.

CO N FLI C T O F I NTE R E S T S
We declare we have no competing interests.

DATA AVA I L A B I L I T Y S TAT E M E N T
No data were used.