Evolution of Multihost Parasites

EVOLUTION INTERNATIONAL JOURNAL OF ORGANIC EVOLUTION PUBLISHED BY THE SOCIETY FOR THE STUDY OF EVOLUTION Vol. 58 March 2004 No. 3 Evolution, 58(3), 2004, pp. 455–469 EVOLUTION OF MULTIHOST PARASITES SYLVAIN GANDON Génétique et Evolution des Maladies Infectieuses, UMR CNRS/IRD 2724, Institut de Recherche pour le Développement, 911 Avenue Agropolis, 34394 Montpellier Cedex 5, France E-mail: gandon@mpl.ird.fr Abstract. Multihost parasites can infect different types of hosts or even different host species. Epidemiological models have shown the importance of the diversity of potential hosts for understanding the dynamics of infectious disease (e.g., the importance of reservoirs), but the consequences of this diversity for virulence and transmission evolution remain largely overlooked. Here, I present a general theoretical framework for the study of life-history evolution of multihost parasites. This analysis highlights the importance of epidemiology (the relative quality and quantity of different types of infected hosts) and between-trait constraints (both within and between different hosts) to parasite evolution. I illustrate these effects in different transmission scenarios under the simplifying assumption that parasites can infect only two types of hosts. These simple but contrasted evolutionary scenarios yield new insights into virulence evolution and the evolution of transmission routes among different hosts. Because many of the pathogens that have large public-health and agricultural impacts have complex life cycles, an understanding of their evolutionary dynamics could hold substantial benefits for management. Key words. Epidemiology, evolution, parasite, transmission, virulence. Received July 2, 2003. Accepted October 23, 2003. Multihost parasites can infect and exploit different types egies of the different habitats by, for example, evolving more of host. These types refer to different variants (i.e., genotypes intense exploitation (virulence evolution) of better-quality or phenotypes) within the same host species or to different hosts. Second, the parasite may evolve habitat choice strat- host species (Taylor et al. 2001; Woolhouse et al. 2001; Hay- egies (transmission evolution) to infect better-quality hosts. don et al. 2002; Holt et al. 2003). In particular, most emerging The evolution and the coevolution between virulence and human, domestic animal, and wildlife diseases are caused by transmission may yield very different parasite life cycles. For parasites infecting multiple host species (Taylor et al. 2001). example, evolution in multihost environments may yield one Several epidemiological studies have shown how the mul- (or several) specialist strategies able to exploit only a single tiplicity of potential hosts can affect the dynamics of infec- host type, and/or a generalist parasite strategy able to exploit tious disease (Anderson and May 1991; Dushoff 1996; Hess all these different hosts. Which factors govern the ultimate 1996; Woolhouse et al. 1997, 2001, 2002; Diekmann and evolutionary and coevolutionary outcomes? Heesterbeek 2000; Haydon et al. 2002; Roberts and Hees- Here, I present a general theoretical framework for the terbeek 2003; Holt et al. 2003). This theoretical knowledge study of parasite life-history evolution in a multihost context. may help to design intervention measures. In particular, iden- This framework is derived from simple epidemiological mod- tifying and managing reservoirs of multihost parasites plays els and can be used to derive evolutionary stable virulence a crucial role in effective disease control (Haydon et al. 2002). and transmission strategies. This analysis demonstrates the Despite the proliferation of epidemiological studies, the importance of epidemiology (the relative quality and quantity evolutionary consequences of multihost life cycles remain of different types of infected hosts) and of the constraints largely overlooked as classical models of virulence evolution among the different evolving traits (both within and between focus on simpler, single-host systems (Frank 1996; Wool- different hosts). I illustrate the potential use of this model house et al. 2001). Because the machinery required for in- through different examples under various ecological and evo- fection, exploitation, and transmission is likely to vary from lutionary assumptions. I begin with an analysis of the evo- one host to another, the selective pressures acting on parasites lution of parasite exploitation strategies and virulence under in different hosts may also vary. How should a parasite re- different transmission patterns. Next, I focus on the special spond to this heterogeneity of their environment (i.e., host case of the evolution of indirect (e.g., vector-borne) trans- diversity)? First, the parasite may alter its exploitation strat- mission and its coevolution with parasite virulence. These 455 q 2004 The Society for the Study of Evolution. All rights reserved. 456 SYLVAIN GANDON different evolutionary scenarios illustrate the diversity of host-parasite life cycles. They show how epidemiology may act on life-history evolution and, reciprocally, how life his- tories may feed back on the epidemiological dynamics of the interaction. These complexities emerging from multihost models yield new and testable predictions on the evolution of parasites. In particular, these models yield new insights for the understanding of virulence evolution. The implica- tions for public-health policies and virulence management are discussed. FIG. 1. Schematic representation of parasite life cycle with two LIFE CYCLES AND EPIDEMIOLOGICAL DYNAMICS different types of hosts. These two types of hosts may have different intrinsic mortality rates (d1 and d2). They may also suffer differ- The parasite may infect n different types of host. Each host entially from being infected, yielding different parasite-induced type may have different intrinsic mortality, di, and, when mortality rates (i.e., virulences a1 and a2) and different recovery infected, they may have different recovery rates, gi. The par- rates (g1 and g2). The parasite transmission pattern is described by asite life-history traits may also vary among different hosts. the four transmission rates that refer to within-type (b11 and b22) The transmission rate from one individual host to the next, and between-type (b12 and b21) transmission. bji, may depend on both the type of origin, j, and on the recipient type, i. The virulence of the parasite, ai (the induced population, and when R0 , 1, it will always go extinct before host mortality rate) may also vary across the different hosts. producing any epidemic. More complex situations with high- This yields the following system of n differential equations er number of hosts can be analyzed using similar methods (where the dot refers to differentiation with respect to time): (Diekmann et al. 1990; Diekmann and Heesterbeek 2000). ẏ i 5 x i O b y 2 (d 1 a 1 g )y , j ji j i i i i (1) Some simplification may occur depending on the pattern of transmission. Suppose, for example, that transmission is the product of two functions: bji 5 pjfi, where pj measures where yi and xi refer to the density of infected and uninfected the production of propagule of the parasite infecting a host hosts of type i, respectively. In matrix form this yields ẏ 5 type j, and fi is the susceptibility of the host type i (see m·y, with y 5 (y1, y2, . . . , yn) and m 5 B 2 D, where B is scenario 1, below). In this situation b12b21 2 b11b22 5 0, a matrix whose elements are bjixi, the expected number of which yields: secondary infections of host type i per infected host of type j, and D is a diagonal matrix whose elements are di 1 ai 1 b11 b22 R0 5 x̂1 1 x̂ , (3) gi, the sum of mortality and recovery rates for each type of d1 1 a1 1 g1 d2 1 a2 1 g2 2 infected host. The matrix m can be used to derive the in- which is the sum of reproductive ratios on each host (An- stantaneous growth rate of the parasite population (Appendix derson and May 1991; Dushoff 1996; Gandon et al. 2001a, 1). Alternatively, the matrix M 5 BD21 can be used for the 2003). Note that this sum involves only within-type trans- derivation of a per generation growth rate of the parasite mission despite the fact that between-type transmission oc- population (Appendix 1). In particular, the basic reproductive curs. ratio of the parasite (the per generation growth rate of the Imagine another situation where the parasite sequentially parasite introduced in a naive host population) is given by exploits the two different types of hosts. This may occur when the dominant eigenvalue of M. the parasite is sexually transmitted through heterosexual con- For the sake of simplicity, in the remainder of this paper, tacts (from one sex to another) or with vector-borne parasites I will only consider the simpler case with two hosts. Figure (e.g., from vertebrate to invertebrates, see scenario 2 below). 1 gives a schematic representation of this life cycle. In this In these situations bii 5 0 (for all i), which yields: case the basic reproductive ratio is: !(d 1 a 1 g )(d 1 a 1 g ) x̂ x̂ . b12b21 b11 b22 R0 5 1 2 (4) R0 5 x̂1 1 x̂ 1 1 1 2 2 2 2(d1 1 a1 1 g1 ) 2(d2 1 a2 1 g2 ) 2 In contrast with equation (3), the basic reproductive ratio is 5 (b12b21 2 b11b22 ) a product (instead of a sum) of two quantities which describe 1 x̂ x̂ between-type transmission. This product reflects the obli- (d1 1 a1 1 g1 )(d2 1 a2 1 g2 ) 1 2 gation for the parasite to exploit these two hosts sequentially. ]6 2 1/ 2 1 [ b11 2(d1 1 a1 1 g1 ) x̂1 1 b22 x̂ 2(d2 1 a2 1 g2 ) 2 (2) Note that the square root comes from the fact that the com- pletion of the whole life cycle requires two generations: one generation from one host to the next and another generation to go back to the original host (Roberts and Heesterbeek where the x̂i values are the equilibrium densities of the dif- 2003). It is also interesting to note that the situation in which ferent types of hosts in the absence of the parasite. The above all bii 5 0 is analogous to the case in which the parasite quantity can then be used to determine if the parasite can infects a single host but produces free-living stages. Here, maintain itself in the host population. If R0 . 1, the parasite the parasite appears sequentially in two states: (1) within will be able to create an epidemic in a previously virgin infected hosts; and (2) in the environment (as a free-living  MULTIHOST PARASITES 457 propagule). If no direct transmission occurs (i.e., b11 5 0) dzj/dzi between traits. The use of the chain rule on equation and if propagules cannot reproduce in the environment (i.e., (5) yields: b22 5 0), this yields an expression of the basic reproduction ratio very similar to equation (4) (e.g., Bonhoeffer et al. C¹r* 5 0, (6) 1996). where 0 is the vector of n(n 1 2) zero elements, C is the n(n The importance of life-cycle architecture to the basic re- 1 2) 3 n(n 1 2) matrix of regression coefficients Cij, and ¹ productive ratio has long been recognized (Anderson and is the gradient operator (]/]z*1 , (] /]z* 2 , . . . ), where everything May 1991; Dushoff 1996; Woolhouse et al. 2001, 2002; Hay- is evaluated at the point where ai*, 5 ai, bij* 5 bij, and gij* don et al. 2002). Next, I emphasize the importance of such 5 gij. The matrix C is thus a function of the state z of the life-cycle geometry for parasite evolution. resident population. The constraints between the different parasite traits may change as the population evolves (i.e., C EVOLUTIONARY DYNAMICS may change as the population proceeds toward the ESS equi- In the above analysis, the parasite life-history parameters librium). However, note again that equation (6) provides only (ai, bji, and gi) are fixed quantities. However, virulence, trans- the condition for an evolutionary internal equilibrium. A fully mission and recovery will evolve if there is genetic variation dynamical theory of evolutionary change (allowing to track in the parasite population. Consider a mutant parasite with the speed of evolution of the different traits) requires further life-history traits that differ from the resident parasite pop- information regarding the additive genetic variance of each ulation, where z* 5 (z* trait (Lande 1982; Charlesworth 1993; Abrams 2001; Day 1 , z* 2 , . . . ) is the vector of mutant traits and z 5 (z1, z2, . . . ) is the vector of resident traits. As an and Proulx 2004). In particular, note that G 5 CV, where G example, these vectors may be of size n(n 1 2) (i.e., n trans- is the matrix of additive genetic covariances among the dif- mission rates, plus one virulence, plus one recovery rate, in ferent traits and V is the vector of additive genetic variance each of the n hosts). The initial dynamics of a mutant intro- of each trait. In the present paper, however, I assume there duced in a monomorphic resident population can be described is sufficient genetic variance (sufficient to reach the equilib- by ẏ* 5 m*·y*, with y* 5 (y* rium obtained with eq. 6) and will focus only on the analysis 1 , y*2 , . . . ) and where m* is analogous to m but refers to the mutant parasite (Appendix of factors that may modify this ultimate evolutionary out- 2). The fate of the mutant strategy (extinction or invasion) come. At this ultimate equilibrium different modeling ap- can be derived from its initial growth rate, which is given proachs all yield conditions very similar to equation (6). by the dominant eigenvalue, r*, of m* (Appendix 2). The Quantitative genetics yield the classical result of selection recurrent invasion and fixation of mutants may ultimately on multivariate traits: G¹r* 5 0 (Lande 1982; Charnov 1989; lead to an evolutionarily stable strategy (ESS). The following Iwasa et al. 1991; Charlesworth 1993). The canonical equa- condition must be satisfied for z to be at an evolutionary tion of adaptive dynamics (Dieckmann and Law 1996) yields equilibrium: mys¹r* 5 0, where m is half the mutation rate, y is the prevalence of the parasite, and s is the variance-covariance dr* dz*i) z5z* 5 0, for all i ∈ [1, n(n 1 2)]. (5) matrix of the multivariate distribution of mutation (within this framework, the constraints between traits are assumed to emerge from the mutation process). Note however, that equation (5) is the condition for an in- To facilitate the interpretation of equation (6), I replace r* ternal evolutionary equilibrium only. Additionally, higher or- by an alternative fitness function (e.g., Taylor and Frank der conditions must be used to check if this equilibrium is 1996; Frank 1998): locally and globally stable (Taylor 1989; Geritz et al. 1998; Kisdi and Geritz 1999; Gandon et al. 2003; Leimar, in press). w* 5 O v m* u 5 O c m*, i,j j ij i i i i (7) Global and/or local instability may lead to more complex situations (e.g., evolutionary bistability, evolutionary branch- where vj is the individual reproductive value of parasites ing). Some of these complexities will be encountered and infecting an individual host of type j, m* ij is the element at discussed in the analysis of the different examples presented the ith column and jth line of m*, and ui is the density of below. infected hosts of type i (when the parasite has reached a stable In the absence of any constraints (e.g., if each trait can distribution between the different types of hosts). The vectors evolve independently of the other traits), parasite evolution u and v are dominant right and left eigenvectors of m, re- would lead to a minimization of virulences (ai) and recovery spectively (see Appendix 1). Note that m* is a function of rates (gi) and to a maximization of transmission rates (bij). both mutant and resident strategies (z* and z, respectively), Indeed, the parasite always benefits from longer duration of whereas u and v depend only on the resident strategy. The the infection and higher transmission. However, I assume final equality in (7) derives from the definition of the class some trade-off will constrain the range of possible pheno- reproductive value of parasites infecting host population of type types. Formally, this means that parasite traits will be cor- i, ci 5 viui, and the weighted sum of transitions between i and related (e.g., transmission and virulence: db11/da1 ± 0) and, j, m*i 5 Sj (vj/vi)m*ij (Taylor and Frank 1996). This yields the consequently, selection on a given trait (e.g., virulence) will following condition for evolutionary equilibrium: be governed both directly by the effect of this trait on par- asite’s fitness and indirectly through the effect of correlated O c [C¹(m*)] 5 0. i i i (8) traits (e.g., transmission). The strength of such indirect ef- fects will depend on statistical regression coefficients Cij 5 The use of equation (8) is particularly insightful because it 458 SYLVAIN GANDON shows that the direction of evolution is given by the sum of the selection acting on traits expressed in different hosts. The the selective pressures acting within the different types of direction of evolution will thus depend on the pattern of hosts, weighted by the reproductive values, ci, of parasites correlation between traits, which could potentially take any infecting these different host populations (for other illustra- form (correlations could be all negative, all positive, or a tions of the use of reproductive values to understand selection mixture of positive, negative, and/or zero). However, in prin- in heterogeneous environments, see also Holt 1996; Frank ciple, it is possible to provide a mechanistic explanation for 1998; Rousset 1999). In other words, evolution may be al- the emergence of a given pattern of correlation. I will focus tered by three factors: (1) C¹(m* i ), the selection occurring here on two contrasting situations that illustrate cases with in the different hosts (this includes both direct and indirect positive or negative between-host types correlations. selection); (2) vi, the quality of these hosts for the parasite First, imagine that the same parasite machinery is required (i.e., the individual reproductive values of parasites); and (3) for the exploitation of both hosts but that some hosts are ui, the prevalence of the parasite among these different hosts. more resistant than others (e.g., if the immune system is more This last point indicates how epidemiology could feed back efficient in reducing within-host growth rate). Infection by on parasite evolution. the same parasite would thus result in different levels of As pointed out above, the relative intensity of direct and exploitation in the two hosts, yielding also different levels indirect selection is governed by C. Figure 2A gives a sche- of virulence, recovery, and transmission. A mutant parasite matic representation of C when the parasites infect two types that adopts a more intense exploitation strategy would in- of hosts. It shows that constraints may occur within each type crease its exploitation on both hosts, and this would lead to of host (between virulence, recovery, and transmission, as a positive covariance between traits expressed in different indicated by the gray cells in Fig. 2A) and/or between dif- hosts. For example, MacKinnon and Read (1999, 2003) found ferent types of hosts. that more virulent strains of Plasmodium chabaudi produce more transmission stages (within-host trade-off between vir- Within-Type Constraints ulence and transmission) and that they are more difficult to If parasite phenotypes in one host do not covary with phe- clear (within-host trade-off between virulence and recovery). notypes in the other, evolution proceeds independently in the They also found that the most virulent strains in immuno- two hosts. Here, as in classical models of virulence evolution logically naive mice are also more virulent, transmissible, (with only one host), parasite evolution is only constrained and difficult to clear in semi-immune mice (Mackinnon and by within-host trade-offs. Read 2003). This generates positive (virulence, transmission) It is often assumed that transmission and virulence are two and negative (recovery) genetic covariances between parasite phenotypic expressions of an underlying pleiotropic trait traits expressed in naive and semi-immune mice (Fig. 2B). (e.g., host exploitation, parasite growth rate). This yields a Best and Kerr (2000) obtained similar results using different positive relationship between the benefit of exploitation strains of myxoma virus to infect laboratory rabbits (naive (transmission) and its cost (virulence): db* 11 /da* 1 . 0. There host) and naturally resistant rabbits. is some empirical data on several very different host-parasite Second, imagine a situation in which different machineries systems (Fenner and Fantini 1999; MacKinnon and Read are required for the exploitation of the two hosts. This may 2003) supporting this hypothesis. This relationship yields well be the case if the two types of hosts are different species intermediate values of evolutionarily stable virulence and representing different resources for the parasite (e.g., malaria transmission if it has the additional property transmission parasites where asexual growth occurs in the vertebrate host saturates with high virulence (d2b* 2 11 /da* 1 , 0). The empirical and sexual reproduction in the vector). Under such a scenario, data supporting this hypothesis remains weak (probably be- one may expect no genetic covariation between traits ex- cause statistical tests of such saturating relationships are very pressed in different hosts. However, if the optimal exploi- demanding). tation of one type of host (adaptation to this host) is asso- Similarly, recovery rates could also be linked to virulence ciated with a reduced ability to exploit another host (i.e., and transmission because the ability to clear a parasite will trade-off between the exploitation of the two hosts), this also depend on its within-host growth rate (which also im- could result in negative genetic covariances. For example, pacts on virulence and transmission). In particular, it is often Davies et al. (2001) observed a trade-off in the reproductive assumed that faster reproducing parasites are more difficult success of schistosomes in their mammalian and molluscan to clear (Anderson and May 1982; Frank 1996). There is hosts (Fig. 2C). Further evidence of negative between-hosts good empirical evidence supporting this hypothesis (Ander- correlations in parasite fitness come from serial-transfer ex- son and May 1982; Fenner and Fantini 1999; MacKinnon periments. When parasites are serially transmitted from one and Read 2003). A single trade-off between virulence and host to another host of the same type, the virulence in this recovery may also yield intermediate levels of evolutionarily host type increases but often with an accompanying decrease stable virulence (Anderson and May 1982; Frank 1996). of virulence (i.e., attenuation) in other types of host (Ebert However, in many situations, it would be more relevant to 1998). envision a trade-off in virulence with both transmission and The two contrasting situations presented above illustrate recovery. how mechanistic differences in the exploitation of the dif- ferent hosts (i.e., whether the parasite uses the same ma- Between-Type Constraints chinery to exploit different hosts) influence the pattern of When some correlation exist between different hosts, the genetic covariances between traits. This point has previously evolution of a trait expressed in one host depends also on been raised at the within-host level where a better under-  MULTIHOST PARASITES 459 FIG. 2. Schematic representation of the regression matrix C between parasite life-history traits. (A) The full matrix for the general two- host model as it is presented in Figure 1. I do not give the values below the diagonal because they can be derived from values above the diagonal. I highlight in gray the regression coefficients required for the classical analysis of parasite evolution on a single host. The white cells show that adding another host in the system substantially increases the number of constraints that may act on parasite evolution. Covariances between traits expressed in different hosts have actually been measured in different host-parasite systems. (B) and (C) present qualitative summaries (only the sign of the regression) of results obtained for the rodent malaria (MacKinnon and Read 2003) and for schistosomes (Davies et al. 2001), respectively. In (B) the two types of hosts are naive and semi-immune mice (MacKinnon and Read, 2003). In (C) the two types of hosts are the snail (intermediate host) and the mouse (definitive host). The signs in parentheses indicate nonsignificant regression coefficients. Note that it is classically assumed that within a single host the regression between virulence and transmission is positive, the regression between recovery and virulence is negative, and the regression between recovery and transmission is also negative. Rodent malaria follows these assumption (see B), but not schistosome in the snails because transmission is negatively correlated with virulence (see C). The between-host constraints also differ in these two examples: the correlations of between-type transmission rates is positive in malaria and negative in schistosome. This qualitative difference is highlighted with a dotted square in B and C. standing of the interaction between parasites and the immune point here is to show how transmission routes (the relative system, for example, could help predict the relationship be- amount of within-host-type and between-host-type transmis- tween virulence, recovery, and transmission (Antia et al. sion) and epidemiology (the relative abundance of the two 1994; Ganusov et al. 2002; Gilchrist and Sasaki 2002; André hosts) may affect the evolutionary outcome. et al. 2003; Ganusov and Antia 2003). The generalization of The second evolutionary scenario focuses on the evolution such mechanistic approach to multihost parasites may help of alternative transmission routes via a new host. This sce- us understand the emerging pattern of genetic covariances at nario is inspired from a situation in which a parasite may both the within- and between-host levels (J. B. André and S. infect two different host species (the focal host and a vector). Gandon, unpubl. ms.). First, I study which factors may govern the evolution of In the following, I illustrate the use of the above evolu- vector-borne transmission and, second, I show how the emer- tionary model (eq. 8) through different examples. For the gence of a new transmission route may feed back on the sake of simplicity, I assume no recovery from infection and evolution of virulence. focus on virulence and transmission evolution. Moreover, the functions relating these two traits in the two different hosts SCENARIO 1: VIRULENCE EVOLUTION UNDER DIFFERENT will not emerge from an explicit description of within-host TRANSMISSION PATTERNS dynamics. Instead, I will use general functions derived from a mix between some available empirical knowledge and im- Here I address the evolution of virulence when parasite plicit arguments regarding within-host dynamics. phenotypes in both host types are under the control of a single In the first evolutionary scenario, I focus on the evolution pleiotropic trait, the host exploitation strategy, «. The het- of the virulence of a parasite exploiting two hosts with dif- erogeneity of the host population will affect the evolution of ferent levels of resistance. This scenario is inspired from this trait when the selective pressures acting on it vary among situations in which a fraction of the host population is nat- different hosts. The weights associated with these different urally or artificially (e.g., vaccination) immunized. The main selective pressures are strongly dependent on the relative 460 SYLVAIN GANDON amount of within- and between-type transmission. These dif- lutionary outcome be closer to the optimum for one host over ferent transmission routes will necessarily fall between two the other? Will evolution in such a heterogeneous host en- extreme cases of: (1) no between-type transmission ( bij 5 0 vironment always lead to a single generalist strategy, or could for i ± j, and parasite life cycle consists of two direct cycles it lead to a polymorphic situation with two (or more) strat- on two different hosts); and (2) no within-type transmission egies specialized on the different types of hosts? The answers (bii 5 0 for all i, and parasite life cycle consists of a single to these questions are obtained through the analysis of par- indirect cycle). asite fitness, which itself depends on the densities of each To illustrate these different situations, it is convenient to type of host (see eq. 8). Thus, a full evolutionary analysis assume the following relationships: requires first a complete description of the epidemiological model and, in particular, the dynamics of uninfected hosts. bij[«] 5 pi[«]fij. (9) For the sake of simplicity, I assume as in Gandon et al. (2003) The parameter pi[«] refers to the production of propagules that: in the host of type i. Note that this production is assumed to 1 O b y 2x depend on the host exploitation strategy, «, which also affects parasite virulence (see below). The parameter fij specifies ẋ1 5 l (1 2 p) 2 d1 1 i1 i 1 and (11a) i the amount of transmission between propagules produced in 5 l p 2 1d 1 O b y 2 x , an individual host of type i to other individuals of type j. In other words, the parameter fij governs the shape of the trans- ẋ2 2 i2 i 2 (11b) i mission pattern. In the present example I assume that this transmission pattern is not affected by the host exploitation where l is the rate of host immigration (this parameter refers strategy of the parasite (i.e., fij does not depend on «), but to both immigration and fecundity) and p measures the pro- this assumption will be relaxed below (scenario 2). portion of the second type of hosts (the resistant ones) among The characterization of the selective pressures acting in immigrants. the two different hosts requires further assumptions regarding Figure 3 illustrates the effect of different transmission pat- the within-host constraints and the relationship between vir- terns on the evolution of parasite virulence. I present a simple ulence and transmission. Regoes et al. (2000) devised a two- case where f11 5 f22 5 1 and vary only the value of f12 5 host model where virulence in one host is traded off against f21 between 0.2 and 5.0. This allows me to contrast situations virulence in the second host. They showed that such a neg- where the ratio of between- and within-type transmission ative relationship between virulence levels yields interme- varies. diate values of the evolutionarily stable virulence even in the Figure 3A shows the effect of the frequency of the second absence of any link between transmission and virulence. Here type of host among immigrants, p, on evolutionarily stable I will analyze a different situation where traits expressed in virulence. Not surprisingly an increase in p yields higher the two hosts (virulence and transmission) are positively cor- virulence (because the optimal virulence on the second type related, as in MacKinnon and Read (2003; see the above is higher, a2 . a1), but the effect of p depends strongly on discussion of this work). Following Gandon et al. (2001a, the transmission patterns. When there is more within-type 2003), I assume the following relations: transmission (fii . fij), the evolutionarily stable virulence « is always very close to the optimal virulence on the more p1 [« ] 5 , p2 [«] 5 p1 [(1 2 r)«] and (10a) abundant host. This yields a sharp increase of evolutionarily 11« stable virulence for small variations in p when both hosts are a1 [« ] 5 « , a2 [«] 5 (1 2 r)«. (10b) abundant (p ; 0.5). In other words, this pattern of trans- The logic behind these assumptions is as follows. Host ex- mission favors specialization to the most abundant host. This ploitation allows the parasite to produce propagules (p is an contrasts with the situation in which there is more between- increasing function of exploitation «), but such exploitation type transmission (fii , fij), where intermediate values of has a deleterious effect on the host (virulence, a, increases virulence and more generalist strategies are favored. with exploitation «). These relationships vary among differ- Figure 3B shows the effect of another demographic pa- ent hosts, and the parameter r governs these differences. This rameter on virulence evolution, the intrinsic host death rate parameter could be viewed as a resistance mechanisms of the second type of host, d2. Again, the transmission pattern against the parasite (the parameter r2 in Gandon et al. 2001a, strongly affects the evolutionary outcome. When there is 2003). Higher resistance decreases parasite within-host more between-type transmission (fii , fij), an increase in growth rate and, consequently, its transmission, p, and its the intrinsic mortality of the resistant host (d2) favors higher virulence, a. Note that the above assumptions yield positive evolutionarily stable virulence as one would expect from the covariances between all the parasite life-history traits (as in analysis of classical single-host models of parasite virulence Fig. 2B, with the exception of recovery rates). (Anderson and May 1982; Frank 1996; Dieckmann et al. The above assumptions also yield different optimal viru- 1999). However, when there is more within-type transmission lence strategies, ai, in the two hosts: a1 5 Ïd1 on host type the evolutionarily stable virulence may first increase but then 1 and a2 5 Ïd2/(1 2 r) on host type 2 (Gandon et al. 2001a). decreases with larger values of intrinsic mortality, d2. Again, One would expect that, when both hosts coexist, the selection more within-type transmission favors specialization to the acting on the evolution of the parasite would push the trait most abundant host, and an increase in the mortality of the somewhere between these two optimal values. Will the evo- second host type favors lower virulence when d2 . d1, be-  MULTIHOST PARASITES 461 FIG. 4. Deterministic simulations showing the evolution of par- asite virulence. At the beginning of the simulation the parasite pop- ulation is monomorphic with virulence a 5 0.5. Mutation occurs at a rate m 5 0.01 and allows this trait to evolve. This simulation illustrates a situation in which there is 10 times more transmission within the same host types than between different host types (f11 5 f22 5 1 and f12 5 f21 5 0.1). This transmission pattern leads to an evolutionary branching, yielding the coexistence of two dif- ferent virulent strategies. The ratio of individual reproductive values on the two different types of hosts (v̄1/v̄2, see Appendix 1) can be used to measure the level of specialization of the two strains (Gan- don et al. 2003). The low virulence strain is better adapted to the first host (v̄1/v̄2 ø 2.78 . 1), and the high virulence strain is better adapted to the second host (v̄1/v̄2 ø 0.37 , 1). Other parameter values are as in Figure 3. FIG. 3. Evolutionarily stable virulence (when measured on host 1) against (A) the proportion, p, of host 2 among immigrants and (B) the intrinsic death rate, d2, of host 2. Three different transmission availability of the different hosts. In particular, Gandon et patterns are considered. The dotted line shows a situation in which al. (2001a, 2003) studied a model with fii 5 fij and showed there is more within-type transmission than between-type trans- how p (which could be viewed as a parameter measuring mission (f11 5 f22 5 1 and f12 5 f21 5 0.2). The dashed line vaccination coverage) affects the evolution of parasite vir- shows a situation in which within-type transmission is equal to between-type transmission (f11 5 f22 5 f12 5 f21 5 1). The full ulence. At the other extreme, when fij 5 0 with i ± j, the line shows a situation in which there is less within-type transmission parasite population consists of two subpopulations evolving than between-type transmission (f11 5 f22 5 0.2 and f12 5 f21 in different directions. This favors the emergence and co- 5 1). In all these situations the equilibrium value is always evo- existence of different virulence strategies, a1 and a2, adapted lutionarily stable (i.e., no evolutionary branching). Other parameter values: l 5 20, d1 5 1, d2 5 1, r 5 2/3. to each host. But evolution toward polymorphism may also occur with low values of between-type transmission. For ex- ample, Figure 4 shows a situation in which evolutionary branching may occur and lead to a polymorphic parasite pop- cause the first host (in which optimal virulence is lower) ulation in which two virulence strategies coexist and each becomes more frequent. strain is specialized to a different host (reproductive values More generally, all these results can be explained by the can be used to measure the level of specialization; see caption differences in class reproductive values of parasites infecting of Fig. 4). different types of hosts. Reproductive values are the proper weights associated with the selective pressures acting in these SCENARIO 2: COEVOLUTION OF INDIRECT TRANSMISSION different habitats. For example, with only between-type trans- WITH VIRULENCE mission (fii 5 0), the ratio of class reproductive values is (d2 1 a2)/(d1 1 a1) (Appendix 1). This ratio is independent The previous examples illustrate the importance of the pat- of p, which explains why this parameter has no effect on tern of transmission on virulence evolution. Here, I allow evolution. With a larger fraction of within-type transmission, different transmission patterns to evolve and coevolve with the ratio of class reproductive values depends more on the virulence. As above, I assume the epidemiological dynamics 462 SYLVAIN GANDON described by equations (1) and (11). I will also follow the assumption that transmission rates are the product of two components, the production of propagule and the transmis- sion route (bji 5 pjfji). The parasite can be transmitted di- rectly from one individual to the next (where both individuals are of type 1) or it can be transmitted indirectly via another host species (host 2), which can be used as a vector toward the infection of the first host (the focal host). To keep things simple, this second host species is assumed not to suffer from the parasite (i.e., a2 5 0, because the parasite exploits only the focal host), but this assumption will be discussed later. First, I analyze the evolution of the transmission pattern and explore what factors may favor indirect (e.g., vector- borne) transmission. Second, because vector-borne transmis- sion is likely to affect the evolution of parasite virulence on the exploited host (Day 2001, 2003), I analyze the coevo- FIG. 5. Evolution of new transmission routes in response to a lution between the pattern of transmission and virulence. change in the abundance of the different types of host. The evo- lutionarily stable (ES) between-type level of transmission is plotted against the proportion, p, of the vector among immigrants. Note Evolution of Indirect Transmission that the ratio p/(1 2 p) gives the rate of immigration of the vector relative to the exploited host. The upper line presents a case in Under what conditions will the parasite evolve strategies which the virulence on the first type of host is a1 5 5 (full line). allowing transmission via a new host (e.g., a vector) when Lower virulence (a1 5 1, dashed line) and higher intrinsic host direct transmission may represent a seemingly simpler alter- mortality of the vector (d2 5 3, dotted line) favor lower ES between- native? Of course, in the absence of any constraint on trans- type transmission. Default parameter values: l 5 20, a1 5 1, d1 5 mission, evolution would favor the strategy maximizing both d2 5 1, q1 5 q2 5 0.5. direct and indirect transmission routes. But, as discussed above, it is very likely that different transmission routes will Evolutionary bistability may occur where the two alternative require specific adaptations. For example, a specialization equilibria are two extreme cases: (1) no indirect transmission toward more efficient between-type (indirect) transmission (i.e., the parasite adopts a direct life cycle and exploits a may yield less efficient within-type (direct) transmission. In single host); and (2) no direct transmission (i.e., the parasite the following, I thus assume a trade-off between these dif- adopts an indirect life cycle and exploits the two hosts se- ferent transmission strategies: quentially). Under some situations evolutionary branching f11 [t ] 5 t q1 and (12a) may also occur, leading to the coexistence of different trans- mission strategies (not shown). f12 [t ] 5 (1 2 t ) q2 , (12b) where the parameters q1 and q2 allow consideration of dif- Virulence Coevolution ferent forms of trade-offs. For the sake of simplicity, I assume Next, I explore how different transmission routes can co- that no transmission occurs between vectors (f22 5 0) and evolve with parasite virulence. I assume again that parasite that transmission from the vector to the exploited host is transmission depends on both the production of propagules constant (f21 5 1). I also assume that the production of (p) and the transmission route (f): transmissible stages are constant in the two hosts (p1 5 p2 5 1, but this assumption will be relaxed below). This yields bij[«, t] 5 pi[«]fij[«, t]. (13) the following transmission rates: b11[t] 5 tq1, b12[t] 5 (1 In contrast to the previous model, parasite transmission de- 2 t)q2, b21 5 1, and b22 5 0. pends on two traits that may evolve independently. Figure 5 shows the effect of the abundance of the vector First, the exploitation of host type 1, «, affects the pro- (where the ratio p/[1 2 p] measures the immigration rate of duction of propagules and the virulence in the first type of vectors relative to the immigration rate of exploited hosts) host (p1[«] 5 «/(1 1 «) and a1[«] 5 «). However, it neither on the evolution of between-type transmission. Higher im- affects the transmission from the vector nor the virulence on migration and lower mortality of this second type of host this second host (p2 5 1 and a2 5 0). Second, as in equation (the vector) yields higher level of evolutionarily stable be- (12), the transmission strategy, t, measures the allocation tween-type transmission. Indeed, both larger densities and toward within-type transmission: lower mortality makes it a better vector. Higher mortality of the first type of host (i.e., d1 1 a1) also yields higher evo- f11 [«, t ] 5 t q1 e2m« and (14a) lutionarily stable between-type transmission (not shown) be- f12 [t ] 5 (1 2 t ) q2 . (14b) cause this mortality lowers the efficacy of transmission by direct contact. As above, I assume that no transmission occurs between vec- In Figure 5, I present a case with a convex trade-off (i.e., tors (f22 5 0) and that transmission from the vector to the q1 5 q2 5 0.5). This favors intermediate levels of between- exploited host is constant (f21 5 1). Note the important dif- host transmission. However, other types of constraints (e.g., ference that f11 is now assumed to be a decreasing function linear or concave) can yield complex evolutionary outcomes. of «, while f12 does not depend on «. This is to express the  MULTIHOST PARASITES 463 in the different hosts (where indirect selection depends on correlations among parasite life-history traits) and, as dis- cussed above, this is mainly governed by within-host dy- namics. Second, evolution depends also on the relative qual- ity of the different hosts (i.e., the class reproductive values), via the relative abundance of the different types of infected hosts and the transmission patterns among these hosts. In other words, evolutionary predictions strongly depend on both microscopic (within-host dynamics) and macroscopic (epidemiological dynamics) details of the host-parasite in- teraction. The complexity emerging from the effects of both micro- scopic and macroscopic processes has practical implications for virulence management of multihost parasites. These two processes are likely to vary from one parasite species to an- FIG. 6. Coevolution of the transmission pattern with virulence in other (e.g., cf. Figs. 2B and 2C) or even from one location response to a change in the abundance of the different types of to another if the abundances of the potential host species vary host. The evolutionarily stable (ES) between-type level of trans- in these different locations. General recommendations to lim- mission (in gray) and virulence on the first type of host (in black) are plotted against the proportion, p,, of the vector among immi- it virulence evolution should thus be very cautious and vir- grants. Parameter values: l 5 20, d1 5 d2 5 1, q1 5 q2 5 0.5, m ulence management, like more classical tools against infec- 5 1. tious diseases, should focus on the development of specific strategies against specific pathogens. General models, however, may help to provide a broader fact that morbidity may impose some cost on direct trans- understanding of what shapes parasite life history. In partic- mission but not on vector-borne transmission (Ewald 1983, ular, the generalization of simple single-host models gener- 1994; Day 2001, 2003; Ewald and De Leo 2002). Indeed, the altered behavior of infected host may limit the contact ates new insights into the evolution of both virulence and with some hosts (host 1) but not with others (host 2). In the transmission strategies. present model the parameter m refers to such morbidity cost. Figure 6 presents the effect of the abundance of the vector Virulence Evolution on the evolution of both transmission and virulence. Higher The different evolutionary scenarios presented here illus- vector densities yield more between-type transmission (as in trate how transmission pattern among different hosts may Fig. 5) but also higher virulence. The increase in evolution- affect virulence evolution. This pattern will affect virulence arily stable parasite virulence is due to an increase in the evolution as long as different costs of virulence are associated fraction of vector-borne transmission. Such transmission with the different transmission routes. Before analyzing the route releases the morbidity cost of virulence expressed only evolutionary consequences of various transmission patterns via direct transmission. Note the synergistic effects emerging (i.e., the relative proportion of within- and between-type through the coevolution between transmission and virulence. transmission), it might be useful to contrast different types The evolution of larger between-type transmission increases of virulence costs. First, there might be fixed costs associated the selection for higher virulence (because this reduces the with some transmission routes. For example, virulence may morbidity cost of virulence) and, reciprocally, larger viru- carry a morbidity cost when transmission is direct (Ewald lence tends to select for larger between-type transmission 1994; Day 2001). One may thus expect evolution to yield a (because, as explained above, higher virulence lowers the positive correlation between virulence on the focal host and efficacy of direct transmission). The above results suggests the amount of indirect transmission (Day 2001; Ewald and that the relative abundance of the different types of host De Leo 2002; see also Fig. 6, where transmission and vir- (controlled by the parameter p in Figs. 5, 6) may be one of ulence are coevolving). There is some empirical evidence the key factors explaining the evolution of very different suggesting that, indeed, the case mortality is higher for vec- parasite life cycles. tor-borne and water-borne diseases where morbidity has only little effect on transmission efficiency (Ewald 1983, 1994; DISCUSSION Ewald and De Leo 2002). But these results are based on Single-host models of parasite evolution have been very correlations that could also emerge because of confounding useful for understanding some of the selective pressures act- factors associated with these different transmission modes ing on parasite life histories (Frank 1996; Stearns 1999; Diek- (e.g., vector-borne and water-borne diseases are more prev- mann et al. 2002). However, many parasites live in different alent in developing countries). More controlled comparative environments and exploit different types of host. The mul- studies and experiments artificially manipulating the mode tihost framework presented here is an attempt to provide more of transmission are required to demonstrate the importance general tools to understand the evolution of parasite life his- of different transmission patterns for virulence evolution. For tories. The general condition (8) for evolutinary equilibrium example, Bull et al. (1991) showed experimentally that ver- identifies two main factors acting on this evolution. First, tical transmission selects for decreased virulence. This evo- evolution depends on direct and indirect selection occurring lution results from the fixed cost of virulence associated with 464 SYLVAIN GANDON vertical transmission. Indeed, under this route of transmis- specialization to the most frequent host (Fig. 3A). When the sion, the parasite fails to infect new hosts when the parasite different hosts are equally frequent, small variation in the kills its host before reproduction. abundance of the different host may result in dramatic chang- Second, there might also be dynamical costs associated es of the evolutionarily stable virulence. This variation of with transmission routes via some habitats (e.g., hosts), which host frequency may be due to differences in host immigration emerge from maladaptations to these habitats. This is a dy- rates (Fig. 3A) or to host mortality rates (Fig. 3B). This latter namical cost because the level of maladaptation results from result contrasts with the classical prediction derived from the several factors including underlying constraints among the simplest host-parasite models that higher mortality should different parasite traits, the transmission pattern itself, and select for higher virulence (Anderson and May 1982; Frank the relative abundance of the different hosts. Parasite adap- 1996; Dieckmann et al. 1999). Recent theoretical studies have tation to the most abundant host (Fig. 3A) may lead to mal- shown that other factors (superinfections, predation) may also adaptive exploitation strategies in other, less frequent, hosts. alter this prediction (Gandon et al. 2001a,b; Williams and In these situations the parasite individual reproductive values, Day 2001; Choo et al. 2003). This demonstrates the potential vi, provide a relevant measure of the level of adaptation to impact of the ecological setting on parasite evolution. different types of hosts (Frank 1996, 1998; Gandon et al. Extreme bias toward within-type transmission may result 2001a, 2003). The maladaptation may either result from sub- in evolutionary branching and coexistence of different vir- optimal exploitation of the host (avirulence) or, on the con- ulence strategies. Each of these strategies are specialized to trary, from overexploitation of the host (hypervirulence). the different types of hosts (Fig. 4). Note that evolutionary Ganusov et al. (2002) illustrated this point with a model of branching is favored in situations where the two hosts are parasite evolution that examined the effect of host population equally frequent (not shown) because the density of the less heterogeneity induced by variations in the efficacy of im- frequent host may reach a threshold below which the parasite munity on optimal virulence. In this model the proportion of density cannot be maintained. Evolutionary branching may different hosts is fixed (contrasting with the present frame- also emerge from other processes. For example, Regoes et work, where heterogeneity depends on host demography and al. (2000) showed that concave trade-offs between virulence parasite transmission strategy). In the absence of host het- in the two hosts favors coexistence of different virulence erogeneity, parasites evolve toward a host exploitation strat- strategies. Similarly, in the second evolutionary scenario (i.e., egy that maximizes transmission without incurring mortality. evolution of indirect transmission), concave trade-offs may However, some heterogeneity yields an optimal strategy in also favor the coexistence of different transmission strategies. which some case mortality occurs because parasite occa- The occurrence of multiple or superinfections (Nowak and sionally infect hosts with inefficient immune systems. This May 1994; Gandon et al. 2001b; Pugliese 2002) and variable optimal strategy could appear maladaptive in both the most recovery rates among different hosts (J. B. André and S. sensitive hosts (where infection is lethal) and the most re- Gandon, unpubl. ms.) may also yield evolutionary branching sistant ones (where this strategy does not maximize the du- and virulence polymorphism. ration of the infection). Understanding virulence evolution In contrast, an increase in the relative amount of between- thus requires a characterization of the selective pressures act- type transmission favors more generalist strategies. In these ing outside the focal host. situations virulence evolution is relatively independent of the Biological examples of apparently maladaptive virulence abundance of the two hosts (Fig. 3a) and is mainly governed of parasites living in different environments are increasingly by within- and between-hosts constraints on parasite life- coming to the forefront. For example, it has been suggested history traits. Such between-host constraints may select for that avirulence genes may be retained in Salmonella enterica increased virulence in a given host if it is beneficial in another because they facilitate survival in nonhost environments. In host. For example Davies et al. (2001) pointed out that the comparison with the wild-type parent, mutation of the pcgL schistosome virulence on snails (the vector) may be a pleio- gene increased virulence and growth in vivo but strongly tropic consequence of an increased reproductive output in the reduced survival in vitro under nutrient-limiting conditions mice (i.e., db21/da1 . 0, Fig. 2C). Between-host trade-offs (Mouslim et al. 2002; Foreman-Wykert and Miller 2003). may also select for lower virulence in some focal host. For Also, the virulence of Cryptococcus neoformans, a soil fungus example, the high parasite burdens associated with malaria that can infect mammalian hosts, may be the byproduct of virulence in rodents generate reduced survival in mosquito an adaptation for protection against soil predators such as vectors (Ferguson et al. 2002). Such correlation may impose amoebae (Steenbergen et al. 2001). an extra cost on virulence and thus select for lower virulence There is also empirical evidence that different hosts may strategies in the human host. A laboratory experiment of constrain virulence evolution in the focal host. In humans, Ferguson et al. (2003), however, failed to find an overall the high virulence evolution of many zoonotic pathogens such relation between virulence levels in the different hosts. Nev- as Echinococcus multilocularis is probably driven by selec- ertheless this interesting hypothesis deserves to be tested in tion occurring in the main animal hosts (Woolhouse et al. natural populations of human malaria and with other vector- 2001). A human host infection may thus appear as an acci- borne diseases. The examples discussed above show that the dental event for both the host and the parasite. vector-borne scenario that I considered in the second evo- A reduction of the relative amount of between-type trans- lutionary scenario (i.e., no virulence on the vector) is clearly mission decreases the cost of specialization (i.e., maladaption an oversimplification. Even if vectors are classically assumed in less frequent host) because these less frequent hosts are to suffer weakly from infection, there are multiple examples rarely infected. More within-type transmission thus favors in which parasites have been shown to reduce vector survival  MULTIHOST PARASITES 465 (Buxton 1935; Turell 1992; Anderson et al. 2000; Davies et Another interesting example is provided by other micro- al. 2001; Ferguson and Read 2002) or fecundity (Hacker sporidian species in which the level of virulence (and other 1971; Elsawaf et al. 1994; Hogg and Hurd 1995, 1997; Fer- traits) may be altered not only by the route of transmission, guson et al. 2003). The analysis of these more complex sit- but also by the sex of the infected host. Indeed, male-killing uations deserves further theoretical investigation. microsporidia such as Amblyospora sp. benefit from killing the males through horizontal transmission to the intermediary Transmission Pattern Evolution hosts (various copepode species). When they infect female mosquitoes, however, the same parasite are often avirulent Transmission patterns may evolve in response to variation and achieve transmission via the infection of the offspring in host heterogeneity. Under the mass action law, when a mosquitoes (Hurst 1991). It would be interesting to analyze host is more abundant it becomes more likely to be infected. models with the two routes of transmission and two host sexes It may thus be adaptive to evolve higher transmission to host (i.e., with four different types of hosts) to study the emer- types that are more frequent (Fig. 5). For example, it has gence of these fascinating conditional virulence behaviors. been suggested that the evolution of a new route of trans- mission (direct oral transmissibility between intermediate hosts) in Toxoplasma gondii may be due to the human ag- Further Theoretical Developments ricultural expansion (Su et al. 2003). The analysis of genetic Transient dynamics polymorphism of T. gondii revealed that oral transmission ability emerged within the last 10,000 years. Su et al. (2003) The above framework focused on evolutionary endpoints thus suggested that this new transmission strategy may have and therefore assume both epidemiological and evolutionary been adaptive in the new environment resulting from the equilibrium. Ronce and Kirkpatrick (2001) showed how a emergence of agriculture and, consequently, the high con- transient perturbation of the demographic equilibrium may centration of cats (definitive host) and other mammals (in- alter the evolutionary outcome (i.e., the level of adaptation termediate hosts). More generally, the dramatic diversity of to different habitats) in a general quantitative genetics model. parasite life-cycles ranging from the exploitation of a single With infectious diseases, this equilibrium assumption is like- to many different host species could have evolved from very ly to be violated in many important situations. For example, different ecological and epidemiological settings. The ex- emerging infectious diseases which, by definition, acquired tinction of previously exploited host species or the immi- recently the ability to infect new host species are likely to gration a new host species may drive the evolution of new be far from their optimal life-history strategy (Woolhouse et transmission strategies. Figure 5 illustrates the impact of host al. 2001). In addition, any therapeutic intervention (e.g., vac- demography (i.e., the relative immigration rate of the two cination) will affect the prevalence of the disease and the hosts) for the evolution of between-host transmission. But heterogeneity of the host population. These modifications other transmission strategies could also evolve. The multihost will only reach a new epidemiological equilibrium after sev- framework could be used to study the evolution of free-living eral parasite generations. In all these situations, it would thus transmission (e.g. air-borne, water-borne) or trophic trans- be more satisfying to develop a dynamical framework allow- mission (Lafferty 1999; Brown et al. 2001; Choisy et al. 2003; ing follow-up of changes in both prevalence (epidemiology) Parker et al. 2003). In particular, this formalism may provide and various parasite life-history traits (evolution). Day and some insights into the evolution of host behavior manipu- Proulx (2004) developed a quantitative genetics model for a lation to facilitate transmission (Moore 2002). single-host model and showed how this formalism could be Another potential use of this framework would be to study used to predict the instantaneous direction of evolution under the evolution of vertical versus horizontal transmission. It is different epidemiological situations. This quantitative ge- classically assumed that horizontally and vertically infected netics approach is particularily interesting because it allows hosts are identical (Nowak 1991; Lipsitch et al. 1996) and us to make evolutionary predictions even if the host-parasite that transmission evolution is constrained by a trade-off be- system is far from its epidemiological equilibrium. It would tween vertical and horizontal transmission (for empirical ev- be interesting to extend this framework to multiple host par- idence of such a trade-off see Turner et al. 1998; Vizoso and asites. The power of this approach comes from the possibility Ebert 2004). However, vertically infected hosts, because they of measuring the variance-covariance matrix G of parasite are infected earlier in their development, may have much populations (Davies et al. 2001; Mackinnon and Read 2003; higher parasite density than horizontally infected ones. This see also Fig. 2B, C) and thus derive short-term predictions may alter both the level of parasite virulence and the trans- on their life-history evolution (Day 2003; Gandon and Day mission efficiency. Vertically and horizontally infected hosts 2003). Note that this could only yield short-term predictions may thus appear to be very different habitats for the parasite. because G is likely to change through time because both the For example, Vizoso and Ebert (2004) studied the interaction matrix of regression coefficients, C, and the additive genetic between Daphnia magna and the microsporidian Octosporea variance of parasite traits, V, may evolve. It would thus be bayeri. This parasite can be transmitted both vertically and particularly interesting to follow G across time and, in par- horizontally, but vertically infected hosts have higher lon- ticular, after some medical interventions (e.g., vaccination). gevity and larger spore load than horizontally infected ones. One potential limit to the quantitative genetics formalism This demonstrates the need for models that incorporate such comes from the difficulty arising as soon as the evolutionary between-host heterogeneity to understand the selective pres- equilibrium is not locally and/or globally stable (Abrams sures acting on the evolution of vertical transmission. 2001). 466 SYLVAIN GANDON Host heterogeneities and may cause later relapses after the host has cleared the parasite from the blood (Frank 2002). These different tissue I focused on the analysis of simple scenarios with only tropisms may thus prolong the infection period, increase the two types of hosts. These black-and-white scenarios are in- total parasitemia, and thus the virulence of the parasite. Sec- spired by realistic situations (e.g., vaccinated vs. unvacci- ond, at a larger spatial scale, host metapopulation structure nated hosts, human host vs. insect host for vector-borne dis- may also strongly impact on parasite evolution. For example, eases), but it is important to explore the evolutionary con- if the different types of hosts tend to be clustered together sequences of other sources of host heterogeneity. For ex- (e.g., because of local host dispersal) and if the parasite is ample, I discussed above the situation in which vertically and transmitted by direct contact, transmission will be more likely horizontally infected hosts should be considered as two dif- to occur between the same types of hosts. This biased trans- ferent types of hosts. It is interesting to note that in this mission pattern will promote the evolution of specialized situation susceptible hosts are assumed to be identical and parasite strategies (Figs. 3, 4). But it is difficult to extrapolate host heterogeneity only emerge from the transmission pattern from the simple effect of biased transmission patterns because itself. Another example of this type of infection-driven het- the emergence of competition among related parasites may erogeneity occurs with multiple infections because hosts in- strongly affect evolution (e.g., for the analysis of single host fected with different numbers of strains could be viewed as models of parasite virulence in space see van Baalen 2002). different types of hosts (van Baalen and Sabelis 1995). Spatial structure may also introduce an additional layer of It would also be interesting to study models with a higher heterogeneity in the host population if the abiotic environ- number of different hosts. For example, natural immunity ment of the host varies in the different populations. Hetero- against malaria is slowly acquired in humans. Different age geneity may be produced by phenotypic variations (e.g., in- classes are thus associated with different levels of resistance. creased fecundity and survival in better-quality habitats) but It may be interesting to explore how a perturbation in the also by genotypic variations if the host is allowed to evolve age structure of the host population may affect parasite evo- in the different habitats. The study of host-parasite interac- lution. tions in metapopulations have shown that both local (e.g., The heterogeneity may also emerge from genetic differ- selection within populations) and global processes (e.g., host ences among the host. This would allow host population to and parasite migration among populations) govern the ulti- coevolve with the parasite. Classical host-parasite coevolu- mate coevolutionary outcome (Thompson 1994, 1999; Gan- tionary models fall between two extreme situations. On the don et al. 1996; Hochberg and van Baalen 1998; Dybdahl one hand, some models focus on life-history coevolution be- and Storfer 2003; Nuismer and Kirckpatrick 2003). More tween a single host and a single parasite (e.g., van Baalen generally, the integration of the diversity of selection pres- 1998; Gandon et al. 2002a). On the other hand, other models sures acting at different spatial scales (host tissues, individual focus on gene-for-gene coevolution between multiple hosts host, host type, host population, host habitat, host metapop- and multiple parasites (Hamilton 1980; Frank 1992). The ulation) is a necessary step toward a general theory of the generalization of the above framework to the coevolution coevolution among multiple parasites and their multiple between multihost parasite and multiparasite hosts may allow hosts. us to fill the gap between these two extreme cases (for an attempt to mix gene-for-gene coevolution with virulence evo- ACKNOWLEDGMENTS lution see Gandon et al. 2002b). Note also that the present framework could be easily modified to study the evolution I am grateful to H. M. Ferguson for inspiring discussions of a single host infected by several parasites. For example, on multihost parasites and for helpful comments on an early this extension could be used to study the evolution of various version of the manuscript. I thank T. Day, S. Frank, M. resistance mechanisms. Host evolution depends not only on MacKinnon, and A. Rivero for very useful comments on the the direct costs of resistance (e.g., fecundity, survival) but manuscript. 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Nature 425:480–484. APPENDIX 1: EPIDEMIOLOGICAL DYNAMICS Pugliese, A. 2002. On the evolutionary coexistence of parasite The dominant eigenvalue, r, of m gives the instantaneous growth strains. Math. Biosci. 177/178:355–375. rate of the parasite population after reaching its stable distribution Regoes, R. R., M. Nowak, and S. Bonhoeffer. 2000. Evolution of among the different hosts. In other words, r . 0 when the parasite virulence in a heterogeneous host population. Evolution 54: is in an epidemic regime and r 5 0 refers to an endemic situation 64–71. where parasite prevalence is stable. However, it is often more con- Roberts, M. G., and J. A. P. Heesterbeek. 2003. A new method for venient to manipulate a per generation growth rate because it gives estimating the effort required to control an infectious disease. the number of secondary cases produced by a typical infected host Proc. R. Soc. Lond. B 270:1359–1364. during its entire period of infectiousness. The per generation growth Ronce, O., and M. Kirkpatrick. 2001. When sources become sinks: rate, R, is the dominent eigenvalue of the matrix M 5 BD21 that migrational meltdown in heterogeneous habitats. Evolution 55: projects the population from one generation to the next (Caswell 1520–1531. 2001). Rousset, F. 1999. Reproductive value vs source and sinks. Oikos Let us now consider a virgin host population (i.e., with no par- 86:591–596. asite) at a demographic equilibrium x̂ 5 (x̂1,x̂2. . . ,x̂n), where the Stearns, S. C. 1999. Evolution in health and disease. Oxford Univ. hat denotes the fact that there are no parasite. In this situation, the Press, Oxford, U.K. dominant eigenvalues r0 and R0 of m and M, respectively, give the Steenbergen, J. N., H. A. Shuman, and A. Casadevall. 2001. Cryp- ability of the parasite to invade such a virgin host population (i.e., tococcus neoformans interactions with amoebae suggest an ex- the parasite can invade if r0 . 0 or if R0 . 1).  MULTIHOST PARASITES 469 For example, when there are only two types of hosts (as in the egies ai, bij, and gi). In principle, it is possible to track the evolution main text): of the parasite population whatever the epidemiological state of the resident population (for nonequilibrium situations see the analyses 1b x b x 2 b11 x1 b21 x1 B5 and (A1) of Frank 1996; Day and Proulx, in press). However, I focus here 12 2 22 2 on situations where the mutant parasite is introduced in a resident population at its epidemilogical equilibrium (x̄ and ȳ, see Appendix D51 2, d 1a 1g 1 1 1 0 1). The logic behind this assumption is that epidemiological dy- (A2) 0 d2 1 a2 1 g2 namics is assumed to be much faster than evolutionary dynamics. As for the epidemiological analysis, the invasion of a mutant and the dominant eigenvalue of M at x̂ yields equation (2). This parasite in a resident parasite population may be measured with method can be generalized to a situation with a higher number of instantaneous or per generation growth rates. The initial instanta- potential hosts for the parasite (Diekmann et al. 1990; Diekmann neous rate of increase of the mutant is given by the dominant ei- and Heesterbeek 2000). genvalue, r*, of The utility of the instantaneous rate of increase comes from the fact that the notion of generation may depend on the type of host. m* 5 B* 2 D* In particular, generations will necessarily overlap when the ex- pected duration of an infection varies among hosts. The stable dis- tribution of the different types of infected hosts can be derived from the dominant right eigenvector u of m, which yields: 5 [b* 11 x̄1 2 (d 1 1 a1 b* x̄ 12 2 * 1 g1* ) b* b21 * x̄1 22 x̄2 2 (d 2 1 a* 2 1 g* 1) ] , (A6) where B* and D* are analogous to B and D but refer to the mutant u1 y1 r 1 d2 1 a2 1 g2 2 b22 x2 parasite. 5 5 . (A3) u2 y2 b12 x2 The initial per generation growth rate of a small population of The individual reproductive values of parasites infecting individual mutant parasite introduced in a resident parasite population (at its hosts of different types can be derived from the dominant left ei- endemic equilibrium) is given by the dominant eigenvalue, R*, of genvector v of m (or M), which yields: M* 5 B*D*21. For a parasite infecting two types of hosts this yields: v1 r 1 d2 1 a2 1 g2 2 b22 x2 R(d2 1 a2 1 g2 ) 2 b22 x2 5 5 . (A4) b* b* v2 b21 x1 b21 x1 R* 5 11 x̄1 1 22 x̄2 2(d1 1 a*1 1 g * 1 ) 2(d 2 1 a*2 1 g* 2) Note that when the parasite can invade a virgin host population 5(d 1 a(*b 1bg*2)(db 1ba*) 1 g*) x̄ x̄ (i.e., r0 . 0 and R0 . 1) the system will ultimately reach an endemic * * * 22 * 12 21 11 equilibrium where r 5 0, R 5 1, 1 1 2 1 1 1 2 2 2 ū1 ȳ1 d2 1 a2 1 g2 2 b22 x̄2 ]6 5 5 , and (A5a) 2 1/ 2 ū2 v̄1 5 ȳ2 b12 x̄2 d2 1 a2 1 g2 2 b22 x̄2 , (A5b) 1 [ b11 * 2(d1 1 a* 1 1 g* 1) x̄1 1 b*22 2(d2 1 a*2 1 g* 2) x̄2 (A7) v̄2 b21 x̄1 Both r* and R* can be used to study the evolution of any parasite’s trait (here I only give R* to facilitate comparison with eq. 2). How- with x̄i and ȳi being the equilibrium densities of uninfected and ever, a convenient alternative to the derivation of r* and R* is infected hosts of type i, respectively. provided by the use of w*, which is defined in equation (7). Note that there is another fitness function, W*, which can be derived from M*, as w* is derived from m*. The fitness function w* presents APPENDIX 2: EVOLUTIONARY DYNAMICS the advantage that it decouples selection and parasite class repro- I will focus here on the ability of mutant parasite (with strategies ductive values in the different hosts (see Discussion in the main ai*, bij*, and gi*) to invade a resident parasite population (with strat- text).