vol. 161, no. 5

the american naturalist

may 2003

A Model for the Coevolution of Immunity and Immune Evasion in Vector-Borne Diseases with Implications for the Epidemiology of Malaria

Jacob C. Koella* and C. Boe¨te†

Laboratoire de Parasitologie Evolutive, Centre National de la Recherche Scientifique, Unite´ Mixte de Recherche 7103, Universite´ Pierre et Marie Curie, 7 quai Saint Bernard, CC237, 75252 Paris, France Submitted July 2, 2002; Accepted November 6, 2002; Electronically published March March 21, 2003

abstract: We describe a model of host-parasite coevolution, where the interaction depends on the investments by the host in its immune response and by the parasite in its ability to suppress (or evade) its host’s immune response. We base our model on the interaction between malaria parasites and their mosquito hosts and thus describe the epidemiological dynamics with the Macdonald-Ross equation of malaria epidemiology. The qualitative predictions of the model are most sensitive to the cost of the immune response and to the intensity of transmission. If transmission is weak or the cost of immunity is low, the system evolves to a coevolutionarily stable equilibrium at intermediate levels of investment (and, generally, at a low frequency of resistance). At a higher cost of immunity and as transmission intensifies, the system is not evolutionarily stable but rather cycles around intermediate levels of investment. At more intense transmission, neither host nor parasite invests any resources in dominating its partner so that no resistance is observed in the population. These results may help to explain the lack of encapsulated malaria parasites generally observed in natural populations of mosquito vectors, despite strong selection pressure for resistance in areas of very intense transmission. Keywords: coevolution, host-parasite evolution, resistance, immunosuppression, malaria.

How much should a host invest in defense against parasites? The answer to this question is generally phrased as the evolutionary pressure to balance the evolutionary costs * E-mail: [email protected]. †

E-mail: [email protected].

Am. Nat. 2003. Vol. 161, pp. 000–000. 䉷 2003 by The University of Chicago. 0003-0147/2003/16105-020254$15.00. All rights reserved.

and benefits of resistance (Antonovics and Thrall 1994; Boots and Haraguchi 1999; Roy and Kirchner 2000; Bowers 2001; Bowers and Hodgkinson 2001). While this approach has given important predictions about, for example, the maintenance of polymorphic populations (Boots and Haraguchi 1999), it neglects that parasites can respond (over evolutionary time) to the host’s resistance. Possibilities for an evolutionary response include avoiding a host’s immune response, for example, by Leishmania spp. or Schistosoma spp. (Roitt et al. 1985), or suppressing the immune response, for example, by HIV (Bloom et al. 1992), leprosy (Modlin et al. 1986), or malaria (Urban et al. 1999). The parasite’s evolutionary response sets the stage for coevolutionary interactions between host and parasite. And indeed, recent studies have emphasized the importance of considering the coevolutionary response in theoretical models of host-parasite evolution. In particular, it can lead to an epidemiological feedback between the selection pressures on each partner of the interaction. Thus, host and parasite respond to the evolutionary pressures in a way that modifies the epidemiological situation that, in turn, is responsible for the evolutionary pressures. This feedback can alter the conclusions of models describing the evolution of single species (Frank 1994; Hochberg et al. 2000; Restif et al. 2001) and leads, for example, to the nonintuitive predictions that mutualistic interactions should be favored in unfavorable environments (Hochberg et al. 2000) and that multiple life-history strategies can evolve in a population of hosts responding to parasitism (Restif et al. 2001). A further example concerns the evolution of a host’s resistance. If the host’s resistance coevolves with the parasite’s virulence, two evolutionarily stable outcomes are possible: one in which the parasites are avirulent and the hosts invest only little in resistance, and one with highly virulent parasites and highly resistant hosts (van Baalen 1998). Here, we consider a coevolutionary model of a host’s investment in its immune system and its parasite’s ability

PROOF 2

The American Naturalist

to avoid or suppress the immune response. We focus on a specific example—the interaction between malaria parasites and their mosquito vectors—to ask the question, Why has the mosquito’s immune encapsulation response, an effective defense mechanism against many eukaryotes and microorganisms (Richman and Kafatos 1996), not evolved to resist malaria parasites? Indeed, Anopheles gambiae, the major vector of malaria in sub-Saharan Africa, fails to encapsulate and kill 99.5% of the infections, although it is capable of encapsulating and melanizing other foreign bodies (Schwartz and Koella 2002). The reason for a lack of resistance does not appear to be a lack of selection pressure, since the parasite reduces the mosquito’s reproductive success by reducing the mosquito’s fecundity (Hogg and Hurd 1995a, 1995b, 1997) and its longevity (Anderson et al. 2000; Ferguson 2002). Rather, possible explanations for the lack of resistance are that the parasite avoids immune recognition or suppresses the immune response (Boe¨te et al. 2002). To gain more insight into this problem and into the coevolution of hosts and parasites in general, we describe a model for the coevolution of the mosquito’s immune response and the parasite’s ability to avoid or suppress the response, assuming that the host’s investment in immunocompetence and the parasite’s investment in immune evasion are continuous quantitative traits. Our goals are to find the coevolutionarily stable investments for the host and the parasite, to predict how these investments change with intensity of transmission (i.e., probability of infection), and ultimately to give a possible reason for the apparent lack of resistance in natural populations. To simplify the analysis, we proceed in three steps. First, we find the optimal investment for the parasite assuming a fixed investment by the host, then we find the optimal investment of the host for a given investment of the parasite, and finally we combine the two approaches to find the coevolutionarily stable investments. Although the model is based on the interaction between malaria parasites and their mosquito vectors, the conclusions will be valid for other parasites that are indirectly transmitted via intermediate hosts. The model can therefore give predictions about a host’s resistance against other vector-transmitted parasites than malaria and can help to understand the coevolutionary dynamics of parasite-host interactions in general. It complements two previous models of the coevolution of resistance and virulence: the coevolution of parasitoid virulence and host resistance (Sasaki and Godfray 1999) and the coevolution of parasite efficacy and host resistance (modeled as Lotka-Volterra predator-prey equations; Frank 1994). Note that, as we are interested in the specific interaction between the malaria parasite and the mosquito vector and in host-parasite coevolution in general, we use the words

“host,” “vector,” and “mosquito” equivalently and, to avoid confusion, refer to the second host in the parasite’s life cycle as “human.”

The Model Strategies We assume that the host’s and the parasite’s levels of investment are continuous traits. The hosts invest a level h (0 ≤ h ≤ 1) in their immune efficacy, and the parasites invest a level p (0 ≤ p ≤ 1) into avoiding or suppressing the host’s immune response. We further assume that the potential efficacy of the immune response (i.e., if the parasite does not suppress it) increases monotonically with the host’s investment and that the efficacy decreases as the parasite’s investment increases. The probability E that the host encapsulates and kills a parasite is then E p h j(1 ⫺ p t), where the parameters j and t are introduced to describe the departures from linearity. For the analyses presented here, we assume that j p t p 1. We also assume that both investments are associated with a cost. The host’s investment reduces its reproductive success by a factor gh(h) p 1 ⫺ bh m, where b determines the maximal cost and m describes the departure from linearity (so that low values of m imply a high cost at low levels of investment). The parasite’s investment reduces its infectiousness (the parameter b described below) by an analogous factor gp(p) p 1 ⫺ xp n. Note that the equation for the host’s cost could be modified to describe a conditional cost, that is, a cost that arises only when the immune response is stimulated by infection. With such a conditional cost we reached qualitative conclusions similar to the ones that we describe below so that we do not show the results. Furthermore, in later sections we show and discuss only the results of simulations with a linear parasite response (n p 1), as variations of this parameter had no qualitative effect.

Epidemiological Equations The epidemiological dynamics are described by slight modifications of the classical Macdonald-Ross model of malaria epidemiology (Macdonald 1957; Koella 1991). The human population is split into a proportion x of susceptible individuals, a proportion y of infecteds, and a proportion z of immunes. The changes in the proportions of these three categories are described by the following differential equations:

Coevolution of Hosts and Parasites x˙ p d ⫺ dx ⫺ Vx ⫹ lz, y˙ p Vx ⫺ (n ⫹ d)y,

(1)

˙z p ny ⫺ (l ⫹ d)z.

ˆ ⫺ vˆ ⫺ w)e ˆ ⫺mT ⫺ mv, v˙ p aby(1 ⫺ v ⫺ w) ⫺ aby(1 ˙ p aby(1 ˆ ⫺ vˆ ⫺ w)e ˆ ⫺mT ⫺ mw, w

y . m ⫹ aby

(3)

Note that we here assume that each bite by an infectious mosquito results in an infection in the human host. Although this might be unrealistic, reducing the inoculation rate by the proportion of unsuccessful bites does not change the qualitative conclusions. (Alternatively, we could redefine the parameter b to summarize the efficacy of the parasite over the whole life cycle, combining the infectiousness of humans to mosquitoes and the infectiousness of mosquitoes to humans.) As is customary for epidemiological models, we summarize transmission with the basic reproductive number R0, which equals the number of secondary cases following the introduction of a single infected individual into a susceptible population. The basic reproductive number can be calculated from the condition that the number of infected humans increases when the proportion of infected humans is close to 0. This condition, y˙ p V ⫺ (n ⫹ d)y 1 0 evaluated for y K 1, gives R0 p

Mba 2e⫺mT . (n ⫹ d)m

(4)

Note that R 0 is a function of the host’s and the parasite’s investment (both of which, via the encapsulation rate, will determine b). We define R ∗0 as the basic reproductive number where neither partner invests into defense or counterdefense (i.e., h p p p 0) and use it as an indicator of the intensity of transmission and thus of the probability that the host becomes infected. At equilibrium, the proportion of infected humans (y) can be calculated as

(2)

where yˆ { y(t ⫺ T), vˆ { v(t ⫺ T), and wˆ { w(t ⫺ T). Because the mosquito dynamics operate on a much faster timescale than the human dynamics described by equation (1), the mosquito population can be considered to be at equilibrium with respect to changes in the human population. This allows its dynamics to be collapsed into an equation describing the proportion of infectious mosquitoes as a function of the proportion of infected humans, y: w p bae⫺mT

that is, the number of infectious mosquitoes multiplied by their biting rate, can be calculated as V p Mwa p Mba 2e⫺mT

Susceptibles become infected at the inoculation rate V (the number of infectious mosquitoes multiplied by their biting rate, described in more detail below), infected individuals recover at a rate n to become immune, and immunes lose their immunity and become susceptible again at a rate l. Deaths occur at a rate d (i.e., the life expectancy is 1/d) and are not affected by infection. They are balanced by births into the susceptible class (i.e., the rate of birth is set to d) so that the population size remains constant. Consider next the infection rate of the mosquito vectors. The mosquito population is maintained at a constant density of M mosquitoes per human host. The population is split into a proportion v of latent mosquitoes that have been infected but have not yet developed infectious stages of the parasite (sporozoites), a proportion w of infectious individuals with sporozoites in the salivary glands, and a proportion u p 1 ⫺ v ⫺ w of uninfecteds. Susceptible mosquitoes become infected by biting infected humans at a rate a; a proportion b of these bites lead to infection. Thus, the proportion of infected mosquitoes increases at a rate aby (1 ⫺ v ⫺ w). The newly infected mosquitoes become infectious to humans if they survive the incubation period T required for the development of the parasite. If the mosquito’s mortality rate is m, a proportion e⫺mT survives this period. Thus, of the aby(1 ⫺ v ⫺ w) mosquitoes infected T days earlier, a proportion e⫺mT moves from the latent to the infectious state. The proportions of latent and infectious mosquitoes decrease through mortality. The process of infection can thus be summarized as

PROOF 3

y . m ⫹ aby

Thus, the inoculation rate V of humans (see eqq. [1]),

yˆ p

R0 ⫺ 1 . (n ⫹ l ⫹ d)R 0 /(l ⫹ d) ⫹ ab/m

(5)

Evolutionary Pressure To find the coevolutionarily stable investment strategies, we first find the optimal investments of the host and of the parasite for a given investment by the partner and then combine the two approaches. Optimal investment of the parasite. As we assume that there are no multiple infections in the final host or the vector, the parasite’s strategy that maximizes R 0 will be evolutionarily stable (Bremermann and Pickering 1983; Bremermann and Thieme 1989). The only parameter in

PROOF 4

The American Naturalist

the equation of R 0 (eq. [4]) that depends on the parasite’s strategy is the infectiousness b, which is determined by the proportion of infections that are not encapsulated and by the reduction of the infectiousness due to the cost of investment in immunosuppression. Thus, b p [1 ⫺ E(h, p)]gp(p) p [1 ⫺ h j(1 ⫺ p t)](1 ⫺ xp n).

(6)

Maximizing this equation given the vector’s immune response h defines the optimal level of immunosuppression p with the implicit equation db p 0 ⇒ (n ⫹ t)xh jp n⫹t ⫹ nx(1 ⫺ h j)p n ⫺ th jp t p 0. dp

duced by the cost of investing in the immune response and, if the host is infected, by the parasite’s virulence. If infection is a random process, the probability that a mosquito will become infected (by a parasite that is not encapsulated) during its lifetime is proportional to the nonˆ , zero term of the Poisson distribution 1 ⫺ exp [(⫺ab/u) y] ˆ where y is the prevalence in the human population at equilibrium (given by eq. [5]), b is the infectiousness to the host (eq. [6]), and a/m is the average number of bites per lifetime. Infection decreases the host’s fecundity by the parasite’s virulence a. Taking into account the cost of investing into the immune response, we thus calculate the host’s reproductive success as

{ [ { [

( )]} ( )]}

L p r 1 ⫺ a 1 ⫺ exp ⫺ Thus, the optimal investment of the parasite increases with the investment of the host (fig. 1A). It is, however, independent of the intensity of transmission R ∗0 and, in particular, also of the host’s biting rate a and mortality m, the ratio of which is proportional to the number of times the parasite is transmitted during the life span of the mosquito. Optimal investment of the host. For simplicity, we assume that the host’s measure of fitness is its reproductive success (when the population has reached its dynamic equilibrium) and thus neglect aspects related to the timing of reproduction within the adult life span. Furthermore, we assume that the population is not regulated by densitydependent processes so that we can assume that evolution will maximize reproductive success (Mylius and Diekman 1995). The host’s intrinsic potential to reproduce is re-

p r 1 ⫺ a 1 ⫺ exp ⫺

ab yˆ gh(h) m ab yˆ (1 ⫺ bh m), m

(7)

where r is the reproductive success of uninfected individuals with no investment in immunity. We found the level of investment h that maximizes this equation numerically. Two qualitatively different outcomes of the maximization procedure are possible. First, for strong nonlinearity in the function defining the cost of investment (i.e., with sufficiently high m), the investment by the host evolves to a single stable equilibrium that is determined by the intensity of transmission R ∗0 and by the parasite’s investment in immunosuppression (fig. 1B). As long as the parasite’s investment remains below a threshold (which is deter-

Figure 1: Evolutionary equilibria of the parasite’s investment in immunosuppression and the host’s investment in its immune response. A, Parasite’s optimal level of investment, calculated by maximizing equation (6) as a function of the host’s immune response. The parameters for the cost of immunosuppression are n p 2 , x p 0.4 ; the parameters of the function determining the encapsulation response are j p t p 1 . B, C, Host’s optimal level of investment, calculated by maximizing equation (7) as a function of the parasite’s investment. In both panels, the cost of the parasite’s investment as in A and the epidemiological parameters are a p 0.5 , a p 0.5 , m p 0.1 . In B, the parameters for the cost of the immune response are m p 3, b p 0.3, and the three intensities of transmission (R∗0 ) are indicated in the figure. In C, the cost of the immune response is changed to m p 1.1 and the intensity of transmission is set to R∗0 p 5 . The solid lines give the optimal response, and the dashed line shows the level of investment with minimal reproductive success.

Coevolution of Hosts and Parasites

PROOF 5

Figure 2: Phase plots showing the coevolutionary equilibria of the host’s investment in its immune response and the parasite’s investment in immunosuppression. The initial intensity of transmission R∗0 increases from (A) R∗0 p 2 through (B) R∗0 p 6 to (C) R∗0 p 18 . The cost of investing in immunity is set to m p 1.1; the other parameters are as in figure 1. The isoclines of the host and parasite show the levels of investment that maximize the host’s success (solid lines), minimize the host’s success (dashed lines), and maximize the parasite’s success (dotted line). The coevolutionary equilibrium is given by the intersection of the isoclines. In A and C, the equilibrium is stable; in B, it is unstable. The arrows show the selection pressures for the two partners and thus give an impression of the coevolutionary dynamics.

mined by the intensity of transmission), the host’s investment increases with that of the parasite. Above the threshold, however, the host’s investment decreases as that of the parasite increases; if the parasite completely blocks the host’s immune response (i.e., at p p 1), the host obtains no benefits investing in immunity, and the optimal investment is 0. The association between the host’s investment in immunity and the intensity of transmission R ∗0 depends on the parasite’s level of immunosuppression. At low levels, investment into immunity increases as transmission intensifies, while at high levels, immunity decreases with transmission. The former pattern seems intuitively clear: investment into immunity should increase if the probability of being infected increases. The latter pattern, in contrast, may need an explanation. The reason for the switch in the relationship between immunity and transmission is that as immunosuppression increases, the high investment by the host that would evolve with low immunosuppression becomes less effective so that its benefit decreases to the extent that the high cost of maintaining the immune system becomes prohibitive. Second, if the cost of investing in immunity increases less nonlinearly with the investment (with sufficiently low m), the investment switches abruptly from a very high level at low immunosuppression to a very low level at high immunosuppression. At intermediate levels of immunosuppression, the two (locally stable) equilibria co-occur, with a basin of attraction determined by an intermediate level of investment giving minimal reproductive success (fig. 1C). Coevolutionarily stable strategy. We found the coevolutionary equilibrium with the intersections of the isoclines

described above. As each isocline describes the stable investment of one of the partners, the intersection defines a coevolutionarily stable strategy. Using this approach, we did not intend to simulate the coevolutionary dynamics but only to find the equilibrium. If the cost of immune function increases close to linearly with investment (i.e., for sufficiently low values of m), the coevolutionary process can lead to three qualitatively different types of outcome. If transmission is weak, the investments of the host and the parasite stabilize at intermediate levels (fig. 2A). At intermediate levels of transmission, the parasite’s isocline crosses the line of the host’s minimal reproductive success so that the intersection defines a saddle point (fig. 2B). Therefore, no stable equilibrium is possible. Rather, as indicated by the arrows showing the direction of selection pressure in figure 2B, the host’s and the parasite’s levels of investment cycle around the saddle point. At intense transmission, the investments decrease until neither partner invests any resources in their respective strategies (fig. 2C). Note that the lack of investment by the hosts is coevolutionarily stable, although their evolutionarily optimal strategy (given weak investment by the parasite) would be to invest a great deal in their immune function (the upper line in fig. 2C). As indicated by the arrows, however, the parasites increase their investment in immunosuppression when hosts are immune competent. This eventually drives the system to the lower level of investment in immune function by the host, where immunosuppression is lost because of its cost. If the costs of investment are strongly nonlinear (i.e., for sufficiently high values of m), a stable coevolutionary

PROOF 6

The American Naturalist

equilibrium is reached at any intensity of transmission. As expected, the investment of the host in immunocompetence decreases with decreasing virulence of the parasite. Furthermore, the host’s investment decreases with increasing intensity of transmission R ∗0 , accompanied by decreasing investment by the parasite in immunosuppression (fig. 3). The combined effect of the two coevolutionary changes on the rate of encapsulation is small so that the encapsulation changes only slightly as transmission intensifies (fig. 3). Similar patterns were observed if, rather than varying the intensity of transmission R ∗0 , we varied the individual parameters defining R ∗0 (and at the same time the host’s reproductive success and optimal investment). Thus, the host’s and parasite’s investments decrease, while encapsulation rate changes only slightly, as biting rate a increases or natural mortality m decreases. Discussion Summary of Results The main findings of our model are that the coevolutionary process between a host’s immunity and a parasite’s response can lead to three types of outcomes. First, the general outcome is a stable equilibrium with intermediate levels of investment by the host and the parasite, where both partners invest less as the intensity of transmission increases. This counterintuitive result follows from the nonlinearities intrinsic to the epidemiology of the infection process. If transmission is very intense, the probability that a host becomes infected changes only slightly if the investment into resistance is increased (in particular, if the parasite responds to increased resistance by increasing its own investment into immune evasion). The small decrease of infection (and mortality) cannot balance the high cost associated with the increased investment. In other words, the host trades off the risk of being killed by the parasite against the savings in the costs of having to defend itself against infection. The epidemiological consequence of this is that the low proportion of parasites that are encapsulated changes only slightly or decreases if intensity of transmission changes. Second, if the cost of investing into resistance is sufficiently high and transmission is sufficiently intense, the host invests no resources in its immune response, and accordingly, the parasite invests nothing in a counterresponse (fig. 2C). This may seem counterintuitive, as at low levels of immune evasion the host would profit from a very high level of investment, and indeed, there may be a global maximum at complete investment (fig. 1C). Thus, it is not the high cost per se that prohibits the spread of resistance but rather the coevolutionary process that ensures that the equilibrium with no resistance is maintained; strong resistance will lead to high immune

Figure 3: The coevolutionarily stable equilibrium as a function of the initial intensity of transmission R∗0 . The other parameters are as in figure 2, except for the parameter defining the cost of immunity m p 3. The levels of investment of the host are shown as a solid line, that of the parasite are shown as the dotted line, and the proportion of infections that is encapsulated is shown as the dash-dotted line.

evasion, which in turn will favor low resistance. Third, when the cost of immunity is high and transmission is intermediate, no stable equilibrium is achieved, but the host’s and parasite’s levels of investment cycle around intermediate values. Thus, taking account of the coevolutionary process leads to predictions very different from those obtained from more simple models that consider only the evolution of the host. Thus, one recent model is based on the same epidemiological equations as the ones used here but neglects the coevolutionary response of the parasite; it predicts that resistance will be maintained at a stable level, which increases from 0 at a low intensity of transmission (or very high cost) to close to 100% at intense transmission (Boe¨te and Koella 2002).

Comparison with Population Genetic Models It may be worth comparing our results with those obtained from population genetic approaches to coevolution, as several of their predictions appear similar to ours. Population genetic models generally approach host-parasite interactions from the viewpoint of the genetic interactions determining resistance. In matching allele models, parasites are successful only if none of the resistance alleles correspond to their own virulence alleles (Frank 1996), so that the interaction is highly specific. This type of interaction leads to frequency-dependent selection, where rare host genotypes have an advantage so that cycles of resistance are commonly predicted (Frank 1996). Although our model also predicts cycles of resistance (at intermediate

Coevolution of Hosts and Parasites transmission rates), the underlying mechanism is different, as our model does include genotype-specific resistance and infectiousness. The cycles in our model are due to density dependence in the epidemiological process rather than to frequency-dependent fitness of individual genotypes. In gene-for-gene models, the interaction is less specific, and some parasite genotypes can attack all hosts, and some host genotypes are susceptible to all parasites (Parker 1994). For some combinations of costs of resistance and of infectiousness, the pathogens can evolve to infect all hosts irrespective of their genotype. Once this occurs, host resistance brings no advantage and the genes coding for resistance disappear, which in turn selects for avirulence. Thus, as in our model (when the intensity is sufficiently high), the coevolutionary equilibrium can be at a state of no investment in resistance and no investment in countering resistance. The difference between the approaches is that our model predicts a stable equilibrium at no investment, while the gene-for-gene approach predicts an equilibrium that can be invaded by novel mutations for resistance. Limitations and Generality of Model Obviously, as in any mathematical or nonmathematical model, the quality of the predictions depends on the quality of the assumptions. There are several reasons for believing that the epidemiological aspect of our model captures some aspect of reality. Compartment models of infectious diseases in general have had considerable success in epidemiology (Anderson and May 1991). In particular, compartment models similar to the ones used here can successfully describe epidemiological patterns of malaria (Molineaux and Gramiccia 1980). Similar models are considered helpful in evaluating the sensitivity of malaria transmission to different control measures (Macdonald 1957) and in predicting the effectiveness of vaccine programs (Koella 1991; Gupta and Anderson 1996; Gandon et al. 2001). As in these models, we ignore the genetic basis of the host’s and parasite’s strategies and thus assume that the evolutionary responses are not constrained by the genetic architecture. Perhaps more worrying is the way that we dealt with superinfection. In order to simplify the calculations, we assumed that neither the human host nor the mosquito vector could be infected more than once, leading to the absence of within-host selection. As the probability of multiple infection increases with the intensity of transmission, selection pressure for resistance may be expected to increase as well. One might therefore assume that the possibility of superinfections would reverse our conclusion that the investment by the host tends to decrease as transmission intensifies. However, although we have not mod-

PROOF 7

eled the possibility of superinfection, we expect that this will not be the case. Indeed, the mechanism underlying the coevolutionary pattern is that selection for immunosuppression intensifies as immunocompetence increases. We therefore expect that any increase of resistance due to superinfections would be balanced by increased selection for immunosuppression. Our model shares several results with two previous models describing the coevolution of a host’s resistance and its parasite’s counterresponse (Frank 1994; Sasaki and Godfray 1999). In particular, these models also give three outcomes: stable strategies with no resistance, stable with intermediate resistance, and cycling. The details of the results, however, differ in two main aspects. First, in contrast to our results, the tendency of the system to cycle increased as the parasite’s reproductive capacity (i.e., the intensity of transmission) increased in one of the models (Frank 1994), while in the other (Sasaki and Godfray 1999), cycling is most likely to occur for moderate costs of immunity and immunosuppression. Second, the previous models suggest that no investment by the host is likely to evolve under a wide range of conditions and that no investment by the host can be accompanied by intermediate investment by the parasite in immunosuppression. The latter difference can be easily explained by the difference in the function determining the probability that a parasite can successfully infect its host. While both previous models assumed that this probability is determined by the difference between the two levels of investment, our function is based on the assumption that the host cannot resist any parasite if it invests no resources in resistance, independently of the parasite’s investment. When we changed our encapsulation function, our results conformed to the previous ones: at high costs of resistance, the host evolved to 0 resistance while the parasite evolved to an intermediate investment (results not shown). The former difference emphasizes the difficulties in generalizing results about complex coevolutionary processes to systems with different underlying dynamics. While all three models describe the coevolution of hosts and parasites, one is based on Lotka-Volterra type dynamics (Frank 1994), one on Nicholson-Bailey host-parasitoid dynamics (Sasaki and Godfray 1999), and our own on RossMacdonald dynamics of malaria epidemiology (Macdonald 1957). Apparently, the differences in the underlying population dynamics can give rise to the opposite predictions. While we predict cyclical evolutionary dynamics with high costs and low transmission, Lotka-Volterra dynamics predicts cycles at intense transmission, and Nicholson-Bailey predicts cycles at moderate but not high costs. Thus, while coevolutionary dynamics give rise to com-

PROOF 8

The American Naturalist

plex predictions in several models, the details of the underlying population dynamics can lead to qualitatively different conclusions. A synthesis of these differing conclusions remains to be done. Implications for Malaria Epidemiology and Control The model presented is a first theoretical step toward understanding the low level of refractoriness against malaria in natural populations of mosquito vectors. It suggests that a high cost of resistance, combined with the coevolutionary pressure by the parasite and the generally high intensities of malaria transmission, maintains investment into immunity at a level very close to 0 (fig. 2C). Of course, other mechanisms could also be involved, for example, genotype by genotype interactions between hosts and parasites allowing each host to recognize and melanize only a small fraction of the parasites. There is, however, only weak evidence for such interactions in the malaria-mosquito system: mosquitoes that had been selected for refractoriness against Plasmodium chabaudi are able to melanize strains of Plasmodium falciparum from the New World, but their immune response is less effective against strains from the Old World (Collins et al. 1986). And indeed, although this observation is consistent with genotype by genotype interactions in recognition, it could just as easily be explained if Old World parasites have more effective immunosuppression. The explanation that we offer is made plausible by data concerning the critical aspects of our model. Most importantly, infection by malaria parasites reduces the efficacy of the mosquito’s immune response (Boe¨te et al. 2002), setting the stage for a coevolutionary arms race. It is not yet known whether this reduction has a genetic basis or is associated with a cost to the parasite, but both appear to hold true for parasitoids that suppress the immune response of their host Drosophila melanogaster (Kraaijeveld et al. 2001). It is also starting to be clear that malaria parasites exert considerable selection pressure on their mosquito vectors to become resistant, as they reduce reproductive success in at least two ways: by reducing fecundity (Hogg and Hurd 1995a, 1995b, 1997) and by reducing longevity (Anderson et al. 2000). (Note that, although the parasite’s effect on longevity is still being debated, a recent meta-analysis suggests that, in general, mosquitoes infected with malaria do indeed have a shorter life span than uninfected controls [Ferguson 2002].) Finally, the immune response of insects is generally associated with an evolutionary cost (Kraaijeveld and Godfray 1997; Siva-Jothy et al. 1998; Moret and Schmid-Hempel 2000; McKean and Nunney 2001), and mosquitoes are no exception. Thus, activating the antibacterial immune response with a lipopolysaccharide from E. coli decreases the

fecundity of mosquitoes (Ahmed et al. 2002), and selecting mosquitoes for more rapid development decreases the efficacy of the encapsulation immune response (Koella and Boe¨te 2002). Should our explanation—the coevolution of the mosquito’s resistance and the parasite’s immunosuppression (or evasion)—indeed underlie the lack of resistance against malaria in natural populations, it would have important implications for strategies of malaria control based on genetic manipulations of mosquitoes for higher resistance. The idea of genetic manipulation is to increase the refractoriness of mosquitoes or, in terms of the model described here, to increase the mosquito’s investment (Aultmann et al. 2001). Our model predicts, however, that the parasite would respond over evolutionary time by increasing its effort in immune evasion or suppression (fig. 1). Thus, while the program might initially have some success, in the long term the expected reductions in the encapsulation rate and in malaria transmission would be small. General Conclusions Although our model is based on malaria epidemiology, its conclusions are more general and complement previous approaches to the evolution of defense and counterdefense in host-parasite systems (Frank 1994; Sasaki and Godfray 1999). In particular, it emphasizes, together with the previous models, the importance of taking into account the coevolutionary response of the parasite to an evolutionary change in resistance. Only this coevolutionary pressure allows cyclical dynamics or maintains the levels of investment in resistance and evasion at 0. Furthermore, our model makes clear some of the critical assumptions that have led to earlier predictions and emphasizes the critical role of the underlying dynamics in reaching general conclusions about the coevolutionary process. Acknowledgments We thank O. Restif and O. Kaltz for helpful comments and an anonymous reviewer for useful comments. C.B. was supported by a Bourse Docteur-Inge´nieur from Centre National de la Recherche Scientifique. Literature Cited Ahmed, A. M., S. L. Baggott, R. Maingon, and H. Hurd. 2002. The costs of mounting an immune response are reflected in the reproductive fitness of the mosquito Anopheles gambiae. Oikos 97:371–377. Anderson, R. A., B. J. G. Knols, and J. C. Koella. 2000. Plasmodium falciparum sporozoites increase feedingassociated mortality of their mosquito hosts Anopheles gambiae s.l. Parasitology 120:329–333.

Coevolution of Hosts and Parasites Anderson, R. M., and R. M. May. 1991. Infectious diseases of humans: dynamics and control. Oxford University Press, Oxford. Antonovics, J., and P. H. Thrall. 1994. The cost of resistance and the maintenance of genetic polymorphism in host-pathogen systems. Proceedings of the Royal Society of London B, Biological Sciences 257:105–110. Aultmann, K. S., B. J. Beaty, and E. D. Walker. 2001. Genetically manipulated vectors of human disease: a practical overview. Trends in Parasitology 17:507–509. Bloom, B. R., P. Salgame, and B. Diamond. 1992. Revisiting and revising T suppressor cells. Immunology Today 13: 131–136. Boe¨te, C., and J. C. Koella. 2002. A theoretical approach to predicting the success of genetic manipulation of malaria mosquitoes in malaria control. Malaria Journal 1: 3. Boe¨te, C., R. E. L. Paul, and J. C. Koella. 2002. Reduced efficacy of the immune melanisation response in mosquitoes infected by malaria parasites. Parasitology 125: 93–98. Boots, M., and Y. Haraguchi. 1999. The evolution of costly resistance in host-parasite systems. American Naturalist 153:359–370. Bowers, R. G. 2001. The basic depression rate of the host: the evolution of host resistance to microparasites. Proceedings of the Royal Society of London B, Biological Sciences 268:243–250. Bowers, R. G., and D. E. Hodgkinson. 2001. Community dynamics, trade-offs, invasion criteria and the evolution of host resistance to microparasites. Journal of Theoretical Biology 212:315–331. Bremermann, H. J., and J. Pickering. 1983. A gametheoretical model of parasite virulence. Journal of Theoretical Biology 100:411–426. Bremermann, H. J., and H. R. Thieme. 1989. A competitive-exclusion principle for pathogen virulence. Journal of Mathematical Biology 27:179–190. Collins, F. H., R. K. Sakai, K. D. Vernick, S. Paskewitz, D. C. Seeley, L. H. Miller, W. E. Collins, et al. 1986. Genetic selection of a Plasmodium-refractory strain of the malaria vector Anopheles gambiae. Science (Washington, D.C.) 234:607–610. Ferguson, H. M. 2002. Why is the impact of malaria parasites on mosquito survival still unresolved? Trends in Parasitology 18:256–261. Frank, S. A. 1994. Coevolutionary genetics of hosts and parasites with quantitative inheritance. Evolutionary Ecology 8:74–94. ———. 1996. Statistical properties of polymorphism in host-parasite genetics. Evolutionary Ecology 10: 307–317. Gandon, S., M. J. Mackinnon, S. Nee, and A. F. Read.

PROOF 9

2001. Imperfect vaccines and the evolution of pathogen virulence. Nature 414:751–756. Gupta, S., and R. M. Anderson. 1996. Predicting the effects of malaria vaccines on the population dynamics of infection and disease. Pages 224–276 in S. L. Hoffman, ed. Malaria vaccine development: a multi-immune response approach. ASM, Washington, D.C. Hochberg, M. E., R. Gomulkiewicz, R. D. Holt, and J. N. Thompson. 2000. Weak sinks could cradle mutualistic symbioses: strong sources should harbour parasitic symbioses. Journal of Evolutionary Biology 13:213–222. Hogg, J. C., and H. Hurd. 1995a. Malaria-induced reduction of fecundity during the first gonotrophic cycle of Anopheles stephensi mosquitoes. Medical and Veterinary Entomology 9:176–180. ———. 1995b. Plasmodium yoelii nigeriensis : the effect of high and low intensity of infection upon the egg production and bloodmeal size of Anopheles stephensi during three gonotrophic cycles. Parasitology 111:555–562. ———. 1997. The effects of natural Plasmodium falciparum infection on the fecundity and mortality of Anopheles gambiae in north east Tanzania. Parasitology 114: 325–331. Koella, J. C. 1991. On the use of mathematical models of malaria transmission. Acta Tropica 49:1–25. Koella, J. C., and C. Boe¨te. 2002. A genetic correlation between age at pupation and melanisation immune response of the yellow fever mosquito Aedes aegypti. Evolution 56:1074–1079. Kraaijeveld, A. R., and H. C. Godfray. 1997. Trade-off between parasitoid resistance and larval competitive ability in Drosophila melanogaster. Nature 389:278–280. Kraaijeveld, A. R., K. A. Hutcheson, E. C. Limentani, and H. C. J. Godfray. 2001. Costs of counterdefences to host resistance in a parasitoid of Drosophila. Evolution 55: 1815–1821. Macdonald, G. 1957. The epidemiology and control of malaria. Oxford University Press, London. McKean, K. A., and L. Nunney. 2001. Increased sexual activity reduces male immune function in Drosophila melanogaster. Proceedings of the National Academy of Sciences of the USA 98:7904–7909. Modlin, R. L., V. Mehra, L. Wong, Y. Fujimiya, W. C. Chang, D. A. Horwitz, B. R. Bloom, et al. 1986. Suppressor T lymphocytes from lepromatous leprosy skin lesions. Journal of Immunology 137:2831–2834. Molineaux, L., and G. Gramiccia. 1980. The Garki project: research on the epidemiology and control of malaria in the Sudan savanna of West Africa. World Health Organization, Geneva. Moret, Y., and P. Schmid-Hempel. 2000. Survival for immunity: the price of immune system activation for

PROOF 10

The American Naturalist

bumblebee workers. Science (Washington, D.C.) 290: 1166–1168. Mylius, S. D., and O. Diekman. 1995. On evolutionary stable life histories, optimization and the need to be specific about density dependence. Oikos 74:218–224. Parker, M. A. 1994. Pathogens and sex in plants. Evolutionary Ecology 8:560–584. Restif, O., M. Hochberg, and J. C. Koella. 2001. Virulence and age at reproduction: new insights into host-parasite coevolution. Journal of Evolutionary Biology 14: 967–979. Richman, A., and F. C. Kafatos. 1996. Immunity to eukaryotic parasites in vector insects. Current Opinion in Immunology 8:14–19. Roitt, I., J. Brostoff, and D. Male. 1985. Immunology. Churchill Livingstone, Edinburgh. Roy, B. A., and J. W. Kirchner. 2000. Evolutionary dynamics of pathogen resistance and tolerance. Evolution 54:61–63. Sasaki, A., and H. C. J. Godfray. 1999. A model for the

coevolution of resistance and virulence in coupled hostparasitoid interactions. Proceedings of the Royal Society of London B, Biological Sciences 266:455–463. Schwartz, A., and J. C. Koella. 2002. Melanization of Plasmodium falciparum and C-25 Sephadex beads by field caught Anopheles gambiae (Diptera: Culicidae) from southern Tanzania. Journal of Medical Entomology 39: 84–88. Siva-Jothy, M. T., Y. Tsubaki, and R. E. Hooper. 1998. Decreased immune response as a proximate cost of copulation and oviposition in a damselfly. Physiological Entomology 23:274–277. Urban, B. C., D. J. Ferguson, A. Pain, N. Willcox, M. Plebanski, J. M. Austyn, and D. J. Roberts. 1999. Plasmodium falciparum–infected erythrocytes modulate the maturation of dendritic cells. Nature 400:73–77. van Baalen, M. 1998. Coevolution of recovery ability and virulence. Proceedings of the Royal Society of London B, Biological Sciences 265:317–325. Associate Editor: Curt Lively