## Abstract

Adaptive speciation has been much debated in recent years, with a strong emphasis on how competition can lead to the diversification of ecological and sexual traits. Surprisingly, little attention has been paid to this evolutionary process to explain intrahost diversification of parasites. We expanded the theory of competitive speciation to look at the effect of key features of the parasite lifestyle, namely fragmentation, aggregation and virulence, on the conditions and rate of sympatric speciation under the standard ‘pleiotropic scenario’. The conditions for competitive speciation were found similar to those for non-parasite species, but not the rate of diversification. Adaptive evolution proceeds faster in highly fragmented parasite populations and for weakly aggregated and virulent parasites. Combining these theoretical results with standard empirical allometric relationships, we showed that parasite diversification can be faster in host species of intermediate body mass. The increase in parasite load with body mass, indeed, fuels evolution by increasing mutants production, but because of the deleterious effect of virulence, it simultaneously weakens selection for resource specialization. Those two antagonistic effects lead to optimal parasite burden and host body mass for diversification. Data on the diversity of fishes' gills parasites were found consistent with the existence of such optimum.

## 1. Introduction

Our understanding of adaptive speciation has expanded broadly over the past two decades to describe how ecological interactions can lead to the diversification of ecological and sexual quantitative traits [1,2]. Theoretical developments have contributed to challenge the view that sympatric speciation is of little importance in explaining species diversity [1,3] and have stimulated much empirical research on the diversification of a wide range of organisms, including plants [4,5], fungi [6,7], algae [8,9], fishes [10,11], birds [12,13] as well as insects, crustaceans and microorganisms [14]. Surprisingly, the theory of adaptive speciation has paid virtually no attention to parasitic organisms, even though they represent an important proportion of species diversity [15,16] whose origin is often discussed with respect to their small body size [17–19], close interactions with their host [16–19], short generation time [18,19] and small effective population size [18]. Such a gap in the literature is surprising as the strong parasites' potential to diversify in sympatry [17,19,20,21] is recurrently claimed to result from the ecological interactions parasites have with their host and between them, and which are already known to influence their population dynamics [22,23] and micro-evolution [24–26].

One particular form of adaptive speciation is ‘competitive speciation’, in which intraspecific competition induces diversification of a quantitative trait associated with the use of gradients of resources [27]. Competitive diversification of non-parasite species has been intensively investigated in the past 10 years both theoretically and empirically [1,2], but we still have little knowledge about the possibility for within-host competition to convey parasite speciation [28,29]. Accordingly, we have no clear understanding of the influence of the specificities of the parasite lifestyle on the conditions and rates of competitive speciation. Parasite populations typically live in a fragmented environment as they are associated with host individuals, and their distribution among hosts is well known to be highly aggregated ([30,31] for reviews). Intuitively, fragmentation is expected to influence the level of competitive interactions and this should be further modulated by the level of aggregation. However, the net effect of these two basic features of parasites’ distribution on adaptive diversification remains broadly unknown. Additionally, parasite virulence could interact with the heterogeneous distribution of parasites among hosts to regulate the level of disruptive selection generated by within-host competitive interactions. Virulence can, indeed, induce the death of the most highly infected host individuals and of their parasites, so that wherever competition and disruptive selection pressure are the strongest, their effects on parasite populations could be counterbalanced by the deleterious impact of virulence. To make further progress on our understanding of competitive diversification of parasites, we need a quantitative theory providing clear predictions on the above potential effects of the three nearly universal features of parasite life history: (i) the fragmentation of the population between host individuals, (ii) the aggregation of individuals among the host population and (iii) parasite virulence, defined here as the *per capita* parasite-induced host mortality [32]. Importantly, the number of hosts in a population and the maximum number of parasites per host individual, which are involved in determining (i) and (ii), are well known to be linked to host body mass through empirically parametrized allometric relationships [33–37]. In this paper, we thus aimed at providing theoretical insights into the independent effect of each of the three above features as well as to produce testable predictions that account for those empirical relationships.

We expand the theory of competitive speciation to account for the key features of parasites’ life history. We focused on macro-parasite species that are transmitted by contact between host and egg or larval stages, and that spend the adult stage and reproduce within one single host individual. Typical examples of such parasites to whom the theory presented in this paper applies are worm species from taxa such as monogeneans, cestodes, trematodes and nematodes that infect wild host species, livestock or human (see [38] for a review). We combined the standard theory describing their ecology and control [39–41,32] with the general framework on ecological character displacement [42–49], effectively merging these two separated parts of theoretical evolutionary ecology. We concentrated on the most basic scenario of competitive speciation, the ‘pleiotropic scenario’ [50–52], whereby the phenotypic trait subject to divergent natural selection is called a ‘magic-trait’ because it pleiotropically contributes to non-random mating between the emerging phenotypic clusters of individuals [52,53]. More complex scenarios of diversification, involving the coevolution between traits determining competitive ability and sexual traits serving as clue for non-random mating, have been investigated for non-parasite species [54] and could be relevant for macro-parasites. These, nonetheless, fall beyond the scope of this first quantification of the effect of the main features of macro-parasites lifestyle on competitive diversification. Combining these theoretical results with standard empirical allometric relationships that link the host body mass with host population size [33,34] and parasite load [35–37], we produced testable predictions on the range of host species body mass that maximize the rate of within-host parasite diversification.

## 2. Material and methods

### 2.1. Model for a polymorphic population of macro-parasites

The model considers a population of macro-parasites whereby individuals differ with respect to a quantitative trait determining the part of a gradient of resource they are able to exploit, and, accordingly, the level of competitive interaction between individuals with different quantitative trait values. Although we do not know how frequent such traits occur in macro-parasites, examples include physiological or morphological traits such as parasite body mass [55,56], the size of anchors in monogenean flatworms colonizing fish gills [57] or the morphology of chewing lice in bird feathers [58]. Even though the role of competition in the diversification of these traits is not always clear [57], these traits are thought to be ‘magic traits’, as they can determine both the distribution of individuals along a gradient of resources in host gut [59], gills [60] or plumage [61], and the level of reproductive isolation between clusters of individuals mating within their niches [55,57,62]. ‘Magic traits’ are called so as they pleiotropically determine pre-zygotic isolation (because of assortative mating within the niche), and post-zygotic isolation (because of hybrid lower fitness induced by frequency- and density-dependent competitive interactions) [51, p. 368]. Individuals compete within each host according to a Lotka–Volterra function, following the standard theory of competitive speciation. Surviving parasites reproduce within-host before larvae disperse and colonize new hosts, the two processes being described according to the seminal model of Anderson & May [39] that dominates the ecological theoretical literature on macro-parasites [32,40,41]. We introduced an additional host mortality induced by the parasite and considered that such virulence (*V*) is independent of parasites’ phenotypes therefore assuming that the effect of a parasite individual on its host does not depend on which part of the gradient of resource it exploits. All modelling assumptions are thus highly consistent with both the theory on ecological character displacement and competitive speciation and the theory of macro-parasites’ ecology. We point out that the evolving trait is the quantitative character itself and not the level of virulence, so that our model is rooted in the theory of ecological character displacement, and is not meant to be a model of virulence evolution. We finally add that, although the Anderson & May model [39] was developed for directly transmitted parasites, our evolutionary modelling could potentially apply to macro-parasites with more complex life cycles, as long as the competitive selective pressures occurring within the different intermediate and definitive hosts are not antagonistic.

The model corresponds to an infinite system of ordinary differential equations describing the rate of variation of the number of hosts harbouring *n _{r}* and

*n*parasites with phenotype

_{m}*r*and

*m*, respectively. A model with a higher level of polymorphism could easily be derived, but such an additional complexity is not justified as standard evolutionary analysis are typically achieved by considering the fate of a mutant in its pairwise interaction with the established resident strategy. The recruitment and loss of hosts with

*n*and

_{r}*n*parasites are then related to the demography of the parasites, described by their intrinsic mortality (

_{m}*μ*) and colonization (

*β*) rates, their virulence (

*V*), the intensity of within-host competition (

*α*) and the within-host carrying capacity (

*K*) (see table 1 for more details about these parameters and figure 1 for their use to describe the host–parasite and parasite–parasite interactions). To derive the model, one first derives an infinite set of ordinary differential equations describing the variation in the number of host individuals carrying

*n*parasite individuals with the resident trait value

_{r}*r*[41]. This can be done while keeping

*n*as a constant, 2.1

_{m}Following the standard literature on ecological character displacement, we assumed and . The carrying capacity is then maximal for individuals with an intermediate trait value (*K*(*s*_{0})) as they exploit the centre of the resource gradient where the resource is more abundant. The level of competition between individuals is maximal when they have similar trait values and thus exploit the same part of the gradient. A second set of ordinary differential equations can be derived, to describe the rate of variation of the number while keeping *n _{r}* as a constant. This system is the exact symmetric of the system described by equation (2.1).

Summing over *n _{r}* and

*n*within each of the two infinite sets of equations [41], one can then derive a couple of ordinary differential equations describing the change in the number of parasite individuals of the two competing phenotypes

_{m}*r*and

*m*: 2.2aand 2.2b

### 2.2. The invasion fitness of macro-parasites

The general expression of the invasion fitness *f*(*m,r*) of a mutant with trait value *m* in a population of residents of trait value *r* was derived from equations (2.2*a*) and (2.2*b*), assuming that the residents are at their population dynamics equilibrium (see the electronic supplementary material, appendix A):
2.3with *Z*(*r*) = *S*(*m,r*)/*P*(*m*).

The term *S*(*m,r*) gives the number of resident individuals that mutants are expected to encounter in the hosts they colonize according to the distribution of parasites among hosts. This ‘effective number’ of resident individuals thus accounts for the effect of fragmentation and aggregation on the actual level of direct (competitive) or indirect (host-mediated) interactions. Accordingly, *Z*(*r*) stands for the ‘effective number’ of residents per mutant individual. The quantity *c* is the intrinsic fitness of parasite in the absence of interaction with other parasites and their host, which accounts for the intrinsic rates of survival and reproduction of adults within the host as well as the intrinsic survival of larvae outside of the hosts.

Assuming that mutants tend to infect the same hosts as residents, and that the resident population size is at its equilibrium value, *P*(*r*)*** (see equation (2.4) for a complete expression), the probability for a mutant to colonize a host already infected with *n _{r}* residents is

*n*(

_{r}/P*r*)

***[29]. Combining these probabilities with the partition of residents among hosts, which typically follows a negative binomial distribution (see [31] for a meta-review of field values), one can derive the average number of residents a mutant individual is expected to interact with

Furthermore, solving equation (2.2*a*) = 0, one can obtain the population size equilibrium value
2.4where *k* is the usual measure of parasite ‘aggregation’ among hosts [39]. Here, we note that there is a maximal level of virulence allowing for the population to persist; the size of the residents population *P*(*r*)*** is indeed positive if and only if *V* < *V*^{max} = *c −* 1*/K*(*r*).

The expression of *Z*(*r*) then follows from basic algebra: *Z*(*r*) = *cK*(*r*)*/*(1 + *VK*(*r*)), and one can complete the definition of the fitness function
2.5This function allows anticipation of the fate of a rare mutant emerging in a monomorphic population of resident individuals at their population dynamic equilibrium. This dynamic equilibrium, whose expression is given by equation (2.4), corresponds to a stable node as has been previously demonstrated in theoretical investigations on the effect of aggregation on host–macro-parasites interactions [31,39,40]. Assuming that invasion leads to the replacement of the resident by the mutant, which then grows in abundance until it reaches its own population dynamic equilibrium, the evolution of the quantitative trait involved in the exploitation of the resource gradient can be seen as a step-by-step mutation–substitution process. The adaptive dynamics (AD) framework [63,64] provides an ideal context to infer the outcome and speed of adaptive evolution in these conditions, and has been especially efficient in investigating how frequency- and density-dependent selection resulting from individual interactions can lead to adaptive diversification (see [1] for a review).

### 2.3. The adaptive dynamics and diversification of macro-parasites

#### (i) The conditions of adaptive diversification

The AD framework allows identification of specific values of the trait, called ‘evolutionary singularities’, and the conditions for such singularities to be ‘branching points’, i.e. points where a monomorphic population can adaptively split into two or more phenotypic clusters. It is important to mention that, under the pleiotropic scenario of speciation considered in this paper, these phenotypic clusters can readily be interpreted as incipient species, because the quantitative trait determines simultaneously both pre- and post-zygotic isolation. Conditions for the existence of a branching point [3] are then equivalent to conditions for parasite duplication, that is, sympatric speciation on the same host species [18]. We thus used the AD framework to derive the range of parameter values where macro-parasites are expected to diversify and, accordingly, we predicted the effects of macro-parasite life history on within-host adaptive speciation.

#### (ii) Rate of adaptive evolution

Although most studies focus on the identification of the conditions of adaptive speciation, the AD framework also allows investigation of the speed at which evolution proceeds towards branching points. The ‘canonical equation’ of AD, indeed, describes the rate of evolutionary change of the average phenotype in the population (*F*(*m*)) [65] as the product of the rate of mutation (*η _{m}*), the standard deviation of the distribution of the phenotypic effect of mutations (

*σ*), the size of the population of residents at dynamical equilibrium (

_{m}*P*(

*r*)

***) and the first derivative of the mutant fitness with respect to the mutant phenotype (). Using the definition of

*f*(

*m,r*) and

*P*(

*r*)

***given by equations (2.3) and (2.4), we obtained the canonical equation accounting the specificities of macro-parasites life history: 2.6

In equation (2.6), the term represents the evolutionary rate coefficient depending on the mutation rate (*η _{m}*), the mutational variance and the size of the resident population [65]. The remaining term represents the gradient of selection [65]. The evolutionary rate coefficient describes how evolution is fuelled with the appearance of new phenotypic variants, whereas the gradient of selection quantifies the direction and strength of selection. Importantly, the evolutionary rate and the gradient of selection here depend on the abundance of residents,

*P*(

*r*)

***, and the ‘effective number’ of residents per mutant,

*Z*(

*r*), respectively. The influence of the specificities of macro-parasites life history on the speed of evolution was analysed while keeping mutational parameters constant.

## 3. Results

### 3.1. Specificities of macro-parasites life history and impact on their fitness of invasion

#### (i) Effect of the fragmentation and aggregation of the parasite population

A simple inspection of the mutant invasion fitness (equation (2.5)) shows that it is independent of the size of the host population and of the level of aggregation of parasites. This may seem surprising as a stronger aggregation means that when the mutant colonizes an infected host it is more likely to share it with a larger amount of residents, and thus to suffer stronger competition. However, a stronger aggregation also means that these highly infected hosts are less abundant, and that alternative hosts with no or a low number of parasites are readily available for mutants. In our model, these two opposite effects exactly cancel out. Our model can then be seen as a neutral model similar in spirit to several basic ecological models of predator–prey [66,67], host–parasite [39] or host–parasitoid [68,69] interactions, and we defer to another contribution the test of departures from the neutral assumption of codistribution of mutants and residents (see Discussion).

#### (ii) Effect of virulence

Virulence has a negative impact on fitness as the additional host mortality induced by resident parasites can prevent mutants’ invasion. The first term inside brackets in equation (2.5) quantifies such a reduction in mutant invasion fitness, and can be interpreted as the effect of the (host-mediated) indirect interaction that typically appears between virulent parasites [70]*.* Virulence also has a positive effect on mutant invasion fitness, as it reduces the abundance of residents in hosts surviving infection and thus the competitive pressure exerted on mutants. The last term of equation (2.5) clearly reveals this positive contribution. Importantly, the net result of these antagonistic effects can be worked out by rewriting the fitness function as the product of a function of *V*, and the function obtained for non-virulent parasites:
3.1where *f _{V}*

_{=}_{0}(

*m,r*) stands for the fitness function of non-virulent parasites [29]. This function decreases monotonously with virulence, suggesting that the additional extinction of mutants associated with parasite-induced host mortality dominates the contribution of virulence to mutant invasion fitness.

### 3.2. Conditions and rate of adaptive diversification of macro-parasites

#### (i) Conditions for adaptive diversification

The analysis of mutant invasion fitness within the AD framework leads to relatively simple conclusions, whose mathematical proofs can be found in the electronic supplementary material, appendix B. The unique singular strategy is the trait value where the carrying capacity is maximum *s** = *s*_{0}, and one can show that evolution is expected to proceed towards such strategy as *s** is both a ‘continuously convergent’ and an ‘invasive’ strategy. In other words *s** is, as a mutant, able to invade any resident strategy corresponding to a trait value that is close or distant from *s*_{0}. An additional key result is that *s** is ‘evolutionary stable’ if and only if Accordingly, there are only two alternative outcomes for the evolution of the quantitative trait after it has reached *s**; either *s** is evolutionary stable, or it is not, and one thus expects further evolution. In that respect, the last important result is that a protected polymorphism can always appear in the vicinity of *s**. When *s** is not evolutionary stable, i.e. when , two or more phenotypic clusters will thus emerge and effectively lead to adaptive diversification and speciation. Such evolutionary strategy *s** is then called a ‘branching point’. The difference between these two situations can be further illustrated with standard pairwise invasibility plots (figure 2) and branching diagrams (figure 3). Importantly, the conditions for *s** to be a branching point are exactly the same as those identified for non-parasite species [3].

### 3.3. Rate of adaptive evolution

#### (i) Effect of the fragmentation and aggregation of the parasite population

The effects of the host population size and the level of aggregation on the rate of adaptive evolution appear clearly in figure 4*a*. The rate of evolution increases (linearly) with *H* and decreases monotonically with aggregation (because aggregation is negatively correlated with *k*). Indeed, the more hosts and the less aggregated parasites are, the more abundant resident parasites are, which speeds up evolution as more mutant offspring are produced. This acceleration of evolution appears explicitly in the evolutionary rate coefficient of the ‘canonical’ equation (once *P*(*r*)*** has been replaced by its expression given by equation (2.4)).

We tested in an independent manner the effect of the maximal number of parasites that each host individual can harbour, i.e. the maximum infection intensity, *K*(*s*_{0}). The effect of this maximal burden per host is much less obvious (figure 4*b*) as there is an optimal value, *K*_{opt}(*s*_{0}), leading to the fastest rate of evolution. The expression of this value can be sorted out analytically
3.2

The logic behind the unexpected existence of such an optimum is the following. Any increase in the carrying capacity *K*(*s*_{0}) leads to a higher abundance of residents which, again, increases the evolutionary rate coefficient (the first term of the canonical equation) and speeds up evolution as it leads to a higher production of mutant offspring. However, increasing *K*(*s*_{0}) also affects the gradient of selection (the second term of the canonical equation) in two separate ways. Larger *K*(*s*_{0}) raises the number *Z*(*r*) of resident individuals the mutants interact with, but it also leads to a higher carrying capacity for the mutant, *K*(*m*), which relaxes the strength of competitive interactions. But, because of the deleterious effect of virulence, the abundance of residents (*Z*(*r*) = *cK*(*r*)*/*(1 + *VK*(*r*))) increases in a slower way than the carrying capacity of the mutant . Consequently, the overall effect of larger *K*(*s*_{0}) is a reduction in the strength of competition and in the gradient of selection. This shapes the right part of the relationship shown in figure 4*b* and leads to an optimal value of *K*(*s*_{0}). As expected, equation (3.2) shows that if virulence vanishes this optimal value sharply increases and actually converges toward infinity for non-virulent parasites, which also clearly appears on figure 4*b* when *V* = 0. Importantly, although the speed of evolution clearly varies with *H*, *k/*(*k* + 1) and *σ*_{α}, the optimal value itself does not depend on the level of fragmentation and aggregation of the parasite population.

Although independent assessments of the effects of the number of hosts (*H*) and the effect of the parasite load per host (*K*(*s*_{0})) on the rate of adaptive evolution were necessary to start to grasp the logic behind their effects, these two parameters are known to covary with host individual body mass. We thus investigated the effect of their covariations on parasite evolution. We used the empirically well-informed allometric relationships that link the number of hosts [33,34,71,72] and the parasite load per host [35–37] to the host body mass in order to infer the expected patterns of covariation between *H* and *K*(*s*_{0})*.* Algebraic calculations that the interested reader can find in the electronic supplementary material, appendix C led to the following relationship
3.3where the couple of parameters (*x*_{H}, *y*_{H}) and (*x*_{P}, *y*_{P}) describe the shape of the allometry between the host body mass and host abundance [34], and between the host body mass and parasite load [36], respectively. The larger the ‘scaling exponents’ *y*_{H} and *y*_{P}, the larger the decrease in host abundance and the increase in parasite load with body mass. The ‘allometric coefficients’ *x*_{H} and *x*_{P} set the actual levels of host abundance and parasite load according to the host/parasite taxa (see the electronic supplementary material, appendix C). Thereafter, we focus on the influence of the scaling exponent as these quantities are the most debated in the literature [35,73,74]. As expected, in equation (3.3), *y*_{H} strengthens the negative correlation between host abundance and parasite load per individual, whereas *y*_{P} tends to weaken this relationship.

Rewriting the canonical equation to account for these allometric relationships does not alter the nonlinearity of the relationship between the rate of adaptive evolution and the maximal parasite burden per host (see equation (S9) in the electronic supplementary material, appendix C). We used this new canonical equation along with the estimates of the allometric coefficients for fishes and several other taxa of animal hosts [34,36] to predict the shape of this relationship (figure 5*a*). Interestingly, there still is an optimal value of *K*(*s*_{0}) leading to the fastest rate of evolution, and a nonlinear relationship also appears in empirical data on the diversity of monogenean parasites with the body length of their West African cichlid fishes hosts. We used the same data as [75] to estimate the richness of monogenean species collected in each cichlid fish host species, as a measure of the rate of within-host diversification. We collected the body length at maturity of each fish species using the online Fishbase database [76], as an index of the parasite infra-populations they can carry. We then plotted the diversity of monogenean species collected in [75] with the body length of their corresponding fish host species. The empirical relationship appears in figure 5*b* and shows that the host species with intermediate body length (13.5 cm) is colonized by the highest diversity of *Cichlidogyrus/Scutogyrus* species (15 species), in qualitative agreement with our theoretical prediction. Although a simple analytical expression of the optimal parasite load (similar to equation (3.2)) can no longer be obtained, it is worth mentioning that the optimum *K*_{opt}(*s*_{0}) now depends on the key allometric coefficients *y*_{H} and *y*_{P} that define the relationship between the number of host *H* and the maximal parasite burden per host *K*(*s*_{0}). Raising *y*_{H} lowers the host population size *H* and, subsequently, the number of residents, so that the negative impact that increasing the maximal parasite burden per host *K*(*s*_{0}) has on the rate of adaptive evolution is shifted towards larger parasite loads. The optimal value *K*_{opt}(*s*_{0}) thus increased with *y*_{H} (result not shown). On the contrary, *y*_{P} has a positive effect on *H* and on the number of resident parasites, and thus *K*_{opt}(*s*_{0}) is shifted towards lower values when *y*_{P} increases (result not shown). However, the low elasticity measures around the standard value of *y*_{H} and *y*_{P} showed that we should expect little quantitative variations in this optimum with respect to these allometric coefficients.

#### (ii) Effect of virulence

Parasite virulence has a twofold negative impact on the rate of adaptive evolution as it simultaneously lowers *P*(*r*)*** and *Z*(*r*) because of the parasite-induced host mortality. The evolutionary rate coefficient and the gradient of selection are thus both negatively affected which leads to a decline of the overall rate of adaptation with *V*. Importantly, low levels of virulence can then substantially increase the value of *K*_{opt}(*s*_{0}) (figure 6). As macro-parasites are typically slightly virulent [77–79], even small variations in parasite-induced host mortality could have a great impact on the parasite load for which the evolutionary rate is maximized.

## 4. Discussion

We expanded the general theory of ecological character displacement and competitive speciation to macro-parasite species and investigated the effect of fragmentation, aggregation and virulence on the evolution of a quantitative trait determining the parasite ability to compete within the host for the exploitation of a resource gradient.

The conditions for competitive diversification of macro-parasite species were found to be the same for virulent and non-virulent parasites, and identical to those obtained for non-parasite species [3]. Although our modelling assumed sexual reproduction while macro-parasites have an important diversity of reproductive systems, which includes parthenogenesis, self-fertilization and inbreeding between clonal individuals [19,20], previous work on non-parasitic species suggests that this should not affect the above conclusion. Under the pleiotropic scenario considered here, asexual and sexual organisms were indeed shown to diversify in exactly the same conditions [3]. This suggests that the conditions for diversification owing to competitive interactions are somewhat universal, and also confirmed previous findings on the lack of effect of aggregation on macro-parasite life-history evolution [29,32]. On the other hand, the rate of adaptive evolution driven by within-host competition was readily affected by the key features of the macro-parasite lifestyle. Adaptation was shown to be faster for parasites infecting hosts species with large population size, i.e. highly fragmented parasite populations, and for weakly aggregated parasites. A larger number of host individuals with parasites broadly spread across hosts, indeed, leads to a larger parasite population [30,39,80], which speeds up evolution (by increasing the emergence of mutants) despite a reduced level of competition within each host individual. Accordingly, the rate of competitive diversification is expected to be larger for parasitic than for non-parasitic species as the latter can be seen as the limit case of a highly aggregated population colonizing a single host. Virulence was shown to have a twofold negative impact on the rate of adaptive diversification as it lowers the total number of parasite and thus the emergence of mutants, and decreases the strength of selection because of the death of the most highly infected host individuals within which competition can initiate ecological character displacement. Non-virulent macro-parasites are thus expected to diversify more rapidly than virulent ones. Finally, our analysis led to the unanticipated conclusion that the speed of within-host competitive diversification is higher for host species with intermediate levels of parasite load. An increase in the maximal parasite load per individual indeed fuels evolution by increasing the total number of emerging mutants, but, because of the deleterious effect of virulence, it simultaneously weakens competition and the strength of selection for resource specialization. The balance between these two antagonistic effects leads to an optimal parasite burden corresponding to the higher rates of competitive diversification.

The use of allometric relationships that link host body mass with host population size [33,34] and parasite load [35–37], allowed for more specific and testable predictions on the rate of within-host competitive diversification. Most importantly, we showed that host species with intermediate individual body mass are expected to serve as hotspots of within-host duplication of parasites, which can be explained as follows. When host body mass increases, the host population is typically made of less individuals infected with larger parasite infra-population. This leads to the production of more mutant parasites, but simultaneously increases the deleterious effect of virulence. When host body mass is too high, the latter effect dominates the former, and this slows down parasite adaptive diversification. An important assumption of our modelling is that virulence does not change with host body mass. If larger hosts were to be more tolerant than smaller hosts, for example because they might have more resources/tissue to spare, a similar parasite load in a large host might have a lower impact than on a smaller one. This could clearly make larger host species more prone to parasite duplication. Whether or not one should still expect an intermediate (though larger) host body mass leading to a greater parasite diversification, or a steady increase in the rate of parasite diversification with host body mass, will depend on the quantitative details of the relationship between host body mass and virulence. Interestingly, previous analyses have suggested that monogenean diversity can be largest in big hosts [81] or that diversity within a genus can be independent of fish size [82]. In this study, phylogenetic data on fish gill parasites [75], whose life-history fits with the competitive diversification scenario [57], displayed a humped relationship between the number of parasite species and the host body length similar to the theoretical predictions derived in this paper. Additional specific studies on other parasite taxa are thus needed to offer broader support to this theoretical finding, and to investigate whether or not these differences are linked to different relationships between host body mass and virulence. The theoretical developments described, in this paper, represent the first attempt to take advantage of the well-documented allometric relationships established between body mass and various life-history traits (see [71] for a review) to improve predictions derived from the standard framework of AD [63,64]. Because this mathematical framework has allowed many insights into the importance of density- and frequency-dependent selection on the evolution of key life-history traits, such as dispersal [28,83] or diapause [84,85] in heterogeneous and/or stochastic environments, such an approach could potentially bring significant additional insights into a variety of evolutionary ecology topics. This could be especially relevant to investigate evolution of complex systems such has vector-borne diseases involving multiple hosts [86] and/or vector species [87].

The theoretical results derived in this contribution clearly show that virulence can freeze the adaptive evolution of a quantitative trait involved in competition between macro-parasites. Our analysis does not however consider that the level of virulence itself can evolve. Within-host competition could then generate a selective pressure for higher parasite efficacy to exploit host resources [88–91]. The generality of this process has been questioned with respect to the details of the host–parasite interaction [92–94], but the possibility that parasite life-history traits evolve to avoid competition and the potential coevolution of those traits with parasite virulence has been broadly overlooked. Although this requires specific efforts to compound the theories on virulence evolution and on ecological character displacement, some predictions can be made from our results. If virulence was to evolve in the first place, then it would constrain the ecological trait evolution resulting in some level of ecological maladaptation, which could, in turn, reinforce the evolution of virulence by maintaining competition between types. Such a positive feedback loop would facilitate the evolution of highly virulent parasites. On the contrary, if the ecological character was to evolve before virulence, then adaptive diversification would lead to a lower level of competition between types of parasites and would reduce the strength of selection for virulence. On the other hand, if one was to consider the evolution of virulence, then an interesting point is that such evolution has been shown to be significantly affected if parasites have sublethal effects on the host and that, correlatively, infection decreases within-host parasite fitness [93]. This could, indeed, be the case as many macro-parasites are well known to have such sublethal effects, typically affecting their host growth [95,96] or rate of reproduction [97,98], and because parasite development and reproduction [99–101] can, indeed, be restricted in infected hosts. Multiple infections could then actually select for reduced (rather than increased) virulence [93], leading to other original patterns of coevolution between ecological traits involved in competitive interactions and virulence.

Our evolutionary analysis assumes that mutant and resident parasites are co-aggregated among the host population. Nevertheless, there is a rich literature demonstrating that dispersal of individuals among distinct resource units can reduce the strength of deleterious interactions and allow for persistence of competitors through competition–colonization trade-offs (see [102–104] for reviews). This has been demonstrated for a very broad range of organisms, including parasite species [105–107] and non-parasite species of various taxa [108–112]. Macro-parasites facing a competitive challenge could thus adapt to exploit specific resources without any change in the pool of host individuals they infect, as demonstrated in this paper, or they could evolve to infect a subset of host individuals that are less colonized by competitors. Infections of alternative sets of hosts by different phenotypes of the same parasite population have been documented. For instance, in the trematode *Schistosoma mansoni* transmitted in the Caribbean island of Guadeloupe, two different timings in the emission of cercariae have evolved to match the activity patterns of two definitive host species: human and rodent [113]. In plant pathogens, such phenotypic divergence in the temporal patterns of pathogens’ emergence fits different subsets of conspecific host plant individuals that differ in the time of their yearly vegetative growth [28]. Diversification of adults in their use of resources within each host individual, and diversification of larvae in their ability to infect individuals within the host population can thus be seen as two sides of the same ecological coin. Such a situation where the same ecological conditions can result in the evolutionary divergence of alternative traits have already been identified, for example, for sexual dimorphism and head shape/body size [114,115]. In such cases, coevolution between alternative traits is unlikely because whichever evolves first dissipates the disruptive selection necessary to drive evolution of the other [114]. One could argue that evolution of larval infection specificity is more likely as avoiding competition with conspecifics by infecting weakly parasited hosts could benefit both larval and adult stage, thus providing a higher selective advantage. However, infecting hosts with low parasite loads also restrains the opportunity to mate [116], leading to rare phenotype disadvantage that has been repeatedly shown to impede adaptive diversification and speciation [47,48,117,118].

To conclude, more investigations on the coevolution between within-host use of resources, within-population use of host individuals, and virulence are required to elaborate on the premises of the adaptation of the theory of ecological character displacement and competitive speciation to macro-parasites that we presented in this paper. Such developments would provide theoretical foundations to better understand the relative occurrence of parasite duplication and host specialization. This would surely lead to new quantitative insights into the evolution of virulence of macro-parasites with the long-term perspective of addressing key aspects of host–macro-parasite coevolution.

## Acknowledgements

This work has benefited from an 'Investissements d'Avenir' grant managed by Agence Nationale de la Recherche (CEBA, ref. ANR-10-LABX-25-01). This work was performed within the framework of the LABEX ECOFECT (ANR-11-LABX-0048) of Université de Lyon, within the programme 'Investissements d'Avenir' (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR).

- Received November 28, 2013.
- Accepted January 13, 2014.

- © 2014 The Author(s) Published by the Royal Society. All rights reserved.