Louise Solveig Nørgaard

Giacomo Zilio

Camille Saade

Claire Gougat-Barbera

Matthew Hall

Emanuel Fronhofer

Oliver Kaltz
email: oliver.kaltz@umontpellier.fr

Louise Solveig

Giacomo Zilio2#

Camille Saade2

Claire Gougat-Barbera2

Matthew D Hall1

Emanuel A Fronhofer2

Oliver Kaltz2

An evolutionary trade-off between parasite virulence and dispersal at experimental invasion fronts

Keywords: Paramecium caudatum, Holospora undulata, host-parasite interactions, experimental evolution, disease, epidemics, eco-evolution, range expansion, dispersal syndrome, horizontal, vertical transmission

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SIGNIFICANCE STATEMENT

What drives parasite evolution in spatially expanding epidemics? Many parasites require dispersal of infected hosts to reach new patches, and this may produce specific adaptations enhancing spatial spread.

We performed experimental range expansions in an aquatic model system, with natural dispersal of infected hosts. Parasites from experimental range fronts were less virulent and interfered less with host dispersal, but also invested less in horizontal transmission than parasites from the range core. Thus, dispersal adaptation at the front may come at a cost of reduced horizontal transmission, a trade-off rarely considered in theoretical models on parasite virulence evolution. These results have important implications in the context of emerging diseases, and for parasite evolution during biological invasions or other spatial non-equilibrium scenarios.

INTRODUCTION

In an increasingly connected world, and with changing environments and habitats, we are facing the risk of infectious diseases spreading outside their natural range and over large geographic scales [START_REF] Bahl | Temporally structured metapopulation dynamics and persistence of influenza A H3N2 virus in humans[END_REF][START_REF] Pettersson | Re-visiting the evolution, dispersal and epidemiology of Zika virus in Asia article[END_REF][START_REF] Findlater | Human mobility and the global spread of infectious diseases: a focus on air travel[END_REF][START_REF] Chinazzi | The effect of travel restrictions on the spread of the 2019 novel coronavirus (COVID-19) outbreak[END_REF][START_REF] Tatem | Global transport networks and infectious disease spread[END_REF]. This issue is of concern to human health, agriculture and wildlife conservation, and understanding the ecological and evolutionary drivers represents a major challenge to epidemiologists and evolutionary biologists [START_REF] Parratt | Infectious disease dynamics in heterogeneous landscapes[END_REF][START_REF] Penczykowski | Understanding the ecology and evolution of host-parasite interactions across scales[END_REF][START_REF] Clark | Climate, host phylogeny and the connectivity of host communities govern regional parasite assembly[END_REF]. Due to their short generation time and large population sizes, parasites have the potential to evolve rapidly, and therefore one important question is whether changes in transmissibility or virulence already occur while an epidemic is progressing [START_REF] Holmes | The evolution of Ebola virus: Insights from the 2013-2016 epidemic[END_REF]. Classic theory predicts evolutionary optima for these traits only in large, spatially homogeneous populations at equilibrium [START_REF] Cressler | The adaptive evolution of virulence: a review of theoretical predictions and empirical tests[END_REF][START_REF] Alizon | Virulence evolution and the trade-off hypothesis: History, current state of affairs and the future[END_REF], but these conditions are unlikely to be met during an epidemic [START_REF] Andre | Virulence evolution in emerging infectious diseases[END_REF][START_REF] Gandon | Evolutionary Epidemiology and the Dynamics of Adaptation[END_REF]. In patchy real-world populations, parasites experience extinction-recolonization dynamics typical of metapopulations, with epidemic spread critically depending on population connectivity and the mobility and dispersal of infected hosts [START_REF] Keeling | Dynamics of the 2001 UK Foot and Mouth epidemic: Stochastic dispersal in a heterogeneous landscape[END_REF][START_REF] Viboud | Synchrony, waves, and spatial hierarchies in the spread of influenza[END_REF][START_REF] Dudas | Virus genomes reveal factors that spread and sustained Ebola epidemic[END_REF][START_REF] Ferrari | The dynamics of measles in sub-Saharan Africa[END_REF][START_REF] North | The dynamics of disease in a metapopulation: The role of dispersal range[END_REF][START_REF] Jousimo | Ecological and evolutionary effects of fragmentation on infectious disease dynamics[END_REF]. Although fundamental for epidemiology, it is still unclear how these spatio-temporal aspects affect concomitant evolutionary processes, and whether they might even lead to specific parasitic adaptations enhancing the spatial spread of the epidemic (see [START_REF] Griette | Virulence evolution at the front line of spreading epidemics[END_REF][START_REF] Leventhal | Evolution and emergence of infectious diseases in theoretical and real-world networks[END_REF][START_REF] Osnas | Evolution of pathogen virulence across space during an epidemic[END_REF] Recent theory has begun to develop a conceptual framework to investigate parasite evolution in spatially explicit, non-equilibrium settings [START_REF] Lion | Evolution of spatially structured host-parasite interactions[END_REF]. Assuming a classic virulence-transmission trade-off (24,[START_REF] May | Epidemiology and genetics in the coevolution of parasites and hosts[END_REF] and local feedbacks between epidemiology and selection, several models predict that more virulent parasites will evolve in highly connected "small-world" landscapes [START_REF] Boots | Large shifts in pathogen virulence relate to host population structure[END_REF][START_REF] Kamo | The evolution of parasite dispersal, transmission, and virulence in spatial host populations[END_REF][START_REF] Kamo | The role of trade-off shapes in the evolution of parasites in spatial host populations: An approximate analytical approach[END_REF] or at the front of advancing epidemics [START_REF] Griette | Virulence evolution at the front line of spreading epidemics[END_REF], where host exploitation and transmission is not limited by local depletion of susceptible hosts ("self-shading"). These predictions are consistent with observed changes in the predominance of a highly virulent honeybee virus at the front of progressing epidemics in New Zealand [START_REF] Mondet | On the front line: Quantitative virus dynamics in honeybee (Apis mellifera L.) colonies along a new expansion front of the parasite Varroa destructor[END_REF], and potentially also with observations for parasites and pathogens of amphibian species [START_REF] Kelehear | Rapid evolution of parasite life history traits on an expanding range-edge[END_REF][START_REF] Phillips | Do pathogens become more virulent as they spread? Evidence from the amphibian declines in Central America[END_REF].

Yet, not all host-parasite systems show this pattern. For instance, the geographic spread of a bacterial pathogen of North American house finches was associated with decreased virulence in the newly invaded areas [START_REF] Hawley | Parallel patterns of increased virulence in a recently emerged wildlife pathogen[END_REF]. Likewise, in monarch butterflies, hosts that sustain long or frequent migrations were found to harbour less virulent parasites [START_REF] De Roode | Host plant species affects virulence in monarch butterfly parasites[END_REF]. This may be explained by the way parasite dispersal enters into the equation. Namely, if parasites travel with their infected hosts, exploitation of host resources may reduce dispersal, thereby introducing a novel dispersal-virulence trade-off. Osnas et al. (2015) [START_REF] Osnas | Evolution of pathogen virulence across space during an epidemic[END_REF] show that such trade-off can lead to selection favouring more prudent and dispersal-friendly parasites at the moving edge of an epidemic that escape more virulent and transmissible parasites from the core of an epidemic. This latter idea mirrors classic principles from metapopulation theory and metacommunity ecology, based on trade-offs between competitive ability and colonisation/dispersal [START_REF] Griette | Virulence evolution at the front line of spreading epidemics[END_REF][START_REF] Calcagno | Coexistence in a metacommunity: the competition-colonization trade-off is not dead[END_REF][START_REF] Oliveri | Metapopulation Genetics and the Evolution of Dispersal[END_REF][START_REF] Nørgaard | Infection in patchy populations: Contrasting pathogen invasion success and dispersal at varying times since host colonization[END_REF]. It also relates to recent work on invasive species and range expansions, where dispersal evolution plays a key role in determining the rate of spatial diffusion [START_REF] Kubisch | Where am I and why? Synthesizing range biology and the eco-evolutionary dynamics of dispersal[END_REF]. In this sense, parasites may evolve 'invasion syndromes', with characteristic changes in morphology, life history or transmission strategies [START_REF] Kelehear | Rapid evolution of parasite life history traits on an expanding range-edge[END_REF][START_REF] Phillips | Do pathogens become more virulent as they spread? Evidence from the amphibian declines in Central America[END_REF][START_REF] Dunn | Parasites and biological invasions: Parallels, interactions, and control[END_REF], thereby creating a positive feedback loop between rates of dispersal and rates of spatial spread of infection.

Although the study of naturally expanding parasites remains the ultimate litmus test of the theory, controlled experiments can verify important assumptions and serve as proof of principle [START_REF] Brockhurst | Experimental coevolution of species interactions[END_REF]. For example, we can manipulate demographic conditions in experimental microcosms to mimic the front and core of an expanding epidemic [START_REF] Nørgaard | Infection in patchy populations: Contrasting pathogen invasion success and dispersal at varying times since host colonization[END_REF] or artificially change levels of population mixing to study epidemiological or evolutionary processes [START_REF] Brockhurst | Experimental coevolution of species interactions[END_REF]. Indeed, studies of the latter type found that experimentally shifting populations from local to global "dispersal" favoured more virulent parasites [START_REF] Boots | Local interactions select for lower pathogen infectivity[END_REF][START_REF] Kerr | Local migration promotes competitive restraint in a host-pathogen "tragedy of the commons[END_REF][START_REF] Berngruber | Spatial structure, transmission modes and the evolution of viral exploitation strategies[END_REF], as predicted by theory [START_REF] Lion | Evolution of spatially structured host-parasite interactions[END_REF][START_REF] Boots | Small worlds" and the evolution of virulence: infection occurs locally and at a distance[END_REF]. [START_REF] Yin | Evolution of bacteriophage T7 in a growing plaque[END_REF] [START_REF] Yin | Evolution of bacteriophage T7 in a growing plaque[END_REF] further showed that phage diffusion on bacterial lawns is associated with the appearance of faster replicating mutants in the periphery. However, to our knowledge, there are no studies addressing experimental evolution of parasites from an explicit metapopulation perspective, under natural dispersal of a host and its parasite.

For (micro-)organisms with directed movement, experimental landscapes can be created to study metapopulation processes or range expansion dynamics with natural dispersal [START_REF] Friedenberg | Experimental evolution of dispersal in spatiotemporally variable microcosms[END_REF][START_REF] Ochocki | Rapid evolution of dispersal ability makes biological invasions faster and more variable[END_REF][START_REF] Fronhofer | Eco-evolutionary feedbacks during experimental range expansions[END_REF]. Here, we employed such an approach to investigate the experimental evolution of spatially spreading parasites, where all parasite dispersal is host-mediated. Using two-patch dispersal arenas for the ciliate Paramecium caudatum infected with the bacterial parasite Holospora undulata, we mimicked a range expansion scenario, with a front population of hosts (and parasites) dispersing into a new microcosm during each selection event, and a core population constantly remaining in place (and losing emigrants; see Fig. 1). After 55 episodes of dispersal selection, we then assayed evolved front and core parasites under common garden conditions on naive hosts. Multiple traits were measured, namely the parasites' effect on host dispersal, investment in horizontal transmission and their impact on host replication and survival. We further obtained additional independent estimates of parasite traits by fitting a simple epidemiological model to time series data (population density, infection prevalence) from the experimental assay.

Because parasite persistence in the front populations depended entirely on host dispersal, we predicted that front parasites would evolve minimal impact on host dispersal, or even increase dispersal of infected hosts [START_REF] Lion | The evolution of parasite manipulation of host dispersal[END_REF]. Such dispersal adaptations could involve a decrease in parasite virulence [START_REF] Osnas | Evolution of pathogen virulence across space during an epidemic[END_REF] and generate an evolutionary trade-off with investment in horizontal transmission, not expected to occur in the core populations. Our results were broadly consistent with these predictions, and we conclude that differential dispersal selection pressures arising at the core and front of a range expansion can lead to marked divergence of parasite life-history traits and the emergence of a 'parasite dispersal syndrome'.

RESULTS

Evolved parasites from the five front and five core selection lines were extracted and the inocula used to infect naïve hosts (three genotypes). Several traits were measured for these newly infected assay cultures (for timing of assays see Table S1 and statistical analyses Tables S2,S3).

Infected host dispersal

On average, hosts infected with front parasites dispersed twice as much (mean dispersal rate: 0.24 ± 0.05 SE x 3h-1) as those infected with the core parasites (0.12 ± 0.02 SE; Fig. 2A). This effect of selection treatment was significant (χ12 = 4.9, p = 0.027; Table S2). The distribution of the differences between model predictions for front and core treatments (small panel, Fig. 2A) also shows that higher frontparasite dispersal is the most frequent predicted outcome (>98%; mean front-core difference: 0.12, 95% CI [0.08; 0.35]). This general trend was consistent on all three host genotypes tested (Fig. S4; Table S3). Fig. S4 further shows that levels of front-parasite dispersal were similar to reference data for uninfected hosts, whereas core parasites generally reduced dispersal.

Using video analysis, we investigated variation in two parameters of Paramecium swimming behaviour: swimming speed and trajectory variation (tortuosity). We found no evidence that infection with core or front parasites had significant effects on these two parameters (p > 0.25; Table S2, neither when tested on host genotypes individually S3; Fig S5 ,S6). Moreover, mean levels of swimming speed or tortuosity were not significantly correlated with infected dispersal rates (r ≤ 0.15, n = 29, p > 0.4), indicating that dispersal was not directly affected by these aspects of swimming behaviour (see also path analysis below).

Parasite life-history traits

Infectivity. Measurements of infection prevalence early after inoculation (day 4) inform on parasite horizontal transmission potential (infectivity). Core parasites had slightly higher infection success (selection line average proportion of infected hosts: 0.59 ± 0.05 SE) than front parasites (0.51 ± 0.03 SE; Fig. 2B). Although not formally significant (effect of selection treatment: χ12 = 2.43, p = 0.118; Table S2; predictive difference distribution front-core infectivity: mean = -0.08, CI [0.02; -0.18]; Fig 2B; see also Fig. S7 for genotype specific responses), this trend was consistent with higher estimates of the transmission parameter for core parasites in an epidemiological model fitted to our experimental data (see below; Fig. 4).

Investment in horizontal transmission (infectiousness). It takes several days until infected hosts

produce horizontal transmission stages and become infectious. In our assay, the first infectious hosts appeared on day 6 p.i., and their frequency then increased over the following week, reaching up to 100% (Fig. 2C). Over this period, populations infected with front parasites produced a lower proportion of infectious hosts (mean: 0.41 ± 0.03 SE) than did populations infected with core parasites (0.53 ± 0.03 SE; effect of selection treatment: χ12 = 13.2, p <0.001; Table S2; predictive difference distribution frontcore infectiousness: mean = -0.10; CI [0.04; -0.23]; Fig. 2C). There was also a difference in timing: on average, core parasites produced the first infectious hosts c. 1 day earlier than did front parasites (day 6 vs day 7) and subsequently showed a faster increase in the proportion of infectious hosts (treatment x time interaction: χ12 = 13.54, p < 0.001,Table S2; Fig. 2C). These differences in total investment and/or timing broadly hold on all three host genotypes tested (Table S3; Fig. S8).

Virulence. We isolated single infected individuals from the core and front infected assay cultures and measured the impact of infection on host division and survival over a 20-day period. Exposed, but uninfected, controls were isolated from the same assay cultures and run in parallel.

Host division. By day 10, 87% of the infected singletons had accomplished at least one division (266 / 305 replicates; mean maximum cell number observed over this period: 8.5 ± 0.6 SE). Analysis of maximum cell density revealed a significant selection treatment x infection status interaction (χ12 = 16.9, p > 0.001; Table S2). Namely, hosts infected with front parasites reached nearly twice as high maximum densities (10.9 ± 1.3 SE) than those infected with core parasites (5.9 ± 0.9 SE; contrast front vs core: t601 = 4.7, p < 0.0001; predictive difference distribution front-core: mean = 4.6, CI [1.4; 9.6]; Fig. 3A).

Host survival. As for host division, there was a significant selection treatment x infection status interaction for host survival (χ12 = 7.4, p = 0.006; Table S2). By day 20, infections with front parasites had experienced a 50% lower mortality (mean proportion of infected replicates extinct: 0.19 ± 0.05 SE) than infections with core parasites (0.37 ± 0.1 SE; contrast front vs core: t601 = 3.75, p > 0.001; predictive difference distribution front-core: mean = 0.30, CI [0.04;0.62]; Fig. 3B). Moreover, effects on host division and on host survival were positively correlated: parasites which allowed more host division also allowed higher host survival (means per parasite selection line: r = 0.84 ± 0.19, n = 10, p = 0.003).

Thus, core parasites generally had negative effects, whereas front parasites only had little, or even positive, impact on their hosts reproduction and survival (Fig. 3A and3B), and these opposing trends were consistent across the three host genotypes tested (Table S2; Fig. S9 &S10).

Path analysis

Using path analysis, we explored the direct and indirect contributions of different traits to the observed variation in infected host dispersal (Fig. 4A). Host division (= maximum cell density) was the only trait with a significant direct effect on host dispersal (F1,20 = 6.16, p = 0.022; Fig. 3B); thus, lower virulence was associated with higher dispersal rates of infected hosts. Horizontal transmission investment (= cumulative infectiousness) had a moderate indirect effect on dispersal via its significant negative relationship with virulence (F1,23 = 4.47, p = 0.0456; Fig. 3C). Swimming behaviour (speed, tortuosity) had no significant direct effect on dispersal, and were themselves only very marginally affected by virulence or infectiousness (Fig. 4A).

Epidemiological model fits

By fitting an epidemiological model to the population-level data from the assay replicate cultures (infection prevalence and population density), we obtained independent estimates of parasite parameters. In the model, we integrated the basic features of the infection life cycle, assuming simple population growth and regulation (Beverton-Holt type model, 49) and parameterising virulence as the reduction in host fecundity.

The model captured the main trends in the demographic and epidemiological dynamics observed in the cultures. This is illustrated in Fig. 5A, showing the model fits for the densities of infected and uninfected hosts for the 63D host genotype (for the other two host genotypes, see SI 4, Fig. S11). Parameter estimates confirm the main trends found in our experimental assays. Namely, the model fits show that front parasites have lower virulence, lower transmission rate and longer latency time than core parasites (Fig. 5B-D), a pattern largely consistent for the three host genotypes tested (Fig. S11).

DISCUSSION

In times of global epidemics [START_REF] Bahl | Temporally structured metapopulation dynamics and persistence of influenza A H3N2 virus in humans[END_REF][START_REF] Chinazzi | The effect of travel restrictions on the spread of the 2019 novel coronavirus (COVID-19) outbreak[END_REF][START_REF] Hawley | Parallel patterns of increased virulence in a recently emerged wildlife pathogen[END_REF] it is important to know how parasites evolve while spreading through a landscape or entire continents. Recent theory suggests that spatial 'viscosity' and connectedness generate eco-evolutionary feedbacks, with important consequences for parasite virulence evolution and the speed of epidemics [START_REF] Lion | Evolution of spatially structured host-parasite interactions[END_REF]. However, so far little attention has been given to the fact that many parasites travel together with their dispersing hosts, which may considerably affect evolutionary predictions [START_REF] Kamo | The role of trade-off shapes in the evolution of parasites in spatial host populations: An approximate analytical approach[END_REF][START_REF] Lion | The evolution of parasite manipulation of host dispersal[END_REF][START_REF] Osnas | Evolution of pathogen virulence across space during an epidemic[END_REF].

To address this issue, we performed a simplified range expansion experiment, with natural dispersal of infected hosts. Our 'range front' and 'range core' treatments imposed differential selection on host dispersal (see 52) and resulted in divergent parasite phenotypes: front parasites allowed for higher dispersal of their infected hosts, were less virulent and showed reduced investment in horizontal transmission, compared to the parasites from the core selection treatment. These patterns were largely robust between the three naive host genotypes tested, and additionally confirmed by results from an epidemiological model that we fitted to time-series data obtained from our assay cultures.

Evidence for a virulence -dispersal trade-off

Our experimental result of multi-trait changes joins empirical observations of "invasion syndromes" in naturally spreading diseases, such as avian malaria in Europe [START_REF] Pérez-Tris | Dispersal increases local transmission of avian malarial parasites[END_REF] or lungworms of invasive cane toads in Australia [START_REF] Kelehear | Rapid evolution of parasite life history traits on an expanding range-edge[END_REF]. Lungworms at the invasion front, for example, exhibit distinct life-history traits (reduced age at maturity, larger infective and free-living larvae), possibly representing adaptations to invasion history [START_REF] Kelehear | Rapid evolution of parasite life history traits on an expanding range-edge[END_REF]. We replayed such an invasion history, by mimicking the spatial progression of an isolated population in our range front treatment, which was expected to favour parasites that succeed in dispersing together with their infected hosts. This explains why our front parasites were found to facilitate higher host dispersal. Importantly, higher host dispersal was associated with higher host replication and survival, indicating a dispersal -virulence trade-off (Fig. 2 and3). Reduced virulence, in turn, was associated with reduced horizontal transmission potential (Fig. 2C), consistent with previous findings in this system [START_REF] Nidelet | Effects of shortened host life span on the evolution of parasite life history and virulence in a microbial host-parasite system[END_REF][START_REF] Magalon | Host growth conditions influence experimental evolution of life history and virulence of a parasite with vertical and horizontal transmission[END_REF][START_REF] Restif | Condition-dependent virulence in a horizontally and vertically transmitted bacterial parasite[END_REF] and reflects a virulence-transmission trade-off for this parasite. Thus, we conclude that the evolution of higher parasite dispersal in front parasites came at the cost of reduced horizontal transmission, a trade-off resulting from a reduction in virulence.

The idea that parasite exploitation strategies can be shaped by the interplay between local transmission and global dispersal was formalised in a theoretical model by Osnas et al. (2015) [START_REF] Osnas | Evolution of pathogen virulence across space during an epidemic[END_REF]. They showed that implementing a trade-off between virulence and the capacity of infected hosts to disperse, favours less virulent strains at the front of an epidemic, escaping the more competitive (and more virulent) strains through faster dispersal [START_REF] Osnas | Evolution of pathogen virulence across space during an epidemic[END_REF]. Such a selection scenario may explain observed geographic patterns of virulence for a bacterial pathogen of North American house finches [START_REF] Hawley | Parallel patterns of increased virulence in a recently emerged wildlife pathogen[END_REF], and it is qualitatively consistent with our results.

Trait relationships: Proximate causes of infected dispersal rate

Just like parasites can alter their hosts behaviour to increase transmission [START_REF] Moore | Parasites and the behaviour of animals[END_REF], they may also evolve to manipulate host dispersal [START_REF] Lion | The evolution of parasite manipulation of host dispersal[END_REF][START_REF] Martini | Infection of an insect vector with a bacterial plant pathogen increases its propensity for dispersal[END_REF]. However, we find little evidence for manipulation to increase the dispersal. Consistent with previous observations of negative effects of infection in this [START_REF] Fellous | Parasitic infection reduces dispersal of ciliate host[END_REF] and other systems [START_REF] Nørgaard | Infection in patchy populations: Contrasting pathogen invasion success and dispersal at varying times since host colonization[END_REF][START_REF] Nørgaard | Can pathogens optimize both transmission and dispersal by exploiting sexual dimorphism in their hosts?[END_REF][START_REF] Bradley | Parasites hinder monarch butterfly flight: Implications for disease spread in migratory hosts[END_REF][START_REF] Goodacre | Microbial modification of host long-distance dispersal capacity[END_REF], core parasites reduced host dispersal, whereas infection with front parasites produced levels of dispersal comparable to uninfected Paramecium. Path analysis indicates that virulence is the main direct predictor of host dispersal in our assays. Investment in horizontal transmission had an indirect effect via decreased virulence. Although intuitively straightforward through a weakening of infected hosts, the mechanistic link between virulence and dispersal remains unclear.

We found no effect of infection on swimming behaviour, nor was there a direct link between swimming behaviour and dispersal, which is frequently observed in other protists [START_REF] Fronhofer | Eco-evolutionary feedbacks during experimental range expansions[END_REF]. Possibly, infection influences other dispersal-relevant traits, such as the vertical distribution in the water column [START_REF] Fels | Ecological and genetic determinants of multiple infection and aggregation in a microbial host-parasite system[END_REF][START_REF] Bauer | The acanthocephalan parasite Polymorphus minutus alters the geotactic and clinging behaviours of two sympatric amphipod hosts: The native Gammarus pulex and the invasive Gammarus roeseli[END_REF], determining the proximity of individuals to the opening that leads to the other tube in the dispersal arena (see Fig. 1).

Contrasting scenarios: Dispersal to new sites vs access to new hosts

While our results suggest more prudent parasites might be spreading at invasion fronts, other theoretical models and experiments reach opposite conclusions. [START_REF] Griette | Virulence evolution at the front line of spreading epidemics[END_REF] [START_REF] Leventhal | Evolution and emergence of infectious diseases in theoretical and real-world networks[END_REF], for example, predict highest levels of virulence at the front of an epidemic wave, where transmission is not limited by the availability of susceptible hosts, thereby favouring the most 'rapacious' variants. Following this line of argument, experiments with viruses and bacteriophages have studied virulence evolution by artificially manipulating dispersal or population connectivity [START_REF] Boots | Local interactions select for lower pathogen infectivity[END_REF][START_REF] Kerr | Local migration promotes competitive restraint in a host-pathogen "tragedy of the commons[END_REF][START_REF] Berngruber | Spatial structure, transmission modes and the evolution of viral exploitation strategies[END_REF]. [START_REF] Kerr | Local migration promotes competitive restraint in a host-pathogen "tragedy of the commons[END_REF] pipetted bacteria and phage either to adjacent wells or to more distant wells on a multi-well plate, in analogy to our 'core' and 'front' treatments [START_REF] Kerr | Local migration promotes competitive restraint in a host-pathogen "tragedy of the commons[END_REF]. Contrary to our results, their latter treatment of unrestricted dispersal resulted in the evolution of more virulent phages, confirming the prediction that erosion of spatial structure in 'small worlds' favours more transmissible and more virulent parasites [START_REF] Kamo | The evolution of parasite dispersal, transmission, and virulence in spatial host populations[END_REF][START_REF] Kamo | The role of trade-off shapes in the evolution of parasites in spatial host populations: An approximate analytical approach[END_REF][START_REF] Lion | Are parasites "'prudent'" in space?[END_REF].

One reason for these contrasting results is that in [START_REF] Kerr | Local migration promotes competitive restraint in a host-pathogen "tragedy of the commons[END_REF] [START_REF] Kerr | Local migration promotes competitive restraint in a host-pathogen "tragedy of the commons[END_REF], dispersal was artificial and cost-free, eliminating a possible virulence-dispersal trade-off. Secondly, our experiment considered a different spatial scenario where infected hosts disperse into empty space, more characteristic of a biological invasion. This means that higher dispersal was not rewarded with more access to susceptible hosts, as assumed in the above models [START_REF] Griette | Virulence evolution at the front line of spreading epidemics[END_REF][START_REF] Lion | Are parasites "'prudent'" in space?[END_REF]. Future experiments can test whether we still find reduced virulence in the front selection treatment, if infected hosts disperse into patches already occupied by uninfected hosts.

Taken together, these examples illustrate the different ways in which spatial spread and dispersal of parasites can be approached both conceptually and experimentally, with very different evolutionary outcomes. We argue that particular attention should be given to how parasites disperse through a landscape, namely because dispersal itself may be the target of selection [START_REF] Nørgaard | Infection in patchy populations: Contrasting pathogen invasion success and dispersal at varying times since host colonization[END_REF][START_REF] Osnas | Evolution of pathogen virulence across space during an epidemic[END_REF].

More vertical transmission at invasion fronts?

We used the replication of infected hosts as a measure of virulence. However, for this parasite, host replication is also equivalent to vertical transmission, because reproductive stages are passed on to daughter cells during mitosis. In this sense, parasites in our front selection treatment underwent a shift from horizontal transmission towards higher levels of vertical transmission. This is due to an underlying developmental trade-off, where reduced conversion of reproductive into infective stages decreases the negative effects on host replication [START_REF] Restif | Condition-dependent virulence in a horizontally and vertically transmitted bacterial parasite[END_REF][START_REF] Kaltz | Host growth conditions regulate the plasticity of horizontal and vertical transmission in Holospora undulata, a bacterial parasite of the protozoan Paramecium caudatum[END_REF], but simultaneously reduces horizontal transmission capacity.

Magalon et al. (2010) observed a similar increase in the efficacy of vertical transmission of this parasite

in frequently disturbed populations [START_REF] Magalon | Host growth conditions influence experimental evolution of life history and virulence of a parasite with vertical and horizontal transmission[END_REF]. In fact, their study can be re-interpreted as a range expansion experiment, with the disturbance treatment mimicking the frequent recolonization events occurring at the front [START_REF] Burton | Trade-offs and the evolution of life-histories during range expansion[END_REF] and the less disturbed control treatment reflecting more stable conditions in the core (see Fig. 1 in 55). The explanation for the evolutionary shift towards vertical transmission is that the demographic oscillations at the invasion front, with frequent periods of low host density and high host fecundity, increase the contribution of vertical transmission to the total transmission success [START_REF] Ebert | The epidemiology and evolution of symbionts with mixed-mode transmission[END_REF].

Because vertical transmission is a means of 'reproductive insurance', we would generally expect it to evolve in association with parasite dispersal syndromes in expanding populations or in highly disturbed habitats [START_REF] Su | Dynamics of host-parasite interactions with horizontal and vertical transmissions in spatially heterogeneous environment[END_REF]. We note, however, that in our present experiment both core and front populations went through density bottlenecks, making the dispersal constraint the main selective driver.

Conclusions

Our results show that different segments of an epidemic wave may be under divergent selection pressures. Namely, we find evidence that dispersal selection at an experimental invasion front leads to reduced virulence. This contrasts with observations in certain natural epidemics [START_REF] Mondet | On the front line: Quantitative virus dynamics in honeybee (Apis mellifera L.) colonies along a new expansion front of the parasite Varroa destructor[END_REF][START_REF] Kelehear | Rapid evolution of parasite life history traits on an expanding range-edge[END_REF], while confirming others [START_REF] Hawley | Parallel patterns of increased virulence in a recently emerged wildlife pathogen[END_REF][START_REF] De Roode | Host plant species affects virulence in monarch butterfly parasites[END_REF]. This calls for more detailed investigations of the role of dispersal for epidemic spread and its implications for the evolution of parasite life-history traits. Our relatively simple statistical modelling exercise suggests that time series data from natural populations represent a useful resource for such a challenge. Establishing a better understanding of the interaction between demography and rapid evolutionary change in spreading populations is crucial for the management of emerging infectious diseases and disease outbreak in the wild, biological invasions and other nonequilibrium scenarios.

MATERIALS AND METHODS

Study system

Paramecium caudatum is a filter-feeding freshwater protozoan ciliate from still water bodies in the Northern Hemisphere [START_REF] Wichterman | The biology of Paramecium[END_REF]. It has a germline micronucleus and a somatic macronucleus. Our cultures are maintained asexually in a lettuce medium with the food bacterium Serratia marcescens at 23C, allowing 1-2 population doublings per day [START_REF] Nidelet | Direct and correlated responses to selection in a host-parasite system: Testing for the emergence of genotype specificity[END_REF]. The gram-negative alpha-proteobacterium Holospora undulata infects the micronucleus of P. caudatum, and can be transmitted both horizontally (by s-shaped infective spores, 15 µm) upon host death or during cell division, and vertically, when reproductive bacterial forms (5 µm) segregate into daughter nuclei of a mitotically dividing host (73). After ingestion by feeding Paramecium, infective spores invade the micronucleus, where they differentiate into the multiplying reproductive forms. After one week, reproductive forms begin to differentiate into infective spores [START_REF] Fels | Ecological and genetic determinants of multiple infection and aggregation in a microbial host-parasite system[END_REF][START_REF] Nidelet | Direct and correlated responses to selection in a host-parasite system: Testing for the emergence of genotype specificity[END_REF]. Infection with H. undulata reduces host cell division and survival [START_REF] Restif | Condition-dependent virulence in a horizontally and vertically transmitted bacterial parasite[END_REF] and also host dispersal [START_REF] Fellous | Parasitic infection reduces dispersal of ciliate host[END_REF].

Long-term experiment

Similar to Fronhofer and Altermatt (2015), we imposed dispersal selection in 2-patch microcosm arenas (Fig. 1, see also SI 1), built from two 14-mL plastic tubes, interconnected by 5-cm silicon tubing, which can be blocked using a clamp (see Fig. S1). We define dispersal as the active swimming of Paramecium from one microcosm to the other via the connective tuber (i.e., the dispersal corridor).

The experiment was seeded from an uninfected host line ("63D", haplotype b05) from our laboratory that had been under "core selection" (see below) for three years and shows characteristically low dispersal propensity (O.K., unpublished data). This 63D mass culture was infected with an inoculum of H. undulata prepared from a mix of various infected stock cultures (for details, see SI 2). All parasites in this mix originate from a single isolate of H. undulata established in the lab in 2001.

In the front selection treatment, we placed Paramecium in one tube ("core patch") and opened the connection for three hours, allowing them to swim into the other tube ("front patch"). Paramecium from the front patch were recovered and cultured in bacterised medium, allowing for natural host population growth and parasite transmission. After one week, we imposed another dispersal episode, again recovering only the Paramecium from the front patch, and so on. The core selection treatment followed the same alternation of dispersal and growth periods, except that only Paramecium from the core patch were recovered and propagated (Fig. 1, and SI 1). We established five infected 'core selection' lines and five infected 'front selection' lines that were maintained for a total of 55 cycles of dispersal. To minimise potential effects of host (co)evolution, we extracted infectious forms from each selection line after cycle 30, inoculated a new batch of naïve 63D hosts and continued the experiment for another 25 cycles. For details of the experimental protocols, see SI 1.

Parasite assays

At the end of the selection experiment, we extracted parasites from core and front selection lines to inoculate new, naïve hosts. We then assayed parasite effects on host dispersal, infection life-history and virulence. To obtain a general picture of trait expression, we tested the evolved parasites on naïve 63D hosts (same genotype as used in long-term experiment), as well as on two other genotypes, C023 and C173 (provided by S. Krenek, TU Dresden, Germany). Companion assays of evolutionary adaptations arising in the host are reported elsewhere [START_REF] Zilio | Travelling with a prasite: the evolution of resistance and dispersal syndrome dyring experimental range expansion[END_REF].

All assays were performed on a cohort of infected replicate cultures, over the course of three weeks under common-garden conditions (Table S1). To initiate the cultures, we placed ≈ 5 x 103 cells of a given naïve host genotype in 1.4 mL of bacterised medium in a 15-mL tube, to which we added the freshly prepared inoculum of a given evolved parasite line (≈ 1.5 x 106 infectious spores, on average).

On day four post-inoculation (p.i.), when infections had established, we split the cultures into three technical replicates and expanded the volume to 30 mL, by adding bacterised medium. A total of 90 replicate cultures were set up (2 selection treatments x 5 parasite selection lines x 3 host genotypes 3 technical replicates).

Dispersal of infected hosts

From day 14 to 19 p.i., we assayed dispersal rates of hosts infected with core and front parasites, using linear 3-patch arenas where the Paramecium disperse from the middle tube to the two outer tubes (Fig. S2). Arenas were filled with ~2800 individuals in the middle tube and after 3 h of dispersal, we subsampled the middle tube (0.5 mL) and the pooled two outer tubes (3 mL) to estimate the number of non-dispersers and dispersers under a dissecting microscope. Furthermore, from ≈20 arbitrarily picked individuals stained with 1% lacto-aceto orcein (LAO fixation; Fokin and Görtz, 2009) we determined the proportion of infected dispersers and non-dispersers (phase-contrast, 1000x magnification), from which we then calculated the dispersal rate of infected hosts for each replicate culture (number of dispersed infected hosts / total number of infected hosts per 3 h). Each of 88 available replicate cultures was tested once. For statistical analysis, we excluded 13 replicates with very low population density and/or infection prevalence (<10%), which prevented accurate estimation of dispersal of infected individuals. Dispersal was not significantly affected by assay date (χ22 = 2.56, p > 0.25), and this factor was therefore omitted from further analysis.

Parasite life-history traits

Infectivity. On day 4 p.i., we estimated infection prevalence in the 30 inoculated cultures, using LAO fixation of ≈20 individuals, as described above. This measurement describes 'parasite infectivity', i.e., the capacity to successfully establish infections [START_REF] Fels | Ecological and genetic determinants of multiple infection and aggregation in a microbial host-parasite system[END_REF].

Epidemiology and parasite development. From day 6 to 13 p.i., we tracked population density and infection prevalence in the 90 replicate cultures, using a blocked sliding window (day 6-8, 11-13) such that each parasite x host genotype combination was measured once per day. As infections developed, we also tracked changes in the proportion of infectious hosts, when reproductive forms are converted into infective spores. These data were used for the fitting of an epidemiological model (see below). Furthermore, we specifically compared core and front parasites for their levels of infectiousness (= proportion of infectious hosts) between day 6 and day 11 p.i.. This time window describes the timing and level of investment into horizontal transmission by the initial cohort of infected hosts [START_REF] Nidelet | Direct and correlated responses to selection in a host-parasite system: Testing for the emergence of genotype specificity[END_REF].

Virulence. Early after inoculation of the initial 30 assay cultures (day 4 p.i.), we isolated single infected and uninfected individuals from each culture and let them multiply for 9 days in 2-mL tubes under permissive common-garden conditions. From these small monoclonal cultures, we started the virulence assay by placing single individuals in PCR tubes filled with 200 L of medium. We assessed cell division on day 2 and 3 (visual inspection), on day 10 (from 50-L samples) and on day 20 from the total volume. A total of 645 replicates were set up, with 8-12 infected and uninfected replicates from each of 28 of the 30 assay cultures. For further details, see SI 2 and Fig. S3. Swimming behaviour. From the above monoclonal lines, we placed 200-µL samples (containing 10-20 individuals) on a microscope slide and recorded individual movement trajectories using a Perfex SC38800 camera (15 frames per second; duration 10 s). For each sample, the mean net swimming speed and swimming tortuosity (standard deviation of the turning angle distribution, describing the extent of swimming trajectory change) was determined, using the BEMOVI package [START_REF] Pennekamp | BEMOVI, software for extracting behavior and morphology from videos, illustrated with analyses of microbes[END_REF]. This assay was performed for infected and uninfected monoclonal lines from 29 assay cultures, with 1-2 samples per monoclonal line (106 replicates in total).

Statistical analysis

Statistical analyses were performed in R (ver. 3.3.3; R Development Core Team, available at www.rproject.org) and in JMP (SAS Institute Inc. (2018) JMP®, Version 14, N.C.). To analyse variation in parasite traits, we used generalised linear mixed-effect models [START_REF] Bates | Fitting linear mixed-effect models using lme4[END_REF]. Binomial error structure and logit link were used for analysis of infected host dispersal (proportion dispersers), infectivity (proportion infected individuals on day 4 p.i.), and horizontal transmission investment (proportion infectious hosts day 6-11 p.i.). Normal error structure was used for analysis of swimming speed and tortuosity. For the virulence assay, we analysed variation in host division (= maximum cell density per replicate; Poisson error structure and log link) and survival (= replicate alive / dead on day 20; binomial error structure and logit link).

In all analyses, parasite selection treatment (front vs core) was taken as a fixed effect and host genotype and parasite selection line identity as random factors. Day p.i. was integrated as a covariate in the analysis of infectiousness. In the virulence analyses, replicate infection status (infected / uninfected) was included as a fixed factor. Analysis of variance (type II) was used to test for significance of fixed effects (car package; Fox and Weisberg, 2018). In complementary comparisons, we used ANOVA model predictions (and their variance) for core and front treatments to establish predictive distributions of the front-core difference (e.g. Fronhofer et al., 2017). For these distributions, we calculated the mean difference and confidence intervals. Finally, we performed multiple regressions (path analysis) to assess how infected host dispersal was affected by the following traits: horizontal transmission investment (HTI, area under the curve of the proportion of infectious hosts from day 6 -11 p.i.), virulence (infected host division) and swimming behaviour (tortuosity and net swimming speed). This analysis was based on trait means for 25 combinations of parasite selection line and host assay genotype. To meet assumptions of normality, certain trait means were transformed (log2 for host division, arcsine for dispersal, square root for HTI). To correct for overall effects of host genotype, we first fitted univariate analyses for each trait, and then performed the regressions on the residuals. Standardised beta regression coefficients were taken as path coefficients.

Epidemiological model fitting

We fitted a simple epidemiological model to the above population density and infection prevalence data recorded in our assay replicate cultures (day 6-13 p.i.). The aim was to obtain additional independent estimates of parasite parameters (Table 1), namely virulence, but also the transmission parameter or latency time, i.e. the time to onset of production of infectious forms (Rosenbaum et al., 2019).

Model structure. We model the density of uninfected (S) and infected (I) hosts using ordinary differential equations (ODEs). In the absence of parasites, we consider that uninfected Paramecium growth follows the continuous time version of the Beverton-Holt model [START_REF] Thieme | Mathematics in population biology[END_REF].

𝑑𝑆 𝑑𝑇 = ( 𝑏 1+𝛼𝑁 -𝑑) 𝑆 (1)
where b is the birth rate, d the death rate and α the competition term. N is the total number of individuals (S +I), which is equal to S in the absence of the parasite. In the presence of infected individuals, uninfected individuals become infected at a rate proportional to the number of infected and uninfected individuals at a rate β: Finally, vertical transmission of the parasite is not necessarily 100%, and some of the Paramecium "born" from infected individuals could be free of parasites due to incomplete vertical transmission. We name γ the proportion of successful vertical transmission:

𝑑𝑆 𝑑𝑇 = ( 𝑏 1+𝛼𝑁 -𝑑) 𝑆 -𝛽𝑆𝐼 (2)
𝑑𝑆 𝑑𝑇 = ( 𝑏 1+𝛼𝑁 -𝑑) 𝑆 -𝛽𝑆𝐼 + ( 𝑏(1-𝑣) 1+𝛼𝑁 𝛾) 𝐼 (6)
𝑑𝐼 𝑑𝑇 = ( 𝑏(1-𝑣) 1+𝛼𝑁 𝛾 -𝑑) 𝐼 + 𝛽𝑆𝐼 (7)
Since the majority of infected individuals were not yet producing infectious forms at the beginning of the time series, we added another parameter, τ, which is the latency before an infected individual becomes infectious (i.e., capable of horizontal transmission):

𝛽 = 0𝑖𝑓𝑡𝑖𝑚𝑒 < 𝜏 (8)
Model Fitting. We fitted the epidemiological model to the data using Bayesian inference and the rstan

R

Core selection treatment

Front selection treatement

SI 1: Long-term selection protocol

Dispersal arenas consisted of two 14 mL plastic tubes (the core and front patch, Fig. S1) interconnected by a 5 cm silicon tube of 0.6 mm inner diameter (corridor). The protocol for a dispersal event is as follows. Step 1: We first fill the entire arena with 9.5 mL of fresh growth medium, then block the corridor with a clamp. Step 2: one of the two tubes ("core patch") is topped up to 13 mL with 8 mL of medium containing cultures of Paramecium caudatum ('Paramecium', hereafter), while the other tube ("front patch") is topped up to 13 mL with medium only. Step 3: we remove the clamp for 3 h allowing the Paramecium to actively disperse from core to front patch or to stay in the core patch. Step 4: after blocking the corridor again, population densities in core and front patches are determined from 200-µL samples, with the number of individuals counted under a dissecting microscope. From these counts we can estimate the dispersal rate. Using a mix of parasite inocula we infected naïve Paramecium of the 63D genotype to set up five front selection and five core selection lines (see main text for details on host and parasite origins). The long-term selection protocol is as follows (for illustration, see Fig. 1 in main text).

(i) In the front selection treatment, densities in the core patch prior to dispersal were set to c. 2000 individuals. After the 3 h of free dispersal, only Paramecium that dispersed to the front patch were maintained, transferred to a 50-mL plastic tube and cultured for one week in 20 mL of bacterised lettuce medium, before the next dispersal and selection event occurred. On average, c. 350 individuals dispersed at a given dispersal event. When we observed fewer than 100 dispersers, we topped up numbers to 100 by adding non-dispersers. Over the one week of culture, populations grew back to carrying capacity (c. 4-5 x 10 3 individuals) and epidemiological processes were acting freely. Then a new episode of dispersal occurred, as described above.

(ii) In the core selection treatment, we followed the same protocol as above, but only Paramecium that stayed in the core patch were maintained and regrown in 20 mL of medium. Furthermore, numbers of transferred core individuals were adjusted so as to match those in the front selection treatment at the beginning of the one-week growth period.

After 30 dispersal/growth cycles, we extracted infectious forms from each selection line and used them to inoculate a new batch of 63D hosts. This was done to minimise effects of host evolution in the experiment and to continue parasite evolution on naïve hosts for another round of 25 cycles. Because carrying capacity in this new round (c. 3-4 x 10 3 individuals) was lower than in the first 30 cycles, we relaxed the dispersal protocol. Instead of adjusting the density prior to dispersal, we topped up the core patch with the maximum possible volume (8 mL; step 2, see above) to ensure that at least 10 3 were placed in the tube.

SI 2: Assay details

After inoculation of three naive host genotypes (63D, C023, C173) with evolved core and front parasites, a series of assays were performed over a 3-week period. In this section, we present an overview of the timing of the assays (Table S1) and further details on the experimental protocols.

Table S1. Timing of measurements for the different parasite traits in the assay. The assay was started by inoculating naive cultures of three host genotypes with parasites from 5 core and 5 front selection treatments (30 combinations in total). Timing of each assay is expressed in days post inoculation (p.i.). On day 4 p.i., the initial 30 inoculated replicates were split into three technical assay replicates, giving a total of 90 assay replicates. For certain traits, not all replicate cultures were available, or data are missing. The 'Number' columns indicate the number of combinations and replicate assay cultures available for each analysis. 'Total n' refers to the total number of data points in the analysis (raw data). Paramecium for the singleton assay were isolated from the initial 30 inoculated assay cultures. For details on trait measurements, see SI below and main text.

Trait

Infectivity

Inoculum preparation. To extract infectious forms of Holospora undulata from an infected culture, the infected Paramecium are transferred to 50-mL Falcon tubes and centrifuged at 1500 g for 20 minutes. The supernatant is removed, and the concentrated individuals placed in 1.5 mL Eppendorf tubes containing 1 mm glass beads. Using a Qiagen TissueLyser they are then vortexed and crushed (1:45 minutes at 30 oscillation frequency) to liberate infectious forms of the parasite. The concentration of infectious forms is then determined at 200x magnification under a microscope (Leica DM LB2), using a hemocytometer.

Infectivity assay. Inocula of the evolved parasites selected for high or low dispersal (see Fig. S2; front and core, respectively) were prepared, as described above. Their capacity to establish infections (= infectivity) was tested on samples of unselected naïve hosts, represented by three genotypes: 63D, C023 and C173. Prior to inoculation, cultures of the three genotypes were concentrated by using mild centrifugation (15 min at 300 g). We placed ≈ 5 x 10 3 cells of a given host genotype in 1.4 mL of bacterised medium in a 15 mL tube, to which we added the freshly prepared inoculum of a given evolved parasite line. Inoculum dose ranged from c. 0.3 -1.4 x 10 3 infective spores per µL (median: 1 x 10 3 ), depending on the identity of parasite selection line. These doses represent an ad libitum administration; typically, infection success reaches a plateau for doses > 0.2 spores per µL [START_REF] Fels | Ecological and genetic determinants of multiple infection and aggregation in a microbial host-parasite system[END_REF]. In the present experiment, a preliminary logistic regression with binomial error structure (logit link) revealed no significant effect of spore dose on infection success (χ1 2 = 10.812, p = 0.147).

Dispersal assay

In the assay, we used 3-patch arenas (50-mL Falcon tubes; Fig. S3) instead of the usual 2-patch arena. These arenas allowed us to use larger numbers of Paramecium and, by letting them disperse from the middle tube into the two outer tubes, we increased the total number of dispersers. To further increase the resolution of dispersal estimates, we concentrated the cultures 12 h prior to the assay, by gentle centrifugation at 300 g for 15 minutes. For the dispersal assay, we first filled the 3-patch system with 20 mL of fresh medium, and then blocked the two corridors with clamps (see steps 1 and 2 in Fig. S1). We then added ≈2800 individuals to the middle tube and topped it up to 25 mL with fresh medium. The outer tubes were topped up to 25 mL with fresh medium only, and the corridors were then opened for 3 h to allow for free dispersal. At the end of the 3-h dispersal period, we determined population density and infection prevalence, for samples from the central tube (500 µl) and from the combined two outer tubes (3 mL). From these estimates we calculated the dispersal rate of infected hosts, as explained above. Of the 90 inoculated replicate assay cultures, 88 were tested (two tubes were found to be uninfected). For statistical analysis, we excluded 13 replicates with very low population density and/or low infection prevalence (<10%), which prevented accurate estimation of dispersal of infected individuals. We also assayed a small number of uninfected control cultures (three tubes per host genotype) for comparison with dispersal rates in infected tubes. For unknown reasons, these replicates showed considerable variation; we therefore regrouped these observations with measurements from previous experiments to inform on the general range of dispersal rates observed for these genotypes (see Fig. S4). We did not carry out formal statistical comparisons with infected dispersal rates observed in our assay. 125

Virulence assay

For the virulence assay, we isolated single infected and uninfected individuals from the replicate assay cultures on day 4 p.i and allowed them to multiply in 2-mL Eppendorf tubes with bacterised medium, under permissive common-garden conditions. After one week, we determined infection status of these monoclonal cultures (LAO fixation). On day 13 p.i., we started the assay by placing single individuals in PCR tubes filled with 200 mL of bacterised 135 medium (Fig. S3). We checked tubes daily for presence or absence of live cells for 20 days. In addition, cell density was determined on day 2 and 3 (by counting cells through the plastic tubes), on day 10 (from 50-mL samples) and on day 20 (total volume). Except for 50 µL of medium added on day 10, no resources were supplied. 150

The assay was performed for 28 of the 30 combinations of parasite selection line and host genotypes, with 8-12 infected singletons tested per combination. Of the 322 infected replicates, 17 died within less than 24 h (possibly due to transfer handling) and were excluded from 155 statistical analysis. In the same way, excluded 23 early deaths of the 323 uninfected singletons.

SI 3: Results

The assays of the evolved parasites were performed on naïve Paramecium representing three host genotypes (63D, C172, C023). The parasites had evolved on the 63D genotype in the selection experiment, but had never been exposed to any of the other two genotypes. In our main statistical analyses, we considered host genotype as a random effect, as the experimental tests were not specifically meant to address differences among the host genotypes. These results are summarised in Table S2. To inspect the generality of selection treatment effects, we also performed analyses, treating host genotype as a fixed effect and including the selection treatment x host genotype interaction (Table S3). They are accompanied by a more detailed presentation of trait expression, with separate panels for each host genotype (Fig. S4-S10). These additional analyses showed that, with few exceptions, differences between core and front parasites were consistent across the different hosts (i.e., treatment x host interactions were non-significant), even though in some cases more or less pronounced. For details of trait definitions and measurements, see main text.

  individuals also display Beverton-Holt dynamics, but their birth rate can be decreased, hence we multiply b by a term(1 -v), where v is the virulence of the parasite:

Fig. 1 .

 1 Fig. 1. Experimental design of the long-term selection experiment, using 2-patch dispersal

Fig. 2 .

 2 Fig. 2. Dispersal and infection life-cycle traits of evolved parasites from core selection (blue)

Fig. 3 .

 3 Fig. 3. Estimates of virulence of evolved parasites from core selection (blue) and front selection

Fig. 4 .

 4 Fig. 4. Relationships between parasite traits. (a) Path analysis testing direct and indirect effects

Fig. 5 .

 5 Fig. 5. Fit of the epidemiological model. (a) Fit of the epidemiological model (equations 6-8)

  Louise Solveig Nørgaard 1,2#* , Giacomo Zilio 2# , Camille Saade 2 , Claire Gougat-Barbera 2 , Matthew D. Hall 1 , Emanuel A. Fronhofer 2 & Oliver Kaltz 2* 1 School of Biological Sciences and Centre for Geometric Biology, Monash University, Melbourne 3800, Australia 10 2 ISEM, University of Montpellier, CNRS, EPHE, IRD, Montpellier, France.

Figure S1 .

 S1 Figure S1. Protocol for setting up dispersal events in 2-patch dispersal arena. Step 1: filling dispersal arean up until dispersal corridor with fresh growth medium. Step 2: block corridor with a clamp and add cultures of Paramecium to patch 1 and fresh media to patch 2. Step 3: remove clamp and allow for acrive dispersal from patch 1 to patch 2 during a three-hour period. Step 4: block dispersal corridor and assess population densities and infection status in patch 1 and 2.

Figure S2 .

 S2 Figure S2. Linear 3-patch arenas used for the dispersal assays. Paramecium was

  140

Figure S3 .

 S3 Figure S3. Protocol for virulence assay. On day 4 post inoculation of replicate cultures with front (ref) or core (blue) parasites, infected and uninfected individuals were isolated and allowed to grow as small monoclonal cultures. Single

Figure S6 .Figure S8 .Figure S9 .

 S6S8S9 Figure S6. Swimming trajectory changes (tortuosity = standard deviation of turning angle distribution) of three naïve Paramecium genotypes (63D, C173, C023), when uninfected or infected with core parasites (blue) or front parasites (red). Filled circles and error bars represent mean model predictions ± 95% confidence interval. Open symbols represent means over two technical replicates. Different symbols refer to different parasite selection lines (5 lines per selection treatment).

SI 4 :Figure S11 .

 4S11 Figure S11. Fit of the epidemiological model (equations 6-8) to infected and uninfected host density time series data in the core and front treatment for host genotype (A) C173 and (B) C023. Dashed lines show observed density trajectories, solid lines

Table 1 .

 1 package (version 2.19.2). Using data from previous experiments (O. Kaltz, unpublished data), we first fitted the Beverton-Holt model (Eq. 1) to growth curves of uninfected populations to estimate the distributions of b, d and α for each host genotype. These distributions were used as priors for fitting the full model (Eq. 6, 7, 8) on infection data. The model was fitted separately for each of the six combinations of host genotype and parasite selection treatment. For simplicity, we fitted a single set of parameters (b, d, α, b, β, γ, τ) over the different selection lines (with different initial conditions fitted over each line). Priors distributions can be found in Table1. Apart from b, d and α, we used lowly informative priors that largely encompass expected values (v and γ priors are uniform over possible Model parameters, their signification and the priors used for fitting.

	Parameters Term		Priors
	b	Birth rate		Posteriors from fitting eq. (1)
				on non-infected population
	d	Death rate		data
	α	Intraspecific	competition
		coefficient
	v	Virulence (decrease in b)	Uniform (0, 1)
	β	Horizontal transmission rate	Lognormal (-5, 0.9)
	γ	Vertical transmission rate	Uniform (0.5, 1)
	τ	Latency time		Uniform (144, 240)

values, τ prior is uniform over previously observed latency values, β prior follows a lognormal distribution an order of magnitude wider than expected values). Fits were realized using the No U-Turn Sampler (NUTS) with default rstan values and multiple chains (three chains per fit, each of total length: 15 000 and warm-up length: 5 000).

Table S2 .

 S2 ANOVA results from GLMM models of all measured traits (dispersal, swimming speed and tortuosity, infectivity, infectiousness and virulence). Parasite selection line and host genotype were added as random factors, all other factors were considered fixed. We performed backward model simplification, with sequential removal on non-significant terms in the model.Terms in the "Fixed effects" category represent the minimal adequate model; sequentially removed terms appear in the "Eliminated terms" category. For each analysis, we indicate the number of replicates used in the analysis and the number of host genotype x parasite selection lines they represent (3 x 10 = 30 combinations inoculated, some of which were not available for certain analyses).

	Table S2 (cont.)
	(e) Infectiousness
	Random effect:	Var
	Selection line	0.11
	Host genotype	0.32
	Fixed effects:	d.f.	χ 2	p
	Selection treatment	1	13.2	<0.001 ***
	Time	1	178.1	<0.001 ***
	Treatment x time	1	13.5	<0.001 ***
	N = 88, data from 30/30 host genotype x selection line combinations
	(f) Maximum host density
	Random effect:	Var
	Selection line	0.10
	Host genotype	2.50
	Fixed effects:	d.f.	χ 2	p
	Infection status	1	1.7		0.194
	Selection treatment	1	4.9		0.027 *
	Treatment x Infection status (a) Dispersal Random effect: N = 605, data from 28/30 host genotype x selection line combinations 1 16.9 Var Selection line 0.43 (g) Host survival	<0.001 ***
	Host genotype Random effect:	0.39 Var
	Fixed effects: Selection line Selection treatment Host genotype Fixed effects: N = 75, data from 28/30 host genotype x selection line combinations d.f. χ 2 1.07 1 4.9 2.50 d.f. χ 2 Infection status 1 <0.1 (b) Swimming speed Selection treatment 1 3.4	p p	0.027 * 0.987 0.065
	Random effect: Treatment x Infection status	Var 1	7.4		0.006 **
	Selection line Host genotype N = 605, data from 28/30 host genotype x selection line combinations <0.001 <0.001
	Eliminated terms:
	Selection treatment	1	0.67		0.414
	Infection status	1	1.25		0.262
	Treatment x infection status	1	0.33		0.943
	N = 106, data from 29/30 host genotype x selection line combinations
	(c) Tortuosity
	Random effects	Var
	Selection line	<0.001
	Host genotype	<0.001
	Eliminated terms:
	Selection treatment	1	0.03		0.857
	Infection status	1	<0.01		0.981
	Treatment x infection status	1	0.11		0.737
	N = 106, data from 29/30 host genotype x selection line combinations
	(d) Infectivity
	Random effects	Var
	Selection line	0.03
	Host genotype	0
	Fixed effects:	d.f.	χ 2	p
	Selection treatment	1	2.43		0.118
	N = 30, data from 30/30 host genotype x selection line combinations

Table S3 .

 S3 ANOVA results from GLMM models of all measured traits (dispersal, swimming speed and tortuosity, infectivity, infectiousness and virulence). Parasite selection line was treated as a random effect, all other factors were fixed effects. We performed backward model simplification, with non-significant terms sequentially removed from the model ("eliminated terms"). For each analysis, we indicate the number of replicates and the number of host genotype x parasite selection lines they represent (3 x 10 = 30 combinations inoculated, some of which were not available for certain analyses).

	Host genotype	2	0.01		0.991
	Treatment x genotype	2	4.33		0.114
	N = 30, data from 30/30 host genotype x selection line combinations
	(e) Infectiousness
	Random effect:	Var
	Selection line	0.08
	Fixed effects:	d.f.	χ 2	p
	Selection treatment	1	13.6	<0.001 ***
	Time	1	176.1	<0.001 ***
	Host genotype	2	28.9	<0.001 ***
	Treatment x time	1	16.8	<0.001 ***
	Treatment x host	2	10.1		0.006 **
	Eliminated terms:
	Host x time	2	3.5		0.167
	Treatment x host x time	2	2.2		0.317
	(a) Dispersal N = 88, data from 30/30 host genotype x selection line combinations
	Random effect: Selection line (f) Maximum host density Fixed effects: Random effect: Selection treatment Selection line Host genotype Fixed effects: Treatment x genotype Infection status Selection treatment N = 75, data from 27/30 host genotype x selection line combinations Var 0.41 d.f. χ 2 Var 1 7.0 0.09 2 607.5 d.f. χ 2 2 22.8 1 2.03 1 5.4 Host genotype 2 264.9	p p <0.001 *** 0.007 ** 0.153 <0.001 *** 0.019 * <0.001 ***
	(b) Swimming speed Treatment x Infection status	1	19.1	<0.001 ***
	Random effect: Treatment x host	Var 2	61.7	<0.001 ***
	Selection line Fixed effects: Eliminated terms: Selection treatment Infection status x Host Host genotype Treatment x Infection status x Host Treatment x genotype N = 605, data from 28/30 host genotype x selection line combinations 2866 d.f. χ 2 1 0.6 2 2.7 2 0.05 2 1.5 2 10.2	p	0.258 0.404 0.457 0.974 0.006 **
	(g) Host survival
	Eliminated terms: Infection status Random effect: Infection status x genotype Selection line Treatment x infection status Fixed effects: Treatment x infection status x genotype Infection status Selection treatment N = 106, data from 29/30 host genotype x selection line combinations 1 1.1 Var 1 <0.1 0.98 1 0.9 d.f. χ 2 2 0.7 1 0.01 1 4.0 Host genotype 2 75.0	0.286 0.979 0.319 0.911 0.684 0.043 * <0.001 *** p
	(c) Tortuosity Treatment x Infection status	2	8.2		0.004 **
	Random effects: Treatment x Host	Var 1	25.9	<0.001 ***
	Selection line Fixed effects: Eliminated terms: Selection treatment Infection status x Host Host genotype Treatment x Infection status x Host	<0.01 d.f. 1 2 2 2	χ 2 0.6 0.2 1.0 1.8	p	0.882 0.800 0.598 0.398
	Infection status N = 605, data from 28/30 host genotype x selection line combinations 2 <0.1		0.932
	Treatment x genotype	2	4.6		0.095
	Infection status x genotype	2	3.7		0.157
	Treatment x infection status	1	0.1		0.713
	Treatment x infection status x genotype	2	3.8		0.147
	N = 106, data from 29/30 host genotype x selection line combinations
	(d) Infectivity
	Random effects:	Var
	Selection line	0.03
	Table S3 (cont.)
	Fixed effects:	d.f.	χ 2	p
	Selection treatment	1	2.44		0.118

Acknowledgements

This work was supported by the 2019 Godfrey Hewitt mobility award granted to LN by ESEB, and by the Swiss National Science Foundation (grant no. P2NEP3_184489) to GZ. This is publication ISEM-YYYY-XXX of the Institut des Sciences de l'Evolution.

Data accessibility

If the manuscript is successfully accepted for publication, data will be available at Dryad or Figshare.

Author contributions

OK, LN and GZ conceived the study. OK, LN, GZ, MH, and EAF helped design the experiments. LN, GZ, CGB and OK performed the experimental work., LN, GZ, MH, OK and EAF performed the statistical analysis. EAF, CS and OK developed, and CS analysed the epidemiological model. All authors interpreted the results and contributed to the writing of the manuscript. Tortuositytrajectory variation

Supplementary Information

An evolutionary trade-off between parasite virulence and

Net swimming speed