R Alami

T Simcon

Planning robust motion strategies for a mobile robot

This paper reports on a recent work we have conducted concerning the development and the implementation of a robust motion planner for a mobile robot in a polygonal environment and in presence of uncertainty in robot control and sensing. Such a planner takes ezplicitly into account the uncertainty in robot control and produces a robust motion plan composed of sensor-based motion commands. The main originality ofthis approach is that it is able to account for a set of motion commands which may accumulate errors. It is based on a geometric analysis of the reachability and it generates motion strategies which may allow the robot to reduce its uncertainty.

A/ In the two-phase approach, a motion plan (or more generally a task plan) is first generated assuming no uncertainty and then, this plan is analyzed and patched in order to finally produce a robust task plan.

The analysis is mainly baaed on the propagation of uncertainty through the plan and its consequences on plan correctness [21, 14, 2, 15, 19, 22, ?, 18, 101. The plan is then modified by inserting complementary actions or sensor readings allowing to reduce uncertainty.

Introduction

While the problem of planning collision-free motions has received considerable attention, there has been only a limited number of contributions where uncertainties are taken explicitly into account in the planning process. However, uncertainties arising from sensor noise, control error and inaccurate models, constitute an integral part of the planning problem for a real robot moving in a real environment.

Consequently, the use of motion planners which do not take explicitly into account uncertainty is limited to situations where the uncertainties can be dealt with by simply growing the obstacles. This cannot be the case in assembly tasks, or in situations where the initial uncertainty is greater than the task tolerances.

Other challenging problems arise for mobile robots which are not equipped with an absolute relocalization procedure and which may accumulate position errors. Indeed, in such situations, as the error cannot be bounded by a fixed value, a growing of the obstacles is not sufficient.

One may argue that uncertainty may be reduced by reading and interpreting sensory data at execution time, allowing to build a new plan after executing a portion of the original plan, etc.. .This is certainly insufficient when it is necessary to reason in advance , taking into account the capacity of the available sensing functions (visibility, range, specularity, *this work is supported by the CEC Esprit 3 Project 6546 PROMotion uncertainty.. .), in order to generate a plan which allows to acquire the necessary knowledge to guide the robot towards the goal. Indeed, if the robot accumulates errors during its motion, it may even reach situations where it is "lost".

This paper reports on a recent work we have conducted concerning the development and the implementation of a robust motion planner for a mobile robot in a polygonal environment and in presence of uncertainty in control and sensing. Such a planner takes explicitly into account the uncertainty in robot control and produces a robust motion plan composed of sensor-based motion commands. The main originality of this approach is that it considers a set of motion commands which may accumulate errors. It is based on a geometric analysis of the reachability and it generates motion strategies which may allow the robot to reduce its uncertainty.

The paper is organized as follows. In section 2, we briefly discuss related work. Section 3 defines more precisely the problem we propose to tackle. In section 4 and 5, we describe how we perform a geometric analysis of the reachability taking into account the uncertainties, and how this analysis is used by the planner (section 6). We finally present some experimental results and discuss possible extensions.

Background and Related work

We do not have here the ambition to provide a detailed analysis of the relevant literature. The reader may refer to a very interesting state of the art and discussion in [ll, 12, 91.

Roughly speaking, the problem has been tackled in the literature following two general approaches: several contributions are based on a two-phase approach, while other contributions stem from the preimage backchaining approach.

When a plan cannot be patched, a backtrack can occur when planning is based on skeleton or script selection [START_REF] Lozano-Perez | Robot programming[END_REF]. The main interest of such an approach is that it can applied to problems which can be more general than motion planning (e.g. assembly, manipulation) and to robots with a high number of degrees of freedom. Its main drawback is that it is based on an a priori decomposition of the planning process and on the assumption that, in most situations, the plan can be locally patched.

B/

The second approach is the preimage backchaining approach which is based on the geometry of the Configuration Space. It has been originally proposed by [START_REF] Lozano-Perez | Representation and propagation of positionning uncertainties through manipulation robot programs[END_REF] and analyzed or extended through several contributions [7, 5,4, [START_REF] Latombe | Robot Motion Planning[END_REF]121. The underlying assumption is that it is necessary to take uncertainty explicitly into account in the planning process itself since it can have drastic consequences on the plan structure.

A preimage for a given motion command and for a given goal region (subset of the C-space), is a set of free configurations from which the command can be started and which guarantee that the robot will reach the goal region and stop inside it. Given a goal region and a start region,preimage backchaining consists in finding a sequence of commands (i.e. a plan) such that the inverse sequence allows an iterative construction of preimages starting from the goal and resulting in a preimage which contains the initial region.

While this problem, in its general formulation gives a useful computational framework, it raises "discouraging" complexity issues [4]. However this, by no means, affects its interest. It remains to find relevant instances of the general problem: 0 which integrate new sensor modalities (proximity 0 which provide sub-classes of the problem with 0 or which allow to implement algorithms of prac-

The problem that we have defined and the algorithm that we propose to solve it fall in these categories.

Note that we also need more elaborate models of different sensor modalities in order to be able to compute where (in the C-Space) they can be used and the nature of the measure they can provide together with its (pre-computed) estimated uncertainty. This should of course be done, taking into account the sensor characteristics (position relative to the robot frame, range, specularity.. .) in a given environment [6, 201. 3 Problem statement

The robot and the environment

Let us assume that the robot is a point moving in the plane amidst polygonal obstacles denoted by a set of oriented edges ej. We assume that the environment is perfectly known.

The robot is equipped with a position sensor (dead reckoning), and a proximity sensor which allows to detect contact with obstacles and to follow walls (edges). sensors, vision) and control algorithms [3, 81; "better" properties [START_REF] Lazanas | Landmark-based robot navigation[END_REF]; tical use even though they are not complete.

The error on position depends on past history (trajectory) and results in cumulative uncertainty.

We assume that the robot initial and final positions are in the free space or along a known edge with an associated uncertainty represented either by a disk or by an interval. The planner will provide a plan which allows, at any moment to know if the robot is at an uncertain position p: in the free space; p = ( 2 , y, E ) , where x, y denote the coordinates and E the value of the maximum error of the position sensor (dead reckoning)'; in the contact space, on a known edge ej; p = ( 2 , ~) where x denotes the nominal position along e, and E the value of maximum error; 0 or on a known obstacle vertex; the uncertainty is then set to zero'.

The commands and their models

There are several available motion primitives which are modelled by the type of initial situations where they can be applied, the final situation they can reach and the envelope of possible actual trajectories they can induce (Fig. 1):

0 MOVEDISTANCE(6), d ) 0 FOLLOW-WALLDISTANCE(d, [LEFT I RIGHT] ) 0 FOLLOW-WALL-UNTIL-VERTEX ( [LEFT I RIGHT]
These primitives are based on dead-reckoning and contact (or proximity) sensors for primitives designed to maintain contact (or k e d distance) with an edge. 2/ When the robot reaches without ambiguity an edge (after a IIOVE~TILXONTACT), the new uncertainty is modelled as an interval whose endpoints correspond to the intersection of the edge with the envelope of all possible trajectories.

3/ When the robot is commanded to follow an edge

(FOLLOWYALLDISTAICE) , we assume that the maximum value of the positioning error, increases linearly:

E ( Z ) = a.]].
-eo11 + EO with a E [0, 1 1 (Fig. 2-a).

4/ When the robot reaches a vertex (after a FOLLOWYALL-UITIL-VERTEX), E is reset to zero. If, from the reached vertex, the robot follows again the same edge (in the opposite direction) or an adjacent edge, using FOLLOW-WALLDISTANCE, the maximum value of the positioning error will again increase linearly, but with an initial value equal to zero: This will allow the planner to produce, when necessary, re-localization strategies along a given edge. In order to ensure a coherence between the different commands, we take: a = tan(h6). However, the algorithm we propose does need such an assumption.

~( 2 )

The planning problem

Given an initial and a goal position, in the free space or along a known edge together with their uncertainties (represented by a disk or by an interval), the planner should generate a sequence of motion commands whose execution guarantees to reach the goal with the desired uncertainty if the actual errors lie inside the control uncertainty cone AO.

We restrict the plan, except the initial and final steps, to contain a sequence of commands which allow the robot to follow edges or to reach an edge starting from another one.

In order to implement such a planner, we need a basic step which computes if a given entity (a disk or an edge) can be reached from another entity using the available commands. If a command exists, the entities will be said adjacent.

Informally, a target entity end, can be reached from an uncertain position p, if there exists at least one direction 6 such that, taking into account a given value of the uncertainty cone AO: 0 C1: the robot cannot miss entj (i.e. all possible paths inside the uncertainty cone, for all possible initial configurations, intersect e n t j ) ; entj is said to be Strongly visible from p; 0 C2: the robot cannot collide any other entity entk (i.e. no possible path inside the uncertainty cone, for all possible initial configurations intersect another entity before its intersection with e n t j ) ; if it collides an entity entk, entk is said to be Weakly visible from p; We develop, in the next sections, the computation of the disk-edge adjacency and edge-edge adjacency. While the first is quite simple ( §4), the second gives rise to the possibility of characterizing the adjacency from a complete edge and not only from an uncertain position on an edge ($5). This is possible because we have a knowledge on the evolution of uncertainty along an edge. It will provide us with a coherent way to combine and to compute the parameters for MOVE-UNTIL-CONTACT, FOLLOW-WALLDISTAICE and FOLLOW-WALLJJMTIL-VERTEX commands.

Disk-Edge Adjacency

This adjacency can be easily computed as illustrated by Fig. 3. The strong visibility is satisfied from at most one range of O values, while the weak visibility can correspond to one range of O values for each entity in the environment different from the target entity. The adjacency will be then verified for a set of O ranges corresponding to the set difference between the strong visibility range and the weak visibility ranges. The O- ranges are determined using the tangents to the disk going through the edges endpoints. Figure 4 shows an example of workspace and the adjacencies computed by the algorithm. Let us consider that the robot arrived on a given edge ei at position (zo,~,). We want to characterize the parameters of the motion commands which allow to reliably reach the other edges of the environment from this position. Some of these edges can be directly Figure 4: An example of diskledge adjacency reached with a MOVE-UNTIL-CONTACT using a computation similar to the case described in $4. However there can also be other edges which are not directly "visible" from the current position but which can be reached if the robot first executes a FOLLOWYALLDISTANCE along ej from zo to another position z. In some other cases, the additional uncertainty induced by FOLLOWYALLDISTANCE will be too important and a re-localization (using FOLLOW-UNTIL-VERTEX) will be required. In this section, we first introduce a notion of visibility between edges; then we explain how this notion is used to decompose the (z,O)-space (which parametrizes the set of motion commands) into regions where the reachability of specific edges is guaranteed. These regions allow to determine the adjacencies between the edges of the environment.

Visibility regions

An edge e, is said to be strongly (resp. weakly) visible from a position z along ei and for a commanded motion in direction 0, if for any (resp. some) uncertain position 5 E [z -~( z ) , z + ~( z ) ] ,

the straight line issued from 5 in direction 0 intersects the edge e,. The regions of the (2, B)-space which verify this definition.are called the strong (resp. weak) visibility regions from ej to ej; they are respectively denoted S V j and WVj.

These regions are limited by two curves Bmrn(e) and Bma,(z). For a linear evolution of the uncertainty ~( z ) , it can be easily shown that the tangents of these extrema1 orientations also depend linearly on z. Thus, SVj and WVj can be simply represented in the (e, tan(8))-space by trapezoidal regions. Figure 5 shows an example which illustrates the construction of the visibility regions.

Note that more complex situations occur when the start edge is intersected by the support line of ej. In this case, SVj and WVj may possibly consist of several

Adjacency regions

The adjacency regions dj from ej to ej, consist of the (z,0) values such that the motions issued from any uncertain position z f c(z) along ej, and in any direction O f A0 are guaranteed to endup on e, ; that is, the robot will not miss ej and it will not be stopped on its way by another edge. We describe below the two steps of the algorithm we implemented in order to compute the dj regions.

The first step is performed without considering the directional uncertainty A(?. In this case, dj clearly corresponds to the sub-regions of SVj which are not contained into the union of the wvk regions associated to the edges lying between ei and e,. A, is first initialized to SVj ; then it is iteratively decomposed by considering each of the wvk. The basic operation of each iteration consists in computing the set difference between two regions. This computation can be easily performed by considering their representations in the (e, tan(O))-space; it results in decomposing each trapezoid into at most four trapezoidal regions.

The second step is needed to account for Ae. Hence, the adjacency regions dj only contain the points (z, 0) such that (2, tan(0 f A0) belongs to the trapezoids produced by the first step. Using the equations of the upper and lower lines defining each trapezoid, we derive the expression of the curves which limit the corresponding sub-region of dj .

The Planner

The planner is given a set of polygonal obstacles, a value for the angle uncertainty cone AO, the initial and final positions represented by two discs Cr and CG. The search space is a directed graph G of uncertain positions p = ( 2 , y, E). The nodes are the initial and final positions pr and p~ and a discrete set of positions lying on the edges of the environment. An arc between two nodes correspond to a given motion command as defined in $3.2.

The planner initially constructs a graph G containing only the two nodes associated to pr and PG. In a first step, it simply tries to connect them by checking that the half-lines D 1 and DZ issued from PI (Fig. 7) If not, the initial node is expanded in order to generate a discrete set of positions lying on the "visible" edges of the environment. These successors are created for the extrema1 values of the legal &ranges. The arcs issued from PI correspond to a MOVElJliTILXOITACT motion command.

do
The other nodes of the graph are incrementally created during the search of a minimum-cost path connecting pr to PG. The costs assigned to the arcs are simply computed from the length of the nominal path connecting two adjacent nodes, and the search is carried out by a classical A* algorithm. Each iteration of the algorithm consists in expanding the "best" node of the OPEN list. We now describe the expansion of a current node denoted Pcur lying on an edge ecur. If Pcur can be directly connected to PG, the expansion simply consists in linking both nodes with a MOVEDISTAHCE arc and the planner returns success. Otherwise, the successors are generated as follows: pcur ie first connected with FOUOUYIJTIL-VERTEX motions to the two endpoints of edge ecur. As the robot is assumed to perfectly detect a corner of the environment, a null uncertainty is associated to both corresponding nodes ( p f e f l and Pright for the example of For all the other edges ej, the adjacency regions computed from eCbr to ei are used to generate motion commands guaranteed to reach the edge ei. Three cases can occur: 0 The set of adjacency regions Ai is empty (ie. the edge is too short to be reachable from eeur with the current uncertainty or it is completely obstructed by other edges): no successors are associated to this edge. This is the case of edge el on the example.

0 The location Pcur along the edge ecur is such that one (or more) feasible range of orientations exists in the Ai's regions (case illustrated by the A2 region shown in Fig. 8-b). A successor is then created for each of the two extrema1 orientations of the ranges (e: and 0; for the example). These new nodes are connected to Pcur by MOVE-UHTIL-COIOTACT commands.

0 When the vertical line issued in the (z,O)-space at the current z position does not intersect any cells of the Ai regions (case illustrated by the A3 regions of Fig. 8-b associated to the edge e3), the robot first needs to follow ecur toward the left (resp. the right) until it reaches a position denoted p' (resp. p") on the figure, and corresponding to the beginning of the nearest legal range. From this intermediate position p' (resp. p") reached via a FOLLOWDISTANCE command, a MOVEYNTILXONTACT motion command issued in direction 0: (resp. e;) allows to generate the successor p: (resp. p;) on edge e3.

Figure 8-c shows the successors created for the environment of Fig. 8-a; it also indicates the motion commands produced to connect Pcur to these nodes. The algorithms presented above have been implemented in C on a Sun Sparc 10 computer. We ran the planner on several workspaces, with various sizes of the initial and goal regions (€1 and 6 ~) and with different values of the directional uncertainty Ad.

Experimental Results

Figures 9, 10 and 11 illustrate some results obtained for a same polygonal workspace containing 98 edges. The black polyline joining the initial and goal regions represent the nominal trajectory and the grey regions show the areas that may by swept by the robot during the execution of the motion commands because of the uncertainties.

The first example (Fig. 9) was run for small values of both initial and control uncertainties (A0 = 5deg.).

Note that the positional uncertainty is reset at the end of the FOLLOWYIOTIL-VERTEX commands (positions p2, p4 and p6) because of the vertex based re-localization.

Only 35 nodes were developed during the search and the solution was obtained in half a second after the computation of the adjacency regions between the edges which required 6 seconds on a Sparc 10 workst at ion. The second example was run with the same value of A0 but with a larger radius for the initial disk. In this case, the initial uncertainty is too important to directly reach the polygon displayed at the center of the figure. After a first motion guaranteed to stop on the left-down wall of the workspace, and a precise vertex localization at position p2, this large polygon can be reliably reached with the next MOVE-UNTIL-CONTACT command (position p3). Figure 11 : Same example with a larger control uncertainty Finally, the third example was run with A0 set to 10 degrees. The small obstacles around the goal region cannot be used anymore to localize the robot and a completely different motion strategy is required as illustrated by Fig. 11. Note that the solution produced by the planner contains two FOLLOWDISTAIfCE commands between pz (resp. p6) and p3 (resp. p7). In both cases, the edge containing p4 (resp. ps) could not be reached directly from position pz (resp. p6) and the planner used the adjacency regions between the corresponding edges to compute the first position at which the next IIOVEYIfTIL-COBTACT command was guaranteed to succeed.

For the two last examples, 46 and 78 nodes were respectively developed during the search and the so- lution was obtained in both cases after less than one second of computation.

Discussion and Extensions

The main originality of the approach described above is its ability to produce robust motion plans composed of sensor-based motion commands which may accumulate errors, and to determine where the robot needs to re-localize in order to guarantee a successful execution of the trajectory.

Although the edge-edge adjacency described in 5 5 captures exactly all the guaranteed motions between two given edges of the workspace, the planner described in § 6 is not complete since the number of paths explored is a finite set (discrete points (z,8) selected into the computed adjacency regions). However, the planner becomes complete if we restrict the class of solutions to strategies where a vertex re-localization is systematically performed after the HOVE-UHTIL-COITACT commands (the errors do not depend anymore on the complete past history). Note that in this case, and when the error A8 tends to zero, the search space of the algorithm degenerates to a classical visibility graph.

The algorithm described in this paper solves a relatively simple instance of the motion planning problem in presence of uncertainty. We are currently investigating several extensions of the approach. Some of them are rather straightforward; the algorithms can be easily adapted to deal with a circular robot and to relax the assumption of a perfect proximity sensor. Another interesting extension would be to consider the information which can be provided by other types of sensors (distance to the obstacle, orientation of the edges) and to explore the possibility of producing conditional strategies.

Nevertheless, there are numerous situations where it should be enough to use a planner like the one we described, which is really able to find in a very reasonable time, non-trivial sensor-based motions strategies for a mobile robot equipped with proximity sensors.

Figure 1 :of the different primitives 1 /

 11 Figure 1: Model of the different primitives 1/ When the robot is commanded to move in a given direction 6 (MOVEDISTANCE, MOVE-UNTIL-CONTACT), the robot follows a path such that the tangent to the 'the disk centered on (z,g) with a radius equal to c may 2it is straightforward to extend it to a fixed value overlap obstacles

= a. 2 (

 2 Fig 2-b and 2-c).

Figure 2 :

 2 Figure 2: Evolution of the uncertainty along an edge

Figure 3 :

 3 Figure 3: 0-ranges associated to the &&-edge adjacency

Figure 5 :

 5 Figure 5: Strong and Weak visibility regions

Figure 6 - 1315 Figure 6 :

 613156 Figure 6-b shows a simple environment and the adjacency regions A7 computed between the edges el and e7. The external contours correspond to the boundary of the adjacency regions before "shrinking" by 110.

Figure 7 :

 7 Figure 7: a/ PG and PI are connected. b/.and .c/ PG and p~ cannot be connected (b/ potential coheon with the environment, c / final error too large)

Fig. 8 Figure 8 :

 88 Fig. 8 which illustrates the node expansion mechanism).

Figure 9 :

 9 Figure 9: uncertainty

Figure 10 :

 10 Figure 10: Same example with a larger initial uncertainty


Giacomo Zilio

Oliver Kaltz

Jacob C Koella
email: jkoella@gmail.com

Resource availability for the mosquito Aedes aegypti affects the transmission mode evolution of a microsporidian parasite

Keywords: Experimental evolution, Horizontal transmission, Microsporidia, Mixedmode transmission, Vertical transmission, Virulence

come

Introduction

Transmission is a key step in the parasite life cycle. It determines the spread and maintenance of infection in the host population, and therefore represents a main component of the parasite's fitness [START_REF] Schmid-Hempel | Evolutionary Parasitology: The Integrated Study of Infections, Immunology, Ecology, and Genetics[END_REF]. Vertical and horizontal transmission are two distinct ways of accomplishing the passage from one host to another, with very different epidemiological and evolutionary implications (Sachs et al. 2011a, b;[START_REF] Ebert | The epidemiology and evolution of symbionts with mixed-mode transmission[END_REF]. The success of vertical transfer of infection from parents to their offspring (e.g., via seeds or eggs) depends on the reproductive output of the infected host. This alignment of host and parasite fitness should therefore favour low levels of virulence [START_REF] Frank | Models of parasite virulence[END_REF]. In contrast, horizontal infectious spread (e.g., via specialised transmission particles) is not limited to individuals that are in a parent-offspring relationship, and potentially reaches any susceptible host in the population. Not necessarily relying on host reproduction, horizontal transmission can therefore be associated with considerable levels of virulence [START_REF] Frank | Models of parasite virulence[END_REF]. While these general considerations are straightforward for the two modes in isolation, we still know little about the evolutionary ecology of parasites that combine horizontal and vertical transmission.

Various types of parasites adopt such a mixed-mode transmission strategy, including phages [START_REF] Weitz | Viral invasion fitness across a continuum from lysis to latency †[END_REF], medically relevant viruses (HIV, hepatitis B and C viruses, Zika, Dengue, Chikungunya) and bacteria (Borrelia miyamotoi, Rickettsia rickettsia) [START_REF] Burgdorfer | Trans-stadial and transovarial development of disease agents in arthropods[END_REF][START_REF] Narita | Vertical transmission of human T cell leukemia virus type I[END_REF][START_REF] Ebert | The epidemiology and evolution of symbionts with mixed-mode transmission[END_REF][START_REF] Contopoulos-Ioannidis | Mother-to-child transmission of Chikungunya virus: a systematic review and meta-analysis[END_REF][START_REF] Da Costa | Evidence of vertical transmission of Zika virus in field-collected eggs of Aedes aegypti in the Brazilian Amazon[END_REF][START_REF] Lai | Vertical transmission of zika virus in Aedes albopictus[END_REF][START_REF] Sambado | Mixed transmission modes promote persistence of an emerging tick-borne pathogen[END_REF][START_REF] Teixeira | Simultaneous circulation of zakat, dengue, and chikungunya viruses and their vertical co-transmission among Aedes aegypti[END_REF]. If there is no interaction between the two modes of transmission, having both should be better than having one [START_REF] Lipsitch | The population dynamics of vertically and horizontally transmitted parasites[END_REF][START_REF] Ferdy | Diversification of transmission modes and the evolution of mutualism[END_REF]. However, due to physiological or developmental constraints [START_REF] Ebert | The influence of host demography on the evolution of virulence of a microsporidian gut parasite[END_REF][START_REF] Messenger | Virulence evolution in a virus obeys a trade-off[END_REF][START_REF] Van Den Bosch | Evolutionary bi-stability in pathogen transmission mode[END_REF]), investing in one transmission mode often reduces transmission with the other. Thus, the two transmission pathways cannot be optimized independently of each other and evolution will favour combinations that maximize the overall transmission success.

The evolutionary adjustment of mixed-mode strategies likely depends on environmental factors and ecological conditions (e.g., temperature, resource availability, spatial structure, host density, co-infection and competition) because these can alter the opportunities for horizontal and vertical transmission [START_REF] Antonovics | The evolution of transmission mode[END_REF][START_REF] Su | Dynamics of host-parasite interactions with horizontal and vertical transmissions in spatially heterogeneous environment[END_REF]). These environmental factors set the stage for the evolution of vertical versus horizontal transmission, and consequently, the evolution of trade-offs or context-dependent shifts in transmission [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]. Accordingly, theory has introduced the ecological context by comparing predictions for different contact rates (opportunities for horizontal transmission) or host birth rates (for vertical transmission) [START_REF] Lipsitch | The population dynamics of vertically and horizontally transmitted parasites[END_REF][START_REF] Lipsitch | The evolution of virulence in pathogens with vertical and horizontal transmission[END_REF]. Further, a number of experimental evolution studies blocked one or the other transmission pathway in several host-parasite systems, and observed subsequent increases or decreases in virulence or transmission capacity, in line with theoretical predictions. Promoting vertical transmission resulted in lower virulence and shifts from parasitism to commensalism [START_REF] Bull | Selection of benevolence in a host-parasite system[END_REF][START_REF] Sachs | A shift to parasitism in the jellyfish symbiont Symbiodinium microadriaticum[END_REF], whereas promoting horizontal transmission induced shifts towards parasitism and higher virulence [START_REF] Sachs | A shift to parasitism in the jellyfish symbiont Symbiodinium microadriaticum[END_REF][START_REF] Clec | Phenotypic shift in Wolbachia virulence towards its native host across serial horizontal passages[END_REF].

So far only few studies have employed more realistic ecological scenarios, without a priori enforcing one or the other transmission mode. Using experimental microcosms of an aquatic model system, [START_REF] Magalon | Host growth conditions influence experimnental evolution of life history and virulence of a parasite with vertical and horizontal transmission[END_REF] mimicked conditions of frequent host population expansion, where periods of high host birth rate provide ample opportunity for vertical transmission. This resulted in an evolutionary shift towards increased investment in vertical transmission of the parasite [START_REF] Magalon | Host growth conditions influence experimnental evolution of life history and virulence of a parasite with vertical and horizontal transmission[END_REF], and eventually led to the near-complete loss of the horizontal pathway [START_REF] Dusi | Long-term selection experiment produces breakdown of horizontal transmissibility in parasite with mixed transmission mode[END_REF]. In a bacteria-phage system, population mixing increased opportunities for horizontal transmission, and led to more virulent, predominantly horizontally transmitting variants [START_REF] Berngruber | Spatial structure, transmission modes and the evolution of viral exploitation strategies[END_REF]). Yet, experimentally increasing the density of susceptible Escherichia coli cells for 500 generations did not lead to the predicted evolution of higher horizontal transmissibility of a "parasitic" plasmid [START_REF] Turner | Tradeoff between horizontal and vertical modes of transmission in bacterial plasmids[END_REF]. These results suggest that predictions about the evolution of transmission pathways may be complex, especially when eco-epidemiological and evolutionary processes and feedbacks are allowed to act freely.

Here, we focus on the role of resource availability for the evolution of mixed-mode parasites. This environmental component has received surprisingly little attention in this context, even though it has strong effects on host-parasite interactions [START_REF] Mojica | Factors affecting virus dynamics and microbial host-virus interactions in marine environments[END_REF]. Resource availability affects the growth of the parasite within its host, the host's immune response (reviewed in [START_REF] Pike | On the diverse and opposing effects of nutrition on pathogen virulence[END_REF]) and the virulence of infections and transmission investment [START_REF] Bedhomme | Virulence reaction norms across a food gradient[END_REF][START_REF] Restif | Condition-dependent virulence in a horizontally and vertically transmitted bacterial parasite[END_REF][START_REF] Cornet | Impact of host nutritional status on infection dynamics and parasite virulence in a bird-malaria system[END_REF][START_REF] Cressler | Disentangling the interaction among host resources, the immune system and pathogens[END_REF]. Nutrient availability can also drive indirect demographic feedbacks, via population density, regulating the extent of horizontal and vertical transmission [START_REF] Mojica | Factors affecting virus dynamics and microbial host-virus interactions in marine environments[END_REF][START_REF] Jover | The elemental composition of virus particles: implications for marine biogeochemical cycles[END_REF].

The microsporidian Edhazardia aedis is an obligate parasite of the mosquito Aedes aegypti. It has a relatively complex, developmentally programmed mixed-mode strategy, with horizontal and vertical transmission occurring at different stages of the host life cycle. Edhazardia aedis is transmitted horizontally among mosquito larvae or vertically through the eggs of infected females [START_REF] Becnel | Development of Edhazardia aedis (Kudo, 1930) N. G., N. Comb. (Microsporida: Amblyosporidae) in the Mosquito Aedes aegypti (L.) (Diptera: Culicidae)[END_REF]. During its development within a host, the parasite has a fixed program alternating the production of two types of spores associated with vertical or horizontal transmission (Fig. 1a). Shortly after horizontal infection of a larvae via ingestion of uninucleate spores, binucleate spores that spread from the gut into different parts of the body are produced at relatively low density. If the infected larva develops fast enough, this stage of infection allows the transition from the juvenile to the adult stage. In females, infection of gonads by binucleate spores then gives rise to vertically infected eggs and subsequently to infected larvae, which again produce uninucleate spores that are released for horizontal transmission upon larval death (Fig. 1a). Another horizontal transmission pathway is possible when larval development is slow, giving the parasite the time to go through its developmental sequence from uninucleate to binucleate to again uninucleate spores within the same larval individual, bypassing vertical transmission (Fig. 1a). This "shortcut" horizontal pathway may be frequent in natural habitats, typically characterised by low resources [START_REF] Christophers | Aëdes aegypti (L.) the Yellow Fever Mosquito: its Life History, Bionomics and Structure[END_REF]), whereas the above alternating horizontal-vertical pathway requires more resource-rich conditions, allowing fast enough larval development.

The fixed developmental program of the parasite may represent a strategy to deal with unpredictable and ephemeral ecological conditions which are likely characterised by ample variation in the resources available for the mosquito. This kind of parasite development ensures some level of vertical transmission under good conditions, when host fecundity is high, and avoids the risk of relying on vertical transmission from hosts with low fecundity under poor conditions. Indeed, previous work demonstrated that investment in either vertical or "shortcut" horizontal transmission can be modulated by the experimental manipulation of resource condition, via the modification of rates of host development [START_REF] Agnew | Life history interactions with environmental conditions in a host-parasite relationship and the parasite's mode of transmission[END_REF][START_REF] Zilio | Host genotype and environment affect the trade-off between horizontal and vertical transmission of the parasite Edhazardia aedis[END_REF][START_REF] Zilio | Sequential co-infections drive parasite competition and the outcome of infection[END_REF]. While these experiments typically span a single infected host generation, the present study explored the scope for evolutionary modification of the parasite's strategy set when facing the same resource conditions over multiple generations.

Using a controlled serial infection protocol, we passaged the parasite over several mosquito generations in treatments with either high or low resource levels, while precluding evolution of the host. Resource levels were manipulated in the aquatic environment in which infected larvae developed. The focus of our experiment was on resource-induced changes in one particular segment of the infection life cycle: juvenile development and the transition to the adult stage (Fig. 1b). The goal was to assess whether these predictable changes in the rate of the host's development produced evolutionary responses in the parasite's vertical and horizontal transmission potential. In particular, high food levels lead to faster development of infected larvae, a higher chance to reach the adult stage and higher adult fecundity [START_REF] Zilio | Host genotype and environment affect the trade-off between horizontal and vertical transmission of the parasite Edhazardia aedis[END_REF], thereby potentially increasing the prospects of vertical transmission. Hence, our main prediction was that if the parasite evolves in an environment with ample resources, it can predict effective vertical transmission; it should therefore adjust the developmental switch from uni-to binucleate spores that occurs within the first days of infection. This evolution would be visible as an increase of vertical transmission in particular when the parasite is tested in an environment with low food. In contrast, in the low-food evolutionary treatment, larval development is slow, so the parasite's developmental switch may become delayed. Consequently, we expected evolution at low food to lead to less vertical transmission potential when the parasite is tested at high food.

After 10 host generations, we assayed evolved parasites under high-food and low-food test conditions, by measuring several components of vertical and horizontal transmission (Fig. 2). This allowed us to test the above predictions about the evolution of the vertical pathway, but also to analyse possible correlated responses to selection in the horizontal pathway, which was a priori not under direct selection in our experiment.

Materials and methods

Experimental system

The yellow fever mosquito Aedes aegypti (obtained from Patrick Guérin, University of Neuchâtel) is found throughout the tropics and subtropics. It is an important vector of several human diseases and its genetics, physiology, and ecology of A. aegypti are well known [START_REF] Christophers | Aëdes aegypti (L.) the Yellow Fever Mosquito: its Life History, Bionomics and Structure[END_REF][START_REF] Nene | Genome sequence of Aedes aegypti, a major arbovirus vector[END_REF]). The larvae grow in natural or artificial containers and during their development are often challenged by periods of nutrient restriction and competition. The eggs can be stored for some months at standard lab conditions (Munstermann 1997).

The microsporidian parasite Edhazardia aedis (provided by J. J. Becnel, USDA, Gainesville, USA) can complete its development only in A. aegypti. It has a complex infection The number of juveniles not emerging, the probability of these individuals carrying uninucleate spores, the uninucleate spore load and the juvenile survival. b For vertical transmission we measured five transmission proxies: The number of females emerging, the probability of these females carrying binucleate spores, binucleate spore load, wing size (fecundity) and longevity life cycle (Fig. 1a), with mixed-mode transmission [START_REF] Desjardins | Contrasting host-pathogen interactions and genome evolution in two generalist and specialist microsporidian pathogens of mosquitoes[END_REF][START_REF] Grigsby | Propagation of the microsporidian parasite edhazardia aedis in aedes aegypti mosquitoes[END_REF]. It produces uninucleate spores for horizontal transmission and binucleate spores for vertical transmission; these spores are morphologically distinguishable (see Fig. 1a). Mosquito larvae ingest uninucleate spores with their food, resulting in the infection of the gut and epithelial cells. Uninucleate cells eventually give rise to binucleate cells, which subsequently spread to other tissues. Binucleate spores invading the oocytes of a female are responsible for vertical transovarial transmission. Male adults represent a transmission dead-end. On average, 95% of the eggs laid by an infected female result in infected larvae [START_REF] Becnel | Edhazardia aedis (Microspora: Culicosporidae) effects on the reproductive capacity of Aedes aegypti (Diptera: Culicidae)[END_REF]. Once the eggs hatch, a new generation of uninucleate spores is produced in the growing larvae. Most of these larvae die before emergence, releasing uninucleate spores in the aquatic environment and starting a new round of horizontal transmission, when ingested by uninfected larvae (the spores remain infective for about 48 h outside the host [START_REF] Nasci | Effect of per os Edhazardia aedis (Microsporida: Amblyosporidae) infection on Aedes aegypti mortality and body size[END_REF]). Horizontal transmission is also possible when, within a larva, the parasite first produces binucleate spores (initiated c. 4 days post infection) and then uninucleate spores, which kill the host. This "shortcut" horizontal transmission, bypassing the vertical transmission, typically occurs under restricted ecological conditions with low food availability. Low food slows down host development and delays emergence into adults [START_REF] Agnew | Life history interactions with environmental conditions in a host-parasite relationship and the parasite's mode of transmission[END_REF][START_REF] Zilio | Host genotype and environment affect the trade-off between horizontal and vertical transmission of the parasite Edhazardia aedis[END_REF]). The parasite is then more likely to produce new uninucleate spores. In contrast, permissive conditions, which let the larva develop rapidly, favour host emergence and the parasite life cycle here matches with the one of the host; the parasite produces binucleate spores and the females produces eggs. Thus, whether a new infection kills the juveniles with the release of uninucleate spores or whether the infection proceeds to binucleate spore production depends strongly on the ecological conditions [START_REF] Agnew | Life history interactions with environmental conditions in a host-parasite relationship and the parasite's mode of transmission[END_REF][START_REF] Duncan | The consequences of co-infections for parasite transmission in the mosquito Aedes aegypti[END_REF][START_REF] Zilio | Host genotype and environment affect the trade-off between horizontal and vertical transmission of the parasite Edhazardia aedis[END_REF]), but the host genetic background plays also a role [START_REF] Zilio | Host genotype and environment affect the trade-off between horizontal and vertical transmission of the parasite Edhazardia aedis[END_REF]. We here assay whether, in addition, the parasite can adapt the developmental switch from uninucleate to binucleate spores according to the host's environment.

Experimental design

All experiments were run in a climate chamber set to 26 °C, 70% humidity and a photoperiod of 12 h light and 12 h dark.

Experimental evolution

We let E. aedis evolve for 10 generations (ca. 1 year, see Fig. 1b) under high-food or lowfood conditions. Each food treatment was replicated in five independent cage populations. We started each generation by synchronously (i.e., at reduced air pressure) hatching eggs from our baseline mosquito colony and haphazardly assigning 200 larvae to each selection line. The larvae of each line were reared for the first four days in groups of 50 individuals in four petri dishes (8 cm diameter) containing 30 mL of deionized water. In the high-food treatment, they were fed daily with a standard amount of TetraMin baby™ fish food (age 0 (i.e., day of hatching): 0.06 mg/larva, age 1: 0.08 mg, age 2: 0.16 mg, age 3: 0.32 mg, age 4: 0.64 mg, from age 5 onwards: 0.32 mg); in the low-food treatment, they received half of the high-food diet. Seventy-two hours after hatching, we added 2 × 10 5 uninucleate spores (in 1 mL water) to each petri dish. This spore dose produces nearly 100% infection without causing high juvenile mortality. The spores had been harvested by crushing and homogenizing 7-day old, vertically infected larvae that had hatched 7 days earlier than the day of infection in an Eppendorf tube with 1 mL of deionized water. The concentration of the spores was determined with a hemocytometer and a phase-contrast microscope (Zeiss Axio Lab.A1). For the first generation, we used spores from our standard batch of parasites; for later generations we used the spores obtained in the previous generation for each line.

Twenty-four hours after exposure to the parasite, all larvae from a given line were transferred to a 200 × 150 × 50 mm plastic tray containing 1 L of deionized water; each tray thus represented a different line of parasite. The pupae were moved to 30 × 30 × 30 cm size cages containing a 10% sugar solution for food and an oviposition cup with a filter paper. No sexual transmission is known, but to avoid any potential bias we removed all infected males with an aspirator just after emergence (males emerge earlier than females) and replaced them with uninfected males from the colony. Thus, infected females only mated with uninfected males. The mosquitoes were blood fed for 10 min on GZ's arms five and seven days after the day when 75% of the individuals of a given line had pupated. The filter papers with newly laid (vertically infected) eggs were removed every 2 days and stored in a petri dish in a climate chamber until the start of a new parasite generation.

Final test: parasite assay conditions

Using parasites from the last batch of vertically infected eggs obtained at generation 10, we tested each parasite line under high-food and low-food conditions on naive mosquitoes. During the experimental evolution we lost one low-food line (all host females died before laying eggs), leaving 5 high-food selection lines and 4 low-food lines for the test. No uninfected control was included in the final test. This parasite is very virulent and a control would have not added much information; independently of the food treatment the uninfected mosquitoes would have differed strongly in any measure of reproductive success. For example, in another study in which juvenile conditions (without parasite) were the same as in our experiment [START_REF] Zeller | Effects of food variability on growth and reproduction of Aedes aegypti[END_REF], uninfected adult females lived, on average, 60 days and more than 80% of 185 females were still alive at day 23 (no difference between HF and LF). In contrast, in this study only 13 out of 300 (4%) of the infected females with Edhazardia aedis were still alive 23 days after emergence.

The final test was split into two blocks starting three weeks apart. Eggs from the naive baseline colony were simultaneously hatched and 2627 deliberately picked larvae (1299 in block 1; 1328 in block 2) were individually reared in 12-well tissue-culture plates filled with 3 mL of deionized water. In each block half of the larvae were assigned to a highfood diet, and the other half to a low-food diet. Forty-eight hours after hatching, each larva received 400 uninucleate spores (in 100 µL water) from one of the 9 parasite lines (from 140 to 154 individuals per line and food test environment). The spores had been obtained by hatching the vertically infected larvae of the evolved parasite lines seven days before the day of infection, as described above. We moved the pupae into 50-ml tubes and provided the emerging adults with cotton-wool soaked with 10% sugar solution, which we replaced every 6 days. We checked the mosquitoes (larvae, pupae and adults) daily, transferred dead mosquitoes into 2 mL Eppendorf tubes and stored them at -20 °C until further investigation. Female wings were removed and mounted on microscope slides, digitally scanned and measured with the software IMAGEJ. We stopped the tests 23 days after hatching and the remaining individuals were frozen at -20 °C.

We counted the spores and determined the type of spores in each individual by adding 0.1 mL of deionized water, homogenizing the samples with a TissueLyser LT-QIAGEN, sampling 4 µL of the obtained solution with a hemocytometer and assaying the solution with a phase contrast microscope (Zeiss Axio Lab.A1). The treatment status of the samples was unknown to the observer (GZ) during the counting. We considered and measured 5 traits as components of the vertical transmission potential: The number of females emerging, the probability of these females carrying binucleate spores, binucleate spore load, wing length as proxy for fecundity [START_REF] Koella | Variability in the relationship between weight and wing length of Anopheles gambiae (Diptera: Culicidae)[END_REF][START_REF] Leisnham | Interpopulation differences in competitive effect and response of the mosquito Aedes aegypti and resistance to invasion by a superior competitor[END_REF][START_REF] Farjana | Effect of body size on multiple blood feeding and egg retention of Aedes aegypti (L.) and Aedes albopictus (Skuse) (Diptera: Culicidae)[END_REF] and longevity. For the horizontal transmission we measured 4 traits: The number of juveniles not emerging and dying in the aquatic environment, the probability of these individuals carrying uninucleate spores, the uninucleate spore load and the juvenile survival.

Statistical analysis

We first analysed variation in each individual transmission component (5 vertical and 4 horizontal components; Fig. 2). For these analyses, we used generalized linear models with appropriate error structure (binomial or poisson) and corresponding link functions (logit or log). For analysis of female longevity, we employed parametric survival analysis (Weibull function, right censoring). For the age at death of juveniles, we used standard ANOVA, with least-square fitting. All models included the effects of evolution treatment, test food conditions and parasite selection lines (nested within evolution treatment), and their possible interactions. We further included experimental block in the final test. Analogous to sums of squares, deviances (2 × log-likelihood ratio) were used to perform Quasi-F tests [START_REF] Schmid | Effects of maternal and paternal environment and genotype on offspring phenotype in solidago altissima l[END_REF].

Second, we used multivariate techniques to summarise the individual transmission components into a combined measure, referred to as vertical or horizontal "transmission potential". To this end, we averaged each transmission component per parasite selection line and test food treatment (9 lines × 2 food levels = 18 means) and performed MANOVAs of vertical and horizontal transmission potential, with evolution treatment and test food treatment as factors. We further performed Principal Component Analyses (PCA) to visualise the differences between treatments in multi-trait space. The values obtained for the first PC axis were then taken as estimates of the vertical and horizontal transmission potential, respectively; in an additional MANOVA we used these vertical and horizontal PC1 values to test whether the relationship between vertical and horizontal transmission potential differed between evolution and test food treatments. For example, a significant evolution treatment effect could indicate an evolutionary trade-off between the two transmission modes. All analyses were conducted with the JMP 14 statistical package (SAS Institute Inc. 2018).

Results

In the final test, 1957 out of 2627 individuals (74%) died as juveniles, with mortality being higher under low-food than high-food test conditions (87 vs. 61%). Of the remaining 670 individuals emerging to adulthood 300 were females (44% of the emerging adults), 243 reared under high food, and 57 under low food. A summary of the results from univariate analyses can be found in Tables 1 and2.

Vertical transmission components

High-food test conditions resulted in increased values of the vertical transmission components (significant Test food effect, Table 1). Compared to low-food conditions, there was a four-fold increase in the number of emerging females (Fig. 3a), an up to twofold increase in the fraction of these females carrying binuclear spores for vertical transmission (Fig. 3b), and a doubling of the binucleate spore load (Fig. 3c). Furthermore, high-food conditions produced a c. 10% increase in wing size of females with binucleate spores, which corresponds to an increase in their fecundity, i.e., the number of (potentially) vertically infected eggs.

Evolution treatments explained some of the observed variation in vertical transmission components, through statistically significant interactions with test environment (Test food × Evo treat interaction; Table 1). Specifically, high-food parasite selection lines tended to enhance vertical transmission under low-food conditions. Thus, females infected with high-food parasites tended to be more likely to carry vertical binucleate spores (Fig. 3b, although Test food × Evo treat interaction non-significant), and allowed these females to become larger and live longer than did low-food parasites (Fig. 3d,e). In contrast, highand low-food parasites showed very similar effects under high-food test conditions (except for longevity; Fig. 3e).

Horizontal transmission components

Low-food test conditions resulted in increased values of three of the four horizontal transmission components (significant Test food effect, Table 2). Compared to high food conditions, there was a 40% increase in the number of juveniles that failed to emerge and died at the aquatic stage, where horizontal transmission occurs (Fig. 3f), a three times larger . f The number of juveniles not emerging and dying in the water, g the probability of the dead juveniles carrying uninucleate spores, h the uninucleate spore load of the juveniles (spores/0.9μL) and i their survival (in days). Big symbols and bars are the overall mean and standard errors, small symbols are the mean for each parasite selection line. Red and blue symbols represent evolution in permissive (Evo HF) and restricted ecological (Evo LF) conditions respectively. Full and empty symbols are the conditions of the final test, corresponding to high (Test HF) and low (Test LF) food levels fraction of these individuals carried uninucleate, horizontally transmitted spores (Fig. 3g), and uninucleate spore loads were about three times higher (Fig. 3h).

Evolutionary treatments explained relatively little of the observed variation in the horizontal transmission components. If anything, under high-food test conditions, some highfood selection lines prevented more larvae to reach the adult stage (Fig. 3f), increased uninucleate spore loads (Fig. 3h) and kept the larvae alive for longer (Fig. 3i), compared to low-food parasites. However, none of these individual trends were statistically significant (Test food × Evo treat interactions; Table 2).

Multivariate analysis: vertical and horizontal transmission potential

Principle Component Analysis (PCA; Figs. 4 and5) showed that all components contributed roughly equally and in a concerted fashion to the description of the explained variance (similar length and direction of arrows in Fig. 4; see also Table S1-4 for PC axes loadings). For both horizontal and vertical transmission, there was a near-complete separation of points defined by the test food conditions (open vs. closed symbols; Fig. 4). Accordingly, the MANOVA revealed a highly significant Test food effect (Table 3). Thus, using the PC1 values as an index of "transmission potential", we found that low-food test conditions strongly increased horizontal transmission potential (Fig. 4b), whereas high-food test conditions strongly increased vertical transmission potential (Fig. 4a).

For vertical transmission, visual inspection of the PCA (Fig. 4a) showed that high-food parasites (red symbols) were grouped in-between low-food parasites (blue symbols). This is supported by the MANOVA, revealing a significant Evo treat x Test food interaction (Table 3). Thus, while there was considerable overlap under high-food test conditions, the vertical transmission potential of high-food parasites exceeded that of low-food parasites when tested under low-food conditions (Fig. 5a).

For horizontal transmission, the PCA did not show a clear-cut grouping of highfood and low-food parasite selection lines (red vs. blue symbols; Fig. 4b), although the MANOVA yielded a trend for overall evolutionary treatment effect (Table 3). This indicates a higher horizontal transmission potential of high-food parasites, despite considerable scatter produced by the individual selection lines (Fig. 5b).

A second MANOVA analysed the relationship between horizontal and vertical transmission potentials. A significant Test food effect (Table 4) indicated an environmental tradeoff between transmission potentials: low-food conditions increased the horizontal transmission potential and reduced the vertical transmission potential, while conversely high-food conditions increased the vertical transmission potential and decreased the horizontal transmission potential (Fig. 5c). This negative relationship held for both high-food and low-food parasites. In contrast, the evolutionary relationship varied with the test conditions (marginally significant Evo treat x Test food interaction; Table 4): Under low-food test conditions, the sign of the relationship tends to be positive, with high-food parasites having both higher horizontal and vertical transmission potential than low-food parasites. Under high-food test conditions, the sign tended to be negative, with high-food parasites having a higher horizontal potential and a lower vertical potential than low-food parasites (Fig. 5c).

Discussion

Environmental factors and ecological conditions can set the stage for the evolution of parasite transmission modes [START_REF] Antonovics | The evolution of transmission mode[END_REF][START_REF] Drew | Microbial evolution and transitions along the parasite-mutualist continuum[END_REF]. We allowed the microsporidian parasite Edharzardia aedis to evolve in its mosquito host Aedes aegypti reared at high or low food conditions. Resource availability alters the development of infected larvae and thereby the probabilities of entering the vertical or horizontal transmission pathways.

After passaging the parasite for 10 host generations, we detected signatures of evolutionary responses to the contrasting environments. This namely concerned the vertical transmission potential, while the horizontal component remained relatively unaffected. Some of these changes are related to the developmental regulation of the production of two spore types, affecting investment in vertical or horizontal transmission. One of the main results was the corroboration of our main prediction: When the parasite evolved in an environment enabling rapid development, it should adjust the developmental switch from uni-to binucleate spores within the first days of infection. As expected, this was visible as an increase of vertical transmission, in particular when the parasite was tested in an environment with low food.

Evolution of vertical transmission (VT) potential

When food is abundant, juvenile mosquitoes have higher survival and reach the adult stage ca. 2 days earlier than under low-food conditions [START_REF] Zilio | Host genotype and environment affect the trade-off between horizontal and vertical transmission of the parasite Edhazardia aedis[END_REF]. This should provide ample opportunity for vertical transmission, as infected hosts rapidly leave the aquatic environment, have higher fecundity and lay eggs with a high probability of being vertically infected [START_REF] Becnel | Edhazardia aedis (Microspora: Culicosporidae) effects on the reproductive capacity of Aedes aegypti (Diptera: Culicidae)[END_REF]. Corroborating previous results [START_REF] Zilio | Host genotype and environment affect the trade-off between horizontal and vertical transmission of the parasite Edhazardia aedis[END_REF][START_REF] Zilio | Sequential co-infections drive parasite competition and the outcome of infection[END_REF], we show here that infected individuals raised under high-food conditions had a higher VT potential compared to those raised under low food. We therefore expected selection on the parasite to match the fast host development and facilitate vertical transmission. Indeed, parasites evolved in permissive conditions showed generally high VT potential (Fig. 5a). Even when tested at low food, these parasites maintained intermediate trait values (open-red symbols, Figs. 4a and 5a), higher than those of parasites evolved and tested in low-food conditions (open-blue symbols) and more similar to values observed under high-food test conditions (filled symbols). This mainly involved a higher probability of carrying binucleate spores for the emerging females (Fig. 3b), higher fecundity (Fig. 3d), and increased longevity (Fig. 3e). Developmental mechanisms and within-host dynamics, such as changes in the fidelity of VT or delayed switch from VT to HT type of cells [START_REF] Magalon | Host growth conditions influence experimnental evolution of life history and virulence of a parasite with vertical and horizontal transmission[END_REF], may explain how the high-food parasites achieved better VT potential. During host development, E. aedis moves through several tissues relying on specific protein modification and trafficking to finally arrive in the ovaries, where binucleate spores accomplish the infection of the eggs for vertical transmission [START_REF] Desjardins | Contrasting host-pathogen interactions and genome evolution in two generalist and specialist microsporidian pathogens of mosquitoes[END_REF]. During evolution, these different steps might be fine-tuned and optimised, thereby increasing the VT potential. Inspection of the individual VT components suggests indeed an adjustment of the developmental switch from uni-to binucleate spores, as we observed here for the high food evolution treatment under low food test (Fig. 3b). Higher adult female fecundity and longevity (Fig. 3d ande, red open symbols) may also be a consequence of this earlier switch: it could reduce the accumulation of uninucleate spores, which are known to be the more virulent forms [START_REF] Agnew | Virulence, parasite mode of transmission, and host fluctuating asymmetry[END_REF].

We would have expected high-food parasites to have some advantage in their "own" high-food environment. However, there was no clear sign of differentiation between highfood and low-food parasites when tested at high food (Fig. 3b). It could be that, in our final assay, the highly permissive conditions masked the expression of genetic variation, a common observation in mosquito-parasite systems [START_REF] Koella | Food availability and parasite infection in¯uence the correlated responses of life history traits to selection for age at pupation in the mosquito Aedes aegypti[END_REF][START_REF] Bedhomme | Virulence reaction norms across a food gradient[END_REF][START_REF] Fellous | Cost of co-infection controlled by infectious dose combinations and food availability[END_REF]. Possibly, differences in the developmental switch of the parasite could be detected through high-resolution time series, tracking the onset of binucleate spore production during juvenile development. Additional adaptation might be seen in an assay covering the complete vertical pathway from egg production to the survival of the vertically infected offspring. This could also include measurements of behavioural components, such as blood feeding and oviposition, which are known to be affected by this parasite [START_REF] Zettel Nalen | Oviposition substrate selection by Florida mosquitoes in response to pathogen-infected conspecific larvae[END_REF].

Evolution of horizontal transmission (HT) potential

Low-food test conditions slowed down juvenile development and increased the death of infected hosts before reaching the adult stage. We show here that the delayed emergence was associated with a higher HT potential (Fig. 3a). This immediate (ecological) effect is due to the fixed developmental program of the parasite. In slowly developing juveniles (larvae or pupae), the parasite has already gone through the binucleate stage and is producing uninucleate HT spores [START_REF] Agnew | Life history interactions with environmental conditions in a host-parasite relationship and the parasite's mode of transmission[END_REF][START_REF] Zilio | Host genotype and environment affect the trade-off between horizontal and vertical transmission of the parasite Edhazardia aedis[END_REF].

There was no evidence for responses to selection in the horizontal transmission components, as parasites from high-food and low-food treatments did not significantly differ in HT potential. Unlike other studies [START_REF] Stewart | An empirical study of the evolution of virulence under both horizontal and vertical transmission[END_REF][START_REF] Sachs | A shift to parasitism in the jellyfish symbiont Symbiodinium microadriaticum[END_REF][START_REF] Clec | Phenotypic shift in Wolbachia virulence towards its native host across serial horizontal passages[END_REF], our experiment was not designed to impose direct selection on the HT pathway. The "shortcut" horizontal transmission was blocked, and all infections had to go vertically in order to reach next cycle of selection. Contributions from this horizontal pathway could be included, for example, by collecting uninucleate (HT) spores from naturally killed juveniles and adding these to the inocula used to start a new infected cohort. Future experiments should aim at protocols allowing the interplay between food conditions and epidemiological processes over the entire infection life cycle (Fig. 1b). The ultimate (but challenging) solution would be to let long-term populations self-maintain in cages, only provisioning them with regular blood meals and letting females oviposit in miniaturised ponds placed inside the cage, with high or low food levels.

Trade-off between horizontal and vertical transmission

Our multivariate analyses indicate an ecological trade-off between HT and VT potential, with high HT potential under low food test conditions and high VT potential under high food test conditions. However, there was no corresponding evolutionary trade-off, such that an evolutionary increase in VT potential would cause a correlated decrease in the HT mode, which is commonly assumed in theoretical models [START_REF] Lipsitch | The evolution of virulence in pathogens with vertical and horizontal transmission[END_REF] and found in certain selection experiments [START_REF] Magalon | Host growth conditions influence experimnental evolution of life history and virulence of a parasite with vertical and horizontal transmission[END_REF][START_REF] Dusi | Long-term selection experiment produces breakdown of horizontal transmissibility in parasite with mixed transmission mode[END_REF]. In fact, if anything, an increase in VT potential of high-food parasites was accompanied by a higher HT potential (at least in tests under low-food conditions; Fig. 5c), a pattern also observed in other studies [START_REF] Van Frankenhuyzen | Vertical transmission of Nosema fumiferanae (Microsporidia: Nosematidae) and consequences for distribution, post-diapause emergence and dispersal of second-instar larvae of the spruce budworm, Choristoneura fumiferana (Clem.) (Lepidoptera: Tortricidae)[END_REF][START_REF] De Roode | Strength in numbers: high parasite burdens increase transmission of a protozoan parasite of monarch butterflies (Danaus plexippus)[END_REF]).

As discussed above, the absence of an evolutionary trade-off could be explained by the fact that our experiment did not allow direct evolutionary responses of the HT pathway. Nevertheless, our data show such a trade-off also does not arise from negative correlated responses to selection on the VT mode. This suggests that the VT mode can evolve independently of the ("shortcut") HT mode, despite the VT vs HT decision the parasite "needs to make" in each individually infected larva. Interestingly, the infection life cycle in this system further suggests that increased vertical transmission (i.e., more vertically infected offspring) is also positively associated with rates of HT via the second pathway, which is accomplished through the killing of the vertically infected offspring (Fig. 1).

More generally, in systems with mixed-mode transmission parasites the evolutionary relationship between the VT and HT modes may be less straightforward [START_REF] Kover | Trade-off between virulence and vertical transmission and the maintenance of a virulent plant pathogen[END_REF] than assumed in conceptual models. With a more complex life cycle, trait relationships are not as unequivocal and different aspects of virulence may not provide a "common currency" linking the two transmission modes, especially when the traits are expressed at different developmental stages (here delayed juvenile development vs reduced adult fecundity).

Resource availability and the ecological theatre

Anthropogenic activities and global change have massive impacts on the amount and distribution of organic matter and nutrients in natural communities. For host-parasite interactions, these changes may affect opportunities for parasite transmission and the expression of virulence-related traits, with huge implications for the spread of epidemics and evolution [START_REF] Becker | Linking anthropogenic resources to wildlife-pathogen dynamics: a review and meta-analysis[END_REF][START_REF] Altizer | Food for contagion: synthesis and future directions for studying host-parasite responses to resource shifts in anthropogenic environments[END_REF][START_REF] Civitello | Assessing the direct and indirect effects of food provisioning and nutrient enrichment on wildlife infectious disease dynamics[END_REF]. Here, we investigated the role of food availability, an ecological variable so far largely overlooked in the context of transmission mode evolution. Yet, resources have long been recognised as a central element for host-parasite interactions, due to their impact on development and virulence of the parasite, or the immunity or tolerance of the host [START_REF] Lopez-Pascua | Antagonistic coevolution across productivity gradients: an experimental test of the effects of dispersal[END_REF][START_REF] Zeller | The role of the environment in the evolution of tolerance and resistance to a pathogen[END_REF][START_REF] Pike | On the diverse and opposing effects of nutrition on pathogen virulence[END_REF]). These internal (within-host) effects, together with more indirect between-host effects via host density, likely feed back on epidemiological dynamics and evolutionary trajectories [START_REF] Hite | Resource-driven changes to host population stability alter the evolution of virulence and transmission[END_REF]. For example, in a study on Hamiltosporidium tvaerminnensis and Daphnia magna, combining field work with laboratory experiments, [START_REF] Narr | Nutrient availability affects the prevalence of a microsporidian parasite[END_REF] concluded that nutrient-rich habitats can favour investment in vertical transmission and may ultimately result in the evolution of lower virulence in their parasite. Even though our results are in line with this prediction, we urge caution in making generalisations. Our study was primarily focused on the evolutionary match between parasite infection life cycle and resource-mediated changes in host development. How changes in host demography add to the equation requires further investigation, both theoretically and experimentally. Predicted outcomes likely depend on the biology of the interacting species and the precise ecological scenario. For example, nutrient-rich habitats may not only increase fecundity (and thus VT potential), but also sustain higher host density. Thus, in a population at equilibrium, only a small fraction of the vertically infected offspring may successfully establish and most transmission be horizontal due to high contact rates [START_REF] Kover | Trade-off between virulence and vertical transmission and the maintenance of a virulent plant pathogen[END_REF]. On the other hand, resources are notoriously variable in time and space. In a metapopulation, parasites evolving in productive environments may flood and replace those adapted to poor environments [START_REF] Hochberg | Antagonistic coevolution over productivity gradients[END_REF][START_REF] Koella | Coevolution of parasite life cycles and host life-histories[END_REF], so that selection on transmission pathways may ultimately depend on the spatiotemporal distribution of different habitat types [START_REF] Saikkonen | The persistence of vertically transmitted fungi in grass metapopulations[END_REF][START_REF] Su | Dynamics of host-parasite interactions with horizontal and vertical transmissions in spatially heterogeneous environment[END_REF]. The metapopulation context could also be highly relevant to our host-parasite system, where oviposition sites and water bodies are highly ephemeral [START_REF] Agnew | Life history interactions with environmental conditions in a host-parasite relationship and the parasite's mode of transmission[END_REF]. The "shortcut" horizontal transmission represents events of local transmission for the parasite, whereas the vertical transmission is associated with the dispersal of infected adult mosquitoes to new patches and oviposition sites, thereby contributing to the global transmission of the parasite.

Conclusions

Many relevant parasites have a mixed mode of vertical and horizontal transmission, but we are still lacking a good picture of how their dual strategy allows them to respond to environmental heterogeneity. Here we demonstrate effects of resource availability on host and parasite development. Permissive food conditions appeared to have favour the evolution of increased VT potential in this eukaryotic parasite, and these changes did not seem to come at the expense of the parasite's horizontal transmission potential. Understanding the eco-evolutionary processes affecting vertical and horizontal transmission, and how these can scale up from within-host to population-level dynamics, remains one main challenge.

Fig. 1

 1 Fig.1Model system and experimental protocol. a Life cycle of the microsporidian parasite Edhazardia aedis and of its host Aedes aegypti (modified from[START_REF] Agnew | Life history interactions with environmental conditions in a host-parasite relationship and the parasite's mode of transmission[END_REF]. The parasite has a fixed developmental program alternating the production of two spore types. The production of a new batch of uninucleate spores after the infection of a juvenile requires first the production of binucleate spores. "Shortcut" horizontal transmission occurs when juveniles (larvae or pupae) die in the aquatic environment; vertical transmission occurs via infected females laying infected eggs. Once the new generation of vertically infected larvae emerges, they either die and new events of horizontal transmission occur, or they emerge to become adults with the potential for vertical transmission. b Protocol of the experimental evolution part of the study. At each generation, uninfected larvae from the stock colony were horizontally infected with uninucleate spores obtained by hatching eggs and harvesting the vertically infected larvae from the previous generation. Infected larvae were raised under permissive high-food conditions (red, Evo HF) or restricted low-food conditions (blue, Evo LF), which resulted in fast or slow development into adults and thereby changing the match with parasite development. The rearing of the vertically infected larvae and the infection of the next generation followed a standardized protocol (main text)

Fig. 2

 2 Fig. 2 Transmission components of the parasite. a For the horizontal transmission we measured four transmission proxies: The number of juveniles not emerging, the probability of these individuals carrying uninucleate spores, the uninucleate spore load and the juvenile survival. b For vertical transmission we measured five transmission proxies: The number of females emerging, the probability of these females carrying binucleate spores, binucleate spore load, wing size (fecundity) and longevity

Fig. 3

 3 Fig. 3 Means of the a-e vertical and f-i horizontal parasite components. a The number of adul females emerging, b the probability of the females carrying binucleate spores, c the binucleate spore load (spores/0.9μL), d the wing size (in cm; proxy for fecundity and number of eggs laid) and e the longevity (in days). f The number of juveniles not emerging and dying in the water, g the probability of the dead juveniles carrying uninucleate spores, h the uninucleate spore load of the juveniles (spores/0.9μL) and i their survival (in days). Big symbols and bars are the overall mean and standard errors, small symbols are the mean for each parasite selection line. Red and blue symbols represent evolution in permissive (Evo HF) and restricted ecological (Evo LF) conditions respectively. Full and empty symbols are the conditions of the final test, corresponding to high (Test HF) and low (Test LF) food levels

Fig. 4

 4 Fig. 4 PCA for the a vertical and b horizontal transmission components. The first two principal component axes (PC1 and PC2) are shown. Each arrow represents a single trait/component used for the PCA. The length and the direction of the arrow indicate which vertical and horizontal transmission traits/components are driving the separation between treatments. Each point represents the average value of a given parasite line in multivariate space: Evolved in permissive (Evo HF, red) or restricted (Evo LF, blue) ecological conditions; tested in the high (Test HF, full circles and solid lines) or low (Test LF, empty circles and dashed lines) food. The ellipses are the 95% containment probability region for the four treatments

Fig.

  Fig. Reduction of the several traits measured for the horizontal and vertical transmission components to one dimension (PC1) after PCA and multivariate analysis. Synthetic measurement of a parasite vertical and b horizontal transmission potential. For visualization, PC1 vertical transmission values were multiplied by -1, in order to have positive values corresponding to higher transmission. c Relationship between the synthetic measurement of horizontal and vertical transmission. Red and blue symbols represent evolution in permissive (Evo HF) and restricted (Evo LF) ecological conditions respectively. Full and empty symbols are the conditions of the final test, corresponding to high (Test HF) and low (Test LF) food levels. Big symbols and bars are the overall mean and standard errors, small symbols are the mean for each parasite selection line

Table 1

 1 Analyses of variation in 5 vertical transmission components. For each term in the statistical model, we report the deviance (Dev) explained by this term and the corresponding quasi-F tests. Selection line was nested in the Evo treatment. For each trait, we indicate the sample size used for the analysis (n). The effects of Test food, Evo treat × Test food and Selection line were tested against the Line × Test food interaction (or the residual term); Evo treat was tested against Selection line; Line × Test food interaction was tested against the residual term

	Analysis based on females that produced binucleate spores
	a

Table 2

 2 Analyses of variation in 4 horizontal transmission components. For each term in the statistical model, we report the deviance (Dev) explained by this term and the corresponding quasi-F tests. For each trait, we indicate the sample size used for the analysis (n). For numerator / denominator in the F-tests, see Table1

	Line × Test food Test block	-Dev = 1.0 F 1,24 = 1.0 p = 0.3273	Dev = 0.86 F 7,1938 = 0.86 p = 0.3539 Dev = 6.85 F 1,1938 = 6.85 p = 0.0090	Dev = 0.30 F 7,172 = 0.30 p = 0.5846 Dev = 0.03 F 1,171 = 0.03 p = 0.8627	Dev = 19.21 F 7,172 = 4.17 p = 0.0427 Dev = 6.59 p F 1,171 = 1.38 = 0.2417
	Selection line	Dev = 1.58 F 7,25 = 1.58 p = 0.1874	Dev = 1.74 F 7,7 = 2.02 p = 0.1870	Dev = 0.21 F 7,7 = 0.7 p = 0.6752	F p Dev = 17.57 7,7 = 0.91 = 0.5479
	Evo treat × Test food	Dev = 1.03 F 1,25 = 1.03 p = 0.3199	Dev = 1.01 F 1,7 = 1.17 p = 0.3153	Dev = 0.43 F 1,7 = 1.43 p = 0.2707	F p Dev = 43.64 1,7 = 2.27 = 0.1756
	Evo treat	Dev = 3.89 F 1,7 = 2.46 p = 0.1608	Dev = 1.07 F 1,7 = 0.61 p = 0.4604	Dev = 0.62 F 1,7 = 2.95 p = 0.1296	F p Dev = 60.33 1,7 = 3.43 = 0.1065
		1,25 = 46.34
	Component Test food	Number of juveniles not emerging (n = 36) Dev = 46.34 F p < 0.0001	Probability of carrying uninucleate spores (n = 1957) Dev = 64.01 F 1,7 = 74.73 p < 0.0001 uninucleate spores load a (n = 190) Dev = 5.24 F 1,7 = 17.47 p = 0.0041	Juvenile survival (n = 190) F p Dev = 38.65 1,7 = 2.01 = 0.1992	a Analysis based on juveniles that produced uninucleate spores

Table 3

 3 Multivariate analyses (MANOVA) including all the horizontal transmission (HT) and vertical transmission (VT) components measured, which correspond to the HT and VT potential. The df(N), df(D) indicate the numerator and denominator degrees of freedom for F-tests

	Source	HT potential			VT potential
		df(N), df(D)	F	p value	df(N), df (D)	F	p value
	Evo treat	5,10	1.54	0.257	5, 10	1.22	0.364
	Test food	5,10	15.66	0.0001	5, 10	17.59	0.0001
	Evo treat x Test food	5, 10	0.60	0.670	5, 10	3.61	0.039

Table 4

 4 Multivariate analysis (MANOVA) of PC1 horizontal and PC1 vertical transmission potential. The df(N), df(D) indicate the numerator and denominator degrees of freedom for F-tests

	Source	df(N), df(D)	F	p value
	Evo treat	2, 13	2.00	0.174
	Test food	2, 13	59.48	0.0001
	Evo treat x Test food	2, 13	3.67	0.054

Acknowledgements We thank K. Thiévent, G. Hauser, A. Belli, L. Moesch and M. Zeller for their help in the lab and suggestions. We thank P. Schmid-Hempel for early discussion on the design of the study. We also thank two anonymous reviewers for very helpful and constructive criticism. This is publication ISEM-2022-062 of the Institut des Sciences de l'Evolution de Montpellier.

Supplementary Information

The online version contains supplementary material available at https:// doi. org/ 10. 1007/ s10682-022-10184-7.

Author contributions GZ and JCK: conceived the study and designed the experiments. GZ: performed the experimental work. GZ and OK: performed the statistical analysis. All authors interpreted the results, contributed to the writing, read and approved the final version of the manuscript.

Funding Open access funding provided by University of Neuchâtel. No funding was received to assist with the preparation of this manuscript.

Data availability

The datasets analysed during the current study are available in the Zenodo repository, https:// zenodo. org/ record/ 63760 63 Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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