Aatreya Manjulagiri Venkatesh

Didier Bouvard
email: didier.bouvard@grenoble-inp.fr

Pierre Lhuissier
email: pierre.lhuissier@simap.grenoble-inp.fr

Julie Villanova
email: julie.villanova@esrf.fr

3D Analysis of Ceramic Powder Sintering by Synchrotron X-ray Nano-tomography

Keywords: Sintering, Ceramic powders, Synchrotron X-ray nano-tomography, Quantitative image analysis, Grain growth, Pore size distribution, Pore curvature

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3D analysis of ceramic powder sintering by synchrotron X-ray nano-tomography

Introduction

Sintering is undoubtedly the most prominent step in powder processing of ceramics [START_REF] Bordia | Current understanding and future research directions at the onset of the next century of sintering science and technology[END_REF], involving the transformation of a powder or a powder compact into a bulk material of controlled density under thermal energy. The complete process is classically divided into three sequential and overlapping stages, characterized by the formation of so-called necks in between the individual particles in the initial stage, considerable densification resulting from the shrinkage of the interconnected pore channels in the intermediate stage, and eventually the creation of isolated closed pores in the final stage, with concomitant grain growth [START_REF] Kang | Sintering: densification, grain growth and microstructure[END_REF] [START_REF] Rahaman | Ceramic processing and sintering[END_REF].

The experimental studies in the context of powder sintering and the subsequent characterization for a quantitative investigation were largely carried out by classical observation techniques such as optical or scanning electron microscopy (SEM). The micrographs of the traditional SEMs were vital in illustrating various sintering related phenomena, but, from a two-dimensional (2D) perspective with relatively small fields of view. This restricted the assessments of complex sintering parameters, which require rather a three-dimensional (3D) outlook [START_REF] Otsuki | Pore throat size and connectivity determine bone and tissue ingrowth into porous implants: 21 Three-dimensional micro-CT based structural analyses of porous bioactive titanium implants[END_REF]. For instance, 2D images provide insufficient understanding of the complex network of pore morphologies in a microstructure. The 3D interconnected pore channels could appear isolated in 2D sections, giving insufficient or wrong impression on the connectivity and the closure of the pores [5] [6]. This highlights the significance of 3D imaging offered by non-conventional characterization techniques, like X-ray tomography.

In fact, 3D imaging has been proven to be of great value in improving the understanding and modeling of sintering of metallic and glass powders. Various notable works of Lame et al. [START_REF] Lame | Bulk observation of metal powder sintering by X-ray synchrotron microtomography[END_REF],

Nöthe et al. [START_REF] Nöthe | Investigation of Sintering of Spherical Copper Powder by Micro Focus Computed Tomography (μCT) and Synchrotron Tomography[END_REF], Olmos et al. [START_REF] Olmos | Analysing the sintering of heterogeneous powder structures by in situ microtomography[END_REF], and Kieback et al. [START_REF] Kieback | Investigation of sintering processes by tomography[END_REF] have employed X-ray micro-tomography (μCT) apparatus to compute and follow-up relevant sintering parameters. These works, for instance, have employed a resolution of around 1.5 μm pixel size to detect critical sintering related features in the metallic particles of approximately 50 μm in size. This ratio of the order of 1/20 to 1/40 between the resolution and particle size has been found to be a good trade-off amongst the high resolution required to precisely quantify necks and curvatures and the low resolution required to capture particle agglomeration and rearrangement. The insights offered by the characterization of various such tomography outcomes were also found to better validate the sintering theories, as the ones proposed by Delannay et al. [START_REF] Delannay | Experimental validation of a new model for the initial stage of sintering of single phase systems[END_REF].

For ceramic powders, the same results cannot be realized as a considerably higher resolution is required to enable particle scale imaging. Indeed, as a result of their small size (around or below 1 μm) and complex architecture, ceramic particles most often form agglomerates. Consequently, prominent X-ray μCT studies over the last two decades on ceramic samples by Bernard et al. [START_REF] Bernard | First direct 3D visualisation of microstructural evolutions during sintering through X-ray computed microtomography[END_REF],

Lu et al. [START_REF] Lu | X-ray computed tomography and mercury porosimetry for evaluation of density evolution and porosity distribution[END_REF], Xu et al. [START_REF] Xu | In situ investigation of ceramic sintering by synchrotron radiation X-ray computed tomography[END_REF] etc. to visualize and quantify microstructural evolutions during sintering have been restricted to the agglomerate level. However, more recently, with the advancement in the X-ray nano-tomography (nano-CT) domain at the synchrotron facilities, microstructural evolutions during sintering at the nano-scale are being investigated, as in Okuma et al. [START_REF] Okuma | Microstructural evolution of electrodes in sintering of multi-layer ceramic capacitors (MLCC) observed by synchrotron X-ray nano-CT[END_REF], paving the way for comprehensive ceramic studies. Particularly remarkable has been the observation of sintering phenomena of glass beads at a sintering temperature of 670°C [START_REF] Villanova | Fast in situ 3D nanoimaging: a new tool for dynamic characterization in materials science[END_REF].

Nevertheless, it is worth noting that the analyses of commonly used ceramic powders are more delicate because of the higher temperatures required (around or more than 1500°C). To the best of our knowledge, none of the various types of tomography, be it post-mortem, ex-situ or in-situchoosing the terminology proposed by Salvo et al. [START_REF] Salvo | 3D imaging in material science: Application of X-ray tomography[END_REF] has been attempted at a resolution good enough for particle length-scale observation of ceramic powder sintering at higher temperatures so far.

In this work, we explore the nano-tomography technique presented by the ID16B nano-analysis beamline at the European synchrotron (ESRF). The beamline offers a phase-contrast based holotomography set-up [START_REF] Cloetens | Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays[END_REF], which allows 3D imaging at the nano-scale (~25 nm voxel size), with fast scan times and with fields of view that are large enough to constitute representative volume elements [START_REF] Martinez-Criado | ID16B: A hard X-ray nanoprobe beamline at the ESRF for nanoanalysis[END_REF]. With this high resolution, we were able to investigate two sets of pre-sintered micron-sized alumina powders in a post-mortem context. 3D images obtained at this resolution were used to investigate densified versions of the alumina powder compacts as well, thus allowing the analysis of intermediate and final stages of sintering. The subsequent quantitative evaluations were utilized to follow the evolution of the morphologies of the grains and the pores and a few associated parameters at different sintering time intervals. The information obtained was further scrutinized by comparing them with classical analytical sintering theories. Furthermore, given that the curvature changes are the foremost phenomena in the sintering process, high resolution 3D renderings were used to plot and analyze curvature maps from a porosity reference framework.

These maps are shown to serve as an indicator to track the evolution of sintering stages.

Materials and Methods

Powder and sample preparation

Two sets of alumina powders, AA-07 and AA-1.3, procured from Sumitomo Chemical Co., Ltd.

with mean particle sizes of around 0.7 μm and 1.3 μm, respectively, were chosen. These sizes fit the investigation criteria of the synchrotron experiments in terms of the expected resolution (~25 nm). Preliminary SEM evaluations show that these so-called advanced alumina powders, produced by an aluminium alkoxide hydrolysis process [20] [21], have an almost isotropic, polyhedral shape and are fairly non-agglomerated (Figure 1).

To assess the sintering advancement of the chosen powders, cylindrical compacts (~8 mm in diameter) obtained by uniaxial pressing of the powders in a die with a stress of ~200MPa, were subjected to sintering experiments in a dilatometry set-up in air. Small quantities of polyvinyl alcohol were used as a binder for better compaction. Thermal cycles were imposed on to the powder compacts at a rate of 5°C/min with a sintering plateau at 1500°C. A 1-hour isothermal hold at 500°C was carried out to remove the binder prior to sintering. The powder compacts were then sintered individually for different time periods up to 120 hours at 1500°C, and the shrinkage and densification attained were recorded. Bulk densities of the sintered compacts and therewith their relative densities were determined using the conventional 'Archimedes' principle, with ethanol as the weighting medium. The compacts were further broken into tiny fragments (about 100 μm in diameter and 1-2 mm in height) for a subsequent investigation using the nano-CT.

Phase-contrast X-ray nano-holotomography

In order to visualize the sintered alumina fragments at the particle scale, X-ray nano-CT experiments were carried out at the ID16B nano-analysis beamline of the ESRF. The beamline is equipped with a set of Kirkpatrick-Baez (KB) mirror systems. These mirrors focus the incoming parallel X-ray beam onto a small beam size of 50*50 nm 2 , which acts as a secondary source [START_REF] Martinez-Criado | ID16B: A hard X-ray nanoprobe beamline at the ESRF for nanoanalysis[END_REF].

The subsequent conic beam advancement results in a geometrical magnification. An energy of 29.2 KeV was used for the experimentations. algorithms to obtain the so-called phase maps (Figure 2 (c)). The filtered 2D phase maps were then fed into the in-house built ESRF PyHST2 software package [START_REF] Mirone | The PyHST2 hybrid distributed code for high speed tomographic reconstruction with iterative reconstruction and a priori knowledge capabilities[END_REF] to reconstruct and render the 3D distribution of the sample (Figure 2 (d)).

Image treatment and analyses

Regions of interest (ROIs) of 1000*1000*1000 voxels were extracted from the reconstructed 3D image stacks. Ring artefacts present were removed with a MATLAB algorithm based on image filtering [START_REF] Lyckegaard | Correction of ring artifacts in X-ray tomographic images Palaeopathology of South African early hominins View project The 1st France-Myanmar Irrawaddy fossil expedition in 2007 View project Correction of Ring Artifacts in X-ray Tomographic Images[END_REF]. A trial-and-error approach was used to find the appropriate parameters. The ROIs were then pre-processed with filters such as fast Fourier transform filter (cut-off frequency of 5%)

to remove high-frequency noise, non-local means filter (strength of 0.5) to reduce left-over noise while keeping the edges sharp etc., in image processing software ImageJ and GeoDict [26] [27].

This was followed by the application of automatic thresholding methodologies (OTSU's method) in order to further integrate the segmented 3D renderings in a quantitative analysis set-up.

However, segmentation of individual features, say, the separation of individual sintered grains, was challenging, especially for image stacks above 75-80% density. Parameters requiring only effective pre-processing and global thresholding operations for their evaluation were hence chosen.

Grain volume fraction measurement

Volume fractions of the grains were first determined from the ROIs with the ImageJ software [START_REF] Schindelin | Fiji: An open-source platform for biological-image analysis[END_REF],

to compare with the relative density estimation from the Archimedes approach.

Grain size and pore size estimation

Next, granulometric analysis in the Geodict image processing platform was employed to estimate the size of the evolving grains [START_REF] Becker | GeoDict (Release 2022)[END_REF]. The algorithm in the GrainFind module of GeoDict first converts the thresholded 3D image stacks into distance maps by Euclidean distance transform (EDT) and then evaluates the diameter of the grains by fitting pre-defined spheres into the grain space. A detailed description of the algorithm and its implementation can be found in [START_REF]GrainFind handbook[END_REF].

Similarly, pore size distributions of the 3D image stacks were carried out by granulometric characterization in the pore space using the PoroDict module of GeoDict [27] [29].

Pore connectivity and pore throat characterization

In order to assess the connectivity in the pore network and their transition into closed porosity, parameters such as pore volume, percentages of open porosity, and percentages of closed porosity were measured using the Analysis_3D plugin in ImageJ [26] [30]. Furthermore, a porosimetric investigation was carried out in the PoroDict module of GeoDict [27] [29]. In contrast to granulometry, here, pre-defined spheres that are fitted into the pore structure are made to pass through from the side of the intrusion to the other side such that it encompasses the entire pore channel. With this, the size of the small pore channels or throats connecting the large pore channels are determined, while needless to say, closed pores do not contribute to the pore throat analyses.

Interface curvature analysis

To track the evolution of pore-solid interface curvature, simplified henceforth as pore curvature, the tools, 'Shape index' and 'Curvedness' proposed by Koenderink et al. [START_REF] Koenderink | Surface shape and curvature scales[END_REF] for graphical representation of 3D shapes were adopted. In contrast to the classical curvature measures like the Gaussian and the mean curvatures, these shape indicators capture the nuances in the variations of local shapes [START_REF] Burr | In situ X-ray tomography densification of firn: The role of mechanics and diffusion processes[END_REF]. The significance of these parameters has been emphasized notably by Shahani et al. [START_REF] Shahani | The dynamics of coarsening in highly anisotropic systems: Si particles in Al-Si liquids[END_REF]. They are independent of each other, with the shape index estimating the local shape profile and the curvedness measuring the amount of curvature of the shape. The significance of these indicators will be further explained in section 3.3. With k1 and k2 as the principal curvatures, the shape index S and curvedness C are defined as follows:

𝑺 = 𝟐 𝛑 𝐚𝐫𝐜𝐭𝐚𝐧 ( 𝒌 𝟏 + 𝒌 𝟐 𝒌 𝟏 -𝒌 𝟐 ) 1 𝑪 = √ 𝒌 𝟏 𝟐 + 𝒌 𝟐 𝟐 𝟐 2
The shape index in Equation 1 can have values in the range from -1 to +1, differentiating convexities from concavities. The curvedness instead, in Equation 2, is a positive value, with 0 indicating a planar surface, quantifying the amount of deviation from a flat plane. Taking these indicators into consideration, pore surfaces of the 3D image stacks were first generated in Avizo software package [34]. Principal curvature values were then computed from the generated surfaces. Using these values, the shape indicators were subsequently calculated in a Python environment, to be further applied to plot curvature maps, i.e., 2D density histogram plots in the (S,C) plane.

Results

Global assessment

Detailed microstructural changes undergone by the sintered materials were revealed, thanks to the high resolution and the large field of view resulting from the multiple distance phase retrieval.

At a global level, many sintering phenomena such as inter-particle neck growth, densification, grain growth, pore rounding, etc. that are stated in the traditional sintering theories at different stages of sintering [START_REF] Bordia | Current understanding and future research directions at the onset of the next century of sintering science and technology[END_REF] [2] [START_REF] Bansal | Ceramics and composites processing methods[END_REF] are clearly observed in the two alumina samples. Figure 3 Figure 4 shows the sintering progression at 1500°C of the relatively smaller alumina powder with 0.7 µm average size ('Al 0.7µm'). Global evaluations suggest that the sintering advances much faster in this case, with grains increasing in size, decreasing in number and the interconnected pores turning isolated towards the end, as in Figure 4 (d). The relative densities were measured to be 89%, 92% and 94% after just 30 min, 1 hour and 10 hours respectively, indicating the final stages of sintering.

Quantitative insights

Classical parameters with regard to the evolution of the grains and the pores corresponding to all the three stages, which are extensively used in the sintering literature, were measured from the 3D data, together with the introduction of some novel parameters.

Density -Grain volume fraction correlation

At each time period, volume fractions of grains extracted from the 3D images, when plotted against the experimentally measured relative density values (Figure 5), show an excellent fit for most of the points for both the alumina samples. This in turn proves the effectiveness of the resolution attained, the representativeness of the ROIs and the subsequent image processing. The fit especially suggests that the samples possess a uniform green density. The agreement between the values at different time periods also provokes interchangeable usage of the terms 'grain volume fraction' and 'relative density' further in this work.

Grain size progression

Advancements in tomography techniques have led to expressing the grain growth phenomenon occurring during sintering in terms of 3D grain size distribution, replacing the earlier quantitative assessments through 2D micrographs and other stereological methods [START_REF] Yeh | Effect of Particle Size Distribution on the Sintering of Alumina[END_REF] [START_REF] Borgh | Microstructure, grain size distribution and grain shape in WC-Co alloys sintered at different carbon activities[END_REF]. Here, the grain size deduction is carried out by granulometry measurements, as described in the previous section 2. [START_REF] Rahaman | Ceramic processing and sintering[END_REF]. Figure 6 (a) and (b) show a fairly narrow original grain size distribution, with a geometrical deviation of 1.17 and 1.2 for Al 0.7µm and Al 1.3µm respectively. De-agglomerated micron and submicron sized powders with uniform narrow size distributions are proven to improve the sinterability [START_REF] Chowdhry | Microstructural evolution during the processing of sodium β-alumina[END_REF] [39] and thereby the densification of the ceramic products to more than 90%, which is very well the case in Figure 6 Also, to be noted is that these distributions do not show a distinct bimodal shape, thus indicating a pattern of normal grain growth for both the samples [START_REF] Rahaman | Ceramic processing and sintering[END_REF]. Average grain sizes were calculated from each of these distributions and their conformity with the scaling law proposed by Herring [START_REF] Herring | Effect of change of scale on sintering phenomena[END_REF] was examined. In accordance with the analysis by Rahaman [START_REF] Rahaman | Ceramic processing and sintering[END_REF], this law correlates the sintering time period required to reach a given particle size, for two powders with similar shapes but different sizes (with say, radii a1 and a2, where a2 = λa1), sintered under the same experimental conditions. The required sintering times 𝑡 2 and 𝑡 1 , in this case, the time 𝑡 2 required by Al 1.3µm

to produce a geometrically similar change as exhibited by Al 0.7µm in time 𝑡 1 , are then interrelated as 𝑡 2 = λ α 𝑡 1 . Here, with λ = ~2, α takes a value of around 3.5, which falls in the acceptable range of values found in the sintering literature. As per Rahaman [START_REF] Rahaman | Ceramic processing and sintering[END_REF], the exponent is 4 for surface diffusion and grain boundary mechanisms and 3 for lattice diffusion.

Another way of evaluating the grain growth involves plotting the evolution of the average grain size as a function of the relative density attained [START_REF] Nettleship | Evolution of the grain size distribution during the sintering of alumina at 1350°C[END_REF]. In fact, average grain size is considered to be the only basic microstructural descriptor necessary to evaluate the microstructural evolution in many analytical estimations. From the distributions in Figure 6

𝑮 𝑮 𝟎 = 𝐚 𝐞𝐱𝐩 ( 𝐛 √𝟏 -𝒇 )

3

Pore size measurements

During sintering, in addition to densification and the corresponding grain size evolution, changes in the pore space occur concurrently. This is evidenced by the decrease in total porosity over the sintering stages. In fact, the pore features play a key role in the physical and mechanical properties of the final sintered product. Quantification of sintering would then be best realized not only by density determinations but also by a thorough understanding of the morphological evolution of porosity in terms of pore size distribution and other associated parameters [START_REF] Varela | Pore Size Evolution during Sintering of Ceramic Oxides[END_REF]. These are realized by way of granulometric analysis here, while, over the years, methods like nitrogen adsorption and mercury intrusion with commercial porosimeters were made use of [36] [46]. Unlike in the grain size distributions in Figure 6 (a) (b), the pore size distribution curves rather appear to be restricted between more or less the same range of values (Figure 7 (a) (b)).

Interestingly, a slight shift to the right is observed in the final curves for both the samples. The average pore size values from each of the distributions were then calculated and plotted against the relative density (Figure 7 (c)). A slight decrease in the values initially followed by an increase was observed in the case of Al 1.3µm, whereas for Al 0.7µm, there was limited variation except for the increase in the values towards the end, above 90% density, consistent with the shift observed in Figure 7 (a) (b). This increase in the average pore size at the end of sintering, as opposed to a drop as in classical theory, could be attributed to coincident grain growth, which leads to pore coalescence. The initiation of this phenomenon seems to be reflected in the sets of images in Figure 4, especially in Figure 4 (d). Further, this variation could be understood by a normalization as in Figure 7 (d), which gathers all the points for both the samples on one master curve.

Taking analytical models into consideration, porosity advancement in the intermediate stage and the final stage of sintering proposed by German [START_REF] German | Coarsening in sintering: Grain shape distribution, grain size distribution, and grain growth kinetics in solid-pore systems[END_REF] follows, 𝑝 = 𝐺 ( [47] [START_REF] Coble | Sintering and Related Phenomena[END_REF], Beere [START_REF] Beere | The second stage sintering kinetics of powder compacts[END_REF], Johnson [START_REF] Johnson | A General Model for the Intermediate Stage of Sintering[END_REF] and Yan et al. [START_REF] Yan | Effect of Grain Size Distribution on Sintered Density[END_REF]. Eudier [START_REF] Eudier | Sintering and Related Phenomena[END_REF] and Svoboda et al. [START_REF] Svobodat | Equilibrium pore surfaces, sintering stresses and constitutive equations for the intermediate and late stages of sintering-I. computation of equilibrium surfaces[END_REF] criticized and disapproved these models in their respective works as these assumptions were not substantiated by enough experimental justifications. Also, in addition to simple theoretical models having a limitation in characterizing the complicated porosity behavior, unlike porosity, the definition of pore size is not so straightforward, much less its way of measurement [START_REF] Nimmo | Porosity and Pore Size Distribution[END_REF].

However, a modification to the analytical expression above was found to give a rather good fit.

Interestingly enough, it holds true for all the stages of sintering for both the samples (Figure 7 (d)).

Pore connectivity and closure

As of the values is also another indication of the homogeneity in the microstructure and the absence of large agglomeration [START_REF] German | Sintering: from empirical observations to scientific principles[END_REF].

Another indicator for pore closure, called connectivity index (CI) is proposed here. It is essentially the ratio of the largest pore volume over the total pore volume. The concept of CI, presented in Babin et al. [START_REF] Babin | Fast X-ray tomography analysis of bubble growth and foam setting during breadmaking[END_REF], was further shown by Burr et al. [START_REF] Burr | Pore morphology of polar firn around closure revealed by X-ray tomography[END_REF] to be better suited for X-ray tomography analysis than the conventional closed porosity ratio to predict the close-off density. The advantages and drawbacks of both these methods are properly discussed in [START_REF] Burr | In situ X-ray tomography densification of firn: The role of mechanics and diffusion processes[END_REF] and [START_REF] Babin | Fast X-ray tomography analysis of bubble growth and foam setting during breadmaking[END_REF]. Accurate determination of pore closure requires high-resolution images, which is incompatible with large fields of view. Consequently, pores that are large with respect to the sample size could appear artificially as open porosity (intersecting the boundary of volume of interest). Closed porosity ratio is thus a biased measure with a smooth variation at pore closure. The connectivity index, meanwhile, is far less sensitive to the sample size and presents an abrupt variation at the closure.

The latter is chosen here to and as shown in Figure 8 (b), the connectivity index is equal to 1 when the porosity is totally open, while it is 0 when all the pores are closed. In particular, a clear drop in the index is observed at a density between 80% and 85% for Al 0.7µm and slightly below 90% for As an additional analysis on the connectivity of the pores, a porosimetric investigation, outlined in section 2.3, was performed to determine pore throats. The two samples exhibit similar patterns, when the average pore throat size is plotted against density (Figure 9 (a)).

The values show a decrease throughout except a sudden increase in the end. This indicates that, at around that density, when the pores tend to close-off, most of the smaller pore throats get closed in the process, while the larger ones remain and would get closed eventually afterwards. Taking the changing grain size into consideration, as in Figure 7 (d), the points show the scaling effect and follow a master curve for both the samples in Figure 9 (b). However, above a relative density of 92%, the normalized pore throat size shows an increase while the normalized pore size does not.

Curvature maps

As illustrated in Figure 10 (a), particles in the initial stage of sintering have tiny necks in between them, with the pores mainly exhibiting a curvature opposite to the curvature of the particles. The process of sintering leads to an intensification in the neck growth phenomenon. This eventually tends to create isolated spherical pores in the final stage with an opposite curvature as against their initial curvature, as in Figure 10 (b). We expect to visualize and capture this 'concave-to-convex' transformation in the pore curvature in the course of sintering [START_REF] Venkatesh | Analysis of Pore Evolution During Ceramic Powder Sintering by Synchrotron X-ray Nano-Tomography[END_REF]. In this regard, the shape indicators, 'Shape index' and 'Curvedness', defined in Equations 1 and 2, are adopted. These shape indictors have been extensively used in the medical community [START_REF] Hu | Shape and curvedness analysis of brain morphology using human fetal magnetic resonance images in utero[END_REF]. Some adaptations were found in metallurgical applications as well [START_REF] Gibbs | The Three-Dimensional Morphology of Growing Dendrites[END_REF]. More recently, Burr et al. [START_REF] Burr | In situ X-ray tomography densification of firn: The role of mechanics and diffusion processes[END_REF] used these indicators to explore snow metamorphism.

The shape index map in Figure 10 Interestingly, somewhere between relative densities of 74% and 81%, there is a clear shift in the maximum density points (Figure 11 (b) (c)).

Adjacent to each of these maps, snapshots of 3D rendering of the pore network corresponding to that particular stage are shown for better visual comprehension. These renderings display only the pore phase, with the ceramic particles appearing as void. The circular contours in the snapshots could be related to the necks between particles. Evolution of the pore curvature is clearly observed with the beginning of the development of isolated closed pores towards the end, as reflected on the shape index map.

With respect to the 3D renderings of the image stacks of Al 0.7µm in Figure 4, since the relative density reaches 89% after just 30 min and further increases progressively to 94% at the end, the curvature maps in Figure 12 This study therefore permits to make a proposition of classifying the stages of sintering in terms of the evolution in pore curvature. While the classical classification of a sintering process involves three sequential stages depending on parameters such as the relative density attained and other associated microstructural evolution, pore curvature advancement clearly reveals two distinct stages. The first stage is characterized by mostly cup-like pores with values of shape indices below 0 and relative densities below, say, around 80%. The second stage pertains to the latter half of the shape index map with the pore curvatures moving towards cap-like pores, after crossing 80% of the density. A transition step occurs in between these two stages, though not precisely observed in the curvature maps.

Moreover, sintering works mainly use conventional curvature parameters such as mean or Gaussian curvature (see for example Wakai et al. [START_REF] Okuma | Interface topology for distinguishing stages of sintering[END_REF]). Various authors in different fields have emphasized the interest in the parameters we chose, notably Shahani et al. [START_REF] Shahani | The dynamics of coarsening in highly anisotropic systems: Si particles in Al-Si liquids[END_REF], for describing coarsening in solid-liquid systems. In the field of sintering, our parameters are particularly useful in the occurrence of grain growth, as the shape index is insensitive to the grain size. It thus allows for a more relevant comparison of the state of the material at various sintering times.

Conclusion

3D investigation of micron-sized ceramic powder systems at the particle length-scale are now feasible, thanks to the ultra-high-resolution capabilities (~25 nm voxel size) offered by upgraded synchrotron facilities. Two sets of alumina powders with particle sizes of 0.7μm and 1.3μm were sintered and observed post-mortem using the nano-CT technique at the ID16B beamline of the European synchrotron, ESRF.

Complete 3D images were obtained for these sets of powders after sintering at a given temperature for various time periods. A comprehensive quantitative analysis was performed on the evolution of grains and pores with increasing sinter density. Several classical trends and some unusual, interesting aspects occurring during the grain and pore growth kinetics were taken note of.

Progression of grain growth was captured and validated with existing sintering theories.

Accompanying pore growth was analyzed in terms of the changes in pore size and pore throat size.

An equation to describe the pore size evolution valid for all the stages of sintering has been proposed. A connectivity index indicator was employed to trace and predict the density range at which the pore channels tend to close off.

Additionally, the data acquired from the 3D images was used to plot and analyze the so-called curvature maps. By virtue of this, a novel way of classifying the stages of sintering in relation to the advancement in pore curvature has been presented. The maps give information on the development of pore shapes throughout sintering, proving to be an indicator to track and assess the effect of sintering mechanisms on microstructural changes.

All of the information acquired may serve as datasets for the calibration of numerical models and for testing their veracity.

However, subtler but important effects at the local level go unnoticed in global analyses. Therefore, further thorough research including many more sintering parameters is needed in order to take into account the collective behavior occurring in a sintering process and to validate the obtained results.

A real-time in-situ tracking of the sintering progression at a similar resolution scale could bring about a substantial improvement in this regard, by exploring relevant details and associated parameters at the particle length-scale. An in-situ analysis would also enable tracking of initial (and perhaps intermediate) stages of sintering by segmenting individual features. These aspects are being dealt with in our ongoing research.

Figure 1 .

 1 Figure 1. SEM observation of alumina powders with particle sizes of around (a) 0.7 µm and (b) 1.3 µm respectively.

Figure 2 .

 2 Figure 2. Principle of nano-CT at ID16B beamline of ESRF: (a) sketch of the experimental set-up, (b) radiographs recorded from the 4-distance image set and (c) phase map obtained by phase retrieval, which are then used in (d) a tomographic reconstruction.

  (a) shows one of the cross-section slices taken from the middle of the image stack (1000*1000*1000 voxels) of the 3D reconstructed alumina of 1.3 µm average particle size (henceforth referred to as 'Al 1.3μm'), sintered at 1500°C with an original relative density of around 60%. Over time (Figure3(b) (c) (d)), we see developments in this original 'green' sample, such as the growth of interparticle necks, particle center-to-center shrinkage and a considerable densification, with the Archimedes relative density 'ρ' reaching 74%, 81%, 91% and 96% after 1 hour, 10 hours, 30 hours and 120 hours respectively. The sintered samples thus appear to span the intermediate (~70 to ~90% of density) and the final stage of sintering (above ~90% density).

Figure 3 .Figure 4 .

 34 Figure 3. One of the cross-section slices of the 3D reconstructed alumina samples of 1.3 µm (a), sintered at 1500°C and observed post-mortem after (b) 1 hour, (c) 10 hours, (d) 30 hours and (e) 120 hours respectively. The relative density values 'ρ' are mentioned on top-left. Scale bar is 5 µm. Alumina grains are in gray, while the black phase is porosity.(a)

Figure 5 .

 5 Figure 5. Correlation between the density of the sintered compact measured by the Archimedes approach and the grain volume fraction obtained by image analysis of the tomographic data for (a) Al 0.7µm and (b) Al 1.3µm, respectively. (a) (b)

Figure 6 .

 6 Figure 6. Evolution of grain size distribution for the two alumina samples, (a) Al 0.7µm and (b) Al 1.3µm, respectively; (c) comparison of average grain size versus density; and (d) average grain size over original grain size versus density for both these samples, along with the corresponding curve fit according to German's equation [42] and the proposed fit.

  (a) (b), the average grain size points are thus extracted and plotted in Figure 6 (c). Also, the average grain size points for the two samples are divided by their original grain size and plotted against the density values as in Figure 6 (d). These points are then compared with the equation proposed by German in [42] [43] for grain size, 𝐺 = 𝐺 𝑜 𝜃 √1-𝑓, where Go is the initial grain size, θ is a constant with a value of 0.6, and f is the grain volume fraction. Trying different values of θ, particularly a value of 0.63 for both our samples, shows a satisfactory match, with goodness-of-fit, R 2 = ~0.8. This value of θ falls in the range of 0.41 and 0.72, as compiled in the recently conducted studies by Paredes et al.[START_REF] Paredes-Goyes | Grain growth in sintering: A discrete element model on large packings[END_REF] for various samples of alumina, with different sizes, sintered at different temperatures. However, an empirical fit below (Equation3), in line with German's equation, appears to show a better agreement. The proposed expression has an R 2 = ~0.96, with two constants, a = ~0.5 and b = ~0.4 respectively.

Figure 7 .

 7 Figure 7. Evolution of pore size distribution for the two alumina samples, (a) Al 0.7µm and (b) Al 1.3µm, respectively; (c) comparison of average pore size versus density; and (d) average pore size over average grain size versus density for both these samples, along with the corresponding curve fit according to German's equations and the proposed fit.

  a link between pore size p, pore volume fraction 𝜀 and grain size G. These analytical relations, particularly the one for intermediate stage, do not yield a good fit when compared to the values obtained in Figure7(c). For instance, initial pore size in Figure7(c) for Al 1.3µm reads 0.61 µm, whereas the porosity relation rather gives 0.3 µm instead. In order to assess this misfit, a packing of spheres with a similar grain size distribution was considered in a discrete element method (DEM) framework, as in Paredes et al.[START_REF] Paredes-Goyes | Grain growth in sintering: A discrete element model on large packings[END_REF]. The packing was rendered in 3D and fed into the granulometry algorithm in GeoDict. This exercise yielded an initial average pore size value of ~0.5 µm, closer to the initial experimental value of 0.61 µm. A probable reason for the misfit could be the assumption related to geometry made in classical theories of the intermediate sintering stage. German[START_REF] German | Coarsening in sintering: Grain shape distribution, grain size distribution, and grain growth kinetics in solid-pore systems[END_REF] assumed grains to have the shape of a regular tetrakaidekahedron with open pore channels residing along the grain edges, as haveCoble et al.

4 Figure 8 .

 48 Figure 8. Evolution of (a) open and closed porosities and (b) connectivity index values versus density for the two alumina samples, Al 0.7µm and Al 1.3µm, respectively. (a) (b)

Al 1 .Figure 9 .

 19 Figure 8 (a), the pores appear to be totally closed at ~95% density.

  (c), adapted from Shahani et al.[START_REF] Shahani | The dynamics of coarsening in highly anisotropic systems: Si particles in Al-Si liquids[END_REF] and Burr et al.[START_REF] Burr | In situ X-ray tomography densification of firn: The role of mechanics and diffusion processes[END_REF], shows local shapes represented in a color scale and categorized into nine different shapes. The shape indices thus distinguish the shapes in the neighboring surface of a point. Cup-like concave shapes would have a shape index of -1, saddle-like cylindrical shapes equal to 0 and cap-like convex shapes +1.Following the generation of pore surfaces in Avizo software and the calculation of shape indicators, these were then represented as curvature maps in the form of 2D histograms. For the 3D renderings of the image stacks of Al 1.3µm in Figure3, the curvature maps show an evolution, as in Figure11. These histograms are scaled with a normalized probability density P(S,C) ranging from 0 in blue to 1 in red. In other words, regions in the map with P(S,C) =1 represent the local surfaces with the highest occurrences of the corresponding shape index and curvedness values. With reference to the shape index map in Figure 10 (c), the original pore network of Al 1.3µm exhibits a variety of shapes in Figure 11 (a), spanning from trough to saddle-like shapes. Eventually, with increase in time, after 30 hours of sintering in Figure 11 (d), the maximum density point P shifts to the right towards dome-like shapes, indicating that the pores are now on the verge of pinching off from the connected pore channels to become isolated.

Figure 10 .

 10 Figure 10. Representation of pore evolution during the sintering process from (a) the initial cup-like pores to (b) the final cap-like pores. (c) Shape index map showing local shapes, adapted from Shahani et al.[START_REF] Shahani | The dynamics of coarsening in highly anisotropic systems: Si particles in Al-Si liquids[END_REF] and Burr et al.[START_REF] Burr | In situ X-ray tomography densification of firn: The role of mechanics and diffusion processes[END_REF].

Figure 11 .

 11 Figure 11. Pore curvature maps for 3D reconstructed alumina Al 1.3µm (in Figure 3) at (a) the initial stage and after sintering at 1500°C and observing post-mortem at (b) 1 hour, (c) 10 hours and (d) 30 hours respectively, along with snapshots of cropped sections of the 3D rendering of the pore network.

  have already undergone the transition observed in Figure11 (b) (c)for Al 1.3µm. The shapes move further to the right at every stage, towards +1 of the shape index, signifying the spheroidization of pores, leading to their closure.The values of curvedness, though, do not evolve much throughout the sintering sequence for both the samples. One could have expected a substantial increase in its values when the sintering was nearing its end, as a result of closed pore shrinkage. However, as proved by Figure7, the pores do not show significant growth at longer times. Curvedness measurement is thus consistent with this previous result. The isolated pore in the final stage of sintering in Figure10(b) are hence assumed to have similar dimensional characteristics as the initial pore in Figure10(a), otherwise often illustrated to be much smaller in sintering literature, in the absence of grain growth.

Figure 12 .

 12 Figure 12. Pore curvature maps for 3D reconstructed Al 0.7µm (in Figure 4) at (a) the initial stage and after sintering at 1500°C and observing post-mortem at (b) 30 min, (c) 1 hour and (d) 10 hours respectively. (a) (b) (c) (d)

Acknowledgements

This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement MATHEGRAM No 813202. The authors also thank the ESRF for the provision of synchrotron radiation facilities (Proposal MA4632).


Giacomo Zilio
email: zilio@gmail.com

Louise S Nørgaard

Claire Gougat-Barbera
email: claire.gougat-barbera@umontpellier.fr

Matthew D Hall
email: matthew.hall@monash.edu

Emanuel A Fronhofer
email: emanuel.fronhofer@umontpellier.fr

Oliver Kaltz
email: oliver.kaltz@umontpellier.fr

Claire Gougat

of the Royal Society B: For Review Only 1 Travelling with a parasite: the evolution of resistance and dispersal syndromes during experimental range expansion

Keywords: Dispersal syndromes, eco-evolutionary dynamics, host-parasite interactions, invasion front, range expansion, resistance

Rapid evolutionary changes during range expansions can lead to the divergence between range core and front populations, with the emergence of dispersal syndromes. Besides intraspecific effects, range expansions may be impacted by interspecific interactions such as parasitism. Yet, despite the potentially large impact of parasites imposing additional selective pressures on the host, their role on range expansions remains largely unexplored. Here, we investigated whether parasites affect the evolution of host dispersal syndromes during spatial spread. Using populations of the ciliate Paramecium caudatum and its bacterial parasite Holospora undulata spreading in microcosm landscapes, we studied experimental range expansions under the presence or absence of the parasite. We found that range expansion and parasite treatments acted independently on the evolution of host dispersal syndromes. Front host populations showed different trait associations between swimming behaviour and population growth parameters than core populations, indicating divergent evolution. The presence of parasites reshaped these trait associations and divergence between front and core, with hosts exposed to the parasite exhibiting overall reduced dispersal, but increased resistance. Our work shows that host-parasite interactions during range expansions can shift the contenders to novel evolutionary trajectories and may influence the speed of the range expansion itself and of spreading epidemics.

Introduction

Species range expansions are increasing in frequency in response to rapidly changing environments [START_REF] Parmesan | A globally coherent fingerprint of climate change impacts across natural systems[END_REF] and becoming crucial to reducing the risk of extinction [START_REF] Thomas | Extinction risk from climate change[END_REF]. While ecological and evolutionary processes have been well explored for single species, we are still lacking a good community perspective of range shifts [START_REF] Kubisch | Where am I and why? Synthesizing range biology and the eco-evolutionary dynamics of dispersal[END_REF][START_REF] Miller | Eco-evolutionary dynamics of range expansion[END_REF]. Species might rarely "travel alone", and it is conceivable that interactions with other organisms facilitate or slow down spatial spread, and add new selection pressures while a species is spreading. Antagonistic species interactions have been suggested a major factor defining species ranges [START_REF] Kubisch | Predicting range shifts under global change: the balance between local adaptation and dispersal[END_REF][START_REF] Legault | Interspecific competition slows range expansion and shapes range boundaries[END_REF]. Parasitism, for example, are ubiquitous and exert strong demographic and evolutionary pressures on the host, which can limit geographic ranges as has been shown in some theoretical models [START_REF] Hochberg | Can natural enemies enforce geographical range limits?[END_REF][START_REF] Holt | Alternative causes for range limits: a metapopulation perspective[END_REF][START_REF] Price | Evolutionarily stable range limits set by interspecific competition[END_REF]. In fact, parasites may re-enforce range limits by reducing dispersal and/or by imposing additional mortality in already small populations at the front. This might be the case in the cane toad [START_REF] Finnerty | The costs of parasite infection: Effects of removing lungworms on performance, growth and survival of free-ranging cane toads[END_REF][START_REF] Kelehear | Rhabdias pseudosphaerocephala infection in Bufo marinus: lung nematodes reduce viability of metamorph cane toads[END_REF] and in other natural systems [START_REF] Antonovics | Spatio-temporal dynamics of bumblebee nest parasites (Bombus subgenus Psythirus ssp.) and their hosts (Bombus spp.)[END_REF][START_REF] Bradley | Parasites hinder monarch butterfly flight: implications for disease spread in migratory hosts: Parasites and monarch flight[END_REF][START_REF] Briers | Range limits and parasite prevalence in a freshwater snail[END_REF]. Adaptation to parasite attack may remove such range limits, but potentially also affect the evolution of other traits known to be selected at range fronts. This could produce eco-evolutionary feedbacks that will not only influence rates of spatial spread of the host species, but also impact parasite propagation in the target species, or spill-over of disease to other species along the way [START_REF] Combe | The rise of the rosette agent in Europe: An epidemiological enigma[END_REF][START_REF] Miller | Parasite spillover: indirect effects of invasive Burmese pythons[END_REF]. Further, parasites can cause knock-on effects on interactions with other species in the community [START_REF] Dunn | Indirect effects of parasites in invasions[END_REF][START_REF] Strauss | Invading with biological weapons: the importance of diseasemediated invasions[END_REF] and affect ecosystem functioning [START_REF] Poulin | Invasion ecology meets parasitology: Advances and challenges[END_REF]. Concomitant with antagonistic species interactions, range expansions often involve stochastic genetic changes in small vanguard front populations (via drift or founder bias), but also targeted evolution of dispersal due to spatial selection, spatial assortative mating and kin competition [START_REF] Phillips | Reid's paradox revisited: the evolution of dispersal kernels during range expansion[END_REF][START_REF] Shine | An evolutionary process that assembles phenotypes through space rather than through time[END_REF]. Dispersal evolution likely entails concerted changes in life-history, behavioural or physiological traits, leading to so-called dispersal syndromes [START_REF] Clobert | Informed dispersal, heterogeneity in animal dispersal syndromes and the dynamics of spatially structured populations[END_REF][START_REF] Cote | Evolution of dispersal strategies and dispersal syndromes in fragmented landscapes[END_REF]. Thus, the underlying genetic architecture and covariation among these traits will be critical to responses to selection at range fronts. Indeed, it has been shown for various biological systems that dispersal is a heritable trait and that covariation with other traits has a genetic basis [START_REF] Saastamoinen | Genetics of dispersal[END_REF], making it possible for selection to drive the divergence between core and front populations [START_REF] Chuang | Expanding population edges: theories, traits, and trade-offs[END_REF][START_REF] Fjerdingstad | Evolution of dispersal and life history strategies -Tetrahymena ciliates[END_REF]. This is illustrated by the introduced cane toad (Rhinella marina) in Australia, where the evolution of dispersal and other lifehistory traits promoted the speed of spread at the invasion front [START_REF] Brown | The straight and narrow path: the evolution of straight-line dispersal at a cane toad invasion front[END_REF][START_REF] Perkins | Evolution of dispersal and life history interact to drive accelerating spread of an invasive species[END_REF][START_REF] Phillips | Invasion and the evolution of speed in toads[END_REF]. Similar results were found for the invasive ladybird Harmonia axyridis [START_REF] Lombaert | Rapid increase in dispersal during range expansion in the invasive ladybird Harmonia axyridis[END_REF], and in laboratory range expansions using experimental evolution approaches [START_REF] Szűcs | Rapid adaptive evolution in novel environments acts as an architect of population range expansion[END_REF][START_REF] Weiss-Lehman | Rapid trait evolution drives increased speed and variance in experimental range expansions[END_REF][START_REF] Williams | Rapid evolution accelerates plant population spread in fragmented experimental landscapes[END_REF]. We currently know relatively little about parasite-mediated selection at range fronts and its consequences for dispersal syndrome evolution [START_REF] Kubisch | Where am I and why? Synthesizing range biology and the eco-evolutionary dynamics of dispersal[END_REF][START_REF] Miller | Eco-evolutionary dynamics of range expansion[END_REF]. While a considerable bulk of literature exists on resistance evolution in host-parasite metapopulations [START_REF] Lion | Evolution of spatially structured host-parasite interactions[END_REF][START_REF] Parratt | Infectious Disease Dynamics in Heterogeneous Landscapes[END_REF], there is no specific theory in the context of range expansion. Intuitively, we may expect that virulent parasites select for increased resistance and that this removes a parasite-imposed range speed limit. Such a case of resistance evolution has been found for populations of the cane toad infested by lung-worms at the range margin [START_REF] Mayer | Rapid divergence of parasite infectivity and host resistance during a biological invasion[END_REF]. Theory further suggests that natural enemies select for changes in host dispersal. For example, parasite-induced fluctuations in host population dynamics can modify environmental predictability and fitness expectations, and consequently favour increased host dispersal [START_REF] Chaianunporn | Concurrent evolution of random dispersal and habitat niche width in host-parasitoid systems[END_REF][START_REF] Chaianunporn | Evolution of dispersal in metacommunities of interacting species[END_REF]. Parasites may also select for plastic responses in dispersal, with sometimes counterintuitive consequences for the spread of infection [START_REF] Deshpande | Host-parasite dynamics set the ecological theatre for the evolution of state-and context-dependent dispersal in hosts[END_REF]. However, few if any studies have considered the joint action of parasite-mediated selection and spatial selection, and hence the interplay between the evolution of resistance and dispersal-related traits. Selection for resistance can be rapid and strong, but also modify genetic correlations with other life-history traits [START_REF] Luong | Costs of Resistance in the Drosophila-Macrocheles System: A Negative Genetic Correlation Between Ectoparasite Resistance and Reproduction[END_REF][START_REF] Sgrò | Genetic correlations, tradeoffs and environmental variation[END_REF], often involving trade-offs [START_REF] Duffy | Ecological feedbacks and the evolution of resistance[END_REF][START_REF] Kraaijeveld | Trade-off between parasitoid resistance and larval competitive ability in Drosophila melanogaster[END_REF] that constrain evolutionary trajectories. Such constrains may also concern dispersal syndromes. Our hypothesis it that dispersal syndrome might be different in the presence of the parasite, especially if there are trade-offs between dispersal and resistance. Using experimental evolution, we investigated the effect of a parasite on the emergence of dispersal syndromes. In a long-term experiment, we mimicked range expansions in interconnected microcosms of the freshwater protist Paramecium caudatum and its bacterial parasite Holospora undulata. In a range front treatment, the paramecia were constantly selected to disperse into a new microcosm, whereas in the range core treatment, only the non-dispersing fraction of the population was maintained. Range and core treatments were established for infected and uninfected populations. Evolved hosts were assayed for six traits, including dispersal, resistance, population growth characteristics and swimming behaviour. We found substantial divergence in multiple phenotypic trait space, attributable to the combined additive effect of our experimental treatments. A dispersal syndrome emerged, with higher dispersal, equilibrium density and movement tortuosity in the front treatment, and higher growth rate and swimming speed in the core treatment. Parasite-mediated selection affected these trait relationships. Namely, front populations evolving with the parasite were more resistant, but also dispersed less than their parasite-free counterparts. The parasite-driven evolution of such novel characteristics may influence the speed of range expansions, but also the risk of spreading epidemics, which can have important implications for biological control, conservation and management decisions.

Material and methods

Study system

Paramecium caudatum is a freshwater filter-feeding ciliate with a world-wide distribution [START_REF] Wichterman | The Biology of Paramecium[END_REF]. Ciliates typically exhibit a nuclear dimorphism: The "germ-line" micronucleus is active during the sexual stage, while the highly polyploid "somatic" macronucleus regulates gene expression during the asexual stage, when replication occurs through mitotic division. In this experiment, clonal populations were maintained asexually (max. 1-2 population doublings per day at constant 23°C) in 50 mL tubes, using a sterilised lettuce medium (1g dry weight of organic lettuce per 1.5l of Volvic TM mineral water), supplemented ad libitum with the bacterium Serratia marcescens as a food resource (referred to as "bacterised medium" or "medium", hereafter). The gram-negative bacterium Holospora undulata is an obligate parasite, infecting the micronucleus of P. caudatum [START_REF] Fokin | Diversity of Holospora Bacteria in Paramecium and Their Characterization[END_REF]. The infection life cycle comprises both horizontal and vertical transmission. Paramecium ingest infectious forms from the aquatic environment, which subsequently colonise the micronucleus and differentiate into multiplying reproductive forms; these reproductive forms are vertically transmitted to the daughter cells of mitotically dividing hosts. The infection life cycle is completed when reproductive forms differentiate into infectious forms, which are then released during host cell division or upon host death. Infection reduces cell division and survival of the Paramecium, as well as dispersal [START_REF] Fellous | Parasitic infection reduces dispersal of ciliate host[END_REF][START_REF] Nørgaard | An evolutionary trade-off between parasite virulence and dispersal at experimental invasion fronts[END_REF][START_REF] Zilio | Parasitism and host dispersal plasticity in an aquatic model system[END_REF]. Experimental evolution of resistance to this parasite was demonstrated in previous longterm experiments and can come at reproductive costs [START_REF] Lohse | Experimental evolution of resistance in Paramecium caudatum against the bacterial parasite Holospora undulata[END_REF][START_REF] Duncan | Temporal variation in temperature determines disease spread and maintenance in Paramecium microcosm populations[END_REF].

Experimental protocols (i) Long-term range expansion experiment Dispersal in two-patch systems

We used two-patch systems for this selection experiment (Supplementary Information, Fig. S1). The systems were built from two 14 mL plastic tubes ("core patch" and "front patch") interconnected by 5-cm silicon tubing (0.6 mm inner diameter) serving as a corridor through which the Paramecium can actively swim. We define dispersal as the active displacement of P. caudatum from the core patch to the front patch. In the long-term experiment, short episodes of dispersal (3h) alternated with periods of population growth and maintenance (1 week). For a dispersal episode, we filled the two-patch system with 9.5 mL of fresh bacterised medium and then blocked the corridor with a clamp. The core patch was filled with c. 8ml of culture containing Paramecium (≈ 2000 individuals), whereas the front patch was only topped up with nonbacterised medium and was thus "empty". After removal of the clamp, Paramecium could freely disperse to the front patch or to stay in the core. After three hours, we blocked the corridor and estimated the cell density in the core and front patch, by sampling up to 1mL from each tube and counting the number of individuals under a dissecting microscope. The dispersal rate is thus the number of dispersers divided by the total number of individuals in the two-patch systems, divided by 3 hours.

Range expansion treatments

Two selection treatments were imposed. In the range front treatment, only Paramecium that had dispersed into the front patch were maintained and allowed to grow for 1 week until the next episode of dispersal. Conversely, in the core selection treatment, only the non-dispersing Paramecium were maintained and allowed to regrow. These contrasting selection protocols were continued for a total of 26 cycles. The front selection treatment mimics the leading front of range expansion or a biological invasion, with populations continuously dispersing into a new microcosm. Populations from the core selection treatment stay in place and continuously lose emigrants. Each new growth cycle was started by placing on average 200 paramecia from front and core selection treatments in 20 mL of fresh bacterised medium, and equilibrium density was then reached within the following 3-4 days. The experiment was conducted with a single host line [START_REF] Nørgaard | An evolutionary trade-off between parasite virulence and dispersal at experimental invasion fronts[END_REF]. This line (63D) had undergone three years of parasite-free core selection prior to the present experiment; initially started from a mix of strains, it has become fixed for a single haplotype [START_REF] Zilio | Predicting evolution in experimental range expansions of an aquatic model system[END_REF].

Parasite treatment

Core and front treatments were established for both infected and uninfected populations. Starting from a 63D laboratory culture, infected and uninfected selection lines were established. The parasites were taken from an ongoing experiment [START_REF] Nørgaard | An evolutionary trade-off between parasite virulence and dispersal at experimental invasion fronts[END_REF] that had already been imposing core and front selection on infected 63D populations for about 8 months (30 cycles). Using standard protocols (see S2), we extracted infectious forms of the parasite from 5 core selection lines and from 5 front selection lines, which were then used to inoculate our new, naive 63D hosts. In other words, we continued core and front selection treatments for the parasite, but replaced the previous hosts by new unselected hosts. In addition to these 10 infected selection lines, we established 3 uninfected front-selection lines and 3 uninfected core-selection lines as controls for a total of 16 selection lines.

(ii) Phenotypic trait assays

At the end of the long-term experiment, phenotypic trait assays for Paramecium from all 16 selection lines were performed under common-garden conditions. Using a micropipette, we arbitrarily picked 4 uninfected paramecia from each selection line and placed them individually in single 1.5 mL Eppendorf tubes filled with bacterised medium, where they were allowed to grow for 2 weeks until small monoclonal lines had established (c. 7-8 asexual generations). Each monoclonal line was then split into three technical replicates and grown for a second common-garden period of 10 days in 50-mL tubes to obtain mass cultures for the phenotype assays (16 selection lines x 4 monoclonal lines x 3 technical replicates = 64 monoclonal lines and 192 replicates, Fig. S3). Of the 64 monoclonal lines, 60 were available to measure 6 phenotypic traits, as follows.

Resistance

To measure resistance, the Paramecium were confronted with parasites from core-selection and frontselection lines. We prepared the inocula by mixing the 5 infected core and 5 infected front selection lines, and extracting infectious forms from the two mixes (for details of the extraction protocol, see S2). For inoculation, c. 5000 paramecia were placed in a volume of 25 mL in a 50-mL tube, to which we added 4.5 x 10 5 infectious forms (core-parasite or front-parasite inoculum). In this way, we set up 4-8 inoculated tubes per host selection line, balanced between the two parasite inocula (16 selection lines x 2-4 monoclonal lines x 2 technical replicates = 120 inoculated tubes). Four days post-inoculation, we fixed c. 20 individuals from each inoculated replicate with lacto-aceto-orcein [START_REF] Fokin | Diversity of Holospora Bacteria in Paramecium and Their Characterization[END_REF] and inspected them for absence or presence of infection using a phase-contrast microscope (1000x magnification). We define resistance as the proportion of uninfected individuals in the sample. Preliminary analysis showed that Paramecium from the four different selection treatments did not differ in their resistance to the mixes of front or core parasites (F 3,12 = 0.44, n.s.); we therefore combined the two inoculum sources into a single "infected" category for the main analysis. Dispersal rate Dispersal was measured in linear 3-patch systems (50 mL tubes; Fig. S4), where the Paramecium dispersed from the middle tube into the two outer tubes (see SI for detailed protocol). This system configuration allowed us to use bigger volumes of culture and thus obtain higher numbers of dispersers than in 2-patch systems. Connections were opened for 3 h, dispersal rates were then estimated by counting the Paramecium in samples from the central tube (500 µl) and from the combined two outer tubes (3 mL). We employed technical replicates that had not been used for the resistance assay, and were kept in 30 mL of fresh medium for several days prior to the dispersal test. One replicate per monoclonal line was tested (60 dispersal tests). Population growth rate and equilibrium density For the population growth assay, we placed groups of 5 arbitrarily picked Paramecium in 15-mL tubes filled with 10 mL of bacterised medium. Over 9 days, we tracked densities in 24-h intervals, estimated from the number of individuals present in 200-µL samples. We set up 6-12 tubes per host selection line (3 tubes per monoclonal line), with a total of 180 tubes tested. For each tube, estimates of intrinsic population growth rate (r 0 ) were obtained by fitting a Beverton-Holt population growth model to each density time series, using a Bayesian approach [START_REF] Rosenbaum | Estimating Parameters From Multiple Time Series of Population Dynamics Using Bayesian Inference[END_REF], see section S5 for details). For certain tubes we obtained unsatisfactory fits of equilibrium density; we therefore decided to use the mean density over the second half of the assay (day 5-9) as a proxy for equilibrium density ( ). A small fraction of 19 tubes failed to produce a coherent growth 𝑁 pattern and remained at very low density for unknown reasons; it was not possible to fit our population growth model to these data, and the tubes were therefore excluded from analysis.

Swimming speed and tortuosity

At the end of the above population growth assay, we analysed swimming behaviour, using an established pipeline of computer vision and automated video analysis to collect this data [START_REF] Fronhofer | Eco-evolutionary feedbacks during experimental range expansions[END_REF][START_REF] Pennekamp | BEMOVI, software for extracting behavior and morphology from videos, illustrated with analyses of microbes[END_REF]. From a given tube, one sample of 119 µL was imaged under a Perfex Pro 10 stereomicroscope, using a Perfex SC38800 camera (15 package [START_REF] Pennekamp | BEMOVI, software for extracting behavior and morphology from videos, illustrated with analyses of microbes[END_REF], which provided individual-based data on swimming speed and the tortuosity of swimming trajectories (standard deviation of the turning angle distribution). Details of the script video analysis are given in S6. Swimming speed and tortuosity were averaged over all individuals in a sample prior to analysis. A total of 60 samples (1 per monoclonal line) was used for analysis, giving 2-4 observations per host selection line.

Statistical analysis

All statistical analyses were performed with R v 4.1.2 [START_REF] Core | R: A language and environment for statistical computing[END_REF]. Focusing on the analysis of trait associations, we constructed a data matrix with the measurements of the 6 traits for 60 monoclonal lines (for resistance, the mean over the two technical replicates was calculated). To impute 10 missing observations in population growth rate and equilibrium density we used the "missMDA" package version 1.16 [START_REF] Josse | missMDA: A Package for Handling Missing Values in Multivariate Data Analysis[END_REF]. Trait distributions were normalised by picking the best transformation ("bestNormalize" package version 1.4.2, [START_REF] Peterson | Ordered quantile normalization: a semiparametric transformation built for the cross-validation era[END_REF]). We then performed a multivariate analysis of variance (MANOVA), with range expansion treatment (core vs front selection lines), parasite treatment (infected vs uninfected control selection lines) and their interaction considered as fixed factors. Selection line identity was included as error term. From this same data set, we also performed univariate analyses for each of the 6 traits. In a second step, to better understand the multivariate results, we performed a principal component analysis (PCA), based on the means per selection line and thus a data matrix of 16 x 6 = 96 observations. To complement graphical inspection of results, we used the first and second components (PC1, PC2) for ad-hoc comparisons between treatments. Finally, we conducted correlations among monoclonal lines analysis using a Bayesian approach with the "rstan" package version 2.19.3 [START_REF] Carpenter | Stan: A Probabilistic Programming Language[END_REF], details in S7). We considered the three biologically relevant pairs of traits: dispersalresistance, r 0 -and speed-tortuosity. 𝑁

Results

We found signatures of selection history in the observed phenotypic variation and covariation (Table 1). Univariate analyses showed significant effects of range expansion treatment and/or parasite treatment on all 6 traits (Table 1). Multivariate analysis of the combination of these traits (MANOVA, Table 1) revealed significant effects of the range expansion (F 1,12 = 8.69, p = 0.005) and parasite treatment (F 1,12 = 8.82, p = 0.005), but not their interaction (F 1,12 = 2.68, p = 0.111). Thus, both selection treatments acted jointly, but largely independently, to produce phenotypic differentiation in the Paramecium. All examined traits contribute to this divergence, with three pairs of traits forming opposite vectors, pulling treatments in different directions in multi-trait space: dispersal-resistance, r 0 -and speed-tortuosity. The presence of 𝑁 parasites changed the intensity and/or sign of the among-line correlation coefficient (Table S1) between these pairs of traits as shown in Figure 2 (full dots vs empty dots). components, we observed along the horizontal PC1 axis a clear effect of the range expansion treatment (front vs core selection), separating the respective clouds of points (red vs blue Fig. 1). This front / core separation was significant both for the parasite-free selection lines (lower two clouds in Fig. 1, F 1,4 = 16.47, p = 0.015), and for selection lines evolving in the presence of the parasite (upper two clouds, F 1,4 = 5.83, p = 0.042). The direction and length of the different arrows in Fig. 1 show that these patterns were mainly driven by opposing trends in movement (speed / tortuosity; highest PC 1 loadings, Table S3). Overall, Paramecium from the front treatment generally had a lower swimming speed (-12%) and more non-linear movement trajectories (+23% tortuosity) than Paramecium from the core treatment (main effects of range expansion treatment: p < 0.009; Table 1). The PCA also indicates opposing trends in demography-related traits (Table S3), with lower population growth rate and higher equilibrium density for front selection lines (Fig. 1). However, univariate analyses show that these trends mainly hold for parasite-free control lines (range x parasite interaction: p < 0.05; Table 1). Along the vertical PC2 axis, phenotypic differentiation was mainly determined by the parasite selection treatment (Fig. 1), thus separating selection lines that had been exposed to the parasite and parasite-free lines. The separation was more pronounced for the range front treatment (upper vs lower red clouds, F 1,4 = 9.74, p = 0.020) than for the core treatment (upper vs lower blue points, F 1,4 = 3.22, p = 0.122). Resistance and dispersal are the key traits associated with the PC2 axis (Table S2), with arrow trajectories indicating higher dispersal for parasite-free lines and higher resistance for lines that had evolved with the parasite (Fig. 1). Univariate analyses confirmed these trends (effects of parasite treatment: p < 0.07; Table 1), but also indicate interactions with the range expansion treatment. Thus, the PCA signal for resistance was mainly due to increased resistance in the front treatment (+ 15%), but not in the core (Fig. 2B; parasite x range treatment: p = 0.056; Table 1). The details of the PCA are provided in Tables S2 andS3. In summary, the experimental treatment combining new front selection conditions with new exposure to parasites produced the strongest phenotypic divergence relative to the negative control treatment (no parasite, no selection for dispersal).

Discussion

Natural populations are currently forced to shift their ranges due to human-induced climatic and environmental changes, which often involves exposure to novel abiotic conditions or confrontation with biotic selection pressures such as parasitism [START_REF] Bowler | Mapping human pressures on biodiversity across the planet uncovers anthropogenic threat complexes[END_REF][START_REF] Morales-Castilla | Forecasting parasite sharing under climate change[END_REF]. Understanding how ecological dynamics affect the evolution and the trajectory of phenotypic traits in a host-parasite context is of major interest and relevance for conservation, controlling infectious disease and epidemic outbreaks [START_REF] Halloran | Emerging, evolving, and established infectious diseases and interventions[END_REF][START_REF] Smith | Global rise in human infectious disease outbreaks[END_REF], as well for the design of proper invasive species management strategies [START_REF] Crowley | Conflict in invasive species management[END_REF]. Importantly, parasites can change the availability of genetic variance to selection as well as the strength and direction of selection. Together with the selective pressures due to range expansion, parasitism will likely produce diverse patterns of divergence and syndromes, leading to changes in the whole host phenotype with trait modifications and the emergence of trade-offs. A multivariate perspective is therefore essential to shed light on how complex traits, like dispersal and resistance, respond to eco-evolutionary pressure in natural populations. In our study, we find substantial multi-trait divergence between core and front populations of an expanding range. Maximum divergence was observed when both new selection pressures were additively combined (front and parasite treatment). Parasites accentuated the difference between core and front populations for some traits, while reducing it for others. Three pairs of traits, typically involved in differentiation at range fronts, acted as opposing vectors in multi-trait space defining the phenotypic divergence between treatments: dispersal -resistance, r 0 -and swimming speed -tortuosity. In particular, front populations 𝑁 evolved with the parasite were more resistant, but dispersed less than their uninfected counterparts. Even though we may currently not know the precise physiology or morphology underlying these trait relationships, our results illustrate how spatial selection and parasite-mediated selection act jointly to produce major shifts in phenotypic trait space, resulting in multi-facetted dispersal syndromes. Below we focus on the evolutionary forces driving the three trait associations and discuss possible feedbacks of such evolutionary changes on range expansion speed.

Parasitism and dispersal syndromes: effects of the parasite at the front Dispersal and resistance

In line with theoretical and empirical results on range expansion dynamics, we found evidence for the emergence of dispersal syndromes, with higher levels of dispersal at the range front compared to core populations [START_REF] Cote | Evolution of dispersal strategies and dispersal syndromes in fragmented landscapes[END_REF][START_REF] Phillips | Invasion and the evolution of speed in toads[END_REF][START_REF] Zilio | Predicting evolution in experimental range expansions of an aquatic model system[END_REF]. However, the parasite imposed a strong additional selection pressure involving resistance as key component. Resistance is indeed a major trait selected under parasitism in the Paramecium -Holospora system [START_REF] Lohse | Experimental evolution of resistance in Paramecium caudatum against the bacterial parasite Holospora undulata[END_REF][START_REF] Duncan | Reverse Evolution: Selection Against Costly Resistance in Disease-Free Microcosm Populations of Paramecium Caudatum[END_REF] as well as in many others [START_REF] Brockhurst | The impact of migration from parasite-free patches on antagonistic host-parasite coevolution[END_REF][START_REF] Lennon | Is there a cost of virus resistance in marine cyanobacteria?[END_REF], but has so far received relatively little attention in a range expansion context. Here, front populations exposed to the parasite exhibited overall increased resistance, but reduced dispersal, relative to parasite-free populations. Additionally, parasites exacerbated the negative correlation between dispersal and resistance at the front (Figure 2, Table 2), indicating the presence of a trade-off. Although exceptions are known [START_REF] Auld | Variation in costs of parasite resistance among natural host populations[END_REF][START_REF] Labbé | Successfully resisting a pathogen is rarely costly in Daphnia magna[END_REF], resistance [START_REF] Schmid-Hempel | Variation in immune defence as a question of evolutionary ecology[END_REF] and dispersal [START_REF] Bonte | Costs of dispersal[END_REF] are usually considered costly traits, suggesting the potential for a trade-off between the two traits. Thus, the energetic costs of mounting an effective (constitutive) defence against the parasite may reduce the resources available for host dispersal. Similarly, the trade-off may have a behavioural component, linking resistance and feeding activity. Paramecia are filter-feeders and become infected when they ingest infectious spores of the parasite together with other food particles. Hence, resistance may be increased by reducing contact rates with the parasite through reduced feeding activity [START_REF] Fels | Ecological and genetic determinants of multiple infection and aggregation in a microbial host-parasite system[END_REF]. Such behavioural aspects of resistance may also include altered swimming behaviour, which could, in turn, affect feeding rates as well as dispersal (see below). The nature of resistance -dispersal trade-offs may vary from system to system. For example, in bacteria, cell surface modification conferring resistance to bacteriophages might come at the cost of reduced motility [START_REF] Koskella | Using experimental evolution to explore natural patterns between bacterial motility and resistance to bacteriophages[END_REF][START_REF] Whitchurch | Escherichia coli contains a set of genes homologous to those involved in protein secretion, DNA uptake and the assembly of type-4 fimbriae in other bacteria[END_REF]. Results from selection experiments indicate that the presence of phage can indeed favour bacterial dispersal evolution [START_REF] Koskella | Using experimental evolution to explore natural patterns between bacterial motility and resistance to bacteriophages[END_REF][START_REF] Taylor | Bacterial motility confers fitness advantage in the presence of phages[END_REF]. However, unlike in our study, there was no clear link with resistance, implying that the two traits evolved independently. This suggests that, apart from mechanical or physiological constraints, the emergence of evolutionary trade-offs also depends on the underlying genetic architecture and relationships with fitness, or on the environmental conditions [START_REF] Deshpande | Host-parasite dynamics set the ecological theatre for the evolution of state-and context-dependent dispersal in hosts[END_REF][START_REF] Zilio | Parasitism and host dispersal plasticity in an aquatic model system[END_REF][START_REF] Boots | The Evolution of Resistance to a Parasite Is Determined by Resources[END_REF][START_REF] Meaden | The cost of phage resistance in a plant pathogenic bacterium is context-dependent[END_REF]. r 0 and 𝑁 On the demographic axis of the multi-trait space, populations at the range front were characterized by high (equilibrium density) and low r 0 (population growth rate), indicating a trade-off typical of classic r-K 𝑁 selection theory (Fig. 1). This negative correlation was particularly pronounced in the parasite treatment (Fig. 2, Table 2). At first sight, this finding appears in contradiction with common ideas about dispersal syndrome evolution (Burton et al. 2010), predicting competitive strategies in the core (high K or ) and opportunistic 𝑁 strategies at range fronts (high r 0 ). However, in our experiment competitive ability is characterised by growth rate, rather than equilibrium density [START_REF] Zilio | Predicting evolution in experimental range expansions of an aquatic model system[END_REF][START_REF] Fronhofer | Eco-evolutionary feedbacks during experimental range expansions[END_REF]. Indeed, the authors showed that rapacious high-growth variants are favoured in the core treatment and more slowly growing variants at the front. This was further corroborated in another study on P. caudatum, using both experimental evolution and predictive modelling, again showing the emergence of high and low r 0 at the range front [START_REF] Zilio | Predicting evolution in experimental range expansions of an aquatic model system[END_REF]. Comparative evidence suggests 𝑁 that this may actually be a widespread pattern [START_REF] Dallas | Predicting cryptic links in host-parasite networks[END_REF]. Parasite-mediated selection reinforced this pattern and further accentuated the divergence between front and core populations (Fig. 1).

Swimming speed and tortuosity

We found decreased swimming speed for Paramecium from the range front treatment, consistent with previous observations [START_REF] Zilio | Predicting evolution in experimental range expansions of an aquatic model system[END_REF]. This is opposite to results in a very similar experiment with another ciliate [START_REF] Fronhofer | Eco-evolutionary feedbacks during experimental range expansions[END_REF] and also seems to contradict observations in other biological systems, where populations at the range front show enhanced movement ability [START_REF] Phillips | Invasion and the evolution of speed in toads[END_REF][START_REF] Weiss-Lehman | Rapid trait evolution drives increased speed and variance in experimental range expansions[END_REF]. However, in our case, speed reduction was associated with increased swimming tortuosity, i.e., the ability of the individuals to change directions while swimming. This could be considered as an upregulated exploratory behaviour that potentially increases the probability to find the dispersal corridor in our dispersal systems. The negative relationship between these swimming behaviours was accentuated by the presence of the parasite at the range front (Figure 2, Table 2). Thus, similarly to the reinforcement of the above dispersal -resistance and r 0 -relationships, parasite-mediated 𝑁 selection also seems to affect the trait architecture of movement behaviour, i.e., the mechanistic basis of dispersal. Evo-to-eco feedbacks: Is the evolution with a parasite slowing down range expansions? The evolution of dispersal syndromes typically produces ecological feedbacks that speed up range expansions [START_REF] Miller | Eco-evolutionary dynamics of range expansion[END_REF]. Parasites, in contrast, may keep in check host populations and thereby limit or slow down range fronts, as generically shown for interspecific (antagonistic) interactions [START_REF] Kubisch | Predicting range shifts under global change: the balance between local adaptation and dispersal[END_REF][START_REF] Price | Evolutionarily stable range limits set by interspecific competition[END_REF][START_REF] Moorcroft | Potential role of natural enemies during tree range expansions following climate change[END_REF]. As discussed above, one of our main results is the emergence of a trade-off between resistance and dispersal. Thus, an intuitive prediction is that, due to lower dispersal, evolution with the parasite slows down the range expansion of infected populations compared to parasite-free populations. This is all the more conceivable given the negative ecological effect of the parasite, via reductions in host density or reduced dispersal [START_REF] Fellous | Parasitic infection reduces dispersal of ciliate host[END_REF]. In natural range expansions, instances of resistance evolution against parasites have been described, e.g., at the range front of the cane toad [START_REF] Mayer | Rapid divergence of parasite infectivity and host resistance during a biological invasion[END_REF]. It is unknown how the resistance evolution in the toad affects dispersal traits, but it seems obvious that, in the face of a detrimental parasite (a lung worm), having the resistance will benefit the range expansion more than not having it. Beyond these simple considerations, however, answers may be more complex [START_REF] Barnett | The impact of parasites during range expansion of an invasive gecko[END_REF], especially when we compare different "strategy sets" (or, dispersal syndromes) in the presence of parasites. Our results suggest that consequences for range expansion speed depend on how the trade-off between dispersal and resistance plays out precisely. If contact rates are high and the parasite virulent, higher levels of resistance may indeed compensate lower dispersal, such that front populations with an evolutionary parasite past might advance faster than their naive, parasite-free counterparts. On the other hand, if enemy-free space can be reached, less resistant variants may actually outrun the parasite and fully profit from their higher dispersal capacity. These scenarios may, for example, relate to biological invasions, where invaders bring along a parasite to which they have already adapted or, like the cane toad, encounter new parasites at the range front. For our experimental system, predictions from the present data remain speculative, because relevant measurements (growth, dispersal, movement) were taken in the absence of infection. A full picture would require estimates of virulence/tolerance or dispersal assays that include infected hosts [START_REF] Nørgaard | An evolutionary trade-off between parasite virulence and dispersal at experimental invasion fronts[END_REF][START_REF] Zilio | Parasitism and host dispersal plasticity in an aquatic model system[END_REF]. Moreover, future experiments can use multi-microcosm landscapes to actually measure range expansion speeds for the different types of hosts and/or epidemiological scenarios. Ideally, these would be accompanied by theory exploring the simultaneous evolution of dispersal and interaction traits [START_REF] Drown | Consumer-Resource Interactions and the Evolution of Migration[END_REF] or accounting for additional factors, such as parasite evolution [START_REF] Nørgaard | An evolutionary trade-off between parasite virulence and dispersal at experimental invasion fronts[END_REF], dispersal plasticity [START_REF] Deshpande | Host-parasite dynamics set the ecological theatre for the evolution of state-and context-dependent dispersal in hosts[END_REF][START_REF] Zilio | Parasitism and host dispersal plasticity in an aquatic model system[END_REF] or the general upregulation of immune responses, known to occur during range expansion [START_REF] Diagne | Contemporary variations of immune responsiveness during range expansion of two invasive rodents in Senegal[END_REF][START_REF] Gardner | Innate immunity of Florida cane toads: how dispersal has affected physiological responses to LPS[END_REF].

Conclusion

Our selection experiment illustrates the possible impact of biotic interactions on evolutionary trajectories during range expansions. Parasite-mediated selection changed the structure of dispersal syndromes, shaping the phenotypic divergence between front and core populations for multiple traits, including dispersal, lifehistory and resistance. Specifically, increased resistance traded off with a decrease in dispersal, which could potentially slow down range expansion. This study focused on the host, but dispersal syndromes may also evolve in the parasite, or even coevolve. This may further complexify the interplay between spatial selection and biotic (co-)evolution, and make it even more difficult to predict the accompanying ecological feedbacks on range expansion dynamics or disease spread. Replicated range expansions under laboratory conditions represent one tool to disentangle these processes. Although being simplified abstractions of the real world, such experiments may also provide baseline information for applied issues of biocontrol or the monitoring of emerging diseases.

Figure captions

Figure 1 PCA for six traits measured for 16 long-term selection lines of P. caudatum, showing the first two principal component axes, PC1 and PC2. The length of the thin arrows inside the graph represents the loading values; the longer the arrow the higher the correlation with the PC axis and the variance explained by that trait. Each point represents the average phenotypic value of a given selection line in multivariate space, with long-term treatment origins specified: range core (blue) vs. range front (red) treatment; evolved in the presence (full circles) vs. absence (empty circles) of the parasite H. undulata. The blue empty circles with dotted ellipsis represent the ancestral host populations. The ellipses represent the containment probability region of the multivariate space for the four treatments. Figure 2 Trait correlations for P. caudatum evolved in range core and range front treatments: (A-B) dispersal -resistance, (C-D) growth rate (r 0 ) -equilibrium density ( ) and (E-F) swimming speed -swimming tortuosity. 𝑁 For each panel, the parasitism treatment is specified: evolved in the presence of the parasite (full dots and lines) vs. parasite-free (dashed dots and lines). The points are the means for 60 monoclonal cultures, isolated from a total of 16 long-term selection lines (for details, see text). Correlations were obtained with Bayesian inference, separately for each combination of range expansion and parasitism treatments. Ellipses are bound to non-linear space and represent the 10, 25, 50, 75 an 90 % CI of the correlation of pairs of traits. Distributions in the small panels represent the posterior distributions of the correlation coefficients, the dashed black line highlight the 0 value, and thus the absence of correlation.

Table 1

 1 MANOVA and ANOVAs for the effect of range expansion treatment (core vs. front) and parasitism treatment (infected vs. parasite-free populations) on six traits, measured for 16 P. caudatum selection lines. P-values < 0.05 highlighted in bold.

			Range expansion		Parasitism		Range x Parasitism
	MANOVA	F 1, 12	p-value	F 1, 12	p-value	F 1, 12	p-value
	All traits	8.69	0.005	8.82	0.005	2.68	0.111
	ANOVA	F 1, 12	p-value	F 1, 12	p-value	F 1, 12	p-value
	Dispersal	1.08	0.318	11.43	0.005	1.86	0.197
	Resistance	9.91	0.008	3.85	0.073	4.44	0.056
	Speed	10.03	0.008	0.05	0.827	0.14	0.713
	Tortuosity	14.82	0.002	3.29	0.094	2.29	0.156
	r 0	3.72	0.077	0.68	0.425	5.25	0.040
	𝑁	2.79	0.120	12.17	0.004	4.76	0.049
	Considering the PCA

http://mc.manuscriptcentral.com/prsb Submitted to Proceedings of the Royal Society B: For Review Only

Submitted to Proceedings of the Royal Society B: For Review Only

Acknowledgements

This is publication ISEM-YYYY-XXX of the Institut des Sciences de l'Evolution -Montpellier.

Funding

This work was funded by the Swiss National Science Foundation (grant no. P2NEP3_184489) to GZ and by the 2019 Godfrey Hewitt Mobility Award granted to LN by ESEB.

data from this study are available at https://doi.org/10.5281/zenodo.5907048 http://mc.manuscriptcentral.com/prsb

Data accessibility

The data from this study are available at https://doi.org/10.5281/zenodo.5907048

Conflict of interest I/We declare we have no competing interests

Statement (if applicable):

CUST_STATE_CONFLICT :No data available.

Ethics

Not applicable

Authors' contributions OK, LN and GZ conceived the study. GZ, LN, MH, EAF, and OK designed the experiments. GZ, LN, CGB and OK performed the experimental work. GZ, LN, OK and EAF performed the statistical analysis. All authors interpreted the results. GZ and OK wrote the first draft of the manuscript and all authors commented on the final version.

Competing interests

The authors declare no competing financial interests.