Estelle Barbot

Mathilde Dufaÿ

Jeanne Tonnabel

Cécile Godé

Isabelle De Cauwer

On the function of flower number: disentangling fertility from pollinatormediated selection

Keywords:

In animal-pollinated angiosperms, the "male-function" hypothesis claims that male reproductive success should benefit from large floral displays, through pollinator attraction, while female reproductive success is expected to be mainly limited by resource availability. As appealing as this theory might be, studies comparing selection strength on flower number in both sexes rarely document the expected asymmetry. This discrepancy could arise because flower number impacts both pollinator attraction and overall gamete number. In this study, we artificially manipulate floral displays to disentangle the fertility versus pollinator attraction components of selection, both in terms of mating and reproductive success. In females, flower number was under strong fertility selection, as predicted in the absence of pollen limitation. In contrast, in males, flower number was mainly under sexual selection, which in turn increased male reproductive success. However, these selection patterns were not different in males with artificially increased floral displays. This suggests that sexual selection acting on flower number in males do not occur because flower number increases pollinator attraction, but rather because more pollen is available to disperse on more mates. Our study illustrates the power of disentangling various components of selection with potentially sex-specific effects for understanding the evolution of sexual dimorphism.

Introduction

Darwin himself introduced the notion of sexual selection, advocating that certain traits are selected because they enhance individual fitness through mating success, i.e. the number of sexual partners [START_REF] Darwin | The descent of man, and selection in relation to sex[END_REF]. According to theory, anisogamy should result in male reproductive success being more limited by gamete acquisition (e.g. through mate acquisition) than female reproductive success [START_REF] Bateman | Intra-sexual selection in Drosophila[END_REF][START_REF] Trivers | Parental investment and sexual selection[END_REF][START_REF] Jennions | Sexual selection[END_REF][START_REF] Lehtonen | Bateman gradients from first principles[END_REF]. Across the animal kingdom, this statement is widely supported by two lines of evidence. First, empirical studies measuring sex-specific Bateman's gradients, the slope of the regression of reproductive success on mating success, generally demonstrate this relation to be steeper in males than in females [START_REF] Janicke | Darwinian sex roles confirmed across the animal kingdom[END_REF]. Second, male biased sexual dimorphism for armament and ornament is pervasive in animal taxa, particularly in reptiles, birds and mammals, suggesting stronger sexual selection on male versus female phenotypes [START_REF] Mori | Sexual dimorphism[END_REF][START_REF] Arnold | Is there a unifying concept of sexual selection that applies to both plants and animals?[END_REF].

The scope for such sex differences in the dependence of reproductive success on access to sexual partners has long been suggested to include all sexually reproducing anisogamous organisms, thus including plants [START_REF] Bateman | Intra-sexual selection in Drosophila[END_REF][START_REF] Arnold | Is there a unifying concept of sexual selection that applies to both plants and animals?[END_REF]. In animals, during the precopulation phase of reproduction, sexual selection can involve (i) competition for the access to sexual partners (usually among males) and/or (ii) choice of sexual partners (usually by females [START_REF] Jennions | Sexual selection[END_REF]). In plants, during the pre-pollination phase of reproduction when pollen is dispersed from anthers to stigmas, sexual selection can operate through male intrasexual competition to access receptive stigmas [START_REF] Moore | Sexual selection in plants[END_REF]. Sexual selection can also take the form of female intrasexual competition to receive viable pollen in the common case of pollen limitation [START_REF] Burd | Bateman's principle and plant reproduction: the role of pollen limitation in fruit and seed set[END_REF][START_REF] Knight | Pollen limitation of plant reproduction: pattern and process[END_REF]. One might thus expect between-sex differences in the intensity of sexual selection to decrease with increasing pollen limitation, as observed in broadcast spawning animals when male gametes become limiting [START_REF] Levitan | Sexual selection in external fertilizers[END_REF].

Yet, the pre-pollination phase of plants strongly differs from sexual selection in animals given that it involves a third party -the pollinators -in a vast majority of angiosperm species [START_REF] Ollerton | How many flowering plants are pollinated by animals?[END_REF]. Sexual selection mediated by pollinators may thus drive the evolution of phenotypic traits linked with pollinator attraction, with obvious parallels with mate attraction in animals [START_REF] Moore | Sexual selection in plants[END_REF][START_REF] Lloyd | Secondary sex characters in plants[END_REF]. In this respect, a wide range of floral traits has been demonstrated to be involved in pollinator attraction, such as nectar quantity [START_REF] Hodges | The influence of nectar production on hawkmoth behavior, selfpollination, and seed production in Mirabilis multiflora (Nyctaginaceae)[END_REF], flower size [START_REF] Ashman | Seasonal variation in pollination dynamics of sexually dimorphic Sidalcea oregana ssp. spicata (Malvaceae)[END_REF][START_REF] Conner | Measurements of natural selection on floral traits in wild radish (Raphanus raphanistrum). I. Selection through lifetime female fitness[END_REF] or flower number (reviewed in [18]). In dioecious plants, i.e. species with separate sexes, sexual dimorphism in floral traits is generally thought to have evolved through differential sexual selection between sexes [START_REF] Moore | Sexual selection in plants[END_REF]19].

In dioecious species, males generally carry more flowers than females, at least in temperate regions, suggesting stronger directional selection on this trait in males than in females [START_REF] Eckhart | Sexual dimorphism in flowers and inflorescences[END_REF][START_REF] Cuevas | Population size, sex-ratio and sexual dimorphism in Fuchsia parviflora (Onagraceae) an endemic dioecious shrub[END_REF][START_REF] Moquet | Temporal dynamics of sexual dimorphism in a dioecious species[END_REF]. Similarly, in hermaphroditic species, flower number has been historically considered as a typical 'male' trait, as earlier work in plants argued that flower number, beyond a certain threshold, served the purpose of the male function only [START_REF] Queller | Sexual selection in a hermaphroditic plant[END_REF][START_REF] Burd | What does the male function hypothesis claim?[END_REF]. Indeed, hermaphroditic plants often display fruit-sets lower than one (i.e. produce many flowers that do not mature into fruits), even in optimal pollination conditions [START_REF] Sutherland | On the importance of male fitness in plants: patterns of fruit-set[END_REF][START_REF] Holland | Testing hypotheses for excess flower production and low fruit-to-flower ratios in a pollinating seed-consuming mutualism[END_REF]. The rationale for this "male-function" hypothesis is based on the common observation that flower number affects pollen donation more than seed production [START_REF] Queller | Sexual selection in a hermaphroditic plant[END_REF][START_REF] Burd | What does the male function hypothesis claim?[END_REF][START_REF] Bell | On the function of flowers[END_REF][START_REF] Skogsmyr | Sexual selection: an evolutionary force in plants?[END_REF]. One process behind this involves pollinator attraction : large number of flowers often increase the number of pollinators visits [START_REF] Conner | Measurements of natural selection on floral traits in wild radish (Raphanus raphanistrum). I. Selection through lifetime female fitness[END_REF]18,[START_REF] Bond | Survival costs and reproductive benefits of floral display in a sexually dimorphic dioecious shrub, Leucadendron xanthoconus[END_REF][START_REF] Morales | Sterile flowers increase pollinator attraction and promote female success in the Mediterranean herb Leopoldia comosa[END_REF]. Thus, if pollen donation depends more on the number of pollinators visits compared to ovule fertilization, large floral displays would mainly benefit male fitness after a certain threshold [START_REF] Queller | Sexual selection in a hermaphroditic plant[END_REF]. Yet, empirical support for the male-function hypothesis remains ambiguous [START_REF] Ashman | Explaining phenotypic selection on plant attractive characters: male function, gender balance or ecological context?[END_REF]. Indeed, several studies quantifying selection on flower number through both sexual functions in hermaphroditic species found either (i) weaker selection on flower number through male function compared to female function [START_REF] Broyles | Paternity analysis in a natural population of Asclepias exaltata : multiple paternity, functional gender, and the "pollen-donation hypothesis[END_REF][START_REF] Sahli | Testing for conflicting and nonadditive selection: floral adaptation to multiple pollinators through male and female fitness[END_REF], (ii) no selection through the male function [START_REF] Conner | Measurements of natural selection on floral traits in wild radish (Raphanus raphanistrum). II. Selection through lifetime male and total fitness[END_REF] or even (iii) negative selection through the male function [START_REF] Hodgins | Natural selection on floral traits through male and female function in wild populations of the heterostylous daffodil Narcissus triandrus[END_REF][START_REF] Van Kleunen | Selection on floral traits through male fertility in a natural plant population[END_REF]. Quantifying the relative effect of flower number through different components of selection in each sex may help understand the current discrepancy between verbal expectations and empirical data.

Selection on flower number may arise through two distinct but simultaneous selective processes. First, flower number can be under sexual selection if individuals with larger display benefit from increased reproductive success through enhanced pollinator attraction (i.e. pollinator-mediated sexual selection), ultimately acquiring a higher number of sexual partners. Second, flower number can be under fertility selection if individuals with larger displays benefit from higher gamete production at the plant level. Comparing the strength of selection between arrays of hand-pollinated and open-pollinated plants has allowed to partition the effect of pollinator-mediated and fertility selection on flower number in a number of study systems [START_REF] Sandring | Pollinator-mediated selection on floral display and flowering time in the perennial herb Arabidopsis lyrata[END_REF][START_REF] Trunschke | Interaction intensity and pollinatormediated selection[END_REF][START_REF] Chen | Pollinator-mediated selection on flowering phenology and floral display in a distylous herb Primula alpicola[END_REF][START_REF] Caruso | A meta-analysis of the agents of selection on floral traits[END_REF]. One important caveat of this approach, however, is that it focuses on female fitness exclusively, precluding any explicit test of the male-function hypothesis [START_REF] Ashman | Explaining phenotypic selection on plant attractive characters: male function, gender balance or ecological context?[END_REF]. A powerful method to alleviate this issue is the use of phenotypic manipulation [START_REF] Campbell | Using phenotypic manipulations to study multivariate selection of floral trait associations[END_REF]. In animals, experiments manipulating traits thought to be involved in mate acquisition has proven to be an effective method in sexual selection studies [START_REF] Moore | Balancing sexual selection through opposing mate choice and male competition[END_REF][START_REF] Cothran | Phenotypic manipulation provides insights into the function of a sexually selected trait in a freshwater crustacean species complex[END_REF][START_REF] Katayama | Sexual selection on wing interference patterns in Drosophila melanogaster[END_REF][START_REF] Safran | The maintenance of phenotypic divergence through sexual selection: an experimental study in barn swallows Hirundo rustica[END_REF]. While phenotypic manipulation has allowed to explain the evolution of various floral traits through pollinator-mediated selection [START_REF] Cuartas-Domínguez | Pollinator-mediated selection and experimental manipulation of the flower phenotype in Chloraea bletioides[END_REF][START_REF] Barrio | Sex-dependent selection on flower size in a largeflowered Mediterranean species: an experimental approach with Cistus ladanifer[END_REF][START_REF] Pellegrino | Functional differentiation in pollination processes among floral traits in Serapias species (Orchidaceae)[END_REF], this approach

has not yet been applied to explicitly test the male-function hypothesis.

In this study, we performed phenotypic manipulation in order to test whether flower number benefitted more the male rather than the female reproductive success, through its impact on pollinator attraction. By adding dummy flowers on half of the individuals in an experimental population of the dioecious species Silene dioica, at the population flowering peak, we amplified the visual signal displayed by some plants without changing their gamete production. Such approach allows disentangling pollinator-mediated from fertility components of selection on flower number with a common methodology for both sexes. Within each sex, two components of individual fitness will be considered: (i) the number of offspring produced, referred to as reproductive success hereafter, which corresponds to the number of seeds for females, and to an estimate of the number of sired offspring for males, obtained through paternity analysis and (ii) the number of acquired mates, referred to as mating success hereafter, which corresponds to the number of genetic mates for both sexes. Because female reproduction is supposed to be limited mainly by resource availability for ovule production and maturation, at least when pollinators are not a limiting factor, we predict that neither female reproductive success, nor its relationship with the number of real flowers, should be impacted by our treatment (control vs. enhanced visual signal). We however hypothesize that female mating success can be affected by our treatment if the addition of dummy flowers enhances pollinator attraction and mate acquisition. In males, we predict that enhancing the visual signal to pollinators should increase both mating and reproductive success, and possibly strengthen the relationship between the number of real flowers and mating/reproductive success assuming that the benefit of displaying a showier signal increases with the number of gametes produced at the plant level.

Material and methods

Study system

Silene dioica (L.) Clairv. is a short-lived perennial herb of the Caryophyllaceae family. This dioecious plant is widespread throughout northern and central Europe [START_REF] Baker | Melandrium dioicum (L. emend) Coss. & Germ[END_REF][START_REF] Jalas | Atlas florae europaeae: distribution of vascular plants in Europe. 7. Caryophyllaceae (Silenoideae)[END_REF]. Sex determination is genetic, with males being the heterogametic sex [START_REF] Warmke | Sex determination and sex balance in Melandrium[END_REF][START_REF] Ming | Sex chromosomes in land plants[END_REF].

The species is sexually dimorphic for flower number and size, with males being more conspicuous than females [START_REF] Moquet | Temporal dynamics of sexual dimorphism in a dioecious species[END_REF][START_REF] Kay | Differences between sexes in floral morphology, nectar production and insect visits in a dioecious species, Silene dioica[END_REF]. Silene dioica is insect-pollinated and displays a generalist pollination system with bees and hoverflies as main pollinators [START_REF] Baker | Melandrium dioicum (L. emend) Coss. & Germ[END_REF][START_REF] Westerbergh | Gene flow and pollinator behaviour in Silene dioica populations[END_REF].

Plant material and experimental design

Plant material was generated using seeds collected in three forests from the same region where the experiment was conducted (Lille University in France, 50°36'27.9''N 3°08'36.3''E), in order to reach a sufficient sample size while avoiding the inclusion of half or full-sibs. All individuals were sown in a greenhouse and placed in separate 0.7-L pots filled with a standard soil mixture.

An array of 172 plants with 1:1 sex-ratio was kept in an insect-proof greenhouse until the beginning of the experiment. The surface area of the experimental plot was of 50 m² and local density was 3.3 individuals.m -², mirroring typical densities observed in nature. No wild populations of Silene dioica were growing in the vicinity. At the flowering peak (31th May 2019), plants were randomly assigned to our two treatments and placed in the experimental garden for ten days with individual spatial positions arranged to follow a grid pattern where sexes and treatments were alternated.

In the control group (C), flower number was left unmanipulated. It included 43 females (FC) and 43 males (MC). In the treatment group (T), which also included 43 females (FT) and 43 males (MT), the visual signal was amplified by adding enough dummy flowers to double the flower number of each individual (i.e. different numbers of dummy flowers were thus used depending on individual flower production). Dummy flowers were created using crepe paper which was selected based on its color spectra to approach average S. dioica petals' reflectance, and circles of 3.5cm diameter were cut in the paper with the closest spectra and rolled to roughly mimic S. dioica's flower shape and size (Figure S1). These dummy flowers were then tied on plants using an invisible nylon thread.

In addition to these open-pollinated plants, a group of 20 females (FHP) were placed in the same experimental garden over the same period and artificially handpollinated to quantify pollen limitation of female reproductive success. All open flowers were supplemented every other day with pollen from a pool of males from the same initial collection, isolated in a greenhouse. Each FHP female received pollen from an average of 20 different males over the course of the experiment, with two males being used for each pollination session for each FHP female. After ten days, all females (FT, FC and FHP) were placed in an insect-proof greenhouse until fruits reached maturity and could be collected, typically two to three weeks after flower opening.

Pollinator observations

In order to verify our expectation that dummy flowers increased pollinator attraction, pollinator visitation patterns were reported and compared between treatments. We conducted observations on groups of ten neighbouring plants through three observational sessions of 20 minutes spread over the course of the experiment. Accordingly, each plant was observed for a total of sixty minutes. For each pollinator entering the group under scrutiny, the identity of the visited plants and the number of visits per plant were noted. A visit was defined as a clear contact between the insect and the reproductive structures of a flower. For each plant, three variables were derived from these observations (Figure 1): (i) whether a plant was visited or not over the course of the sixty minutes, defined hereafter as visitation, (ii) the number of visiting pollinators (i.e. the number of independent insects visiting a given plant), and (iii) the total number of visits (i.e. the total number of contacts between any pollinator and the reproductive structures of a given plant). Note that we did not observe any contact between pollinators and a fake flowers.

Trait measurement

Floral traits -A total of twelve floral traits were measured on all plants. Three traits were measured three times during the course of the experiment and averaged across dates: [START_REF] Darwin | The descent of man, and selection in relation to sex[END_REF] the number of open flowers, (2) corolla width and (3) calyx height. The nine remaining traits were measured once, just before the beginning of the experiment: (4) nectar volume, (5) sugar concentration, (6) petal colour luminance, [START_REF] Mori | Sexual dimorphism[END_REF] petal colour saturation, [START_REF] Arnold | Is there a unifying concept of sexual selection that applies to both plants and animals?[END_REF] petal reflectance in UV wavelengths, (9) petal length, [START_REF] Burd | Bateman's principle and plant reproduction: the role of pollen limitation in fruit and seed set[END_REF] petal largest width, [START_REF] Knight | Pollen limitation of plant reproduction: pattern and process[END_REF] petal area and (12) petal cleft length. Details about floral trait measurements are available in appendix (Text S1; Figure S4).

Gamete production -

The number of gametes per flower was assessed for both sexes.

For females, ovule number was assessed by imaging the contents of a random sample of fruits. For males, pollen quantity was estimated on two anthers using a particle counter. Details about estimation of gamete production in each sex are available in appendix (Text S1).

Female reproductive success

Seed production was assessed on half of the mature fruits (one to six fruits per plant) using image processing, as described in Text S1. Germination rates were estimated on a sub-sample of 60 seeds per female that were sown in petri dishes filled with 40mL of 10g/L agar in sterile water (photoperiod 14:10 and temperature 21-15°C) and surveyed during 15 days. For each female, reproductive success over the course of the experiment was then obtained by multiplying three terms: total number of fruits, mean seed number per fruit, and germination rate.

Male reproductive success

Male reproductive success was estimated by genotyping a subsample of offspring.

The number of seedlings genotyped for each female reflected its contribution to the total seed pool (23.6 ± 11.4 seeds genotyped per female). Within each female, seedlings were randomly sampled across fruits. Total genomic DNA from adults (86 females and 86 males) and seedlings (2030 individuals) was extracted, and PCR assays were used to amplify five nuclear microsatellites (Table S1, Text S2). Using genotypes and individual spatial data, we then used a spatially explicit mixed mating model (MEMM model, [START_REF] Tonnabel | Sex-specific selection on plant architecture through "budget" and "direct" effects in experimental populations of the wind-pollinated herb, Mercurialis annua[END_REF]) to assess variation in male reproductive success and in pollen dispersal kernels, as described in Text S3.

Estimation of mating success

We performed categorical paternity assignments using CERVUS 3.07, allowing for a 2% genotyping error and using an 80% confidence criterion [START_REF] Marshall | Statistical confidence for likelihood-based paternity inference in natural populations[END_REF][START_REF] Kalinowski | Revising how the computer program cervus accommodates genotyping error increases success in paternity assignment[END_REF]. To assess the number of effective mating partners for each female and male (i.e. genetic mating success), we used a bootstrapping procedure that sampled 8 seeds per mother 1000 times. Fixing the number of offspring per mother allows avoiding the establishment of an artificially positive correlation between reproductive and mating success that would solely reflect variation in seed production across females [START_REF] Anthes | Measuring and interpreting sexual selection metrics: evaluation and guidelines[END_REF]. The mean number of effective mating partners by individual across bootstraps was used in the analysis. All data (pollinator visits, floral traits, male and female reproductive and mating success, as well as pollen dispersal distances) is available on Dryad (doi:10.5061/dryad.0rxwdbs4d).

Statistical analysis

Phenotypic homogeneity between groups -Prior to all analyses, we removed one male from the treatment with manipulated flower number (MT) because it produced over one standard-deviation more flowers than the second most-floriferous male individual. One female was also removed from dataset because it did not produce any seeds (FC). For each sex, a multivariate analysis of variance (MANOVA) was then performed to ascertain that values for the thirteen measured traits (twelve floral traits and gamete number, see above) were homogeneous within sex and among treatments, using Wilks' Lambda statistic.

Assessing pollen limitation in the experimental plot -The occurrence of pollen limitation was tested by assessing whether the treatment (control FC, manipulated FT or hand-pollinated FHP) affected seed set. Seed set was calculated for each dissected fruit as seed number divided by ovule number. Comparisons were performed using a generalized linear model with a binomial distribution. A random individual effect was added because several fruits were sampled for each female (lme4 package, [START_REF] Bates | Fitting linear mixed-effects models using lme4[END_REF]), and a likelihood ratio test was used to test the effect of pollination treatment, by comparing models without vs. with pollination treatment as a fixed effect.

Testing the effect of phenotypic manipulation on pollinator visits, pollen dispersal distances, reproductive success and mating success -In the following models, we included as fixed effects (1) the first axis of a PCA on all morphological floral traits, (2) the number of real flowers, and (3) gamete number per flower. The latter two were explicitly included in models as fixed effects to account for fertility variation between plants while the former described the general floral phenotype of individuals. PCAs were performed on males and females separately. The first axis accounted for 27.6% of floral traits' variance in females and 29.8% in males. We only retained the first axis of the PCA on basis of the broken-stick method ( [START_REF] Jackson | Stopping rules in principal components analysis: a comparison of heuristical and statistical approaches[END_REF]; Figure S2). In both sexes, this first axis mainly represents flower size variation (Figure S2).

Pollinator visits -Three groups of generalized linear models were built to explain pollinator attraction, one for each estimate (visitation, number of pollinators visits, total visits). For each model, likelihood ratio tests were used to test the significance of the following fixed effects: (i) the number of real flowers, (ii) the first axis of PCA defined above, (iii) treatment, (iv) sex and (v) the interaction effect between treatment and sex, by comparing the likelihood of models including or not those effects.

Because pollen production can also play a role in pollinator attraction [START_REF] Duffy | Effects of pollen reward removal on fecundity in a self-incompatible hermaphrodite plant[END_REF], additional models testing for the effect of gamete production and its interaction with sex were also built. Visitation was modelled using a GLM with a binomial distribution. For models explaining either the number of pollinators or the total number of visits, GLMs with negative binomial distributions were retained based on their greater AIC values compared to hurdle or zero-inflated models (i.e. accounting for overdispersion and/or excess of zeros).

Pollen dispersal distance -Variation in mean pollen dispersal distances among males was assessed using multiple linear regressions including the following explanatory variables: (i) the number of real flowers, (ii) the number of gametes per flower and (iii) the first axis of PCA defined above. Separate analyses were first performed on control males (MC) and on manipulated males (MT). Then, a second analysis on both groups of males was performed to test differences between groups.

T-tests were conducted on estimates to assess their significance in separate models, and likelihood ratio tests were used to test the effect of interactions between treatment and each of the three explanatory variables in the complete model. Prior weights were set up to take into account uncertainty of a posteriori individual mean pollen dispersal distance estimated using the MEMM model (Text S3).

Patterns of selection on flower number -

We used structural equation modelling (SEM, [START_REF] Kline | Principles and practice of structural equation modeling[END_REF]) which allows to jointly assess the direct and indirect effects of floral traits (number of real flowers, gamete number and first PCA axis) on both mating and reproductive success. Specifically, we evaluated how floral traits affected mating success (Figure 2) while testing the relationship between mating success and reproductive success (i.e. indirect effect of floral traits on reproductive success through mating success; Figure 2). We also evaluated the direct relationship between floral traits and reproductive success, independently of an indirect effect through mating success (Figure 2). This was done on two separate datasets, one for each sex, using piecewiseSEM package in R [START_REF] Lefcheck | piecewiseSEM: piecewise structural equation modelling in R for ecology, evolution and systematics[END_REF]. We then performed a multigroup analysis using local estimation of the parameters for each sex, which is carried out in two steps. The first step provides statistics for each treatment × variable interactions using type III ANOVA to assess which selection patterns were similar between groups (i.e. treatment × variable interaction effects that are not significant). The second step provides correlation estimates, and significant treatment × variable interaction are free to vary between each group. Estimates were then plotted on the network using semPlot package in R [START_REF] Epskamp | semPlot: unified visualizations of Structural Equation Models[END_REF].

Another aim of the study was to evaluate if enhanced pollinator attraction through phenotypic manipulation resulted in higher mating success (MS) and/or reproductive success (RS). To that aim and in addition to the SEM analyses, we tested for a main effect of the treatment on MS and/or RS, which cannot be achieved using SEMs. We thus built multiple linear models, predicting either reproductive or mating success, again considering males and females separately. Apart from the treatment variable, we tested for the same independent variables than those included in the SEM analyses, i.e. number of real flowers, number of gametes per flower and the first PCA axis. In models predicting reproductive success, mating success was added as an additional explanatory variable. Significance of estimates were assessed using T-tests for separate models, and likelihood ratio tests were used to test effects of (i) treatment as main effect, (ii) treatment × trait interactions, as well as (iii) treatment × mating success interaction in reproductive success models. Uncertainties in the estimation of male reproductive success were again accounted for by modelling prior weights using a posteriori distributions of the MEMM model. The analyses were performed using as response variables either relative reproductive or mating success (i.e. estimates were divided by the mean), and used standardized trait values as explanatory variables (i.e. traits were centred and scaled), following standard recommendations [START_REF] Lande | The measurement of selection on correlated characters[END_REF][START_REF] De Lisle | On the standardization of fitness and traits in comparative studies of phenotypic selection[END_REF]. Relativization and standardization were performed per sex and across treatments, since the methods used to estimate fitness differed between sexes.

Results

No evidence for pollen limitation

We found no evidence of pollen limitation in our experimental garden. Handpollinated females (FHP) did not show higher seed sets than open-pollinated females (FC: 0.

Phenotypic manipulation increased pollinator visitation

A total of 280 pollinators were observed, including Syrphidae (60.7% of visitors), Bombus species (28.6%), Halictidae (6.8%) and Lepidopterae (3.9%). Pollinators were more attracted by males than females as revealed by a significant sex effect for all three descriptors of pollinator visitation patterns: visitation ( χ 1). MANOVAs on the thirteen measured traits did not indicate phenotypic differences between treatments (females: F 15,67 =1.34 , P=.20 ; males : F 15,62 =0.71 , P=. 77 ), so any effect of treatment on visitation patterns should be ascribable to the phenotypic manipulation. Results showed that dummy flowers did not increase visitation ( χ 1,160 2 =1.82 , P=.17 ), but increased both the number of visiting pollinators and the total number of visits ( χ ). When included in the models, gamete number had no effect on pollinator attraction, and did not modify the results described above.

Pollen dispersal distance was influenced by the number of real flowers Across treatments, average pollen dispersal distance was 1.50 meters (± 0.32 SD) within our experimental garden. Mean pollen dispersal distance did not differ between control (MC) and manipulated (MT) males ( χ 1,77 2 =0.44 , P=.51 ; Figure S3).

Mean pollen dispersal distance increased with the number of real flowers in the manipulated group. This effect was weaker in the control group, although the effect of the interaction between the number of real flowers and treatment was not significant (Table 1). Neither the number of gametes per flower nor PC1 (representing variation in flower size) affected pollen dispersal distances in both groups.

Selection patterns differed between sexes

Results from SEM analyses and linear models were globally congruent. Estimates and statistics from linear models are thus reported in supplementary (Table S2). SEM analyses showed the same selection patterns in control and manipulated females (Table 2). In both groups, we detected a significantly positive direct effect of the number of real flowers on both reproductive and, to a lesser degree, mating success (Table 2, Figure 2A), as well as a significant positive effect of the number of gametes per flower on reproductive success. In both groups of females, MS and RS were not significantly correlated. In the linear model, treatment did not increase reproductive success (i.e. treatment as main effect was not significant; χ 1,74 2 =1.23 , P=. [START_REF] Bell | On the function of flowers[END_REF] ), but significantly increased mating success ( χ 1,76 2 =4.97 , P=.26 ).

In both control and manipulated males, the number of real flowers was significantly positively correlated with plant mating success (Table 2; Figure 2B). Because the SEM analyses also detected a strong correlation between MS and RS in males, this suggests an indirect effect of real flower number on reproductive success. The only difference detected between manipulated and control males concerned the correlation between the number of gametes per flower and reproductive success:

Discussion

The current study aimed at exploring the male-function hypothesis [START_REF] Queller | Sexual selection in a hermaphroditic plant[END_REF][START_REF] Bell | On the function of flowers[END_REF], by measuring the relationship between flower number and fitness in both sexes, through its potential impact on pollinator attraction. Specifically, our aims were (i) to investigate the impact of flower production on reproductive and mating success in male and female plants of S. dioica, and (ii) to explore whether an experimental enhancement of the floral signal would mainly impact selection patterns in males, highlighting the role of flower number in pollinator attraction and pollen export.

Adding dummy flowers indeed increased pollinator attraction, enabling us to test our predictions. As expected, we found that neither female reproductive success, nor its relationship with flower number were impacted by this enhanced attraction. We also found that this manipulation increased female mating success (in terms of mate acquisition), but with no detected impact on seed production. In males, contrarily to our hypotheses, we found no effect of enhanced attraction to pollinators on either reproductive or mating success. Whereas large flower numbers seem to be associated with a higher mating success, we found no difference in this selection pattern between control and manipulated males. The reach of these results for the historical discussion on the male function hypothesis are discussed below.

Pollination context

Seed production was not statistically different between open-and hand-pollinated plants, suggesting that female reproductive success was not limited by pollen receipt in the experimental garden. In such conditions, according to sexual selection theory, one expects fitness of male plants to depend more on their ability to attract pollinators compared to that of females [START_REF] Moore | Sexual selection in plants[END_REF][START_REF] Burd | Bateman's principle and plant reproduction: the role of pollen limitation in fruit and seed set[END_REF], provided that pollinator attraction is associated with the probability to reach sexual partners.

The strongest determinant of pollinator attraction was clearly sex (males received on average twelve-fold more visits than females), confirming previous observations in S.

dioica [START_REF] Kay | Differences between sexes in floral morphology, nectar production and insect visits in a dioecious species, Silene dioica[END_REF][START_REF] Carlsson-Granér | Floral sex ratios, disease and seed set in dioecious Silene dioica[END_REF]. It should be noted that this preference for male S. dioica plants is known to be at least partly driven by the high degree of sexual dimorphism for flower number [START_REF] Moquet | Effects of sexual dimorphism on pollinator behaviour in a dioecious species[END_REF]. This effect of flower number on pollinator attraction is confirmed in our study: adding dummy flowers resulted in an overall increase in the number of pollinators attracted, as well as in the total number of visits.

Female reproductive success was mainly driven by gamete production

In females, the number of real flowers was shown to positively affect reproductive success, and this effect was similar in both manipulated and control plants. This observation, along with the fact that no pollen limitation was detected, suggests that the benefit for the female function of carrying more flowers is only linked to a higher ovule production at the plant level, and not to any effect on pollinator attraction. In other words, our results support the sole effect of fertility selection on the number of flowers, in alignment with general expectations from sexual selection theory. Our analysis also revealed positive selection on the number of ovules per flower, but no selection on flower size (a trait often associated with pollinator attraction [START_REF] Ashman | Seasonal variation in pollination dynamics of sexually dimorphic Sidalcea oregana ssp. spicata (Malvaceae)[END_REF][START_REF] Conner | Measurements of natural selection on floral traits in wild radish (Raphanus raphanistrum). I. Selection through lifetime female fitness[END_REF]).

Taken together, these findings support that, as long as the pollination context is favourable, traits that increase female reproductive success are associated with fertility, as found in several other plant species [START_REF] Sandring | Pollinator-mediated selection on floral display and flowering time in the perennial herb Arabidopsis lyrata[END_REF][START_REF] Chen | Pollinator-mediated selection on flowering phenology and floral display in a distylous herb Primula alpicola[END_REF][START_REF] Delph | Sexual, fecundity, and viability selection on flower size and number in a sexually dimorphic plant[END_REF].

In our experiment, female mating success increased both when plants received more pollinator visits (treatment effect) and when they carried more real flowers. These two effects are likely to emerge from mechanistic aspects of pollen dispersal. On the one hand, an increase in the number of independent pollinator visits is expected to increase the diversity of pollen arriving on the stigmas. On the other hand, because producing more flowers implies that more ovules are available for fertilization, an increase in flower number should result in a parallel increase in the number of mates.

However, because female mating and reproductive success were uncorrelated, a result equivalent to non-significant Bateman gradients found in females of many animal species ( [START_REF] Janicke | Darwinian sex roles confirmed across the animal kingdom[END_REF] but see exceptions within) and in another plant species [START_REF] Tonnabel | Do metrics of sexual selection conform to Bateman's principles in a wind-pollinated plant?[END_REF], the detected positive effects on mating success did not translate in an increase in reproductive success. In other words, females did not benefit from an increased seed number because they accessed more sexual partners, confirming that only fertility selection occurred in females of our experiment.

Males do not seem to benefit from enhanced pollinator attraction Contrary to our expectations, artificially enhanced floral display did no impact male reproductive success or patterns of selection on floral traits. The only difference between control and manipulated male plants concerned selection on the number of pollen grains per flower, with control plants experiencing negative selection on this trait, whereas manipulated plants seemed to experience positive selection. Although we could not find any satisfactory explanation for this difference between control and manipulated plants, this effect is unlikely to be driven by treatment differences in pollinator attraction, since the quantity of gamete per flower had no significant impact on pollinators visits in our analyses. While a negative trade-off between pollen quantity and quality could contribute to the observed change in selective patterns between control and manipulated males, our previous evaluation of pollen phenotypes suggests that this correlation is rather positive [START_REF] Moquet | Temporal dynamics of sexual dimorphism in a dioecious species[END_REF].

In both categories of males, the number of real flowers positively impacted mating success. In strong contrast with the patterns observed in females, however, mating and reproductive success were strongly associated, reflecting the positive Bateman gradient that is often observed in male animals [START_REF] Janicke | Darwinian sex roles confirmed across the animal kingdom[END_REF] and in a couple of plant species [START_REF] Tonnabel | Do metrics of sexual selection conform to Bateman's principles in a wind-pollinated plant?[END_REF][START_REF] Johnson | The effects of quantitative fecundity in the haploid stage on reproductive success and diploid fitness in the aquatic peat moss Sphagnum macrophyllum[END_REF]. Thus, although flower number did not have any detectable direct effect on male reproductive success, our results support an indirect effect through mating success: male plants with more (real) flowers tended to have a better access to mates, which in turn significantly increased the number of seeds they sired. This part of our results thus seems consistent with the expectation of flower number being under sexual selection in males. Whereas observational studies cannot assess whether such selective pattern is mediated by an increased pollinator attraction or an increased gamete production, our manipulation of floral display -that increased pollinator attraction only-allowed us going further. Under the hypothesis of a male function through pollinator attraction, we were expecting differences between manipulated and control males. Our results did not fit our expectations. Manipulated males did not benefit from increased mating or reproductive success, and they appeared to experience the same selection patterns on real flower number compared to control males. This suggests that the possible benefit of exhibiting a high number of flowers in males is not mediated by pollinator attraction per se. One likely explanation for our results is that producing many flowers results in larger pollen loads on pollinators (e.g. through increased visit time, [START_REF] Jones | Pollinator-mediated selection on a flower color polymorphism in experimental populations of Antirrhinum (Scrophulariaceae)[END_REF]) and, ultimately, in reaching a larger number of females. The fact that the number of real flowers was positively associated with longer dispersal distance in both control and manipulated males indirectly supports this hypothesis. Pollen production at the plant level is a trait that typically falls in the realm of what is sometimes referred to as "the grey zone" of sexual selection [START_REF] Alonzo | Grey zones of sexual selection: why is finding a modern definition so hard?[END_REF], since it can both be argued to be mainly under fertility selection or under sexual selection.

This study documented extremely restricted pollen dispersal distances (typical for entomogamous species, [START_REF] Hardy | Fine-scale genetic structure and gene dispersal in Centaurea corymbosa (Asteraceae) I. Pattern of pollen dispersal[END_REF][START_REF] Llaurens | High paternal diversity in the self-incompatible herb Arabidopsis halleri despite clonal reproduction and spatially restricted pollen dispersal[END_REF][START_REF] Van Rossum | Fluorescent dye particles as pollen analogues for measuring pollen dispersal in an insectpollinated forest herb[END_REF]), which might weaken the opportunity for sexual selection, since male-male competition would typically occur among directly neighbouring individuals. Nevertheless, our result support that males producing more flowers gain higher fitness at through enhanced access to females. It thus seemed that sexual selection played a part in the evolution of flower number in males of Silene dioica, whereas selection on the same trait in females was undoubtedly based on fertility selection. Nonetheless, this difference between males and females could not be attributable to a differential in the relationships between male vs. female fitness and pollinator attraction. Taken together, our results are thus not congruent with the male-function hypothesis, when interpreted as an advantage of producing many flowers to the male function through an increased capacity of attracting pollinators [START_REF] Moquet | Temporal dynamics of sexual dimorphism in a dioecious species[END_REF][START_REF] Holland | Testing hypotheses for excess flower production and low fruit-to-flower ratios in a pollinating seed-consuming mutualism[END_REF].

Tables Table 1: Effect of floral traits on pollen dispersal distances and differences between groups.

Figures

Figure 1: Illustration of the three proxies used to characterized pollinator visits (A) : visitation, the number of visiting pollinators and the total number of visits. Boxplots representing the number of visiting pollinators (B) and the total number of visits (C), according to sex and treatment. P-values for the treatment effect are represented with * < 0.05 and ** < 0.01. Males (MC: yellow, MT: orange) were more visited than females (FC: light green, FT: dark green), and both sexes were more visited with the addition of dummy flowers. Means are represented with white points.

2 =0. 10 ,

 210 whereas this correlation was marginally positive in manipulated plants, it was negative in the control group. In the linear model, neither the average reproductive nor mating success were affected by the treatment (respectively χ 1,74 2 =0.87 , P=.[START_REF] Hodgins | Natural selection on floral traits through male and female function in wild populations of the heterostylous daffodil Narcissus triandrus[END_REF] and χ 1,76 P=.[START_REF] Llaurens | High paternal diversity in the self-incompatible herb Arabidopsis halleri despite clonal reproduction and spatially restricted pollen dispersal[END_REF] ).

Figure 2 :

 2 Figure2: Results from multigroup SEM analyses in females (A) and males (B). Each trait can have (I) a direct effet on MS and/or RS, as well as (ii) an indirect effect on RS, depending of the strenght of the relationship between RS and MS (i.e. Bateman gradient), through a direct effect on MS. Estimates for each correlations are plotted with associated P-values in brackets, with green arrows for positive values and orange arrows for negative values. Covariances between traits are represented with double headed dotted arrows. In the SEM analyses, only one correlation differed between control (C) and manipulated (T) group, with estimates plotted in grey for the correlation between gamete number per flower and reproductive success in males.

  62 ± SE 0.012; FT: 0.64 ± SE 0.011; FHP: 0.59 ± SE 0.018; χ 2,556 2 =1.45 , P=.48 ).

Table 2 :

 2 Estimates (± SE) from linear models are reported for each effect in both groups (MC and MT). are reported from likelihood ratio tests to assess the interaction between treatment and each trait. P-value in bold are significant. The proportion of variance explained by each model is reported using adjusted R-squared ( R S F-stats (type III ANOVA) for multigroup SEM analyses

	721
	722
	723
			Control males (MC)	P	Manipulated males (MT)	P	Treatment × trait	P
			R S 2 =-0.014		R S 2 =0.11		R S 2 =-0.048
	β Number of real flowers	0.0045 ± 0.0038	.24	0.012 ± 0.0045	.014	χ 1,77 2	=1.60	.21
	β Gametes number per flower	8.4 × 10 -7 ± 1.7 × 10 -6	.62	4.4 × 10 -7 ± 1.8 × 10 -6	.80	χ 1,77 2 =0.029	.87
	β PC1		0.016 ± 0.024	.51	0.031 ± 0.025	.22	χ 1,77 2	=0.65	.65
	724 725 726 727	Note: 2	).

Acknowledgements

We would like to thank E. Klein for letting us access the MEMM model. We thank S. P. De Lisle for precious advice about reproductive and mating success relativization and trait standardization in selection gradient analysis. We also thank Céline Devaux, Eric Imbert and François Rousset for their advice about the analyses. This work has been performed using infrastructure and technical support of the "Plateforme Serre, cultures et terrains expérimentaux -Université de Lille". We are grateful to Eric Schmitt for the support in plant collection maintenance. For laboratory assistance, we thank L. Debacker, S. Flourez and N. Le Roux.

Funding

This work is a contribution to the CPER research project CLIMIBIO. The authors thank the French Ministère de l'Enseignement Supérieur et de la Recherche, the Hauts de France Region and the European Funds for Regional Economical Development for their financial support to this project. JT was funded by a Marie-Sklodowska-Curie grant (#844321).

Data accessibility

Data are available on Dryad: https://dx.doi.org/10.5061/dryad.0rxwdbs4d [START_REF] Barbot | Data from: on the function of flower number: disentangling fertility from pollinator-mediated selection[END_REF].


Wijdane Kaiss
email: wijdanekaiss@gmail.com

Khalifa Mansouri
email: khmansouri@hotmail.com

Franck Poirier
email: franck.poirier@univ-ubs.fr

Personalized e-learning recommender system based on a hybrid approach

Keywords: Recommender system, Personalization, Elearning, Hybrid recommendation techniques

In recent years, the development of recommendation systems has aroused growing interest in many areas, especially in e-learning. However, the lack of support and personalization in this context leads the learners to lose their motivation to continue in the learning process. To overcome this problem, we focus on adapting learning resources to the needs of learners using a recommender system. Thus, most of the existing studies in this area don't take into account the differences in the characteristics of learners. This problem can be mitigated by incorporating additional learner information into the recommendation process. Additionally, many recommender techniques experience cold start and rating sparsity issues. This article presents our proposed recommendation system in order to provide learners with appropriate learning resources to follow the learning process and maintain their motivation. We propose hybrid recommender system that combines recommendation techniques to solve the problem of retrieving relevant learning resources for learners and that can alleviate both the cold-start and data sparsity problems. Using this hybridization between different techniques is useful in the personalization of the learner's profile. We consider different learner characteristics such as their preferences, their goal, and their level of knowledge, hence resulting in the generation of more accurate recommendations.

I. INTRODUCTION

The rapid progression of technology has affected many aspects of our lives, especially those related to education. The impact of the COVID-19 pandemic has resulted in the shift of learning from traditional school classrooms to online learning environments [START_REF] Georgia | Transition to Online Education in Schools during a SARS-CoV-2 Coronavirus (COVID-19) Pandemic in Georgia[END_REF], [START_REF] Sun | Coronavirus pushes education online[END_REF]. E-learning environments are gaining popularity in higher education, particularly for distance learning. Ideally, they provide free access and open participation to learners around the world via the Internet and other technologies [START_REF] Bylieva | Online Group Student Peer-Communication as an Element of Open Education[END_REF]. E-learning offers online courses and learning resources in various categories such as computer science, mathematics, engineering, etc. E-learning environments do not automatically detect the most suitable resources for each learner's real needs such as the type of learning objects (e.g. video, images, text, etc.), the language of teaching, what they want to learn, the need to work with peers or individually, etc. This is the common problem of search ability which corresponds to the difficulty of finding the right resources among a very large number without cognitively overloading the user [START_REF] Raj | Architecture of an Adaptive Personalized Learning Environment ( APLE ) for Content Recommendation[END_REF]. In other words, recommendations must be personalized to meet the wide diversity of learners and target the most appropriate resources for the learning domain.

However, the lack of accompaniment and personalization in this context leads learners to lose their motivation and leave the learning process which can reduce their success rate in elearning systems. Therefore, it is crucial to develop recommendation systems to help learners access the right elearning resources. In recent years, many efficient and effective recommender techniques have been considered to solve the problem of retrieving relevant learning resources for learners. The various aspects of recommender techniques are discussed below. But not each technique has the capabilities to overcome the problems of cold start, scalability and sparsity.

To overcome these problems, our paper aims to improve the performance of recommender system in e-learning in order for learners to succeed in their learning experiences, by adapting learning resources to learners' needs that change as they progress in their studies, to improve learners' satisfaction and help them achieve their goals effectively in less time and at lower cost.

In order to improve the accuracy of recommendation, we propose a hybrid recommendation technique that generally combines the best features of several recommendation techniques such as content based [START_REF] Dwivedi | Learning path recommendation based on modified variable length genetic algorithm[END_REF], collaborative filtering [START_REF] Bourkoukou | E-LEARNING PERSONALIZATION BASED ON COLLABORATIVE FILTERING AND LEARNER[END_REF], knowledge-based, context aware, group recommendation [START_REF] Rahman | A Personalised Group-Based Recommendation Approach for Web Search in E-Learning[END_REF], skill-based, ontology-based [START_REF] Tarus | Knowledge-based recommendation : a review of ontology-based recommender systems for e-learning[END_REF], case based reasoning, fuzzy-based, and many others, to provide higher performance and overcome the disadvantages of each technique. We propose a model that consists of three layers, namely a user interface, a database server and a recommendation engine.

In the following section, we will present a brief review on recommendation techniques relevant to this work, and discusses related work about e-learning recommender systems. Section 3 presents the architecture of our proposed system. Subsequently, we will describe our hybrid recommendation approach step by step in section 4. Then, we will end our article with a conclusion and a presentation of our future research work.

II. RELATED WORK

This section offers a brief overview of the recommendation techniques that are pertinent to this study as well as some related e-learning recommender system research.

A. Recommendation techniques

Recommender systems are useful for recommending relevant items to users. For generating recommendations, several techniques have been proposed and used.

Content-Based:

The system learns to recommend items that are similar in content characteristics to those the user liked in the past. The principle of the content-based recommendation is based on the calculation of the similarity of the characteristics of the items associated with the compared objects [START_REF] Dwivedi | Learning path recommendation based on modified variable length genetic algorithm[END_REF]. Content based recommenders can be classified into attribute-based technique [START_REF] Koper | Personal recommender systems for learners in lifelong learning networks : the requirements, techniques and model Hendrik Drachsler[END_REF] and case-based reasoning [START_REF] Adomavicius | Toward the Next Generation of Recommender Systems : A Survey of the State-of-the-Art and Possible Extensions[END_REF]. Case-based reasoning techniques recommend items that have the highest correlation to previous items appreciated by the learner, whereas attribute-based techniques recommend items based on the correspondence of their attributes with the learner profile [START_REF] Klašnja-Mili | Recommender systems in e-learning environments : a survey of the state-of-the-art and possible extensions[END_REF].

Collaborative filtering: This technique recommends to the active user the items that other users with similar preferences liked in the past [START_REF] Kim | Improvement of collaborative filtering using rating normalization[END_REF]. Similarity in preference of two users is calculated based on the similarity of users rating history [START_REF] Ekstrand | Collaborative Filtering Recommender Systems[END_REF]. A rating measures the degree of interest in an item by a user. The calculation of similarity between users is the principle of collaborative filtering Knowledge-based: This technique recommends items to users based on domain knowledge of how items meet user preferences [START_REF] Colombo-Mendoza | Expert Systems with Applications RecomMetz : A context-aware knowledge-based mobile recommender system for movie showtimes[END_REF]. In e-learning, knowledge-based technique aggregates knowledge about the learning resources and learners to apply them in the recommendation process [START_REF] Shishehchi | Ontological Approach in Knowledge Based Recommender System to Develop the Quality of E-learning System[END_REF].

Ontology-based:

This technique uses an ontology for knowledge representation [START_REF] Shishehchi | Ontological Approach in Knowledge Based Recommender System to Develop the Quality of E-learning System[END_REF]. In the context of e-learning domain, ontology is used to model knowledge about the learning resource and learner.

Hybrid recommender systems:

This technique combines the characteristics of two or more recommendation techniques e.g. collaborative filtering and content-based filtering systems to benefit from the strengths of each technique and to improve performance [START_REF] Ghauth | Measuring learner's performance in e-learning recommender systems[END_REF].

Demographic-based recommender systems:

This technique aims to categorize the user based on personal characteristics and give recommendations based on demographic classes such as gender, age, education, etc. [START_REF] Morisio | Hybrid Recommender Systems: A Systematic Literature Review[END_REF]. Users with common or similar personal characteristics are likely to have similar item preferences.

Context aware-based recommender systems:

This technique provides personalized services by adapting them to the user's specific contextual situation [START_REF] Adomavicius | Context-Aware Recommender Systems[END_REF]. In E-learning, a learner's contextual information can be their learning style, learning goal, prerequisite, learning progress, available learning time, device, location, etc. [START_REF] Verbert | Context-aware recommender systems for learning: A survey and future challenges[END_REF].

Group recommender system:

This technique recommends items to a group of users instead of an individual [START_REF] Garcia | Preference elicitation techniques for group recommender systems[END_REF]. It analyses a group of students' behaviors and makes recommendations. Different characteristics of the learners are used to group them together.

Skill-based models observe the similarity of skills between learners and group them according to their abilities. Both skillbased and group-based systems use content-based or collaborative techniques to recommend the learning objects after initial grouping [START_REF] Rahman | A Personalised Group-Based Recommendation Approach for Web Search in E-Learning[END_REF], [START_REF] Jagadeesan | Real-time personalization and recommendation in Adaptive Learning Management System[END_REF].

Social network-based recommender systems:

This technique uses information available in social networks to identify user preferences and generate recommendations based on information on user-profiles and relationships between users [START_REF] He | A Social Network-Based Recommender System ( SNRS )[END_REF], [START_REF] Victor | Trust and Recommendations[END_REF]. Facebook and LinkedIn are examples of social media sites using social network recommendations.

B. E-learning recommender systems

Several recommendation systems have been implemented in e-learning, most of them focus on recommending learning materials and objects. Following are some related e-learning recommendation systems.

In [START_REF] Rodríguez | Using Ontological Modeling for Multi-Agent Recommendation of Learning Objects[END_REF], the authors proposed a multi-agent learning object recommendation system based on ontological modeling. In their system, the ontology was used to represent information about learning objects and the profile of the learner according to her/his characteristics. The recommendation used learning style as the main characteristic and applied rules of inference to generate learning objects suitable for learners.

In [START_REF] Mota | OTILIA-An architecture for the recommendation of teaching-learning techniques supported by an ontological approach[END_REF], the authors proposed a knowledge-based recommendation system supported by an ontological modeling approach to help educators design teaching-learning activities.

In [START_REF] Imran | PLORS : a personalized learning object recommender system[END_REF], the authors proposed a personalized learning object recommendation system that supports learners with appropriate learning object recommendations in the course. Based on a collaborative filtering technique, the system provides learning objects that may be relevant to learners based on their previous experiences as well as learning objects visited by similar learners' profiles.

In [START_REF] Approach | Toward Recommending Learning Tasks in a Learner[END_REF], the authors proposed a rule-based recommendation system that allows learners to choose from a pool of learning activities with different levels of difficulty.

The system provides learners with recommendations on which learning activities are suitable for them, given their previous performance, the performance of neighboring learners who have similar characteristics, and activities that learners initially selected. Since information about the learner's performance is essential to provide the appropriate recommendation, the system cannot provide recommendations for the target learner in the first learning unit.

In [START_REF] Pukkhem | LORecommendNet: An Ontology-Based Representation of Learning Object Recommendation[END_REF], the ontology was used in the Learning Object Recommendation (LORecommendNet), which can be utilized to allow machines to interpret and process learning objects in a recommendation system. The learner was mapped to a personalized learning object using the ontology.

Based on the work presented above, we propose to develop a new recommender system in an e-learning context that focuses on learning resources. The choice of recommending personalized resources is due to its importance in satisfying the needs of the learners and respecting their interests, in order to engage them in the learning process.

A review of the literature in this area of study revealed that although many studies on recommending e-learning resources have been conducted using a variety of techniques, a more precise recommendation approach remains to be performed. Many recommender systems depend on one recommendation technique, our system is based on a hybrid knowledge approach that combines several techniques at the same time. The main advantage of hybridizing techniques is to take advantage of each technique's strengths while overcoming the limitations of individual techniques [START_REF] Liu | A hybrid collaborative filtering recommendation mechanism for P2P networks[END_REF]. Therefore, the hybrid approach can mitigate issues like sparsity and cold start issues that limit the performance of recommender systems. Our approach aggregates content-based, collaborative filtering, group-based, context aware-based, demographicbased, ontology-based for domain knowledge representation of the target learner in the recommendation process. Using this hybridization between these different techniques is useful in the personalization of the learner's profile. We consider different learner characteristics such as their preferences, their goal, and their level of knowledge, hence resulting in generation of more accurate recommendations.

III. E-LEARNING ENVIRONMENT RECOMMENDER SYSTEM

ARCHITECTURE

The primary goal of the proposed system is to recommend useful and interesting learning resources to learners based on their preference, their goal, and their level of knowledge in elearning. The architecture of our proposed system includes 3 main layers namely Learner Interface, Database Server, and Recommendation as shown in Fig. 1.

A. Learner Interface Layer

It is the e-learning interface with which learners interact. It takes the inputs information like their behavior information, and sends it to the Learner Activity Log Database. It is also used to visualize the proposed personalized resources filtered after the recommendation process. The module Display Recommended Resources presents recommendations to the learner.

B. Database Server Layer

This includes four databases that store: Learner Activity Log, Learner Resource Rating, Learner Model, and Domain Model. It gathers data to be used by the recommendation engine.

Learner Activity Log creates a Learner Model from the learner characteristics and creates a Learner Resource Rating after preprocessing on the data. The primary questions to addressed are: what the motivation of the learner is, what content they want to learn and how they want to learn. To answer these questions, we need to know specific learner characteristics such as their learning style, goal, and level of knowledge. The initial learner characteristics, such as learning style and goal of learning, have to be collected from the learners through questionnaires. The current level of knowledge of the learner is assessed by carrying out a preevaluation in the domain. Learning style will be initialized based on the Felder-Silverman Learning Style Model (FSLSM) [START_REF] Felder | Learning and Teaching Styles in Engineering Education[END_REF].

The learner's preference data contain implicit feedback (e.g., viewing, clicking, time spent selecting resources, etc…) and explicit ratings (e.g., like/dislike, scores 1-5, comments) on learning resources, which will be pre-treated from Learner Activity Log to perform Learner Resource Rating Database The Learner Model Database represents these various characteristics (learning style, goal, and level of knowledge) of the learners that can be used to generate an individualized learning resources, it is a collection of static and dynamic data about each learner. From an assessment of the learner's knowledge and monitor his or her changing preferences, their profile will be updated.

The Domain Model contains all the knowledge for a particular discipline. Typically, the domain model gives a domain expert's view of domain. The whole course in divided into units or concepts, all consisting on several lessons. A learning unit holds one unit of knowledge and presents different aspects of it with different types of learning object which constitutes multiple external representations such presentations, questions activities, examples, exercises, glossary [START_REF] Bachari | An adaptive teaching strategy model in e-learning using learners' preference: LearnFit framework[END_REF].

C. Recommendation Layer

It is the most important part in the learning process and constitutes the core of our proposed system. The Hybrid Recommendation Engine is the main component that generally combines the best features of several recommendation techniques to provide higher performance, which aims to generate suitable recommendations for a target learner based on learner model and domain model as well as the learner ratings on learning resources. Then, it is necessary to generate the list of the Top N Learning Resources recommendations for the target learner, and display them to the learner. The next section describes the proposed recommendation process step by step.

IV. A HYBRID RECOMMENDATION APPROACH IN E-LEARNING

Recommendation learning resources is fulfilled by following the steps which depicted in Fig. 2. Application of ontology is a key aspect for the success of our personalized recommender system. It can simplify the knowledge structuring by providing a standard based manner for knowledge representation. Ontology has some advantages encouraging us to use it in our knowledge approach. The most important advantage is usability and shareability [START_REF] Shishehchi | A proposed semantic recommendation system for e-learning: A rule and ontology based e-learning recommendation system[END_REF]. Ontology is proposed in this case to describe learner profiles and learning resources. So, it is included in our system to represent learner profile, domain model and learning resources to achieve easier knowledge sharing and reuse. Extract the knowledge about the learning resource and learner's knowledge, is the main task in knowledge based recommender system. We will use the ontology to represent all required knowledge.

A. Learner Ontology

In the proposed system, the ontological model tries to combine all the fundamental concepts between the interactive elements to provide a model that contains several parts; learner, knowledge level, personal data, learning style and domain. Learner profile is very important in adaptive elearning system. Knowledge level identifies the learner knowledge in a specified domain by carrying out a preevaluation. Personal data include all the demographic data (name, age, gender, etc.). Knowing what the learner wants to learn (which domain, specialty, prerequisite, interest) through the questionnaire. Learning styles include any of the four dimensions of the FSLSM namely visual/verbal, sequential/global, active/reflective, and sensing/intuitive [START_REF] Felder | Learning and Teaching Styles in Engineering Education[END_REF] as shown in Table I. To obtain the learner's learning style, an online questionnaire "Index of Learning Styles Questionnaire" [START_REF] Soloman | Index of Learning Styles Questionnaire[END_REF] will be administered to the learner during account registration process. Fig. 3 shows knowledge about the learner.

B. Domain Ontology

A domain model presents and describes how the information content in the e-learning is structured. The whole course in divided into units, all consisting on several concepts. Every concept has one or more learning object(s) and contains learning resources and activities such presentations, examples, questions activities, exercises. Fig. 4 shows the structure of the domain model. The learning resource ontology represents knowledge about the learning resources (see Fig. 5). Knowledge represented in this ontology include learning resource's name, domain, language, the prerequisites required to access, knowledge level which may be: beginner, intermediate and advanced, as well as learning resource format which may be text, image, audio or video, and learning activity such as lecture notes, exams and assignments. In this model, ontology has been used for personalization of learner profile as well as modeling of the learning resource ontology.

C. Learner Resource Rating Matrix

Each learner likes certain learning resources, and the rating value 𝑟 𝑙,𝐿𝑅 is the data associated with each learner l and learning resource LR. 𝑟 𝑙,𝐿𝑅 represents how much the learner l appreciates the learning resource LR. These rating values are collected automatically in the matrix, called Learner Resource Rating Matrix, in which each row 𝑙 𝑖 represents the list of rated learning resources for learner 𝑙 𝑖 , while each column 𝐿𝑅 𝑗 lists all the learners who have rated the learning resource 𝐿𝑅 𝑗 . This matrix uses a 0-to-5 rating scale where the score 0 indicates that the learning resource is not yet explicitly rated or used at all, 1 indicates that the learner is not at all satisfied with the learner resource, 3 indicates that the learner is not moderately satisfied, and finally, 5 means that the learner is strongly satisfied with the selected learning resource.

D. Computing Similarities and Predictions

Once ontology domain knowledge about the learner and learning resources as well as the learner ratings on learning resources has been preprocessed, the recommendation engine analyzes them, and the subsequent step is to group similar learners according to their learning styles, domain, and levels of knowledge in their chosen domain based on similarity computation (as shown in Fig. 7), and compute the similarities of learning resources as well as predictions for the target learner. In computing the similarities, the ratings and ontology domain knowledge are considered.

()

Where 𝑟 𝑙,LR 𝑖 denotes the rating given to learning resource i by learner l, 𝑟 𝑙 ̅ is the ontological mean rating of all the ratings provided by l. i, j ∈ {1,2,...,m}, i ≠ j. Ontological information is utilized in computing the mean rating 𝑟 𝑙 ̅ in the proposed approach.

The ontological similarity 𝑠𝑖𝑚(𝑙 𝑣 , 𝑙 𝑢 ) between two learners 𝑙 𝑣 and 𝑙 𝑢 will be calculated using Pearson Correlation Coefficient (PCC), which outperforms other similarity measurements [START_REF] Aggarwal | Recommender Systems[END_REF]. Equation ( 2) can be used to calculate the PCC between learners v and u: Where r l v ,LR i denote the rating given to LR i by the learner l v , r l v ̅̅̅ is the mean rating of all the ratings provided by learner l v , u and v ∈ {1, 2,...,n}, u ≠ v.

2) Making Prediction

Once we obtain the set of k most similar learners (knearest neighbors) and the k most similar resources using respectively the PCC similarity and Adjusted Cosine Similarity, the next step is to compute predictions of unknown ratings for the target learner. In the case of insufficient ratings, the principle is to predict the rating 𝑟 𝑙 𝑘 ,𝐿𝑅 ℎ providing by target learner 𝑙 𝑘 for a 𝐿𝑅 ℎ (k-nearest neighbors) using the rating given to 𝐿𝑅 ℎ by other similar learners (nearest neighbors) obtained by [START_REF] Sun | Coronavirus pushes education online[END_REF]. The predicted ratings are computed from the k most similar resources (k-nearest neighbors) obtained by (1) that they are rating by similar learners to 𝑙 𝑘 (those who belong to the same group), and the ratings given on it by the target learner. To compute the predictions of ratings, we use the following prediction [START_REF] Bylieva | Online Group Student Peer-Communication as an Element of Open Education[END_REF].

𝑃𝑟𝑒𝑑 𝑙 𝑘 ,𝐿𝑅 𝑖 = ∑(𝑠𝑖𝑚(𝐿𝑅 𝑖 ,𝐿𝑅 ℎ )×𝑟 𝑙 𝑘 ,𝐿𝑅 ℎ ) ∑(|𝑠𝑖𝑚(𝐿𝑅 𝑖 ,𝐿𝑅 ℎ )|) ()
Where Pred l k ,LR i is the predicted rating for unrated resource LR i by the target learner l k , sim(LR i , LR h ) is the similarity between two resources LR i and LR h , and r l k ,LR h is the rating of resource LR h (the neighbors) by the target learner l k .

E. Generating list of recommended learning resources

After creating ontology to represent knowledge semantically about the learner and learning resources, and grouping together the learners using these ontologies (according to their preferred domain, their level of knowledge, and their learning style), and computing the similarities, and after predicting all unknown resources rating in a Learner-Resource matrix, it is necessary to generate recommendations list (top N) for the target learner. It consists of eliminating all resources that do not match the learner's preference and need, like language, knowledge level. The following algorithm shows how generate a list of the top N recommendations. Calculate ontological similarity 𝑠𝑖𝑚(𝑜 𝑙 𝑘 , 𝑜 𝑙 𝑠 ) using () endfor foreach unknown ratings of the target learner:

Algorithm: Generate a list of the top N recommendations

Predict ratings 𝑃𝑟𝑒𝑑 𝑙 𝑘 ,𝐿𝑅 𝑖 using () endfor Filter learning resources according to learner profile return top N recommendation list for target learner 𝑙 𝑘 V. CONCLUSION AND FUTURE WORK Recommender systems play an important role in today's e-learning field. In this article, we have presented the architecture of our proposed system which includes 3 main layers namely Learner Interface, Database Server, and Recommendation, and we have presented a hybrid recommendation technique that generally combines the best features of several recommendation techniques to recommend the most appropriate learning resources to learners based on their knowledge level, their preferred domain, and their learning style. The ultimate goal is to improve the performance of recommender system in e-learning in order for learners to succeed and to improve their learning experience, by adapting learning resources to learners' needs that change as they progress in their studies, to improve learners' satisfaction, maintain learner's motivation, and help them achieve their goals effectively in less time and at lower cost. For our future work, we will implement our recommender system and integrate it into a learning platform. Then, we will evaluate it as an adaptive application that personalizes resources for learners with different profiles who participate in e-learning systems to show that our proposed hybrid approach can obtain better performance and accuracy than the other.

Fig. 1 .

 1 Fig. 1. Recommender system architecture of learning resources in the context of e-learning

Fig. 2 .

 2 Fig. 2. Hybrid recommendation model for e-learning

Fig. 3 .

 3 Fig. 3. The learner model ontology

Fig. 4 .

 4 Fig.4. Hierarchical organization of the domain model[START_REF] Bourkoukou | E-LEARNING PERSONALIZATION BASED ON COLLABORATIVE FILTERING AND LEARNER[END_REF]

Fig. 5 .

 5 Fig. 5. The learning resource ontology

Fig. 6 indicates

 6 Fig. 6 indicates Learner-Resource rating Matrix with n rows and m columns, where n denotes the number of learners L = {l 1 , l 2 , … , l n }, and m denotes the number of learning resources LR = {LR 1 , LR 2 , … , LR m }.

Fig. 6 .

 6 Fig. 6. Learner-Resource rating Matrix

Fig. 7 .

 7 Fig. 7. Grouping of learners according to their preferred domain, their level of knowledge, and their learning style1) Computing similaritiesWe will use Adjusted Cosine Similarity[START_REF] Ricci | Introduction to Recommender Systems Handbook[END_REF] to calculate ontological similarities. The following formula (1) will be used to calculate ontological similarity 𝑖 , 𝐿𝑅 𝑗 ) between two learning resources i and j:

  𝑠𝑖𝑚(𝑙 𝑣 , 𝑙 𝑢 ) = ∑(𝑟 𝑙 𝑣 ,𝐿𝑅 𝑖 -𝑟 𝑙 𝑣 ̅̅̅̅)(𝑟 𝑙 𝑢 ,𝐿𝑅 𝑖 -𝑟 𝑙 𝑢 ̅̅̅̅) √∑(𝑟 𝑙 𝑣 ,𝐿𝑅 𝑖 -𝑟 𝑙 𝑣 ̅̅̅̅) 2 √∑(𝑟 𝑙 𝑢 ,𝐿𝑅 𝑖 -

  Set of learning resources 𝐿𝑅 = {𝐿𝑅 1 , 𝐿𝑅 2 , … , 𝐿𝑅 𝑚 } Set of learners 𝐿 = {𝑙 1 , 𝑙 2 , … , 𝑙 𝑛 } Ontological knowledge 𝑂 = {𝐿𝑒𝑎𝑟𝑛𝑒𝑟, 𝐿𝑒𝑎𝑟𝑛𝑖𝑛𝑔 𝑅𝑒𝑠𝑜𝑢𝑟𝑐𝑒} Learner-Resource Rating 𝑅 = {𝑟 𝑙 1 𝐿𝑅 1 , 𝑟 𝑙 1 𝐿𝑅 2 , … , 𝑟 𝑙 𝑛 𝐿𝑅 𝑚 } Where 𝑅 ∈ {1,2,3,4,5} Output: Generate Top N recommendation List Method: foreach 𝐿𝑅 𝑖 ∈ 𝐿𝑅 , 𝑜 ∈ 𝑂, do: Calculate ontological similarity 𝑠𝑖𝑚(𝑜 𝐿𝑅 𝑖 , 𝑜 𝐿𝑅 𝑗 ) using () endfor foreach 𝑙 𝑘 ∈ 𝐿 , 𝑜 ∈ 𝑂, do:

ACKNOWLEDGMENT

The authors would like to their gratitude to the editors and referees committee of the IEEE Global Engineering Education Conference for their constructive comments and valuable feedback on this work.