Yassine Safsouf
email: yassine.safsouf@isga.ma

Khalifa Mansouri
email: khmansouri@hotmail.com

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

Understand the influence of learning analytics dashboards on learner self-regulation and academic success

Keywords: Learning analytics, Learning experience, Selfregulated dashboards

Since the beginning of the COVID-19 pandemic, many countries have adopted online education as an alternative to face-to-face courses. This has increased awareness of the importance of analyzing learning data left by students to improve and evaluate the learning process. This article presents a new tool, named TaBAT, created to work with different LMSs in the form of dashboards accessible online and allowing teachers to monitor the progress of their learners and at the same time and allow teachers to track the progress of their learners, while allowing learners to develop self-regulation skills and visualize their learning process. The results of a study conducted show that TaBAT helped learners to increase their progress and spend more time in the online course.

I. INTRODUCTION

Learning analytics (LA) is a discipline that aims at exploiting the hidden potential of interaction data generated by the use of learning management systems (LMS) [START_REF] Ferguson | Learning analytics: Drivers, developments and challenges[END_REF]. Its main challenges are to collect learner interaction traces, to analyze them and to propose a display of the analysis results to different users [START_REF] Labarthe | L'analytique des apprentissages numeriques[END_REF]. According to Sclater, the goal of learning analytics is to analyze the digital traces left by learners in order to better understand them and optimize learning [START_REF] Sclater | Learning Analytics Explained[END_REF].

Learning analytics focuses on the detection, collection, analysis and exploitation of digital traces left by learners in their daily activities, in order to understand and optimize learning and environments in which it occurs [START_REF] Siemens | Learning analytics special issue[END_REF]. However, the diversity of existing LMS complicates the task of analyzing this data, which is further amplified by the need to combine data from a variety of sources. The main challenge would be to have a system to analyze learning data in such a way that the precise meaning of the data is easily accessible and could be translated into an understandable format regardless of the LMS or technological environment used.

In this paper, we propose an interpretable visual communication tool, designed as a dashboard for teachers and learners that provides an analysis of learning data to facilitate the monitoring and control of the learning process, with the aim of improving the engagement and success rate of online learners.

In the rest of the paper, we present a literature review in the influence of self-regulated learning theory and learning analytics on online learners' success. Then we share the reports of our tool created in the form of learning trace analysis dashboards. The next section is dedicated to the methodology, data analysis of our tool usage and discussions of these results. Finally, we present a conclusion with some perspectives.

II. RELATED WORK

A. Self-regulated learning theory

Self-regulated learning theory (SRL) defines learning as a dynamic process in which the individual plans, monitors and evaluates his or her learning, applying appropriate strategies to achieve the goals [START_REF] Zimmerman | Self-Regulation, Where Metacognition and Motivation Intersect[END_REF]. It is a set of activities that individuals do by themselves in a proactive way [START_REF] Zimmerman | From Cognitive Modeling to Self-Regulation: A Social Cognitive Career Path[END_REF]. Panadero published an article that presents a review of the six most popular selfregulated learning models [START_REF] Panadero | A Review of Self-regulated Learning: Six Models and Four Directions for Research[END_REF], the article concludes that, most of these models are composed of three essential phases, namely, the preparation phase, the performance phase and the reflection phase. As presented in the model of phases and subprocesses of self-regulation by Zimmerman and Campillo [START_REF] Zimmerman | Motivating Self-Regulated Problem Solvers[END_REF], the preparation phase includes task analysis, planning, goal detection, and goal achievement; the performance phase involves the performance of the actual task completed while monitoring and controlling progress; and the final reflection phase, where the learner self-assesses, reacts, and adapts for future performance.

Many studies agree on the relevance of self-regulated learning as a predictor of academic success in online learning systems. Liaw and Huang investigated learner self-regulation to better understand learners' attitudes toward online learning [START_REF] Liaw | Perceived satisfaction, perceived usefulness and interactive learning environments as predictors to selfregulation in e-learning environments[END_REF]. The results show that the factors perceived satisfaction, perceived usefulness, and interactive learning environments were identified as predictors of perceived self-regulation in the online learning context. In a study on formal and informal learning using social media, the authors showed that the use of social media as pedagogical means, to encourage students to control their autonomies [START_REF] Matzat | Self-regulated learning and social media -a 'natural alliance'? Evidence on students' self-regulation of learning, social media use, and student-teacher relationship[END_REF].

B. Learning analytics dashboards

One of the most common methods of learning analytics is the use of dashboards as a way to provide stakeholders (mainly teachers and learners) with visual interpretations to give them an overview of the learning process [START_REF] Verbert | Learning Analytics Dashboard Applications[END_REF]. Schwendimann defined these tools as a set of single displays that aggregate many indicators about the learning process and/or context into one or more visualizations [START_REF] Schwendimann | Understanding learning at a glance: An overview of learning dashboard studies[END_REF]. These dashboards are generally steering tools that summarize the company's activities and results by process; thus, allowing to supervise the achievement of any set objective [START_REF] Fernandez | Les tableaux de bord du manager innovant: Une démarche en 7 étapes pour faciliter la prise de décision en équipe (Management)[END_REF].

Jivet and colleagues, proposed a literature review to better understand and describe the theoretical underpinnings behind the use of dashboards in educational settings. The study revealed that the most common foundation for the design of analytic dashboards is SRL. This theory is primarily used in the awareness and triggering of reflection, providing some support for the performance and self-reflection phases of the SRL cycle. In research conducted by Nicholas and colleagues to see how dashboards would be able to predict student outcomes at different points in a course. The study shows that learner outcomes can be predicted with a supervised machine learning algorithm. These predictions were integrated into an instructor dashboard that facilitates decision making for learners classified as needing assistance [START_REF] Nicholas | An instructor dashboard for real-time analytics in interactive programming assignments[END_REF].

In this paper we propose the development of a tool able to analyze learning data in a way that provides precise and meaningful dashboards for teachers and learners. We named it TaBAT (for Tableau de Bord d'Analyse des Traces d'apprentissage in French).

III. TABAT TOOL DESCRIPTION

LMS platforms provide a variety of integrated reports based on journal data but they are primarily descriptive. They tell participants what happened but not why and they do not predict outcomes or advise students on how to improve their academic performance. These tools are mostly programmed to work with a single platform.

Created to work with different online platforms, TaBAT is designed as a dashboard accessible online via the following link https://safsouf.net/tabat. It allows us to see what happened during the online course (descriptive aspect), to see which students will or will not succeed in the online course (predictive aspect), to know why students were declared as dropouts (diagnostic aspect) and finally to get information on the actions to be taken to improve students' progress and success in the online course (proactive aspect).

TaBAT presents reports in various diagrams (based on the learning traces generated from the LMS platform in JSON files to ensure interoperability). Two independent views are presented: the student report and the teacher report.

A. Report for the Teacher

The report for the teacher (showed in Figure 1) presents statistical data during the online course. The first page (1) includes the number of students enrolled, the number of sections, activities and resources in the course, the number of students who actively participate in the course, statistics on monthly connections for the current year, as well as statistics on the number of times students consult the activities and resources. The quiz analysis page (2) provides a table that shows, for each student, the list of quizzes taken or not taken, the number of questions answered, the total number of questions, the final score obtained as a percentage, and the time recorded for taking the test.

The assignment analysis page (3) provides a summary of the assignments that may (on time or late) or may not be returned by students.

The dropout page (4) presents a table that displays the list of students with an estimation of the overall time spent on the course, an indicator representing the level of success (based on the results of our theoretical model called e-LSAM (for elearner Success Assessment Model) [START_REF] Safsouf | An analysis to understand the online learners' success in public higher education in morocco[END_REF], [START_REF] Safsouf | A new model of learner experience in online learning environments[END_REF]) and finally a prediction status. This status indicates the result of the prediction either: risk of dropping out, minimal risk or success. A color coding allows to visually differentiate if the assignment is submitted or not, if the quizzes are done or not and the risk of dropping out or not.

B. Report for the Student

The report for the student gives an overall view of each student's progress in the course. The three available interfaces are shown in Figure 2. The first interface (1) gives a positioning of the student's progression level for each section of the course with two other levels: the level of progression of the best student and the level of the average student in the class. It also displays a ranking table of all learners in the class. This interface aims to motivate and support students' metacognition and self-regulation processes.

For the second interface (2), the student can see the details of his/her progress in the course. A chart presented in the form of a vertical progress bar summarizes the student's progress for each section of the course. This interface displays the details of the student's progress in each section.

The last interface (3) is the notification interface. Here the student can view the list of notifications (marked as unread) sent automatically by the system. Notifications are displayed by type, with a message indicating the actions to be taken. A script is scheduled to send notifications automatically twice a day; at 08:00 in the morning and again at 08:00 in the evening.

If the same notification has already been sent and has not been read yet, the sending is not done.

IV. METHODOLOGY AND DATA ANALYSIS

This study aims to test TaBAT and evaluate its impact on self-regulation and prediction of success of two classes of the Higher Institute of Engineering and Business in Morocco. We present here a study based on a quantitative approach, with the aim to present the results obtained after a feedback on the use of the TaBAT tool. The methodology and the results analysis are presented below.

A. Methodology of Study

This study is conducted on a population of 25 students all enrolled in the first year, all of whom take a course entitled "Object Oriented design" over a period of 14 weeks, organized in a blended learning modality on the Moodle 3.8 platform. The course is finalized by a supervised face-to-face exam. In order to respect the sanitary protocol, put in place during the COVID-19 pandemic, the institute has limited the number of students from 10 to 14 per group.

The class is divided into two homogeneous groups, composed of 13 and 12 students randomly. The first group was informed about the experiment to use TaBAT to analyze learning traces (called exposed group), while the second group did not have access (called control group). Table1 summarizes the demographic profile of participants.

B. Data Analysis and Results

The online part of course is composed of 9 sections, with 7 lessons, 3 files to download, 5 URL links to visit, and 2 assignments due on scheduled dates. The analysis of the activity of the TaBAT tool dashboards via the teacher report. Table 2 describes the result of study.

We first note that all students in the first class groups logged into the online course. The second observation concerns the total time spent doing the online course activities. This time is represented in Table 2, cumulated for each group. Students in the exposed group spent more than twice as much time as those in the control group doing the online course. The third observation concerns the performance of both groups, which is represented by the average progress score in the online course. The average obtained of the exposed group is significantly higher than that of the control group.

The fourth observation concerns the analysis of assignment completion. The exposed group had a 100% assignment return rate (returned on time with those returned late), while for the control group, the same rate was 45.83%. The final point concerns student success. In this study, the level of success calculated by the TaBAT is compared to the level of success obtained after the terminal exam. Table 2 shows that TaBAT was able to predict the totality of the success of the learners in the exposed and control groups. This result demonstrates the effectiveness of the success algorithm, based on our theoretical e-LSAM model to predict learners' success early before the end of the online course.

C. Discussion of Study Results

The strong increase in participation of the exposed group in our study gives positive feedback to the TaBAT tool, reflecting the contribution of this tool in helping learners resist distractions, regulate their learning, and monitor their performance. The increase in participation is mainly explained by the proactive actions carried out manually by the teacher or sent automatically by the TaBAT tool, in order to remind learners (through notifications) if they have resources not to consult (file to download or URL to visit) or activities not to carry out (lesson, homework, quiz to do). Not to mention the important role of the learner's report that allows them to selfevaluate and follow meta-cognitive strategies to improve their online performance.

In addition to increased participation and progress in the online course, the number of assignments submitted also increased for the group exposed to the use of the TaBAT tool. This increase is primarily due to the notifications sent automatically by the tool when an assignment is due. These proactive actions allowed learners to remember the due date and have a higher submission rate than the control group.

For predicting learner success, the TaBAT tool was found to be very effective for this role. The results of the study demonstrate the tool's ability to predict learner success online for both groups, compared to their actual success in a classroom situation (after face-to-face testing). These results also show that student performance and success is due in part to their ability to provide effective work at home, better preparing them for in-class exams.

The teacher reported that TaBAT helped him track the participation and progress of students participating in the experiment. Indeed, the dashboards provide the teacher with a comprehensive view of learner activities that allows him/her to monitor learners' progress, consult homework and quiz results, view predictive states (academic success, low or high risk of failure), as well as contact learners directly or schedule automatic reminder notifications to alert them when needed.

V. CONCLUSION AND PERSPECTIVES

The The design, development and and implementation of the TaBAT learning outcomes analysis tool represents the completion of our modeling work, which would identify factors in an attempt to reduce the dropout rate of learners, and at the same time to improve their success in online courses. We proposed in this paper a study to test the effectiveness of the tool in the analysis of learning traces in online courses planned by an engineering school in Morocco. The results of this study confirmed that the use of TaBAT increased the learners' performance, improved their autonomy, and finally improved their academic success.

In our future work we would like to extend the use of TaBAT to other online courses (of different fields and specialties), in order to generalize our experience and to see the impact of the tool on the performance and the real success of learners.

Fig. 1 .

 1 Fig. 1. Dashboards summarizing the report for the teacher.

Fig. 2 .

 2 Fig. 2. Dashboards summarizing the report for the student.

TABLE I .

 I DEMOGRAPHIC PROFILE OF PARTICIPANTS

		Exposed	Control
		group	group
	Male	9	10
	Gender


Estelle Barbot
email: estelle.barbot@protonmail.com

Mathilde Dufaÿ

Isabelle De Cauwer

Sex-specific selection patterns in a dioecious insect-pollinated plant Running title: Sex-specific selection in a dioecious plant

Keywords:

Competition for mate acquisition is the hallmark of any sexual organism. In insect-pollinated plants, competition to attract pollinators is expected to result in pollinator-mediated selection on attractive floral traits. This could overlap with sexual selection if the number of mating partners increases with pollinator attraction, resulting in an improved reproductive success.

In this study, we measured a set of floral traits and estimated individual fitness in male and female Silene dioica in an experimental population. Results align with the predictions of Bateman's principles, in the absence of pollen limitation. In females, natural selection acted on traits that are typically linked with fertility (number of flowers and number of gametes), and selection strength was similar in open-and hand-pollinated females, suggesting a limited role of pollinator-mediated selection. In males, flowering duration and corolla width were positively associated with both reproductive success and number of mates, suggesting that sexual selection has played a role in the evolution of these traits. The use of Bateman's metrics further confirmed stronger sexual selection in males than in females. Taken together, our results shed light on the occurrence of sex-specific patterns of selection in an insectpollinated plant population.

Introduction

Sexual selection (selection arising from competition for mating partners and/or their gametes), along with viability selection (selection for traits that increase survival) and fertility selection (selection for traits that increase the number of offspring per reproductive episode, e.g. via gamete production), constitute the three routes through which natural selection shapes phenotypic traits (Arnold 1994a;[START_REF] Delph | Sexual, fecundity, and viability selection on flower size and number in a sexually dimorphic plant[END_REF]. In animals, precopulatory sexual selection has often been proposed as the ultimate cause for the evolution of extravagant phenotypes in males, in a large array of traits including ornaments, armaments and behaviors [START_REF] Darwin | The descent of man, and selection in relation to sex[END_REF][START_REF] Lande | Models of speciation by sexual selection on polygenic traits[END_REF][START_REF] Jennions | Sexual selection. Evolutionary behavioral ecology[END_REF]. In this matter, Bateman's principles predict that the sex experimenting the stronger sexual selection should display three features. First, it should have the highest variance in reproductive success (i.e. the opportunity for selection , measured as the variance in offspring number).

Second, it should display the highest variance in mating success (i.e. the opportunity for sexual selection , measured as the variance in the number of reproductive partners). Finally, it should exhibit the strongest dependency of reproductive success on mating success (i.e. the Bateman gradient, which quantifies the reproductive benefit of acquiring more mates by regressing reproductive success on mating success, [START_REF] Bateman | Intra-sexual selection in Drosophila[END_REF]Arnold 1994a). Using metrics of sexual selection [START_REF] Jones | On the opportunity for sexual selection, the Bateman gradient and the maximum intensity of sexual selection[END_REF]), a recent meta-analysis on animal species showed that sexual selection is often stronger in males than in females [START_REF] Janicke | Darwinian sex roles confirmed across the animal kingdom[END_REF], which is generally interpreted as a direct consequence of anisogamy [START_REF] Bateman | Intra-sexual selection in Drosophila[END_REF].

Although animal species with sexual dimorphism in secondary sexual characters have been the primary focus of sexual selection theory, there is now a wide acceptance that sexual selection should occur in plants as well (Arnold 1994b;[START_REF] Delph | Trait selection in flowering plants: how does sexual selection contribute?[END_REF][START_REF] Moore | Sexual selection in plants[END_REF]. In plants, competition for access to reproductive partners is expected to take place both before pollination (e.g. male-male competition for access to stigmas or femalefemale competition for pollen delivery; [START_REF] Minnaar | Plant-pollinator interactions along the pathway to paternity[END_REF]) and after pollination (e.g. pollen competition for access to ovules; [START_REF] Murphy | Interaction-independent sexual selection and the mechanisms of sexual selection[END_REF][START_REF] Moore | Sexual selection in plants[END_REF]. Any plant trait that would impact the outcome of competition for mates should thus be under sexual selection.

Because a wide majority of angiosperms rely on insects for mate acquisition [START_REF] Ollerton | How many flowering plants are pollinated by animals?[END_REF], some of the traits under sexual selection in plants are likely to be directly involved in pollinator attraction, but not necessarily all of them (e.g. some traits can be involved in postpollination sexual selection with no link to pollinator attraction, [START_REF] Tonnabel | The scope for postmating sexual selection in plants[END_REF].

Selection on attractive floral traits, arising from competition among plants for pollinators, is usually referred to as pollinator-mediated selection and this should thus at least partially overlap with sexual selection [START_REF] Willson | Sexual selection in plants: perspective and overview[END_REF][START_REF] Delph | Trait selection in flowering plants: how does sexual selection contribute?[END_REF][START_REF] Waelti | How to be an attractive male: floral dimorphism and attractiveness to pollinators in a dioecious plant[END_REF][START_REF] Dai | Sexual selection in a hermaphroditic plant through female reproductive success[END_REF][START_REF] Paterno | The maleness of larger angiosperm flowers[END_REF].

If one applies the framework of sexual selection to animal-pollinated plants, male reproductive success should be more dependent on pollinator attraction than female reproductive success, at least in situations where female reproduction is not limited by pollen availability [START_REF] Stephenson | Male competition, female choice and sexual selection in plants[END_REF]. First, plants are anisogamous organisms, and male reproductive success should thus be more limited by mate acquisition than female reproductive success, as is the case in animals without reversed sex-roles [START_REF] Bateman | Intra-sexual selection in Drosophila[END_REF][START_REF] Willson | Mate choice in plants: tactics, mechanisms and consequence[END_REF][START_REF] Janicke | Darwinian sex roles confirmed across the animal kingdom[END_REF]. Second, a recent study demonstrated that, across hermaphroditic angiosperms, the allometric relationship between flower biomass and sexual organ biomass was steeper for the male than for the female organs, a result that can be explained by a widespread role of male-male competition in the evolution of floral morphology [START_REF] Paterno | The maleness of larger angiosperm flowers[END_REF]. Third, selection on floral traits has been documented to be stronger through male than female function in some hermaphroditic species. This is not a general trend and it may depend on the availability of pollinators (see below) but when selection seems stronger through male function, this may be because these traits promote pollinator attraction, although sexual selection was not directly measured in these studies (e.g. [START_REF] Hodgins | Natural selection on floral traits through male and female function in wild populations of the heterostylous daffodil Narcissus triandrus[END_REF] for corolla width; Briscoe Runquist et al. 2017 for petal area).

These observations thus seem consistent with sexual selection occurring in males, and potentially being stronger than in females, as observed in the animal kingdom [START_REF] Janicke | Darwinian sex roles confirmed across the animal kingdom[END_REF]. Nonetheless, contrary to what is typically seen in female animals, which are rarely sperm limited provided they acquire at least one mating partner (with the exception of animals with external fertilization; Levitan & Petersen 1995), female reproductive success is often pollen limited in angiosperms [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]. This means that both sexual functions can be limited in their access to reproductive partners and that both sexual functions can display a positive Bateman gradient. In other words, under pollen limitation, pollinator-mediated selection should shape attractive traits through both sexual functions in hermaphroditic species, or in both sexes in dioecious species [START_REF] Burd | Bateman's principle and plant reproduction: the role of pollen limitation in fruit and seed set[END_REF]. On the contrary in the absence of pollen limitation, one could expect that attractive traits would be under stronger selection through the male function, or in males in dioecious species (Arnold 1994a).

From the female perspective, one way to estimate the strength of pollinator-mediated selection is to use pollen supplementations: by comparing selection gradients on floral traits in open-pollinated versus hand-pollinated females, one can assess the magnitude of pollinator-mediated selection on these traits [START_REF] Sletvold | Pollinator-mediated selection on floral display and spur length in the orchid Gymnadenia conopsea[END_REF][START_REF] Trunschke | Interaction intensity and pollinator-mediated selection[END_REF].

However, because these methods focus on the female reproductive success, they do not allow any comparison between male and female reproductive functions [START_REF] Barrett | The ecology of mating and its evolutionary consequences in seed plants[END_REF]. One solution to compare sexes would be to estimate the access to reproduction through a measurement of the number of different genetic sexual partners [START_REF] Tomaszewski | Mating consequences of contrasting hermaphroditic plant sexual systems[END_REF], an approach that is commonly used in animal studies. Although the number of genetic sexual partners may underestimate the actual number of mates, because it depends on both access to mates and post-fertilization processes (cryptic female choice and competition among male gametes; [START_REF] Anthes | Measuring and interpreting sexual selection metrics: evaluation and guidelines[END_REF], this estimate has the clear advantage of providing an equivalent measurement of mating success in both males and females. Only two studies estimated the Bateman gradient using the number of genetic sexual partners in angiosperm species and both found that while mating and reproductive success were independent in females, they were strongly positively correlated in males [START_REF] Tonnabel | Do metrics of sexual selection conform to Bateman's principles in a wind-pollinated plant?[END_REF][START_REF] Kwok | Sexual selection on male but not female function in monoecious and dioecious populations of broadleaf arrowhead (Sagittaria latifolia)[END_REF]. Noteworthily, this measurement might not perfectly reflect the number of mating opportunities in plants, in particular in animal-pollinated taxa. Indeed, because each flower constitutes a reproductive tract, mating events can be quite independent among flowers, depending on pollinators' visitation sequences. One could thus expect the number of genetic mating partners to increase with the number of flowers (and thus with the number of ovules for the female function or the number of pollen grains for the male function) and to be an indirect by-product of individual fertility. In such a context, it becomes difficult to distinguish between sexual and fertility selection, a situation which has been referred to as "the grey zone of sexual selection" by [START_REF] Alonzo | Grey zones of sexual selection: why is finding a modern definition so hard[END_REF]. By correcting mating success estimates by individual fertility, one should be able to compare the strength of sexual selection between males and females while minimizing this bias [START_REF] Henshaw | How to quantify (the response to) sexual selection on traits[END_REF].

In this study, we measured a set of floral traits and estimated male and female reproductive success in an experimental population of the dioecious insect-pollinated species Silene dioica. Our objectives were fourfold. First, by regressing reproductive success on floral phenotypes in both sexes, we explored sex-specific patterns of natural selection during one flowering season. In our study, this includes both sexual and fertility selection, but not viability selection since no deaths were observed. Second, by comparing the relationship between reproductive success and floral phenotypes between open-pollinated and handpollinated females, we quantified the relative importance of pollinator-mediated selection in females. Third, we quantified the importance of floral phenotypes for mate acquisition in both sexes by regressing genetic mating success (i.e. the number of genetic mating partners) on floral phenotypes in males and females. In females, this allowed us to compare patterns of pollinator-mediated selection (objective 2) and sexual selection (objective 3), a useful approach to determine whether sexual selection arises from competition to attract pollinators or not. Finally, overall sexual selection was compared between sexes using the metrics derived from Bateman's principles: the opportunity for selection I, the opportunity for sexual selection I S , and a partial Bateman gradient (regression of reproductive success on mating success controlling for flower and gamete production). Studying sexual selection in plants combining several approaches will provide an integrative framework to understand how sexual selection on floral traits parallels with other selection components in plants.

Material and methods

Study system

Silene dioica (L.) Clairv. is a herbaceous short-lived perennial species of the Caryophyllaceae family that is widely distributed throughout most of 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]. It is a dioecious species with XY sex determination [START_REF] Warmke | Sex determination and sex balance in Melandrium[END_REF][START_REF] Ming | Sex chromosomes in land plants[END_REF]). The species flowers during late spring, but is known to sometimes exhibit a second flowering peak at the end of summer [START_REF] Jürgens | Reproduction and pollination in Central European populations of Silene and Saponaria species[END_REF][START_REF] Bopp | Importance of Silene latifolia ssp. alba and S. dioica (Caryophyllaceae) as host plants of the parasitic pollinator Hadena bicruris (Lepidoptera, Noctuidae)[END_REF]. In Lille (France), this second peak is generally brief and presents extremely male-biased sex ratios, so most of the reproduction effectively occurs during the first peak, between end-April and mid-July (pers. obs). This species presents a generalist insect-pollinated system, with Bombus species, Syrphidae, diurnal butterflies and Sphingidae as 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]. Silene dioica has been documented as sexually dimorphic for flower size and number (males > females; [START_REF] Kay | Differences between sexes in floral morphology, nectar production and insect visits in a dioecious species, Silene dioica[END_REF][START_REF] Baena-Díaz | Insights into the genetic architecture of sexual dimorphism from an interspecific cross between two diverging Silene (Caryophyllaceae) species[END_REF][START_REF] Moquet | Temporal dynamics of sexual dimorphism in a dioecious species[END_REF], total nectar production at the flower level (females > males; [START_REF] Hemborg | Different rewards in female and male flowers can explain the evolution of sexual dimorphism in plants[END_REF] and flowering duration (males > females; [START_REF] Hemborg | Seasonal dynamics in reproduction of first-year females and males in Silene dioica[END_REF].

Experimental population

Experimental plants were derived from seeds harvested in three forests during 2015, 2016 and 2017 (site A 50°12'05.4''N 3°44'95.7''E, site B 50°26'06.0''N 3°18'39.5''E and site C 50°23'19.3''N 3°25'24.9''E). Our experimental population thus included three cohorts (one, two and three-year-old plants). Sampling sites were geographically close to each other (i.e. maximum distance of 40 km between sites) and to our experimental garden (< 65 km). Seeds were collected at different study sites to reach a sufficient sample size while minimizing the probability of including half or full-sibs. Plants from all three populations and from all cohorts were repotted every year in new potting mix and kept in the exact same conditions in the greenhouse until the experiment.

Experimental design

Three groups of plants were established in the same common garden. The three source forests and the three cohorts were evenly distributed among these groups. The two first groups were open-pollinated females (OP females hereafter, 98 individuals) and openpollinated males (OP males, 102 individuals) that were left to be naturally pollinated by insects present in the experimental garden. In the third group, composed of hand-pollinated females (HP females, 65 individuals), all open flowers were supplemented three times a week with pollen from a pool of 65 males from the same collection that were kept in a greenhouse. For a given HP female and a given supplementation day, dehiscent anthers were collected on two randomly selected pollen donors and were brushed on the stigmas.

Common garden

The experimental population was set up in a common garden in April 2018 on the campus of Lille University in France (50°36'32.5''N 3°08'40.3''E) during spring 2018. No wild populations of Silene dioica were growing in the vicinity. All individuals were in separate 0.7-L pots filled with a standard soil mixture. Plants were watered every other day, or every day on the hottest days. OP and HP plants were placed separately in two experimental plots 1.5 meter away from each other. Because of inter-individual variance in flowering phenology, the density of flowering plants changed across time (from 2 to 12 individuals per m 2 ). OP females and males were spatially alternated following a grid pattern. Each week, the spatial position of individuals within each plot was randomized while keeping the malefemale alternation.

Plant traits

A total of 18 traits were measured on all plants from the three experimental groups. A summary of the number of observations per trait and experimental group is available in appendix (Table S3). Number of gametes per flower -In females, the number of ovules per flower was estimated at the end of the survey, by dissecting a subsample of fruits per plant. Fruits were collected at maturity, typically two to three weeks after flower opening. At the end of the flowering season, 1004 fruits (one fifth of total fruit production) were randomly chosen and dissected to estimate ovule and seed production for each female (6 to 44 fruit per female, with the number reflecting the females' contribution to the overall fruit production at the population level). Unfertilized ovules and seeds were counted by imaging the fruit content using a high resolution scanner (Epson Perfection V700 Photo, Seiko Epson, Suwa, Japan) and using digital image processing (EBImage package in R; [START_REF] Pau | EBImage -an R package for image processing with applications to cellular phenotypes[END_REF]. Unfertilized ovules and seeds were distinguished on the basis of size (0.062 ± 0.031 mm² for unfertilized ovules versus 0.86 ± 0.12 mm² for seeds). The number of unfertilized ovules and seeds were then summed within each fruit and averaged over all fruits imaged for each OP and HP female, yielding an estimate of female gamete production per flower.

In males, the number of viable pollen grains per flower was assessed on one nearly open bud at the flowering peak. This measurement involved multiplying the proportion of viable pollen grains by the pollen quantity per flower. To do so, each bud was dissected to keep three of the ten anthers. Pollen was removed from the first one and placed on a glass slide with one drop of staining solution to assess the proportion of viable pollen grains under x100 microscope [START_REF] Peterson | A simplified method for differential staining of aborted and non-aborted pollen grains[END_REF]. The two remaining anthers were used to estimate pollen quantity per flower using a particle counter (CASY® Model TT, Roche Innovatis AG, Bielefeld, Germany) and following the protocol described in [START_REF] Dufaÿ | Variation in pollen production and pollen viability in natural populations of gynodioecious Beta vulgaris ssp. maritima : evidence for a cost of restoration of male function?[END_REF].

Floral traits -The remaining 15 traits fall in three categories: (i) non-destructive measurements, performed weekly, (ii) measurements involving the removal and dissection of a flower that were only conducted once, at the flowering peak and (iii) measurements performed at the end of the flowering season.

Weekly measurements -Daily flower display, stem number (i.e. number of branches with at least one open flower), height of the highest open flower (cm), as well as corolla width (mm) and calyx height (mm, measured on two randomly chosen flowers using a digital calliper precise to 0.01 mm and averaged), were surveyed once a week. All the weekly measured traits showed higher variation among than within individuals, as well as a Gaussian distributions across repeated measures, and were thus summarized using an individual mean.

Measurements at the flowering peak -On the evening before measurements, all mature flower buds were marked using watercolor paint, and individuals were isolated under an insect-proof tent in order to exclude nectar feeding pollinators. The next day, one newly opened flower per individual was randomly selected among the marked ones and collected.

On this flower, we estimated the total volume of nectar using 2µL microcapillary tubes.

Nectar sugar content (µg of sucrose equivalent per flower) was then determined using a refractometer (Abbe NAR-1T LIQUID, Atago Co., Ltd., Tokyo, Japan). On the same flower, one freshly dissected petal was used to measure reflected light on average every 0.6 nm within 200-700 nm using a probe connected to an AvaLight-XE ULS2048 spectrometer and to an AvaLight-XE xenon pulsed light source (Avantes, Apeldoorn, the Netherlands). Spectra were calibrated against a fully absorbing black standard and a fully reflecting barium sulfate white standard. Two measures were performed for each individual, one in the center of each petal lobe (i.e. on both sides of the axis of symmetry of the petal). Averaged reflectance spectra were analyzed using the pavo package in R [START_REF] Maia | pavo2: New tools for the spectral and spatial analysis of colour in R[END_REF]. Using Apis mellifera visual systems, which should be representative of bumblebee's perceptions [START_REF] Peitsch | The spectral input systems of hymenopteran insects and their receptor-based colour vision[END_REF]) we extracted cartesian X-Y coordinates from the polygon color space, resulting in two traits for petal color. Finally, to characterize petal size, area and shape, another petal was dissected on each collected flower, taped flat and imaged using a high resolution scanner (Epson Perfection V700 Photo, Seiko Epson, Suwa, Japan). Using ImageJ [START_REF] Schneider | NIH Image to ImageJ: 25 years of image analysis[END_REF], we then measured petal length from the paracorolla to the apical part (mm), largest width (mm), cleft length (mm) and petal area (mm²). Two indexes of petal shape were then calculated: elongation (i.e. length divided by width) and bifidity (i.e. cleft length divided by petal length).

Measurements at the end of the flowering peak -At the end of the flowering season, total flower production was estimated on both sexes by counting all pedicels attached on the stems.

Reproductive and mating success

Females -Seed number per fruit was estimated jointly with ovule number (see above).

Female reproductive success was then estimated by multiplying mean seed number per fruit, total number of fruits and germination rate. Germination rates were estimated on a subsample of seeds (15 to 90 seeds per female according to its relative production) that were sown in petri dishes filled with 40mL of 10g/L agar in sterile water (photoperiod 14:10 and temperature 15-21°C).

Males -Reproductive success was estimated as the total number of seeds sired on a sample of genotyped seedlings, which was determined using paternity analyses. Genotyped seedlings were selected so as to reflect each female's contribution to the total seed pool (for any given female, the proportion of genotyped seeds relative to the total number of genotyped seeds is the same as the proportion of seeds produced relative to the total seed production at the population level) and were sampled across all fruits the female produced during the flowering season. On average, 23 seedlings per mother were genotyped, and this number ranged from a minimum of 6 to a maximum of 56 seedlings per mother.

Total genomic DNA of all adults (200 OP plants) and 2916 seedlings was extracted and single-step multiplex PCR assays were used to amplify five nuclear microsatellites (Text S1 and Table S1). Paternity assignments were conducted using the maximum-likelihood procedure implemented in the software CERVUS v.3.0.7 [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]. Likelihood scores, based on allele frequencies in the experimental population, were calculated for each seedling / potential father couple. To determine whether the paternity of each offspring could be assigned to the father with the highest likelihood, we used the difference in likelihood scores between the two most likely pollen donors (Δ LOD ). The critical value (Δ C ) of Δ LOD below which paternity could not be assigned at 80% was determined using a distribution of Δ obtained from 10 000 simulated pollination events. This distribution was generated using the following simulation parameters: no unsampled pollen donors and 2% of genotyping error. The reproductive success of each male was estimated as the number of genotyped seedlings fathered. Three males did not sire any seeds in the sample of genotyped offspring. We also used the results from the paternity analysis to estimate mating success of each OP female and male as the number of genetic mating partners per individual.

Statistical analyses

The dataset with the 18 floral traits and reproductive and mating success for each experimental group is available on Dryad (https://doi.org/10.5061/dryad.j6q573nh1).

Statistical analyses are organized as follows. First, we evaluated the correlations between all pairs of traits, and then we selected a subsample of traits covering different functional categories and weakly correlated with each other to estimate natural and sexual selection gradients. All linear models verified (i) normal distribution of residuals, (ii) homoscedasticity and (iii) low levels of multicollinearity (i.e. variance inflation factor smaller than 4; [START_REF] Thompson | Extracting the variance inflation factor and other multicollinearity diagnostics from typical regression results[END_REF].

All analyses were conducted in R (R Development Core Team 2019).

Trait variation -Within each of the three experimental groups (HP females and OP females and males), correlations between all 18 measured traits were investigated to explore the phenotypic architecture and to identify trade-offs between traits. Correlations were estimated using the Pearson correlation coefficient and significance was assessed using a ttest with Bonferroni correction. Additionally, phenotypic variation between groups was tested for all floral traits using Likelihood Ratio Tests (LRT) to assess group effect, in order to (i) verify trait homogeneity between OP and HP females and (ii) assess the occurrence of sexual dimorphism between OP females and males.

Standardization -Prior to estimating selection gradients, all floral traits were centeredscaled within groups to allow comparison by removing dimension (i.e. variance(SD)standardized selection gradient; [START_REF] Lande | The measurement of selection on correlated characters[END_REF][START_REF] Matsumura | Standardizing selection strengths to study selection in the wild: a critical comparison and suggestions for the future[END_REF]. Female and male reproductive success were relativized within groups by dividing the absolute reproductive success for each individual by group mean. Mating success was estimated in OP females and males only and were relativized within sex.

Natural selection gradients -Cohort and source forest were included as random effects in the following models and their effect was tested using LRT. Because source forest had weak effects (P > 0.05), this factor was not kept in final models.

The strength and direction of selection was estimated following [START_REF] Lande | The measurement of selection on correlated characters[END_REF] using multiple regression analysis with relative reproductive success (i.e. produced / sired seeds) as dependent variable and standardized trait values as independent variables. The data set was simplified by reducing the number of traits because (i) our statistical power was limited due to sample size and (ii) multicollinearity is known to produce unstable selection gradient estimates [START_REF] Thompson | Extracting the variance inflation factor and other multicollinearity diagnostics from typical regression results[END_REF]. We selected six traits in order to keep a data set with limited correlations and to cover different functional categories: one trait linked with phenology (flowering duration, i.e. the number of weeks the individual produced flowers), one trait that is presumably involved in long distance attraction (plant height, which has been found to positively affect pollinator attraction in other systems; [START_REF] Zu | The effects of becoming taller: direct and pleiotropic effects of artificial selection on plant height in Brassica rapa[END_REF][START_REF] Brunet | The effects of flower, floral display, and reward sizes on bumblebee foraging behavior when pollen is the reward and plants are dichogamous[END_REF], two flower morphology traits (corolla width and calyx height , which are expected to impact both attraction and various aspects of plant-pollinator fit, see for instance; [START_REF] Glaettli | Pollinator responses to variation in floral display and flower size in dioecious Sagittaria latifolia (Alismataceae)[END_REF], and two descriptors of plant fertility (number of gametes per flower and number of flowers produced over the whole flowering season). 64 HP females, 98 OP females and 100 males were measured on all six traits. Of these, three males and one HP female were removed from the analyses because they did not sire / produce any seeds.

Multiple linear regressions of reproductive success on the six selected floral traits were performed (i) group by group, (ii) on a dataset grouping HP and OP females, allowing us to test for the occurrence of pollinator-mediated selection and (iii) on a dataset grouping OP females and males, allowing us to test for sex-specific selection. Significance of selection gradients was assessed using t-tests for group by group models, and LRT were used to test the effect of the group × trait interaction. Since multicolinearity precluded us from fitting all traits in the same analysis, we also estimated selection differentials on each character one by one. Differentials correspond to the slope of simple regressions of reproductive or mating success on each trait taken separately. It thus covers both direct and indirect selection (i.e. selection indirectly acting on a trait due to the correlation between this trait and another one that would be the direct target of selection, see Figure S1).

Sexual selection gradients and indexes -We estimated sexual selection gradients (i.e. direct sexual selection), by regressing relative mating success (i.e. number of genetic sexual partners) in OP females and males on the six standardized traits, using the same method as for natural selection gradients.

Additionally, we used Bateman's three metrics to quantify the overall strength of sexual selection in each sex. First, we estimated the standardized variance in reproductive success, which corresponds to the opportunity for selection I [START_REF] Wade | Sexual selection and variance in reproductive success[END_REF]. Second, we estimated the standardized variance in mating success in each sex, which corresponds to the opportunity for sexual selection I S [START_REF] Wade | Sexual selection and variance in reproductive success[END_REF][START_REF] Wade | The intensity of sexual selection in relation to male sexual behaviour, female choice, and sperm precedence[END_REF]. We tested for differences in reproductive and mating success variances between sexes using Levene tests. Third, we estimated a standardized partial Bateman gradient in each sex, by assessing the slope of the linear regression of relative reproductive success on relative mating success, while controlling for total flower number and mean number of gametes per flower [START_REF] Henshaw | How to quantify (the response to) sexual selection on traits[END_REF].

To estimate Bateman gradients, we used two alternative sampling strategies for estimating female mating success. In a first set of analyses, we used the same estimate of male and female mating success as before, based on the genotyping of a number of seedlings per female that would reflect each female's contribution to the total seed pool (hereafter pro-rata method). Whereas this method has the advantage of not heavily truncating the variance in female MS (see below), it can however create an artificial relationship between mating and reproductive success for females [START_REF] Anthes | Measuring and interpreting sexual selection metrics: evaluation and guidelines[END_REF]). To estimate Bateman gradients without this possible bias, we produced a second estimate of mating success, by using a bootstrapping procedure where we sampled ten genotyped offspring for each female 1000 times (hereafter fixed method). The possible disadvantage of this method is that it sets an upper limit of ten reproductive partners per female. Male mating success was directly deduced from female MS and averaged over the bootstrapping procedure. Finally, to take into account that the variance in female RS can translate into a variance in male RS, we calculated individual RS of each male p (RS m , p ) as the sum of its contribution to each female i Π p (χ i ) weighted by individual RS of each female (RS f ,i ), as follows:

RS m , p = ∑ i=1 I Π p (χ i )×RS f ,i
For each sampling method, we then tested for significance of the Bateman's gradient in each sex using t-tests. We also tested for the differences in the Bateman gradient between sexes by using LRT to test for mating success × sex interaction.

Pollen limitation -The occurrence of pollen limitation was tested on three components of overall female reproductive success by assessing differences between OP and HP females in (i) seed-set (i.e. seed number divided by ovule number over all dissected fruits), (ii) fruit-set (i.e. total fruit number divided by total flower number) and (iii) total number of seeds. Differences in seed-set and fruit-set between OP and HP females were assessed using generalized linear models with binomial distribution and an individual random effect for seed-set as several fruits were sampled per individual. Differences in total seed production were assessed by using a generalized linear model with negative binomial distribution to account for overdispersion (package glmmTMB; [START_REF] Brooks | glmmTMB balances speed and flexibility among packages for zero-inflated Generalized Linear Mixed Modeling[END_REF]. LRT were used to test the effect of pollination treatment.

Results

Trait variation

Correlations between traits in open-pollinated plants -Within each sex, correlations between traits were explored for all possible pairs (153 pairs). Overall, males appeared to be more phenotypically integrated than females (32.0% versus 13.7% of all correlations were significant after Bonferroni correction, Figure 1 and Table S2). In females, significant correlations were mostly positive (22 out of 26 significant correlations), while nearly half of them were negative in males (23 out of 49 significant correlations). Some obvious correlations were observed in both males and females, such as positive correlations between various measurements of flower size (corolla width, calyx height, petal length, width and area) or positive correlations between stem number, flower number (both daily and total) and height (Figure 1 and Table S2). The most notable differences between males and females included (i) a positive correlation between estimates of flower number and flowering duration in males only, (ii) a trade-off between flower size and total flower number, as well as between flower size and flowering duration in males only, (iii) a negative correlation between the number of gametes per flower and total flower number in females and (iv) a negative correlation between viable pollen production per flower and flowering duration in males. Sexual dimorphism -All measured traits were sexually dimorphic, except petal color as perceived by bees (Table 1). Males produced more flowers, both daily and total, flowered longer, were taller and produced larger flowers, both in terms of corolla width and calyx height, than females. The same was true for all petal measurements. Males also had more elongated and bifid petals. The only trait showing female-biased sexual dimorphism was nectar sugar content, with females offering significantly more reward per flower than males.

Homogeneity between open-pollinated and hand-pollinated females

However, because of the difference in flower production between sexes, nectar reward at the plant level was still overwhelmingly more abundant in males than in females.

Natural selection gradients

In females, natural selection gradients were similar in HP and OP plants: in both groups, we detected a significantly positive relation between reproductive success and two traits linked with fertility, total flower number and number of gametes per flower (Table 2). Accordingly, we did not observe any pollinator-mediated selection (i.e. none of the group × trait interactions were significant; Table 2). Regarding selection differentials, we detected significant total selection on the same traits as well as on traits that were strongly correlated with them (Figure S1 and Table S2).

In males we detected significant selection for larger corolla width and longer flowering duration (Table 2). As in females, the patterns detected using selection differentials mirrored those observed with selection gradients (Figure S1) When fitting both sexes in the same model, the selection gradient for flowering duration was stronger in OP males than in OP females (i.e. significant effect of the sex × trait interaction; Table 2 and Figure S2). On the contrary, selection on total flower number and number of gametes per flower was stronger in females than in males. Although selection on corolla width was detected in males but not in females, the sex × trait interaction was only marginally significant (Table 2 andFigure S2).

Sexual selection gradients

We detected sexual selection for more gametes per flower and more flowers in OP females, along with positive sexual selection on both corolla width and flowering duration in OP males (Table 3). The sex × group interaction was significant for flowering duration, as well as for flower number and number of gametes per flower (Table 3 andFigure S3).

Sexual selection indexes

The opportunity for selection I (i.e. standardized variance in reproductive success), as well as the opportunity for sexual selection Is (i.e. standardized variance in mating success), were significantly stronger for OP males than for OP females (0.410 versus 0.168 and 0.286 versus 0.111, respectively). Levene's test on the variances in reproductive and mating success showed significantly stronger variance in males. In OP males, the partial Bateman gradient was significantly positive for both methods (pro-rata method: 1.08 SE ± 0.055, P<.001; fixed method: 1.05 SE ± 0.036, P<.001). In OP females, it was marginally positive for the fixed number method (0.45 SE ± 0.24, P=.067) but significantly positive for the pro-rata method (0.72 SE ± 0.084, P<.001). LRT showed that Bateman's gradients were significantly different between sexes for both methods (pro-rata method: χ 1,183 2 =8.56 , P<.01; fixed method: χ 1,183 2 =7.24 , P<.01; Figure 2), with reproductive success being more correlated with mating success in males than in females.

Pollen limitation

None of the components of female reproductive success indicated pollen limitation (GLMs, seed-set: χ 2 1,2676 =2.67 , P=.10; fruit-set: χ 2 1,159 =0.074 , P=.79; total production of viable seeds: χ 2 1,159 =1.35 , P=.25). OP females produced an average of 29.4 (SD ± 11.8) fruits and 4762.6 (SD ± 1835.2) seeds, and HP females produced 26.3 (SD ± 9.6) fruits and 4336.1 (SD ± 1502.2) seeds.

Discussion

Our study aimed at quantifying the strength of sexual and natural selection on an array of traits in both males and females of a dioecious plant, in which sexual selection is expected to partly occur through the action of pollinating insects. Most traits investigated in the current work displayed male-biased sexual dimorphism. Similar results have been reported in some dioecious plant species, and this has sometimes been interpreted as the possible outcome of sexual selection [START_REF] Delph | Sexual dimorphism in life history[END_REF][START_REF] Eckhart | Sexual dimorphism in flowers and inflorescences. Gender and sexual dimorphism in flowering plants[END_REF][START_REF] Ashman | Sniffing out patterns of sexual dimorphism in floral scent[END_REF]. Indeed, the expression of more conspicuous phenotypes in males may result from stronger selection on traits that increase access to mating partners through pollinator attraction [START_REF] Moore | Sexual selection in plants[END_REF][START_REF] Barrett | Sexual dimorphism in flowering plants[END_REF], an expected difference between sexes when pollen is not a limiting factor for female reproductive success. In Silene dioica, at least one previous study performed in natural populations found no evidence for pollen limitation [START_REF] Carlsson-Granér | Floral sex ratios, disease and seed set in dioecious Silene dioica[END_REF] this was also the case in our experimental garden. Consistent with our expectations, we found that: (i) selection acts on traits associated with fertility in females and on traits associated with mate acquisition in males and (ii) reproductive and mating success are more variable and show a stronger correlation in males than in females.

Patterns of selection on floral traits

Fertility selection acts on flower and ovule number in females -Selection differentials and gradients for total flower number and number of gametes per flower indicated a positive effect of these traits on female fitness. Selection for more flowers through female function is a common pattern in flowering plants [START_REF] Harder | Darwin's beautiful contrivances: evolutionary and functional evidence for floral adaptation[END_REF][START_REF] Caruso | A meta-analysis of the agents of selection on floral traits[END_REF]) and ovule number per flower was also found to be under positive selection in the sister species Silene latifolia [START_REF] Delph | Sexual, fecundity, and viability selection on flower size and number in a sexually dimorphic plant[END_REF].

Comparing selection patterns between OP and HP females allows infererence of the nature of selection on these two traits. Indeed, flower number could affect both pollinator attraction or gamete production at the individual level, and could thus be subjected to both pollinatormediated and fertility selection. In our experimental garden, seed production was not pollen limited, and selection was found to act on the same traits, and with the same intensity in the two groups. In other words, no pollinator-mediated selection was detected and the significant selection on total flower number and gamete number could be entirely attributed to the variance in fertility among females, rather than variance in the ability to attract pollinators. This pattern is however expected to vary widely with ecological conditions. While individual density in our experimental population was within the range of values observed in natura (Barbot et al. pers. obs., Carlsson-Granér et al. 1998), pollinator availability is expected to vary among sites, in particular in the current context of pollinator decline [START_REF] Biesmeijer | Parallel declines in pollinators and insect-pollinated plants in Britain and the Netherlands[END_REF][START_REF] Potts | Global pollinator declines: trends, impacts and drivers[END_REF]). Three fifths of published studies quantifying pollen limitation in angiosperms report significant increases in female reproductive output in hand-pollinated plants [START_REF] Burd | Bateman's principle and plant reproduction: the role of pollen limitation in fruit and seed set[END_REF] and there is evidence that the intensity of selection on attractive traits increases with the magnitude of pollen limitation [START_REF] Ashman | Explaining phenotypic selection on plant attractive characters: male function, gender balance or ecological context[END_REF][START_REF] Sletvold | Experimental reduction in interaction intensity strongly affects biotic selection[END_REF].

Because competition to attract pollinators is one possible component of sexual selection, but not the only one (for instance, sexual selection can also occur through post-pollination processes), comparing the results obtained with pollen supplementations to those obtained with sexual selection gradients should provide some insight on whether and how pollinator mediated selection and sexual selection overlap. We also detected positive sexual selection gradients on both flower number and ovule number. In that case, this link between traits and mating success cannot be attributed to pollinator-mediated selection. In other words, females with low values of mating success did not suffer from a shortage of pollen. Two factors could explain this discrepancy between pollinator-mediated and sexual selection patterns. First, we cannot exclude the action of post-pollination sexual selection, receiving gametes from more diverse partners could promote fecundation and zygote development, for example by enhancing male-male competition [START_REF] Aizen | Expanding the limits of the pollen-limitation concept: effects of pollen quantity and quality[END_REF][START_REF] Pannell | The incidence and selection of multiple mating in plants[END_REF].

Second, a part of this result is likely to emerge from the mechanistic relationship between the total number of available ovules and the number of reproductive partners. This constraint motivated our use of partial Bateman gradients (see below).

Finally, as mentioned earlier, this study provides a picture of sexual selection patterns in females in a non pollen-limited situation. Setting-up similar studies in other situations and/or species will allow covering the wide diversity of ecological situations encountered by insect pollinated plants. In particular, this should allow to investigate whether pollinator-mediated and sexual selection are detected on the same traits when pollen becomes limiting.

Sexual selection acts on corolla width and flowering duration in males -

In males, patterns of natural selection were consistent with those of sexual selection, based on both selection differentials and gradients. Contrary to what was seen in females, we detected no association between the male mating success and components of fertility (i.e. total flower number and gamete number). Moreover, traits that appeared beneficial in terms of mating success were also likely to increase the access of males to their female sexual partners. First, the number of sexual partners increased with corolla width, a trait that has been found to increase pollinator attraction in several other species [START_REF] Ashman | Seasonal variation in pollination dynamics of sexually dimorphic Sidalcea oregana ssp. spicata (Malvaceae)[END_REF][START_REF] Stanton | Consequences of floral variation for male and female reproduction in experimental populations of wild radish, Raphanus sativus I[END_REF][START_REF] Conner | Effects of flower size and number on pollinator visitation to wild radish, Raphanus raphanistrum[END_REF]. In some species, corolla width was also shown to affect flowerpollinator fit and impact the efficiency of pollen removal [START_REF] Conner | Effects of flower size and number on pollinator visitation to wild radish, Raphanus raphanistrum[END_REF][START_REF] Ashman | Sex ratio represents a unique context for selection on attractive traits: consequences for the evolution of sexual dimorphism[END_REF]. It thus seems likely that sexual selection on this trait arises from some pollinator-mediated selection, although this cannot be directly demonstrated in males.

Second, flowering phenology played a major role in access to reproduction in males. While the strong phenotypic correlation between flowering start and flowering duration prevented us of disentangling the effect of these two traits, males that started early (and thus flowered longer) clearly accessed more partners and reached higher siring success than males starting later on in the flowering season. This set of traits increased the flowering overlap with females, a trend that was already documented in Silene latifolia by [START_REF] Delph | Sexual, fecundity, and viability selection on flower size and number in a sexually dimorphic plant[END_REF].

The advantage of an early flowering start in terms of siring success has been reported in several species [START_REF] O'connell | Male and female pollination success in a deceptive orchid, a selection study[END_REF][START_REF] Munguía-Rosas | Meta-analysis of phenotypic selection on flowering phenology suggests that early flowering plants are favoured: Phenotypic selection on flowering phenology[END_REF][START_REF] Forrest | Plant size, sexual selection, and the evolution of protandry in dioecious plants[END_REF][START_REF] Austen | Estimating selection through male fitness: three complementary methods illuminate the nature and causes of selection on flowering time[END_REF]. Here, the possible overlap between pollinator-mediated and sexual selection is less clear. Selection for earlier (and thus longer) flowering may reflect the fidelity of pollinators to individuals on which they had originally been foraging or, since this pattern was also documented in a wind-pollinated species [START_REF] De Cauwer | Disentangling the causes of heterogeneity in male fecundity in gynodioecious Beta vulgaris ssp. maritima[END_REF], the fact that males that flower early have larger floral displays when females start flowering, giving them an edge over competitors starting later during the flowering season.

Contrary to females, we found no trace of selection acting on flower number in males. This is an unexpected result, given the common role of flower number in pollinator attraction in many plant species [START_REF] Conner | Effects of flower size and number on pollinator visitation to wild radish, Raphanus raphanistrum[END_REF][START_REF] Vaughton | Floral display, pollinator visitation and reproductive success in the dioecious perennial herb Wurmbea dioica (Liliaceae)[END_REF], and given the positive impact of flower number on the overall pollen production at the plant level. Flower number has historically been considered as a typical 'male trait', based on the fact that many hermaphroditic species exhibit more flowers than the number of fruits they produce, leading to the idea that these excess flowers would have a male, rather than a female function (reviewed in [START_REF] Burd | What does the male function hypothesis claim?[END_REF]. This view has however been challenged by several experimental studies that found no or even negative selection through male function on this trait [START_REF] Elle | Sex allocation and reproductive success in the andromonoecious perennial Solanum carolinense (Solanaceae). II. Paternity and functional gender[END_REF][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] Lau | Selection through male function favors smaller floral display size in the common morning glory Ipomoea purpurea (Convolvulaceae)[END_REF][START_REF] Van Kleunen | Selection on floral traits through male fertility in a natural plant population[END_REF].

In Silene dioica, the absence of selection could reflect that flower number is, for the observed range of trait values, more or less neutral for male fitness. [START_REF] Moquet | Effects of sexual dimorphism on pollinator behaviour in a dioecious species[END_REF] showed that one major factor explaining why males attract much more pollinators than females is their larger floral displays. However, another study showed that artificially increasing the number of flowers increased pollinator attraction in both sexes without impacting plant reproductive success [START_REF] Barbot | On the function of flower number: disentangling fertility from pollinator-mediated selection[END_REF]). One possibility is thus that the relationship between this trait and male fitness is a saturating one: after a certain threshold producing more flowers does not result in any increase in male fitness. In addition, [START_REF] Barbot | On the function of flower number: disentangling fertility from pollinator-mediated selection[END_REF] found significant selection on flower number in males, when surveying reproductive success over a period of 10 days, suggesting that at this short time scale flower number may indeed increase male reproductive success. When considering the whole flowering season, as we did in the current work, this effect no longer holds and flowering phenology appeared to be the most impacting trait for male fitness.

Estimates of sexual selection

In addition to testing the dependency of mating success on floral phenotypes, sexual selection was also quantified using several indexes that are typically used in animals [START_REF] Klug | The mismeasurement of sexual selection[END_REF][START_REF] Janicke | Darwinian sex roles confirmed across the animal kingdom[END_REF]. We found a greater opportunity for sexual selection in males, consistent with the results recently reported in the wind-pollinated Mercurialis annua [START_REF] Tonnabel | Do metrics of sexual selection conform to Bateman's principles in a wind-pollinated plant?[END_REF]) and insect-pollinated Sagittaria latifolia [START_REF] Kwok | Sexual selection on male but not female function in monoecious and dioecious populations of broadleaf arrowhead (Sagittaria latifolia)[END_REF].

Regarding the Bateman gradients, when mating success was estimated based on the pro-rata sampling method, we detected a significant positive relation between mating and reproductive success in females. This result is at least partly explained by the sampling method (i.e. we sampled more seed in females with high reproductive success). When we correct for this possible bias using the fixed sampling method, the slope was not significant.

In both cases we found a signicantly steeper Bateman gradient for males than for females, as predicted by theory (Arnold 1994a), and as found in three plant species (Johnson and Shaw 2017;[START_REF] Tonnabel | Do metrics of sexual selection conform to Bateman's principles in a wind-pollinated plant?[END_REF][START_REF] Kwok | Sexual selection on male but not female function in monoecious and dioecious populations of broadleaf arrowhead (Sagittaria latifolia)[END_REF] . Again, a stimulating perspective of this work will be to replicate similar experiments in situations where pollen availability limits female reproductive success, in order to test whether these male-female differences in sexual selection decrease in less favorable situations.

Sexual dimorphism evolution

Interestingly, the selection patterns detected in our study are only partly consistent with the sexual dimorphism observed in our model species. On the one hand, our findings of males having wider corollas and flowering for a longer period of time than females are consistent with sexual selection acting on these traits in male plants. On the other hand, the stronger selection on flower number observed in females appears contradictory with the much higher number of flowers displayed by males in this species. In males, and as mentioned previously, maybe flower number is not under selection because this trait does not increase pollen export at least in the range of values that we observe. In females, the fact that positive selection on flower number does not translate into evolution towards larger floral display may be that, due to higher costs of reproduction, females are subjected to stronger trade-offs between components of their fitness. For instance, although not quantified in our study, a trade-off between flower number and survival could maintain the marked sexual dimorphism for this traits even in the face of a strong selection for larger number of flowers in females [START_REF] Obeso | The costs of reproduction in plants[END_REF].

Conclusion

Overall, our findings show that some predictions from sexual selection theory corpus seem to apply well to plants when pollen is not limiting. However, it seems crucial to explicitly consider the specificity of plant reproduction when estimating mating success as mate diversity and interpreting its relationship with reproductive success. First, the fact that each individual typically carries several independent reproductive tracts (i.e. flowers), opens the question of the transferability of classical sexual selection metrics from animals to plants.

Because a high genetic mating success may be an indirect byproduct of fertility in females, one should be cautious when interpreting sexual selection gradients. From the male perspective, one may also question whether genetic mating success accurately reflects access to reproduction in plants. Indeed, multiple pollen dispersal events to several flowers carried by the same female plant can constitute an efficient access to reproduction that would translate in a low genetic mating success. The strong positive Bateman gradient documented on male S. dioica yet suggests that this metrics may satisfactorily capture access to female mates in our study system. The strong correlation between male reproductive and mating successes probably stems in part from the observed variance in flowering duration: longflowering males appear to have maximized their access to reproduction through a greater overlap with flowering females. Studying sex-specific selection on attractive traits through another angle, that of sexual partners acquisition, thus seems to constitute a promising avenue. S2).

Tables

Flowering

  phenology -Flowering phenology was described with two traits: the date of first flowering and flowering duration. Since plants were surveyed once a week, flowering duration is the number of weeks during which at least one flower was open for a given individual.

  -We detected no significant differences between the two groups of females, except for three traits. HP females displayed fewer flowers per day (χ 1,159 2 =4.56 , P=.033), fewer gametes per flower ( , P=.030) and shorter calyxes (χ 1,159 2 =3.91 , P=.048) than OP females.

  of freedom (d.f.) and P-values from t-tests are reported for the significance of sexual selection gradients. Statistics from LRT are reported for interaction terms : (i) between pollination group and trait γ pol (OP versus HP females) to investigate pollinator-mediated selection and (ii) between sex and trait γ sex (OP females versus OP males) to investigate sex-specific selection. The proportion of variance explained by fixed effects in each model is reported using marginal R-squared ( R M 2 ). Values in bold are significant at P < .

FiguresFigure 1 :

 1 Figures

Figure 2 :

 2 Figure 2: Bateman's gradients (i.e. relation between reproductive and mating success) according to the sampling method (A) pro-rata method and (B) fixed method. The distributions of reproductive success and mating success in both sexes are represented respectively along the right and top margins (females in white and males in black). Females are representend with gray lines and empty circles and OP males are represented with black lines and filled circles.

Table 1 :

 1 Trait means ± SD in open-pollinated females and males.Note: Statistics from LRT are reported as well as associated P-values ( P sex ) for differences between OP females and OP males. Values in bold are significant at P < .05.

	Traits	OP females	OP males	LRT	P sex
	Stem number (mean)	1.09 ± 0.45	5.81 ± 3.07	χ 1,197 =193.76	< .001
	Height (cm, max)	47.03 ± 14.68	53.31 ± 12.86	χ 1,197 =13.07	< .001
	Corolla width (mm, mean)	17.93 ± 2.65	20.05 ± 1.87	χ 1,197 =39.62	< .001
	Calyx height (mm, mean)	13.44 ± 1.01	15.66 ± 1.01	χ 1,197 =160.18	< .001
	Nectar sugar content (µg sucrose/flower)	0.71 ± 0.57	0.46 ± 0.3	χ 1,162 =12.71	< .001
	Bees X-coordinate	0.10 ± 0.02	0.095 ± 0.02	χ 1,162 =0.87	.35
	Bees Y-coordinate	0.145 ± 0.02	0.143 ± 0.02	χ 1,162 =0.19	.66
	Petal length (mm)	8.81 ± 1.24	9.23 ± 1.21	χ 1,168 =6.36	.012
	Petal width (mm)	9.02 ± 1.38	9.94 ± 1.51	χ 1,168 =18.08	< .001
	Petal cleft length (mm)	4.1 ± 0.67	4.71 ± 1.13	χ 1,168 =17.34	< .001
	Petal area (mm²)	56.72 ± 15.4	63.52 ± 15.85	χ 1,168 =9.39	< .01
	Petal shape (elongation)	0.98 ± 0.1	0.94 ± 0.11	χ 1,168 =8.21	< .01
	Petal shape (bifidity)	0.47 ± 0.06	0.51 ± 0.09	χ 1,168 =9.31	< .01
	Total number of flowers	30.32 ± 11.84	316.32 ± 150	χ 1,197 =224.71	< 0.001
	Daily flower display (mean)	2.51 ± 1.12	18.59 ± 8.52	χ 1,197 =240.54	< 0.001
	Number of gametes per flower	257.71 ± 46.02	37152.45 ± 17472.81	χ 1,195 =229.49	< 0.001
	Flowering start	4.77 ± 1.79	5.16 ± 1.64	χ 1,197 =6.04	0.014
	Flowering duration (number of weeks)	4.3 ± 1.47	6.79 ± 1.56	χ 1,197 =104.29	< 0.001

Table 2 :

 2 Natural selection gradients estimates ± SE on variance-standardized traits for hand-pollinated females, open-pollinated females and males.

		β HP females R M 2 =0.268	P 56 d.f	β OP females R M 2 =0.157	P 90 d.f	β OP males R M 2 =0.242	P 92 d.f	R M 2	γ pol =0.412	P pol	R M 2	γ sex =0.372	P sex
	Height (mean)	-0.083 ± 0.053	.12	0.008 ± 0.036	.81	0.007 ± 0.073	.92	χ 1,147 2	=0.01	.93	χ 1,183 2	=0.15	.70
	Corolla width (mean)	0.004 ± 0.037	.22	-0.001 ± 0.99	.99	0.13 ± 0.058	.027	χ 1,147 2	=0.52	.52	χ 1,183 2	=3.72	.054
	Calyx height (mean)	-0.056 ± 0.037	.14	-0.034± 0.037	.36	-0.059 ± 0.055	.28	χ 1,147 2	=0.33	.57	χ 1,183 2	=0.30	.59
	Total number of flowers	0.23 ± 0.044	< 0.001	0.26 ± 0.036	< .001	-0.078 ± 0.066	.24	χ 1,147 2	=0.02	.90	χ 1,183 2	=21.87	<.001
	Number of gametes per flower	0.16 ± 0.038	< 0.001	0.22 ± 0.035	<.001	0.023 ± 0.052	.65	χ 1,147 2	=1.07	.30	χ 1,183 2	=9.08	<.0.01
	Flowering duration	-0.045 ± 0.040	.27	0.029 ± 0.036	.42	0.35 ± 0.064	<.001	χ 1,147 2	=1.17

Table 3 :

 3 Sexual selection gradients estimates ± SE on variance-standardized traits for open-pollinated females and males.Note: Degrees of freedom (d.f.) and P-values from t-tests are reported for the significance of sexual selection gradients. Statistics from LRT are reported for γ sex the interaction between sex γ sex (OP females versus OP males) and trait, highlighting sex-specific sexual selection patterns. The proportion of variance explained by fixed effects in each model is reported using marginal R-squared (R M

		β MS OP females R M 2 =0.280	P 90 d.f	β MS OP males R M 2 =0.201	P 92 d.f	R M 2	γ sex =0.353	P sex
	Height (mean)	-0.019 ± 0.033	.55	-0.068 ± 0.060	.26	χ 1,183 =0.22	.64
	Corolla width (mean)	0.011 ± 0.034	.74	0.12 ± 0.048	.011	χ 1,183 =3.75	.0.53
	Calyx height (mean)	-0.009 ± 0.034	.78	-0.041 ± 0.045	.36	χ 1,183 =0.34	.56
	Total number of flowers	0.18 ± 0.033	<.001	-0.062 ± 0.054	.25	χ 1,183 =15.70	<.001
	Number of gametes per flower	0.12 ± 0.032	<.001	0.010 ± 0.042	.81	χ 1,183 =4.15	.042
	Flowering duration	0.031 ± 0.033	.35	0.26 ± 0.053	< .001	χ 1,183 =14.19	<.001

). Values in bold are significant at P < .05.

Acknowledgments

For fruitful discussion related to the project, we thank J. Shykoff, N. Sletvold, C. Devaux and J. Tonnabel. We also thank T. Janicke for his precious comments that helped improving the manuscript. For laboratory assistance, we thank C. Gode. For greenhouse assistance, we thank E. Schmitt, N. Faure, C. Ponitzki and C. Glorieux. We are grateful to V. Mahut, R. Boisserie, N. Le Roux and P. Drouvin for help in collecting the data. We thank A. Duputié for the development of the image analysis script. 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.

Data and materials availability

All data are available in Dryad (https://doi.org/10.5061/dryad.j6q573nh1).

Conflict of interest

The authors declare no conflict of interest.