Fan Li

* Alain Etienne

Franç Ois Vernadat

Ali Siadat
email: ali.siadat@ensam.eu

Comprehensive Performance Expression Model for Industrial Performance Management and Decision Support

Keywords: Performance evaluation, performance analysis, decision making, decision support systems, project management, industrial systems 

Due to proliferation of evaluation criteria and decision data overflow in nowadays fluctuating industrial environments, it is necessary to build a holistic, easy-to-use and efficient methodology for performance evaluation and decision making. More accurate overall performance expressions should not only prove that the selected decision alternative better fits the evaluator's objective at the time of evaluation, but it should also assume that this alternative remains the best solution in the subsequent evaluation periods. To this end, the benefit-cost-value-risk (BCVR) methodology has been developed for performance evaluation and decision support. The objective of this paper is to propose a comprehensive performance expression model to further ease the application of the methodology.

INTRODUCTION

Regarding today's changing global competitive market, companies must simultaneously satisfy multiple stakeholder objectives in industrial projects. However, this endeavour becomes more challenging with the increasing diversity of customer demand [START_REF] Nudurupati | State of the art literature review on performance measurement[END_REF] and emergence of new concept such as Industry 4.0 [START_REF] Hofmann | Industry 4.0 and the current status as well as future prospects on logistics[END_REF] in industrial systems. In addition, objectives and degrees of satisfaction vary among stakeholders. This problem can even be more complicated when some of the objectives contradict each other.

Satisfying objectives requires performance measurement and management methodologies to efficiently evaluate how good the objectives are met [START_REF] Berrah | Towards a unified descriptive framework for industrial objective declaration and performance measurement[END_REF]. To this end, many methodologies and approaches have been proposed so far, such as Activity-Based Costing [START_REF] Cooper | Measure costs right: make the right decisions[END_REF], Balanced Scorecard [START_REF] Kaplan | The balanced scorecard: Measures that drives performances[END_REF], ECOGRAI [START_REF] Bitton | ECOGRAI : méthode de conception et d'implantation de systèmes de mesure de performances pour organisations industrielles[END_REF][START_REF] Ducq | Definition and aggregation of a performance measurement system in three aeronautical workshops using the ECOGRAI method[END_REF], QMPMS [START_REF] Suwignjo | Quantitative models for performance measurement system[END_REF] or Performance Prism [START_REF] Neely | The Performance Prism: The ScoreCard for Measuring and Managing Business Success[END_REF], just to name a few.

Performance measurement and management methodologies evolved with business trends [START_REF] Bititci | Performance measurement: challenges for tomorrow*: performance measurement[END_REF]. Indeed, earlier methods mainly focused on cost or financial evaluation, then later methods integrated financial and nonfinancial performance measurement and, more recently, new methods turned to integrate performance management systems which take into consideration the multidimensional nature of performance through a wide range of performance indicators. Consequently, performance measurement and management problems become ever more challenging due to the proliferation of evaluation criteria and decision data overflow in nowadays fluctuating environments. In addition, companies must rely on integrated, dynamic and relevant performance information to promote a pro-active management style for efficient and effective decision making.

For this purpose, it is necessary to build a holistic, easy-touse and efficient methodology for performance management and decision support. Because the dimensions of benefit, cost, value and risk (BCVR) are the most common and important aspects taken into account (including time) while evaluating an industrial system or project, it has been decided that performance of an industrial system can be comprehensively measured and managed using these dimensions [START_REF] Shah | Value-risk based performance evaluation of industrial systems[END_REF][START_REF] Vernadat | VR-PMS: a new approach for performance measurement and management of industrial systems[END_REF].

Based on these observations,Li (2017) proposed a BCVR based methodology for performance evaluation and decision support of industrial systems. It consists of four main phases (identification, quantification, aggregation and decision support) to generate an overall performance, which is qualitatively and quantitatively expressed on each of the four dimensions.

Overall performance expressions should not only prove that the selected decision alternative better fits the evaluator objective at the time of evaluation, it should also assume that this alternative remains the best solution in the subsequent evaluation periods. Therefore, a comprehensive performance expression model is proposed as a supplementary component of the BCVR based methodology.

The first part of the paper introduces the key concepts of BCVR based comprehensive performance expression. The second part presents the concept of performance variation to adjust the overall performance expression. The last part shows the results of an experimental application to illustrate the proposed model.

BCVR BASED PERFORMANCE EXPRESSION

The key concepts for BCVR based performance expression framework are presented in this section.

Concepts of benefit, cost, value and risk

The concepts of benefit, cost, value and risk as well as industrial performance are popular terms that have been widely used in almost all practice and research contexts. Their definitions vary across different fields of application and it is hard to identify standard definitions that can be adapted to universal situations. Therefore, the specific definitions adopted the particular research context must first be presented.

Benefit can be tangible or intangible. Tangible benefits, which are always on quantitative monetary measurements, can be estimated before the start of a project and measured at the end. Intangible benefits, which are often related to non-financial and subjective aspects, may either be measurable or qualitative. They can be listed before the project starts and can only be ascertained at the end. Because any kind of benefits cannot be systematically expressed in measurable units to become an estimation indicator, they will be expressed in the form of literal expressions. In this paper, benefit is defined as a qualitative list of potential advantages or gains for a stakeholder compared to an objective that is set beforehand for the realisation of an industrial system.

The cost of an industrial project is usually quantitatively expressed and evaluated in monetary terms. In this paper, cost refers to total expenses for the production, distribution and acquisition of the final result (a product, service or deliverable) of an industrial system. The challenging point regarding this evaluation axis is not the proposition of an adapted definition, but the identification of the different measurable elementary costs that can comprehensively represent the overall cost.

The dimension of value is considered as a non-financial term in the proposed methodology. Therefore, value is described as the degree of satisfaction of a set of stakeholder expectations or needs, expressed by the appreciation level of a number of performance indicators.

Regarding the context of project management, risk means the likelihood and consequence of an event occurrence impacting the achievement of some stakeholder objectives.

According to these definitions, the concept of benefit has been defined as a non-monetary term and it is assumed that benefits are expressed as literal expressions in the current approach. The global performance of an industrial project can be quantitatively and independently expressed by following the other three dimensions (cost, value and risk). In addition, it is assumed that all dimensions are independent at a broad level because they are analysed and evaluated separately. However, they can interact at the basic level by sharing common elementary variables. For instance, project delay can be a factor that can negatively impact user satisfaction and budget overrun risk, thus impacting the value and risk axes. The individual model of each dimension should be developed on the basis of a common logic to ease performance measurement.

The concepts of benefit, cost, value and risk will be developed on the basis of individual conceptual models. The objectives are: (1) description of the relations among the different key concepts used in each dimension for the purpose of evaluation and (2) establishment of a basis for software development in the future work to ease the evaluation process.

Figure 1 shows the proposed model of risk with different elements and their interactions using UML (Unified Modelling Language) class diagrams. The global project risk can result from a set of risk components that are related to elementary risk expressions. These components can be further classified into different types and at different levels. A risk component can also be expressed by several subcomponents at the lower level for the purpose of risk assessment. A risk component is impacted by several risk drivers that influence the result of risk measurement. The elementary expressions of risk components should be aggregated into an overall result by using a selected bottomup aggregation method in order to help the stakeholder in making a risk evaluation. The overall expression should also be normalised into a real number between 0 and 1 to make the decision making easier on a normalised scale.

Fig. 1. Individual model for the dimension of risk

The numeric numbers in Fig. 1 indicate the main operations used to process risks. They are: (1) identification of the risk structure regarding the project context, (2) risk assessment with selected estimation methods, (3) generation of the overall risk expression with adapted aggregation methods and quantitative weights and (4) risk evaluation based on the evaluator's preferences.

Using the same logic, the individual model of cost and value can be developed. These individual models show that each dimension is directly measured at the elementary levels to get quantitative expressions for the purpose of performance management and, then, these elementary expressions can be aggregated into one global result per dimension to support the decision making process performed by the evaluator or analyst.

Based on the conceptual models, the main operations (identify, quantify, aggregate and decide) involved in performance evaluation can be identified as the basis for the methodological framework. However, besides the multiple aspects of the selected dimensions, performance expression should also meet other characteristics of performance. Therefore, an analytical framework for BCVR based performance expression is developed in the next section.

BVCR based performance expression

The concept of "industrial performance" is multidimensional and relative in nature [START_REF] Li | Multi-criteria performance management methodology for decision support in industrial project selection problems[END_REF]. On one side, the performance of an industrial project can be assessed from multi points of view, multi levels and multi-criteria. Performance excellence in one aspect of cost, value or risk cannot guarantee the success of an industrial project. In addition, a performance expression depends on the objective to be met. It is also influenced by the time, the way and the conditions under which it is measured and interpreted. From a generic level, industrial performance can be defined by three perspectives: stakeholders, evaluation periods and evaluation variables. The definition is summarised (1). P = (S, T, VA)

(1) Where, -P is the overall performance of an industrial system; -S is a set of viewpoints from selected stakeholder(s) involved in the performance evaluation process;

-T is the time period over which the performance evaluation is carried out. It can be an instant, a life cycle phase or the whole duration of the system or project;

-VA is the set of evaluation variables to be considered. It is assumed that these variables can be categorised along the four dimensions: benefit, cost, value and risk.

Based on the particular context of the problem at hand, the evaluator selects the relevant performance components (i.e. key stakeholders, specific time periods and adequate evaluation variables) to define the scope of the performance evaluation problem. For a decision maker and a specific industrial system or project, an overall performance measure of one decision alternative can be quantitatively expressed as shown in (2).

P = (C, V, R) (2)
Where, C, V and R are the overall cost, value and risk of one specific decision alternative. They are expressed with a single quantitative expression within a range [0, 1]. Bigger numeric result represents better performance in a specific cost, value or risk dimension.

In the BCVR methodology [START_REF] Li | Performance evaluation and decision support for industrial system management: a benefit-cost-value-risk based methodology[END_REF], a visualisation tool is proposed to help the decision maker to graphically evaluate the overall performance compared to the predefined preferences (Fig. 2). This representation is based on the performance measurement of one specific decision alternative for one particular evaluation period. This visualisation and the estimation of overall performance expression can help in the following types of problems: (1) decision support based on benefit, cost, value and/or risk evaluation, this could be a priori analysis such as opportunity assessment of different alternatives while selecting the most appropriate one at the preliminary phase of an industrial system or de facto analysis such as decision making;

(2) performance evaluation at any stage of an industrial system, process or project (a priori, de facto or a posteriori) and (3) monitoring and control of an ongoing industrial project requiring performance evaluation steps at different phases along the life history of the project.

However, it should be noticed that the overall performance expressions for a selected evaluation period may not be accurate enough for the decision maker to compare different decision alternatives. Better performance results can only prove that the selected decision alternative is closer to the evaluator's objective at the time of evaluation, but it cannot assume that this alternative can always be the most performing solution in the subsequent evaluation periods along the project life history. Therefore, the concept of "performance variation" should be introduced to assess the evolution of performance over time.

PERFORMANCE VARIATION

For the purpose of prognosis, an adapted comprehensive performance expression is first introduced in this section. Then, definitions on the concept of performance variation are presented. Finally, the process for decision support by using the comprehensive performance expression is described.

Adapted overall performance expression

It is assumed that the performance expression for decision support should include two parts: (1) performance measurement for one specific time interval and (2) gap of performance variations (GA). The former is the overall value, cost and risk, which are obtained from the aggregation computation in the BCVR based methodology [START_REF] Li | Performance evaluation and decision support for industrial system management: a benefit-cost-value-risk based methodology[END_REF].

The latter is the difference between two overall expressions for one specific alternative in one certain performance dimension over the relevant time interval along a project life history. Finally, the overall performance expression for decision support can be adjusted as shown in (3).

P(A) = {(C, GA c ), (V, GA v ), (R, GA r )} (3)
Where, 𝐺𝐴 𝑐 , 𝐺𝐴 𝑣 and 𝐺𝐴 𝑟 are gaps of performance variations of the three dimensions: cost, value and risk. They should be computed based on different overall performance expressions.

To explain the process to generate the gap of performance variations, a set of concepts are proposed in the following section.

Proposed definitions

Definition 1: Performance variation (PV) is the difference between two results of performance measurement regarding the same alternative in terms of one dimension: cost, value or risk. It is computed by using (4).

PV c = ( C i -C j t i -t j ) , PV v = ( V i -V j t i -t j ) , PV r = ( R i -R j t i -t j ) (4)
Where,

-𝑃𝑉 𝑐 , 𝑃𝑉 𝑣 𝑎𝑛𝑑 𝑃𝑉 𝑟 are performance variations in terms of cost, value and risk;

-𝑡 𝑖 𝑎𝑛𝑑 𝑡 𝑗 are two instants when the performance measures are generated;

-𝐶 𝑖 -𝐶 𝑗 , 𝑉 𝑖 -𝑉 𝑗 𝑎𝑛𝑑 𝑅 𝑖 -𝑅 𝑗 are the differences between two performance measures of the same dimension at the selected moments. In most cases, it is supposed that the numeric expressions of the initial time, cost, value and risk in a decision making problem equal to 0, that is, the results of these elements 𝑡 0 , 𝐶 0 , 𝑉 0 , 𝑅 0 are set to 0.

Based on the type of performance measures, performance variations can be categorised in two types: desired and estimated variations.

Definition 2: Desired variation (DV) is the difference between two measures: (a) the desired quantitative measures at the end of the evaluation period -They are predefined by the decision maker; and (b) the performance expression at the initial instant of the relevant time interval. The mathematical expressions are given by ( 5).

DV c = ( C d -C 0 T -t 0 ) = C d T , DV v = ( V d -V 0 T -t 0 ) = V d T , DV r = ( R d -R 0 T -t 0 ) = R d T ,
with t 0 , C 0 , V 0 , R 0 = 0 (5)

Where,

-𝐷𝑉 𝑐 , 𝐷𝑉 𝑣 𝑎𝑛𝑑 𝐷𝑉 𝑟 are the desired variations in terms of cost, value and risk;

-𝑡 0 , 𝑡 𝑖 𝑎𝑛𝑑 𝑇 are the initial time, measurement moment and the end time of the performance evaluation period;

-𝐶 𝑑 -𝐶 0 , 𝑉 𝑑 -𝑉 0 𝑎𝑛𝑑 𝑅 𝑑 -𝑅 0 are the differences between the performance measure at time 𝑡 𝑖 and the initial performance measure of the same dimension.

Definition 3: Similarly, the estimated variation (EV) is the difference between two expressions: (a) the performance measures which are the outputs of the aggregation computation and (b) the performance expression at the initial instant of the relevant time interval, as shown in ( 6).

EV c = ( C i -C 0 t i -t 0 ) = C i t i , EV v = ( V i -V 0 t i -t 0 ) = V i t i , EV r = ( R i -R 0 t i -t 0 ) = R i t i , with t 0 , C 0 , V 0 , R 0 = 0 (6)
Where,

-𝐸𝑉 𝑐 , 𝐸𝑉 𝑣 𝑎𝑛𝑑 𝐸𝑉 𝑟 are the estimated variations in terms of cost, value and risk;

-𝐶 𝑖 -𝐶 0 , 𝑉 𝑖 -𝑉 0 𝑎𝑛𝑑 𝑅 𝑖 -𝑅 0 are the differences between the performance measure at time 𝑡 𝑖 and the initial performance measure of the same dimension.

Because the performance measures are influenced by the decision maker subjective judgment, the estimated variation should be adjusted.

Definition 4: The estimated variation after adjustment (EVA) is defined to take into consideration the random events which can influence the evaluation of the overall expression of one specific performance dimension along the life history of the system or project. The mathematical expression of the term EVA is given by ( 7).

EVA = EV × ε × c (7)
Where,

-𝜀 is a random number that represents the happening of random events. For the dimension of cost, the number is between -1 and 0, because the overall cost is always accumulated over time and the performance expression is decreasing. However, this number is between -1 and 1 for the dimensions of value and risk, because the overall value and risk can be increased or decreased over time.

c is a positive constant number between 0 and 1 which represents the degree of variance of one particular performance dimension according to the decision maker estimation.

In some cases, the decision maker needs to predict future performance of the project or process in order to improve the management control and generate more effective action plans for future steps. Hereby, the proposed terms can also be used to forecast the overall performance after a considered time interval. The predicted performance can be expressed as shown in (8).

P(A ′ ) = P(A) × (1 + EVA) (8)
Definition 5: To describe the uncertainty of the overall performance in one specific dimension, the term gap of variation (GA) is proposed. It is defined as the absolute value of the difference between desired variation and the maximum absolute value of estimated variation, as shown in ( 9).

GA = |DV -max |EVA|| = |DV -max |EV × ε × c|| (9)
Higher GA means the selected overall performance expression will have higher variation (it may lead to over performance or underperformance) regarding the desired result. However, it depends on the evaluator preference to define the acceptable level of the GA in a particular case.

The overall performance expression can be further applied to ease the decision making process in an industrial system. The detailed information is presented in the following section.

Decision support process

From the previous definitions, a process for decision support based on the comprehensive performance expression can be proposed as shown in Fig. 3.

Fig. 3. Overall performance expression for decision support

Thanks to the graphical presentation, the decision maker evaluates whether the overall performance obtained is acceptable. If there is no preferred solution, the action plan should be modified and a new performance measurement should be generated. If the answer is positive, the aim of the following step is to evaluate the GA to ensure this alternative can have a stable performance in the future phases of the project. With an acceptable GA, the alternative can be considered as a solution with reliable performance along the life history of a system or project. Otherwise, it means that even if the selected decision alternative has the preferred overall performance at the moment of evaluation, strong possibility may exist that the performance be subject to large variation in future phases of the project.

EXPERIMENTAL ILLUSTRATION

The application of the proposed model for comprehensive performance expression is illustrated on an application dealing with decision support in construction projects implementation. The main results are presented in this section.

Background

A building construction company simultaneously implements three construction projects which differ by complexity, duration, budget and variety of works. To make better use of shared material, financial and human resources to achieve higher profits, the company needs efficient performance evaluation for each of these projects during the implementation stage. Therefore, the final objective of the construction company is to achieve higher profit at the end of the implementation phase of the different construction projects. Based on industrial experience, ten evaluation criteria [START_REF] Li | Performance evaluation and decision support for industrial system management: a benefit-cost-value-risk based methodology[END_REF] are selected to generate the elementary performance expression.

BCVR based performance expression

Using the BCVR methodology, the benefits in this decision problem are summarised as: (1) increasing efficiency of the construction company in projects implementation and (2) internal and external improvement of the enterprise image. Then, the overall performance of each construction project can be quantitatively expressed on the following dimensions: cost, value and risk. Table 1 shows the results obtained. To help the decision maker in the comparison of different candidate projects, the overall performance expressions are displayed in the cost-value-risk graph (Fig. 4).

This graph shows that Projects 2 and 3 have much higher value than Project 1, while their cost and risk performance are also better. Regarding Projects 2 and 3, the latter can generate higher value with less risk and cost. Therefore, it can be concluded that the order of priority among these three projects is: Project 3 > Project 2 > Project 1.

Adjusted overall performance expression

To generate the performance variations, the desired expression for all candidate projects in each dimension are firstly defined by the decision maker based on decision preference. Other data such as the constant numbers c are then defined according to previous analyst experience for each dimension (namely, c 1 , c 2 and c 3 ).

Overall performance expressions

Graphical presentation

Is there an preferred alternative?

Evaluation of variations

Whether the gap of variations is acceptable? The implementation phase will last for 12 months. The moment decided for the performance expressions generated with the BCVR methodology is fixed at the end of the third month. It is supposed that the numeric expressions of the initial time, cost, value and risk in this decision making problem equal to 0. Table 2 presents the detailed information of the data used to generate the gaps of performance variations for the preselected Project 3.

Table 2. Gaps of performance variations for Project 3

C d V d R d C i V i R i c 1
c 2 c 3 0.65 0.75 0.65 0.81 0.63 0.57 0.1 0.6 0.3 C 0 V 0 R 0 t 0 t i T GA c GA v GA r 0 0 0 0 3 12 0.03 0.06 0.05 Finally, the adjusted overall performance expressions for Project 3 can be expressed as shown in Table 3. Table 3. Overall performance expressions for Project 3 Overall cost Overall value Overall risk (0.81, 0.03) (0.63, 0.06) (0.57, 0.05) Therefore, Project 3 has limited performance variations compared to evaluator objective. This alternative can always be the most performing solution in the subsequent evaluation periods along the project life history.

In addition, the evolution of the overall performance expressions for Project 3 from the performance evaluation time (t i = 3) to the end of the implementation stage (T=12) can be predicted as shown in Fig. 5. It can be assumed that the overall value of Project 3 can be significantly increased with limited cost and risk variations.

CONCLUSIONS

The proposed model expresses comprehensively the industrial performance at the time of evaluation, as well as the variation of the measures. It helps the decision maker to evaluate whether the preferred decision alternative can always be the most performing solution in the forth-coming performance evaluation periods. In addition, it improves the application of the BCVR methodology in decision support phase. The current proposal is mainly based on linear functions to generate performance variations. However, it is a fairly complex subject to estimate the deviation and liability of the overall performance expressions. Further experimental applications should be applied to verify robustness and improve the mathematical models if necessary.

Fig. 2 .

 2 Fig. 2. Performance expressions in a cost-value-risk graphWith such a 3D graph, the overall cost, value and risk of one decision alternative or more can be presented in a cost-valuerisk space to assist the decision maker to evaluate the performance of different decision alternatives denoted 𝑃 (𝑎𝑛) (with n=1,2,…n) (for example, different solutions or candidate projects) according to their preferences.

  Fig. 4. Plot of overall performance expressions in CVR graph

Fig. 5 .

 5 Fig. 5. Overall performance evolution for Project 3

Table 1 .

 1 Overall performance expressions of all projects

		Project 1 Project 2 Project 3
	Overall cost	0.67	0.79	0.81
	Overall value	0.25	0.60	0.63
	Overall risk	0.27	0.40	0.57


Simone Pádua Teixeira

Marina F B Costa

Paulo Basso-Alves

Finn Kjellberg

Rodrigo A S Pereira

Morphological diversity and function of the stigma in Ficus species (Moraceae)

Keywords: Brood-site pollination, Coevolution, Extra-gynoecial compitum, Synstigma, Moraceae, Nursery pollination

The stigma plays several roles such as pollen hydration and selection, and pollen tube nutrition. In the Ficus-fig wasp mutualism, stigmata have an additional, almost unknown, function by representing a physical interface for both plant and wasp reproduction. We used light and electron microscopy to compare the detailed morphology of the stigmata of nine Ficus species of different sections and with different pollination modes and sexual expressions. Figs were collected at the stage when the stigmata were receptive for pollination. Stigmata in actively pollinated monoecious species have well developed papillae concentrated on the adaxial surface exposed towards the fig cavity. Conversely, the passively pollinated monoecious species have the whole surface of the stigmata covered by somewhat smaller papillae. In both actively and passively pollinated monoecious species these features are consistent, irrespective of style length. In all actively pollinated gynodioecious species, the stigmata of pistillate flowers were tubular or infundibuliform whereas in almost all actively pollinated monoecious species (except F. racemosa) the stigmata were filiform, with one branch or two asymmetric branches. In gynodioecious species the short-styled flowers in "male" figs show a limited receptive surface with small papillae, while the stigmata of long-styled flowers in "female" figs are covered by papillae that extend down the sides of the style, increasing the stigmatic surface. In actively pollinated species, stigmata are cohesive, forming a common surface for pollen tube germination (= synstigma). The synstigma arrangement was quite variable: lax, cohesive or very cohesive, with entanglement by stigmatic papillae and stylar trichomes. Entanglement by stylar trichomes is common in gynodioecious species. The synstigma arrangement did not correlate with phylogeny or breeding system. This study is the first to report a very loose synstigma in actively pollinated monoecious Ficus species. Our analyses revealed that, in Ficus, the synstigma is functionally analogous to an extra-gynoecial compitum. Comparative studies will be required to test further hypotheses about the evolutionary determinants of such variation.

Introduction

The stigma is generally the apical extension of the carpel that receives the pollen grain and intercedes in the germination of the pollen tube [START_REF] Heslop-Harrison | Surfaces and secretions in the pollenstigma interaction: a brief review[END_REF][START_REF] Heslop-Harrison | The angiosperm stigma[END_REF]. Thus, the stigma is the site where pollination ends and the journey of the pollen tube toward the ovule begins [START_REF] Van Went | Fertilization[END_REF]. Although the function of the stigma is the same for all angiosperms, stigma structure (shape, cellular composition and secretion occurrence) and physiology are very diverse [START_REF] Edlund | Pollen and stigma structure and function: the role of diversity in pollination[END_REF][START_REF] Endress | Diversity and Evolutionary Biology of Tropical Flowers, Cambridge Tropical Biology Series[END_REF][START_REF] Heslop-Harrison | The angiosperm stigma[END_REF]. The shape of the stigma, for example, may be of taxonomic value [START_REF] Bigazzi | Stigma form and surface in the tribe Boragineae (Boraginaceae): micromorphological diversity, relationships with pollen, and systematic relevance[END_REF][START_REF] Brown | Stigma types in Bromeliaceae -a systematic survey[END_REF][START_REF] Heslop-Harrison | Stigma characteristics and angiosperm taxonomy[END_REF], in addition to being related to adaptations to pollen grain deposition, such as the plumose stigma in the anemophilous species of Poaceae [START_REF] Heslop-Harrison | The angiosperm stigma[END_REF], or requiring the visit/manipulation of an animal to become receptive to pollen germination [START_REF] Basso-Alves | Pollen and stigma morphology of some Phaseoleae species (Leguminosae) with different pollinators[END_REF][START_REF] Sigrist | Pollination and reproductive biology of twelve species of neotropical Malpighiaceae: stigma morphology and its implications for the breeding system[END_REF].

As a reflection of its morphological variation, the stigma can play several roles [START_REF] Edlund | Pollen and stigma structure and function: the role of diversity in pollination[END_REF], such as hydration of pollen grains [START_REF] Edlund | Pollen and stigma structure and function: the role of diversity in pollination[END_REF][START_REF] Heslop-Harrison | Surfaces and secretions in the pollenstigma interaction: a brief review[END_REF] and nutrition of growing pollen tubes [START_REF] Rejón | The plant stigma exudate[END_REF]. Because of its ability to stimulate or prevent the emission of pollen tubes, the stigma also plays a selective role in the germination of pollen grains (HeslopHarrison, 2000;[START_REF] Rejón | The plant stigma exudate[END_REF]. This control over the access of pollen tubes to style and ovary and, consequently, to ovules, is evidenced by systems of pollen-stigma recognition and compatibility [START_REF] Heslop-Harrison | Pollen-stigma interaction and cross-incompatibility in the grasses[END_REF][START_REF] Heslop-Harrison | The stigma surface in incompatibility responses[END_REF]. It should be noted that the selective role in pollen tube growth is not restricted to the stigma [START_REF] Erbar | Pollen tube transmitting tissue: place of competition of male gametophytes[END_REF][START_REF] Lora | The diversity of the pollen tube pathway in plants: toward an increasing control by the sporophyte[END_REF] but is also performed by the compitum [START_REF] Endress | Syncarpy and alternative modes of escaping disadvantages of apocarpy in primitive angiosperms[END_REF][START_REF] Wang | Extra-gynoecial pollen-tube growth in apocarpous angiosperms is phylogenetically widespread and probably adaptive[END_REF]. The compitum (from the Latin crossing or crossroads) is a term applied to places of convergence of several growing pollen tubes, forming a competition arena. It is found at the intersection of a pistil transmitting tissue in flowers with a syncarpic gynoecium [START_REF] Carr | The functional significance of syncarpy[END_REF][START_REF] Endress | Evolutionary diversification of the flowers in angiosperms[END_REF][START_REF] Erbar | Pollen tube transmitting tissue: place of competition of male gametophytes[END_REF].

Therefore, it seems evident that stigma shape and organization are highly associated with the type of pollination [START_REF] Edlund | Pollen and stigma structure and function: the role of diversity in pollination[END_REF]. However, much greater effort has been expended on elucidating the relationship between pollen and pollination (e.g., [START_REF] Banks | Pollen structure and function in caesalpinioid legumes[END_REF][START_REF] Hesse | Pollen wall stratification and pollination[END_REF][START_REF] Osborn | Pollen morphology and ultrastructure of the Cabombaceae: correlations with pollination biology[END_REF] than between stigma and pollination [START_REF] Heslop-Harrison | The angiosperm stigma[END_REF]. The study of the diversity of stigmata related to various types of pollination [START_REF] Basso-Alves | Pollen and stigma morphology of some Phaseoleae species (Leguminosae) with different pollinators[END_REF][START_REF] Jousselin | The functional implications of active and passive pollination in dioecious figs[END_REF] and breeding systems [START_REF] Katinas | The origin of the bifurcating style in Asteraceae (Compositae)[END_REF][START_REF] Lora | Stigmatic receptivity in a dichogamous earlydivergent angiosperm species, Annona cherimola (Annonaceae): influence of temperature and humidity[END_REF] is thus of great interest in general and for obligate mutualisms such as between fig trees (Ficus) and their agaonid pollinating wasps in particular [START_REF] Galil | On the pollination ecology of Ficus sycomorus in East Africa[END_REF].

Fig trees (Ficus L.) belong to the largest genus of Moraceae, comprising 841 of 1217 described species in the family (The Plant List, 2013). Its representatives are widely distributed in tropical, subtropical and temperate regions [START_REF] Berg | Moraceae diversity in a global perspective[END_REF]. The genus has as synapormorphy a distinct type of inflorescence called a syconium or fig, that consists of an urn-shaped receptacle. Internally the fig is covered by diclinous flowers (= unisexual) [START_REF] Berg | Reproduction and evolution in Ficus (Moraceae): traits connected with the adequate rearing of pollinators[END_REF][START_REF] Verkerke | Structure and function of the fig[END_REF] and presents a single opening to the outside, called an ostiole [START_REF] Berg | Reproduction and evolution in Ficus (Moraceae): traits connected with the adequate rearing of pollinators[END_REF][START_REF] Galil | On the pollination ecology of Ficus sycomorus in East Africa[END_REF]). These plants are involved in a notable specialized pollination mutualism with agaonid wasps [START_REF] Galil | On the pollination ecology of Ficus sycomorus in East Africa[END_REF].

About half the Ficus species are monoecious. Their figs contain staminate and pistillate flowers and therefore they produce pollen and seeds and provide a breeding place for the pollinating wasps. The other Ficus species are structurally gynodioecious but functionally dioecious, i.e., some individuals carry figs with long-styled pistillate flowers which produce only seeds ("female individuals"), while others ("male individuals") have figs with staminate flowers and short-styled flowers that are used by the pollinating wasps to deposit their eggs and which produce practically no seeds. Therefore figs in "male" fig trees produce pollen and wasp offspring [START_REF] Kjellberg | Biology, ecology and evolution of fig pollinating wasps (Chalcidoidea: agaonidae)[END_REF]. Monoecy is probably the ancestral character-state in the genus, with one (or more) change to gynodioecy and two reversals to monoecy [START_REF] Datwyler | On the origin of the fig: phylogenetic relationships of Moraceae from ndhF sequences[END_REF]Jousselin et al., 2003b;[START_REF] Weiblen | Phylogenetic relationships of functionally dioecious Ficus (Moraceae) based on ribosomal DNA sequences and morphology[END_REF].

The Ficus-fig wasp mutualism probably exerts a strong selective pressure over stigma morphology, as the stigma constitutes a physical interface for both plant and wasp reproduction. Indeed, stigma morphology is correlated with the pollination mode of different fig tree species, i.e. active or passive pollination (Jousselin et al., 2003a;[START_REF] Jousselin | The functional implications of active and passive pollination in dioecious figs[END_REF]. About 3/4 of all Ficus species are actively-pollinated. In these species females of pollinating wasps actively collect pollen from anthers before leaving their natal figs and place it in special thoracic structures called pollen pockets, in order to transport it to another fig whose pistillate flowers are receptive to pollination. Once inside a receptive fig, the female wasp removes some pollen from its pollen pockets each time it lays an egg and deposits it on the stigma surface [START_REF] Galil | Note on pollen transport, pollination and protection of ovaries in Ficus sycomorus[END_REF][START_REF] Ramírez -Benavides | Fig wasps: mechanism of pollen transfer[END_REF]. In actively pollinated Ficus species, stigmata can be cohesive, forming a common surface for pollen tube germination (= synstigma). Since actively pollinating wasps are selected to pollinate the flower in which they have just laid an egg, the synstigma seems to play a functional role ensuring seed production by allowing lateral growth of the pollen tube and hence limiting the capacity of wasp to control which flower is fertilized [START_REF] Jousselin | The functional implications of active and passive pollination in dioecious figs[END_REF]. However, in passively pollinated species stigmata are separated and elongated, brushing the surface of the wasp and thus the synstigma is absent.

The objective of the present study was to check at a detailed morphological level the stigmatic features selected in response to the Ficusfig wasp mutualism. To achieve this objective nine species of Ficus from different sections and with different modes of pollination and sexual expressions were compared in terms of stigma morphology. In addition, the morphology of stigmatic papillae in the highly cohesive synstigma of F. religiosa and F. racemosa was evaluated at the ultrastructural level. 2. Materials and methods Nine species from eight Ficus lineages (sections) -F. auriculata (section Sycomorus), F. crocata (section Americanae), F. lyrata (section Galoglychia), F. microcarpa (section Conosycea), F. obtusiuscula (section Pharmacosycea), F. racemosa (section Sycomorus), F. religiosa (section Urostigma), F. septica (section Sycocarpus) and F. ulmifolia (section Sycidium) (Table 1) -were studied. Ficus auriculata and F. racemosa were included as they represent a gynodioecious and a monoecious species, respectively, in sect. Sycomorus. Species names were based on C.C. Berg [START_REF] Berg | Taxonomic studies on Ficus (Moraceae) in the west indies, extra-amazonian Brazil and Bolivia[END_REF][START_REF] Berg | Flora Malesiana. Series I, Seed Plants[END_REF].

For monoecious Ficus species, stigmata of both shorter-and longerstyled pistillate flowers were analyzed. For gynodioecious species we studied long-styled flowers from figs of "female trees", except F. septica for which we studied short-styled flowers from "male trees" and longstyled flowers from "female trees".

Five figs (= inflorescences) of each species studied (from one individual/species) were collected at the stage when stigmata are receptive for pollination. Figs were cut in half and fixed in FAA 50 (formalin:acetic acid:alcohol) [START_REF] Johansen | Plant Microtechnique[END_REF] or in buffered formalin [START_REF] Lillie | Histopathologic Technic and Practical Histochemistry[END_REF] for 24-48 h, dehydrated in an ethanol series and processed for observation by light microscopy (LM), scanning electron microscopy (SEM) and transmission electron microscopy (TEM).

The external morphology of the stigmata was assessed by SEM. Previously fixed samples were dehydrated in an ethanol series, critical point dried in a Bal Tec CPD 030 critical point dryer, placed on stubs over carbon adhesive tape, and sputter coated with gold with a Bal Tec SCD 050 instrument. Images were obtained using a Jeol JSM-6610LV SEM.

Stigma anatomy was studied in samples embedded in methacrylatebased resin [START_REF] Gerrits | The Application of Glycol Methacrylate in Histotechnology; Some Fundamental Principles[END_REF] and cut into 5 μm thick sections with a Leica RM 2245 rotary microtome. Sections were stained with 0.05% toluidine blue in phosphate buffer as a general stain [START_REF] O'brien | Polychromatic staining of plant cell walls by toluidine blue O[END_REF] and with Sudan black B [START_REF] Pearse | Histochemistry, Theoretical and Applied: Preparative and Optical Technology[END_REF] to detect lipophilic substances. Anatomical sections were observed and photographed using a Leica DM 5000 B light microscope coupled to a Leica DFC 320 digital camera. Crystals were observed and shot with a Leica DM5000 B light microscope provided with a polarizing filter (PLM, [START_REF] Johansen | Plant Microtechnique[END_REF].

The ultrastructure of stigmatic cells was analyzed under TEM in Ficus religiosa and F. racemosa. Samples were fixed in Karnovsky's fixative [START_REF] Mcdowell | Histologic fixatives suitable for diagnostic light and electron microscopy[END_REF] for 24 h, post-fixed in 1% osmium tetroxide in 0.1M phosphate buffer (pH 7.2) and embedded in araldite. Ultrathin sections (60 nm thick) were obtained using a Leica Reichert Ultracut S ultramicrotome, collected on copper grids covered with Formvar, contrasted with 2% uranyl acetate and lead citrate for 15 min each [START_REF] Reynolds | The use of lead citrate at high pH as an electron-opaque stain in electron microscopy[END_REF], and examined with a Jeol 100CXII TEM.

Synstigmata were classified into cohesive or lax according to the degree of difficulty in separating fixed samples using a needle.

For simplicity, in gynodioecious species, the fig tree containing figs with long-styled pistillate flowers which produce only seeds we called a "female plant". The one in which figs have staminate flowers producing pollen and short-styled flowers that produce wasp offspring and no or almost no seeds we called a "male plant".

Results

The stigmata of the studied Ficus species are dry but differ in shape, size, and cellular composition of the stigmatic surface (Table 2). In all actively pollinated gynodioecious Ficus species studied the stigmata of pistillate flowers were tubular or infundibuliform (Table 2). Stigmata in actively pollinated monoecious Ficus species (except F. racemosa) have the well developed papillae concentrated only on the adaxial surface exposed towards the fig cavity. Conversely, the passively pollinated monoecious species have the whole surface of the stigmata covered by somewhat smaller papillae. The short-styled flowers of "male plants" show a limited receptive surface with small papillae, while the stigmata of long-styled flowers of gynodioecious species are covered by papillae that extend down the sides, increasing the stigmatic surface.

Ficus auriculata (gynodioecious, active)

The stigma (pistillate flower, female inflorescences) is tubular (Fig. 1A). The contact between the stigmata is lax. A synstigma can be formed by two to several stigmata (Fig. 1B). The external stigmatic surface is formed by papillae containing phenolic compounds and numerous large, central vacuoles (Fig. 1C). No druses (groups of crystals united by their centre and of calcium oxalate, silicates, or carbonate composition) are found.

Ficus crocata (monoecious, active)

The stigma of the shorter-and longer-styled flowers shows two highly asymmetric filiform branches (Fig. 2A) or a filiform branch (Fig. 2B). The contact between the stigmatic branches is tight, forming a cohesive synstigma (Fig. 2C) by the adherence of uni-or bicellular trichomes that compose the whole stigmatic surface (Fig. 2D andE) and the interweaving of branches. The synstigma can be formed of two to ten stigmata. The trichomes are covered by a thin, smooth cuticle and are formed by vacuolated cells (Fig. 2E). The transmitting tissue contains druses (Fig. 2F). No phenolic cells are found.

Ficus lyrata (monoecious, active)

The stigma of the shorter-and longer-styled flowers shows a filiform branch (Fig. 3A), and sometimes a second very shortened branch is apparent (Fig. 3B). The contact between the stigmatic branches is tight, forming a cohesive synstigma (Fig. 3C andD) by the adherence of uni-, bi-or tricellular trichomes that compose the adaxial stigmatic surface (Fig. 3D-F). The trichomes are covered by a thin, smooth cuticle and are formed by vacuolated cells (Fig. 3F).

Phenolic content is frequently observed in the basal cells of trichomes (Fig. 3F). The transmitting tissue contains druses (Fig. 3G).

Ficus microcarpa (monoecious, active)

The stigma of the shorter-and longer-styled has a filiform branch (Fig. 4A,E), and more rarely a second, very shortened branch (Fig. 4B). The contact between the stigmatic branches is lax, forming an atypical synstigma usually involving only two stigmata (Fig. 4C andD). The adaxial stigmatic surface is formed by papillae (Fig. 4D-F) covered with a thin, smooth cuticle (Fig. 4F). The transmitting tissue has some cells that contain druses (Fig. 4G). No phenolics are found.

Ficus obtusiuscula (monoecious, passive)

The stigma of the shorter-and longer-styled flowers displays two filiform branches, often unequal in length: shorter and less exposed in 5C andD). There is no contact between the stigmatic branches and therefore there is no synstigma (Fig. 5E). The stigmatic surface is formed by strongly vacuolated papillae (Fig. 5B, D) covered by a thin, ornamented cuticle. Papillae can have phenolic content (Fig. 5B,D). The length of the stigmatic branches and the papilla distribution are the main differences between the longer-and shorter-styled flowers (Fig. 5). The elongated stigmatic branches of longerstyled flowers reach much longer into the fig cavity than the short stigmatic branches of shorterstyled flowers. Papillae extend down the sides on the stigma of longer-styled flowers (Fig. 5A andB), whereas they are concentrated on the adaxial surface in shorter-styled flowers (Fig. 5C andD). The transmitting tissue has cells that contain druses (Fig. 5F).

Ficus racemosa (monoecious, active)

The stigma of the shorter-and longer-styled flowers is infundibuliform (Fig. 6A-C). The contact between the stigmata is tight, forming a cohesive and continuous synstigma (Fig. 6A) through the entanglement of papillae (Fig. 6B-D). The papillae are covered by a thin, ornamented cuticle. The cohesion between the stigmatic papillae is done by cell walls (Fig. 6E-G), a fact that makes the manual separation of stigmata difficult. In the region of contact between the papillae of different stigmata the middle lamella is discontinuous (Fig. 6F) or even missing (Fig. 6G), indicating that there is union between two cell walls. The transmitting tissue is composed of elongated or isodiametric cells that are vacuolated, have a dense cytoplasm, a conspicuous nucleus and sometimes druses.

Ficus religiosa (monoecious, active)

The stigma of the shorter-and longer-styled flowers has two highly asymmetric filiform branches. There is tight contact between the stigmatic branches, forming a cohesive and continuous synstigma (Fig. 7A) through the entanglement of long papillae that compose the stigmatic surface (Fig. 7B). The papillae are covered by a thin, smooth cuticle (Fig. 7C) and may contain phenolic compounds (Fig. 7B). The transmitting tissue consists of isodiametric cells that can contain druses (Fig. 7D). The cohesion between the stigmatic papillae is done by cell walls (Fig. 7E,F), a fact that makes the manual separation of stigmata difficult. In the region of contact between the papillae of different stigmata the middle lamella is discontinuous (Fig. 7E) or even nonexistent (Fig. 7F), indicating that there is union between two cell walls.

Ficus septica (gynodioecious, active)

The stigma of short-styled pistillate flowers (Fig. 8A) of "male figs" and long-styled pistillate flowers (Fig. 8B) of "female figs" is infundibuliform. There is no contact between the stigmata of short-styled flowers and therefore there is no formation of a synstigma (Fig. 8C). Conversely, the stigmata of long-styled flowers can be solitary or form groups of synstigma (Fig. 8B,D). The stigmata are tightly connected to each other by stigmatic papillae and stylar unicellular trichomes (Fig. 8B). The stigmatic surface is formed by slightly convex cells in short-styled flowers (Fig. 8E). The papillae in long-styled flowers extend down the sides of the stigma (Fig. 8F), are covered by a thin, smooth cuticle (Fig. 8G) and have phenolic content. The transmitting tissue is composed of isodiametric or elongated cells that have a dense cytoplasm and a prominent nucleus (Fig. 8E andF). There are no druses.

Ficus ulmifolia (gynodioecious, active)

The stigma of long-styled flowers of "female figs" is tubular (Fig. 9A). The stigma may be solitary or form a synstigma with several connected stigmata (Fig. 9A-C). The receptive stigmatic surface is formed by papillae (Fig. 9A,C,D) covered by a thin, smooth cuticle (Fig. 9D). The transmitting tissue is composed of elongated or isodiametric cells with a dense cytoplasm and a conspicuous nucleus. No druses or phenolic cells are observed. The fundamental structure of Moraceae pistillate flowers includes a gynoecium formed by two carpels, one of which does not produce an ovule, but can provide a second stigma [START_REF] Eckardt | Untersuchungen über Morphologie, Entwicklungsgeschichte und systematische Bedeutung des pseudomonomeren Gynoeceums[END_REF][START_REF] Payer | Traité d'organogénie comparée de la fleur[END_REF]. In several genera the stigmatic branches are unequal in length and some species have a single stigmatic branch [START_REF] Berg | Systematics and phylogeny of the urticales[END_REF]. Our morphological observations of Ficus should be interpreted within that framework. We show here wide variation in stigma structure among Ficus species. This variation can be analyzed within the context of variation in the fig species' biology and evolutionary history. Four basic types of reproductive systems are present in Ficus and could be expected to lead to convergent stigma adaptations. Ficus species may be monoecious or gynodioecious, and they may be actively or passively pollinated. In actively pollinated species, the wasps load pollen into specialized pollen pockets before leaving their natal fig, and each time they have deposited an egg into an ovule, before removing the ovipositor, they collect some pollen from the pocket and deposit it on the stigmata. In passively pollinated species, the body of the wasps becomes covered with pollen before they leave their natal fig, and when they enter a receptive fig, pollen is passively deposited, often due to the fact that the elongated stigmata brush the surface of the body of the wasp. In monoecious figs, pistillate flowers presenting a shorter pedicel and those located closer have longer styles and produce mainly seeds while pistillate flowers presenting a longer pedicel and located further from the fig wall often host insect larvae instead. Wasp larvae develop at the expense of developing endosperm [START_REF] Jansen-González | Mutualism from the inside: coordinated development of plant and insect in an active pollinating fig wasp[END_REF]. The endosperm may be triploid, initiated through the double fertilization of the fig embryo sac, or diploid, initiated parthenogenetically by the activity of pollinator larvae [START_REF] Leclerc Du Sablon | Observations sur les diverses formes du figuier[END_REF]. Data from a number of species show that passively pollinating wasp species do not benefit from carrying pollen, and that wasp larvae, in general, probably induce the parthenogenetic development of the endosperm, while in actively pollinating species the wasp larvae mainly rely on double fertilization to induce the developement of the endosperm (Beck and Lord, 1988a;[START_REF] Jansen-González | Mutualism from the inside: coordinated development of plant and insect in an active pollinating fig wasp[END_REF][START_REF] Verkerke | Syconial anatomy of Ficus asperifolia (Moraceae), a gynodioecious tropical fig[END_REF][START_REF] Verkerke | Anatomy of Ficus ottoniifolia (Moraceae) syconia and its role in the figfig wasp symbiosis[END_REF]. Our results show that the stigmata of the Ficus species studied show a diversity of morphological traits regarding their format, relative size of their branches and composition of the cellular surface. Despite their diversity, morphological specialization patterns were identified in pistillate flowers depending on the pollination mode. About one third of Ficus species are passively pollinated [START_REF] Kjellberg | Pollination mode in fig wasps: the predictive power of correlated traits[END_REF]. Reconstructions of the ancestral character state have suggested that active pollination has independently reverted to passive pollination at least five times (Jousselin et al., 2003b). In the passively pollinated monoecious F. obtusiuscula, the stigmatic branches of shorterstyled flowers are short with papillae concentrated on the upper surface and not extending down the sides, whereas the longer-styled flowers have two long stigmatic branches with papillae covered by an ornamented cuticle extending further than the short stigmata into the cavity of the fig, increasing the stigmatic extension and thus the chance of being pollinated (see Fig. 10). This is in agreement with the observation of more abundant pollen deposition on longer-styled flowers than on shorter-styled flowers in F. maxima, another species of section Pharmacosycea [START_REF] Jousselin | Flower specialization in a passively pollinated monoecious fig: a question of style and stigma?[END_REF].

Discussion

According to [START_REF] Berg | The subdivision of Ficus subgenus Pharmacosycea section Pharmacosycea (Moraceae)[END_REF], two distinct spatial presentations of the stigmata can be observed in section Pharmacosycea. In subsection Bergianane stigmata of longer-styled and shorterstyled flowers may reach the same height while in subsection Petenense stigmata of longerstyled flowers may project further into the fig cavity than those of shorterstyled flowers. Our observations on F. obtusiuscula as well as our unpublished obervations on F. adhatodifolia contradict this separation since both species belong to subsection Bergianae while the arrangement of flowers corresponds to Berg's description for subsection Petenense. We conclude that there is a single disposition of pistillate flowers in section Pharmacosycea, an arrangement in which the stigmata of longer-styled flowers project into the fig cavity and get most of the pollen while those of shorter-styled flowers do not reach the fig cavity and get little pollen [START_REF] Jousselin | Flower specialization in a passively pollinated monoecious fig: a question of style and stigma?[END_REF]. The phylogenetic placement of section Pharmacosycea within the genus Ficus is still controversial since this section corresponds to a recent diversification from an old stock, but it may be quite basal within Ficus and passive pollination could be ancestral [START_REF] Cruaud | An extreme case of plant-insect codiversification: figs and figpollinating wasps[END_REF], see Fig. 10). Some observations are also available for another passively pollinated Ficus belonging to a clade that is of active pollination ancestry, namely F. curtipes (subgenus Urostigma, section Conosycea) which is pollinated by a species of Waterstoniella [START_REF] Cruaud | Laying the foundations for a new classification of Agaonidae (Hymenoptera: chalcidoidea), a multilocus phylogenetic approach[END_REF]. An active pollination ancestry can be inferred from the presence of relictual pollen pockets in the genus Waterstoniella [START_REF] Kjellberg | Pollination mode in fig wasps: the predictive power of correlated traits[END_REF]. In F. curtipes, the stigmata have highly asymmetric filiform branches (giving a monofid aspect) and not two long stigmatic branches, but project into the fig cavity without forming a syntigma [START_REF] Zhang | Floral characteristics of Ficus curtipes and the oviposition behavior of its pollinator fig wasp[END_REF], and the stigmata of the longer-styled flowers project further than those of shorterstyled flowers into the fig cavity (Li Z., pers. com.). The connection of pollination mode and stigma morphology is evident in section Malvanthera, subgenus Urostigma. Subsections Hesperidiiformes and Malvantherae are representatives of an ancient condition of passive pollination in Malvanthera. In these groups in general traces of pollen pockets are absent in the pollinator species and fig species have stigmata with two long stigmatic branches. In Subsection Platypodeae there is active pollination and a transition to passive pollination. Pollinators representing this recent transition to passive pollination have relictual pollen pockets and their host fig species in general have stigmata with highly asymmetric branches or polymorphic stigmata [START_REF] Rønsted | Phylogeny, biogeography, and ecology of Ficus section Malvanthera (Moraceae)[END_REF]. In conclusion, monoecious species (and their pollinators) that correspond to recent transitions to passive pollination, such as F. curtipes and some species of subsection Platypodeae, probably share some morphological traits of actively pollinated species due to phylogenetic inertia.

The arrangement of stigmata in passively pollinated gynodioecious figs was analyzed in the case of Ficus carica (Beck and Lord, 1988b). In "female plants", the pistillate flowers show stigmata with two elongated branches very similar to those of the longer-styled stigmata of F. obtusiuscula with the presence of papillae all around the stigmatic branches. Pistillate flowers of "male plants" showed stigmata with two much shorter branches. Furthermore, the receptive (LM). Note that the stigmatic branches are shorter and less exposed in shorter-styled flowers and longer facing the syconium cavity in longer-styled flowers. F. Transmitting tissue with druses (PLM). Scale bars: A,C, D, F = 200 μm; B = 100 μm; E = 1 mm surface was reduced as in F. obtusiuscula. There is, however, a major difference since in "male plants" pollen germination and pollen tube growth are poor and may even be stopped by callose plugs, an adaptation that limits seed production in "male figs", while no such observation has been made in monoecious passively pollinated figs [START_REF] Jousselin | The functional implications of active and passive pollination in dioecious figs[END_REF]. Indeed, for the passively pollinated gynodioecious species for which experimental data are available, the proportion of pollen germination is significantly lower on stigmata of short-styled flowers [START_REF] Jousselin | The functional implications of active and passive pollination in dioecious figs[END_REF], and in F. deltoidea, a passively pollinated gynodioecious species, embryo sac fertilization in short-styled flowers is rare because only about 20% of all deposited pollen grains germinate and, among those that germinate, more than 70% of the resulting pollen tubes are blocked by a callose plug [START_REF] Jousselin | The functional implications of active and passive pollination in dioecious figs[END_REF]. Therefore, stigma shape and its cellular composition seem to play a functional role in the mutualism for these species, leading to specialization in seed or wasp production (i.e., pollen-vector) in passively pollinated species. For monoecious actively pollinated species we analyzed Ficus crocata, F. lyrata, F. microcarpa and F. religiosa belonging to lineages that may be of exclusively monoecious ancestry and one species (F. racemosa) belonging to a lineage of gynodioecious ancestry (see Fig. 10). In the species of monoecious ancestry, the stigmata show two highly asymmetric branches, giving the aspect of a single elongated branch. They are not comparable to the stigmata of F. obtusciuscula as they do not project into the fig cavity. Instead they form an imperfect platform and only the side of the stigma turned towards the fig cavity presents numerous conspicuous elongated papillae. While we observed much variation in the precise arrangement of the stigmata, the general pattern was homogeneous. What is heterogeneous is the connectivity between stigmata. In some cases synstigmata are extremely intimate as in F. religiosa, while in other species the connection is lax. The disposition of stigmata in F. racemosa was very different and must be interpreted by comparison with the stigmata of actively pollinated gynodioecious species. In all actively pollinated gynodioecious Ficus species, the stigmata of pistillate flowers were tubular or infundibuliform (see Fig. 10). The short-styled flowers of "male plants" show a limited receptive surface with small papillae, as in F. septica of subgenus Sycomorus (this study) and F. asperifolia of subgenus Sycidium [START_REF] Verkerke | Structure and function of the fig[END_REF], while the stigmata of long-styled flowers of gynodioecious species are covered by papillae that extend ; down the sides, increasing the stigmatic surface [START_REF] Verkerke | Structure and function of the fig[END_REF]present study). In "male figs", the consistently tubular shape of stigmata, without elongated branches and with a limited receptive surface, agrees with their interpretation as an adaptation allowing female wasps to deposit pollen precisely on the stigma of the flower into which their ovipositor is inserted just after laying an egg into the ovule [START_REF] Jousselin | The functional implications of active and passive pollination in dioecious figs[END_REF]. The presence of tubular stigmata in "female figs" may be due to genetic correlations between "male and female plants". In this context, a synstigma can be seen as an adaptation that can favor secondary dispersal of pollen tubes when pollen deposition is limiting. In agreement with a hypothesis of frequent limiting numbers of pollen grains, fig pollen is exceptionally small in size for insect-pollinated plants (about 10 μm), in both actively and passively pollinated Ficus species [START_REF] Wang | Has pollination mode shaped the evolution of Ficus pollen?[END_REF]. This feature suggests selection for increased numbers of pollen grains due to limiting pollen, rather than selections for competitive capacity of the pollen tubes. In agreement, conditions of pollen loading in parental figs were shown to affect the pollination capacity of pollinating wasps in an actively and a passively pollinated Ficus species [START_REF] Kjellberg | Some pollinators are more equal than others: factors influencing pollen loads and seed set capacity of two actively and passively pollinating fig wasps[END_REF]. Variation in cohesiveness of stigmata into forming a synstigma could be interpreted as a result of stronger or weaker selection favoring secondary pollen dispersal by lateral growth of pollen tubes resulting from more or less clumped deposition of pollen by the wasps. An extreme situation for actively pollinated figs can be found in "female figs" of F. montana in which stigmata are perfectly separated (F. Kjellberg, unpublished data). Within Ficus, tubular or infundibuliform stigmata are perhaps found in all actively pollinated gynodioecious species and in all the species belonging to subgenus Sycomorus that have reverted to monoecy, including all species of section Sycomorus subsection Sycomorus, but also F. microdyctia and F. pritchardii [START_REF] Corner | Ficus subg. Pharmacosycea with reference to the species of New Caledonia[END_REF]. Hence, the stigmatic structure documented here in the monoecious Ficus racemosa (and in Ficus sur, [START_REF] Verkerke | Structure and function of the fig[END_REF] is to be explained by the combination of active pollination and dioecious ancestry.

The synstigma arrangement of the Ficus species studied was quite variable. The entanglement of stigmata can be lax (e.g., F. auriculata, F. microcarpa and F. ulmifolia), cohesive (e.g., F. lyrata and F. septica) or very cohesive (F. racemosa and F. religiosa). This synstigma arrangement is clearly not correlated with the phylogenetic position of the species or with their breeding system (see Tables 1 and2, Fig. 10). The entanglement of stigmata can occur by trichomes found on the style or by stigmatic papillae. Entanglement by stylar trichomes is common in [START_REF] Corner | Ficus dammaropsis and the multibracteate species of Ficus sect. Sycocarpus[END_REF] and F. hispida [START_REF] Basso-Alves | Different ontogenetic processes promote dicliny in Ficus L. (Moraceae)[END_REF]] and Sycidium [e.g., F. asperifolia [START_REF] Verkerke | Syconial anatomy of Ficus asperifolia (Moraceae), a gynodioecious tropical fig[END_REF]]. However, intrasection variation in the type of stigma entanglement can occur, as observed in F. racemosa comparatively to F. auriculata (Basso-Alves et al., 2014; present study) and in F. ulmifolia comparatively to F. asperifolia (present study) in which stylar trichomes are absent. Furthermore, stigmata are perfectly separated in "female" F. montana (unpublished observation). An entanglement of stigmata through papillae, forming loose or cohesive synstigmata is generally found in monoecious actively pollinated species, as reported here in F. lyrata, F. microcarpa, F. racemosa and F. religiosa. In F. religiosa and F. racemosa the tight cohesion between papillae is provided by the cell walls. In the region of contact between papillae, the middle lamella is discontinuous or even absent, indicating that there is true union of cell walls. In the other Rosales, an order to which Moraceae belongs (APG IV, 2016), a structure similar to a synstigma was reported in two Procris species (Urticaceae, [START_REF] Weberling | Morphology of Flowers and Inflorescences[END_REF] and in Rosa setigera (Rosaceae, [START_REF] Kemp | Floral development of Rosa setigera[END_REF]. In Procris the congested inflorescence organization seems to promote the union of stigmata in inflorescences with pistillate flowers. In Rosaceae, species belonging to the section Synstylae are characterized by the presence of a column of united styles and a synstigma.

The Ficus gynoecium is functionally apocarpic, since a reduction occurs (i.e., pseudomonomery) that results in a uniovulate pistil per flower [START_REF] Eckardt | Untersuchungen über Morphologie, Entwicklungsgeschichte und systematische Bedeutung des pseudomonomeren Gynoeceums[END_REF]. In taxa that have a syncarpic gynoecium, the region of pollen tube assembly is called a compitum [START_REF] Endress | Evolutionary diversification of the flowers in angiosperms[END_REF] and allows the equitable distribution of the pollen tubes between carpels [START_REF] Endress | Gynoecium structure and evolution in basal angiosperms[END_REF] in addition to acting as a site of selection and competition of the pollen tubes [START_REF] Endress | Syncarpy and alternative modes of escaping disadvantages of apocarpy in primitive angiosperms[END_REF]. In this context, the synstigma of Ficus is functionally analogous to an extragynoecial compitum, as reported for some apocarpic plant groups, such as Austrobaileyaceae [START_REF] Endress | Syncarpy and alternative modes of escaping disadvantages of apocarpy in primitive angiosperms[END_REF][START_REF] Endress | Gynoecium structure and evolution in basal angiosperms[END_REF], Illiciaceae [START_REF] Endress | Gynoecium structure and evolution in basal angiosperms[END_REF], Monimiaceae [START_REF] Endress | Noncarpellary pollination and "hyperstigma" in an angiosperm (Tambourissa religiosa, Monimiaceae)[END_REF][START_REF] Endress | Diversity and evolutionary trends in the floral structure of Tambourissa (Monimiaceae)[END_REF], Nymphaeaceae [START_REF] Endress | Gynoecium structure and evolution in basal angiosperms[END_REF], and Schisandraceae [START_REF] Du | Intercarpellary growth of pollen tubes in the extragynoecial compitum and its contribution to fruit set in an apocarpous species, Schisandra sphenanthera (Schisandraceae)[END_REF][START_REF] Endress | Syncarpy and alternative modes of escaping disadvantages of apocarpy in primitive angiosperms[END_REF][START_REF] Lyew | Pollen tube growth in association with a dry-type stigmatic transmitting tissue and extragynoecial compitum in the basal angiosperm Kadsura longipedunculata (Schisandraceae)[END_REF], in its distribution of pollen components. A common type of extra-gynoecial compitum, found among basal angiosperm lineages, involves abundant stigmatic mucilaginous exudate [START_REF] Endress | Evolutionary diversification of the flowers in angiosperms[END_REF][START_REF] Endress | Noncarpellary pollination and "hyperstigma" in an angiosperm (Tambourissa religiosa, Monimiaceae)[END_REF][START_REF] Endress | Gynoecium structure and evolution in basal angiosperms[END_REF][START_REF] Endress | Diversity and evolutionary trends in the floral structure of Tambourissa (Monimiaceae)[END_REF][START_REF] Wang | Extra-gynoecial pollen-tube growth in apocarpous angiosperms is phylogenetically widespread and probably adaptive[END_REF], this mucillage constituting a medium for pollen germination, selection and distribution. An extreme case of this condition is described as "hyperstigma" in Monimiaceae [START_REF] Endress | Syncarpy and alternative modes of escaping disadvantages of apocarpy in primitive angiosperms[END_REF][START_REF] Endress | Noncarpellary pollination and "hyperstigma" in an angiosperm (Tambourissa religiosa, Monimiaceae)[END_REF]. Indeed, some Monimiaceae species show many affinities with Ficus pollination biology. At least species of Mollinedia, Steganthera and Wilkiea seem to be involved in a breeding-site pollination mutualism with Thysanoptera insects and the gross appearance of their flowers resembles the inflorescence of Ficus [START_REF] Endress | Noncarpellary pollination and "hyperstigma" in an angiosperm (Tambourissa religiosa, Monimiaceae)[END_REF]. However, the Ficus stigma appears to be dry [START_REF] Heslop-Harrison | The receptive surface of the angiosperm stigma[END_REF][START_REF] Ramírez-Benavides | Pollination analogies between orchidaceae, Ficus (Moraceae) and asclepiadaceae[END_REF], and their mutual cohesion is mechanical, similar to that provided by the post-genital union of the distal parts of carpels of Apocynaceae, Malvaceae and Sapindales (Endress et al., 1983;[START_REF] Vieira | Oxypetalum banksii subsp. banksii: a taxon of Asclepiadaceae with an extragynoecial compitum[END_REF].

Conclusions

The main differences in stigma structure documented here in Ficus can be readily explained in adaptive and historical terms. However, within each type of reproductive system (active versus passive pollination, monoecious versus gynodioecious breeding system), variation in synstigma structure is observed, even within sections, suggesting that within a general system, the fine biology of the interaction between figs and wasps may vary. For instance, this study is the first to report a very loose synstigma in actively pollinated monoecious species. Further investigation could replicate species within Ficus groups, especially from subgenus Synoecia, sections Eriosycea and Oreossycea, and subsection Frutescentiae that were not included here. Also, comparative studies will be required to test further hypotheses about the evolutionary determinants of such variation.

Fig. 1 .

 1 Fig. 1. Stigmata of long-styled flowers of Ficus auriculata (gynodioecious, active, "female syconium"). A. Tubular stigmata (SEM). B. Synstigma formed by the entanglement of stylar trichomes and of stigmatic papillae (LM). C. Short phenolic papillae (dark blue content) forming the stigmatic extension (LM). Scale bars: A = 100 μm; B = 1 mm; C = 50 μm

Fig. 2 .

 2 Fig. 2. Stigmata of longer-styled flowers of Ficus crocata (monoecious, active). A. Stigma with two highly asymmetric filiform branches (SEM). B. Stigma with a single filiform branch (SEM). C. Synstigma formed by the entanglement of stigmatic trichomes (LM). D. Anatomy of a synstigma formed by three stigmas (transverse section, LM). E. Detail of a synstigma showing the entangled stigmatic trichomes. Note that they are formed by one or two cells (transverse section, LM). F. Transmitting tissue with druses (longitudinal section, PLM) Symbols: e = stigma. Scale bars: A, B = 100 μm; C = 1 mm; D, F = 100 μm; E = 50 μm.

Fig. 3 .

 3 Fig. 3. Stigmata of longer-styled (A, C, D) and shorter-styled (B, E, F, G) flowers of Ficus lyrata (monoecious, active). A. Stigma with a filiform stigmatic branch (SEM). B. Stigma with two highly asymmetric filiform branches (SEM). C. Cohesive synstigma (LM). D. Synstigma of two stigmata formed by the entanglement of trichomes (SEM). E. Stigmatic trichomes formed by one, two or three cells (LM). F. Trichomes covered by a thin, smooth cuticle and with phenolic content (LM). G. Transmitting tissue with druses (PLM). Scale bars: A, B, E, G = 200 μm; C = 2 mm; D = 100 μm; F = 20 μm

Fig. 5 .

 5 Fig. 5. Stigmata of shorter-styled (A, B) and longer-styled (C, D, E, F, G) flowers of Ficus obtusiuscula (monoecious, passive). A. Stigma formed by two short symetric filiform branches (SEM). B. Stigmatic branches covered by papillae concentrated on the adaxial side (LM). C. Stigma formed by two long asymetric filiform branches (SEM). D. Stigmatic branches covered by papillae spread on the adaxial and abaxial sides (LM). E. Stigmatic branches without contact

.

Fig. 6 .

 6 Fig. 6. Stigmata of pistillate flowers of Ficus racemosa (monoecious, active). A. Cohesive and continuous synstigma (SEM). B. Detail of the synstigma surface formed by the tight entanglement of papillae (SEM). C. Anatomy of the synstigma showing the tight entanglement of papillae (LM). D. Detail of the union of cell walls of several papillae (TEM). E. Two cell walls showing a discontinous middle lamella (TEM). F. Two cell walls showing no middle lamella (TEM). Symbols: cw = cell wall; e = stigma, p = papilla. Scale bars: A = 500 μm B = 100 μm; C = 200 μm; D = 3 μm; E, F = 1 μm.

Fig. 7 .

 7 Fig. 7. Stigmata of pistillate flowers of Ficus religiosa (monoecious, active). A. Cohesive and continuous synstigma (LM). B. Synstigma formed by the entanglement of long papillae (LM). C. Detail of papillae in a connection of two stigmata (LM). D. Druses in the transmitting tissue

Fig. 8 .

 8 Fig. 8. Stigmata of short-styled (A, C, E) and long-styled (B, D, F, G) flowers of Ficus septica (gynodioecious, active). A. Infundibuliforme stigma (SEM). B. Infundibuliform stigma covered by papillae. Note the stylar trichomes (SEM). C. No synstigma is found in a "male syconium"

Fig. 9 .

 9 Fig. 9. Stigmata of a long-styled flower of Ficus ulmifolia (gynodioecious, active). A. Tubular stigmata (SEM). B. Synstigma formed by the entanglement of papillae (LM). C. Several

Table 2

 2 Stigma morphology of the Ficus species studied. SSF = shorter-styled flower, LSF = longerstyled flower, NA = not applicable, + = present, -= absent.

	Species	Floral	Shape	Synstigma	Cuticle	Surface	Druse	Phenolic
		morph		arrangement	thickness and	cellular	occurrence	cell
					ornamentation	composition		occurrence
	Ficus auriculata	LSF tubular	lax, 1 to stigmata several	thin, smooth papillae	-	+
	F. crocata	SSF	2 highly	cohesive, 2	thin, smooth uni or	+	-
		LSF	asymetric	to 10		bicelular
			filiform	stigmata		trichome
			branches
	F. lyrata	SSF	1 filiform	cohesive, 2	thin, smooth uni to	+	+
		LSF	branch; rarely a	to several		tricellular
			second short	stigmata		trichome
			branch
	F.	SSF	1 filiform	lax,	thin, smooth papillae	+	-
	microcarpa	LSF	branch; rarely a	generally 2
			shortened	stigmata
			branch
	F.	SSF 2 short filiform	NA	thin,	short	+	+
	obtusiuscula		branches		ornamented	papillae
		LSF 2 long			papillae
			asymmetric

shorter-styled flowers (Fig.

5A and B

), and long, facing the fig cavity in longer-styled flowers (Fig.

Acknowledgments

We thank Edimárcio S. Campos (Botany Laboratory, FCFRP/USP), José Fig. 10. Phylogenetic hypothesis showing the stigma diversity found in the species studied of Ficus (modified from Cruaud et al., 2012). The terminal branches show the stigma shape and cellular composition in shorter-styled flower (SSF) and longer-styled flower (LSF), the pollination mode (A = ative, P = passive) and the sexual expression Augusto Maulin, Maria Dolores Seabra Ferreira (LMME, FMRP/ USP) and Rodrigo F. Silva (Chemistry Department, FFCLRP/USP) for technical assistance, Priscila C. Costa, Fernando H. A. Farache (FFCLRP/USP) and Lillian J. V. Rodriguez (University of the Philippines Diliman) for some Ficus samples, and Elettra Greene for the English revision. This work was supported by FAPESP (grant numbers 2012/ 02374-2 and 2014/07453-3); CNPq (grant numbers .