Serge Haddad
email: serge.haddadd@lsv.ens-cachan.fr

Lynda Mokdad
email: lynda.mokdad@univ-paris12.fr

Samir Youcef
email: samir.youcef@lamsade.dauphine.fr

Response time of BPEL4WS constructors

Keywords: composite Web service, BPEL constructors, response times, heavy-tailed

Response time is an important factor for every software system and it becomes more salient when it is associated with introducing novel technologies, such as Web services. Most performance evaluation of Web services are focused toward composite Web services and their response time.One important limitation of existing work is in the fact that only constant or service exponential time distribution are considered. However, experimental results have shown that the Web services response times is typically heavy-tailed, in particulary, if there are heterogeneous. So, heavy-tailed response times should be considered in the dimensioning Web services. In this study, we propose analytical formulas for mean response times for structured BPEL constructors such as sequence, flow and switch constructors, etc. The difference with previous studies in the literature, is that we consider heterogenous servers, the number of invoked elementary Web services can be variable and the elementary Web services response times are heavy-tailed.

I. INTRODUCTION

Service oriented computing utilizes services to support lowcost, flexible software. The underlying services are looselycoupled, thus allowing rapid change of such systems. Although a framework for defining the functional interfaces of Web services has been established, non-functional properties remain under-development. The Web services architecture is defined by W3C (The World Wide Web Consortium) in order to determinate a common set of concepts and relationships that allow different implementations working together. The Web services architecture consists of three entities, the service provider, the service registry and the service consumer. The service provider creates or simply offers the Web service. The service provider needs to describe the Web service in a standard format WSDL (Web Service Description Language), which is often XML, and publish it in a central service registry UDDI (Universal Description, Discovery and Integration). The service registry contains additional information about the service provider, such as address and contact of the providing company, and technical details about the service. The service consumer retrieves the information from the registry and uses the service description obtained to bind and to invoke the Web service, using the SOAP (Simple Object Access Protocol) protocol.

Elementary Web services, such as described by WSDL, are conceptually limited to relatively simple functionalities modeled through a collection of simple operations. However, for certain types of applications, it is necessary to combine a set of individual Web services to obtain more complex Web services, called composite or aggregated Web services. This last is possible using BPEL4WS (Business Process Execution Language For Web Services) standard, which is the result of the merger of the previous languages such WSFL (Web Services Flow Language) and XLANG (XML Business Process Language). One important issue within Web service composition is related to their Quality Of Service (QoS), which must be guaranteed for an adhesion clients. Web services quality of services is a combination of several properties and may include availability, security, response time, and reliability of Web services. For this, quantitative methods are needed to understand, to analyse and to operate such large infrastructure.

The goal of our research is to propose an extension of a recent study [START_REF] Haddad | Response-time analysis of composite Web services[END_REF], where we have taken into account different statistical characteristics for the services and a random number of invoked services and Web service response time are supposed exponential with different parameters, contrarily to the models presented by Manascé [START_REF] Menascé | Response-time analysis of composite Web services[END_REF] and Sharf [START_REF] Sharf | On the response time of the large-scale composite Web services[END_REF]. However, most existing work only considers constant or exponential service times. As will be shown in [START_REF] Vallamsetty | Characterization of ecommerce traffic[END_REF] [START_REF] Crovella | Self-similarity in World Wide Web traffic: Evidence and possible causes[END_REF], measurements in the WWW and in e-commerce systems have observed heavytailed server response time distributions. In this study, we take into account the fact that the Web services response time is typically heavy-tailed, like Pareto distribution, which is attributed to the burstiness of arriving requests [START_REF] Vallamsetty | Characterization of ecommerce traffic[END_REF]. More precisely, the objective of this paper is to consider the heavytailed response times in the dimensioning of web service platforms.

The rest of the paper is structured as follows. Section II presents the related work. Section III details the different structured BPEL constructors. Section IV presents analytical formulas for response time of these constructors. In section V, we give the response time formula for multi-choice pattern which is a generalization of switch constructor. Numerical results are given in section VI. Finally, section VII concludes and gives some perspectives to this work.

II. RELATED WORK

Major works in the domain of Web services performance are concentrated towards composite Web services and their response time. Although there have been several studies reported on the workload characetrization of general Web servers, where the response-time distribution is found to be heavytailed, which has been attributed to the heavy-tailed nature of request and response file-sizes [START_REF] Vallamsetty | Characterization of ecommerce traffic[END_REF] [START_REF] Sahinoglu | On multimedia networks: Self-similar traffic and network performance[END_REF]. However, most existing work only considers constant or service exponential time distribution. Only few studies have been taken into account this result on the computation of composite Web services response time. Actually, the execution of a composite service have been studied as a fork-join model in [START_REF] Menascé | Response-time analysis of composite Web services[END_REF], where Web services response time are supposed exponential with the same parameters, excepted one which is slower than others. This model states that a single Internet application invokes many different Web services in parallel and gathers their responses from all these launched services in order to return the results to a client. Sharf [START_REF] Sharf | On the response time of the large-scale composite Web services[END_REF] studies the response time of a centralized middleware component performing largescale composition of web services. This last work is similar to the first study [START_REF] Menascé | Response-time analysis of composite Web services[END_REF], that analyzes the effects of exponential response times. The work is more oriented towards studying fork-join model in order to understand the merger of results from various servers. More recently, [START_REF]Optimal Service Selection Heuristics in Oriented Architectures[END_REF] proposed how service providers can optimally allocated to support activities of business process with topologies that can include any combinaison of BPEL constructors. However, authors are content to propose a general formula for a given composite Web service without giving the exact result when the service of elementary Web services are know. The exact response time of fork and join system, under some hypothesis, can be found in [START_REF] Hahn | Two parallel queues created by arrivals with two demands[END_REF]. However, these last state that the number of servers is equal to two, the job arrival is Poisson process and the tasks have exponential service time distribution. Nelson and Tantawi [START_REF] Nelson | Approximate Analysis of Fork/Join Synchronization in Parallel Queues[END_REF] proposed an approximation in the case where the number of servers is greater or equal to two and homogeneous exponential servers. Thereafter, a more general case is presented in [START_REF] Bacelli | The fork and join Related Systems with Synchropnization constraints: Stochastic Ordering and Computable Bounds[END_REF] [START_REF] Bacelli | Simple computable bounds for the fork-join qeue[END_REF], where arrival and service process are general. An upper and lower bound are obtained by considering respectively G/G/1 and D/G/1 queuing parallel systems. Klingemann and al. [START_REF] Kiczales | Aspect-oriented programming[END_REF] use a continuous Markov chain to estimate the execution response time and the cost of workflow. In [START_REF] Kiczales | Aspect-oriented programming[END_REF], authors propose an algorithm which determines the QoS of a Web service composition by aggregating the QoS dimensions of the individual services, based on a collection of workflow patterns defined by Van der Aalst's and al. [START_REF] Van Der Aalst | Workow patterns[END_REF], where Web services response times are supposed constants. These QoS include upper and lower bounds of execution time as well as throughput. In [START_REF] Bhatti | Simulation-based Response Time Analysis of composite Web Services[END_REF], we have studied end-to-end response time for composite Web services representing a factor of Internet overhead in the execution model, using simulation technique. Contrarily to these previous studies, where the servers are not heterogenous, their number is always constant and their response times are supposed exponential, the aim of this paper is to overcome theses limitations. Thus, we propose analytical formulas for mean response time of composite Web services assuming that servers are heterogenous, the number of invoked elementary Web services can be variable.

III. BPEL CONSTRUCTORS

Business Process Execution Language for Web services (BPEL4WS) has been built on IBM's WSFL (Web Services Flow Language) and Microsoft's XLANG (Web services for Business Process Design) and combines accordingly the features of a block structured language inherited from XLANG with those for directed graphs originating from WSFL [START_REF] Curbera | Business Process Execution Language for Web Services[END_REF]. The language BPEL is used to model the behavior of both executable and abstract processes.

• An abstract process is a not an executable process and which is a business protocol, which use process descriptions that specify the mutually visible message exchange behavior of each parts involved in the protocol, without revealing their internal behavior. • An executable process specifies the execution order between a number of activities constituting the process, the partners involved in the process, the messages exchanged between these partners and the fault and exception handling specifying the behavior in cases of errors and exceptions. In the BPEL process each element is called an activity which can be a primitive or a structured one. The set { invoke, receive, reply, wait, assign, throw, terminate, empty } are primitive activities and the set {sequence, switch, while, pick, flow, scope} are structured activities. In this paper, we are interested on the sequence, flow and switch activities also called constructors. In the following, we give analytical formulas to evaluate the response times to each considered constructor.

IV. RESPONSE TIMES OF STRUCTURED BPEL

CONSTRUCTORS

In this section, we give analytical formulas for mean response times for structured BPEL constructors and we consider the case that the execution time of each elementary Web service s i , of a composite Web service S, is heavy-tailed and we consider also that the number of invoked elementary services are variable. The Pareto function distribution is given by the following equation :

F (t) = 0 t ≤ k 1 -( k t ) α t > k (1)
which has an infinite variance for α < 2 and is then heavytailed. Thus, we consider in the following the control patterns supported by BPEL standard. More specifically, the control patterns considered are: sequence, parallel split (flow), exclusive choice (switch), multi-choice. This last pattern is not directly supported by BPEL, but we can implement it using control links inherited from WSFL.

A. Computation for the sequence constructor

The sequence constructor correspond to a sequential execution of s 1 to s n elementary Web services. The analytical formulas of mean response time E(T sequence ) is given by the following proposition:

Proposition 1: When elementary Web services s i , i = {1..n} are exponentially distributed, the mean response time of composite Web service S is given by:

E(T sequence ) = n i=1 E(T i ) (2)
Proof: The execution time of composite Web service S composed by n elementary Web services is given by: T sequence = n i=1 T i which is easier to derive from equation [START_REF] Menascé | Response-time analysis of composite Web services[END_REF].

Case of homogeneous servers. In the case where T i , i ∈ {1, ..., n} are random variables with Pareto distributions with parameters (α, k) for each T i , the mean response time of composite Web service S is trivial and is given by:

E(T sequence par ) = n kα α -1
Case of heterogenous servers. As we notice before, we overcome the limitation of other studies by considering that the servers are heterogeneous. Thus, we consider that the execution time of k elementary services s i follow a Pareto distribution with rate (α 1 , k 1 ) and the execution time of n -k services follow a Pareto distribution with rate (α 2 , k 2 ). Thus, the response time for a composite Web service S is given by:

E(T sequence par ) = k 1 α 1 α 1 -1 k + k 2 α 2 α 2 -1 (n -k)

B. Computation for the flow constructor

One the most important benefits of the component approach is the interoperability. This inherent interoperability that comes with using vendor, platform, and language independent XML technologies and the ubiquitous HTTP as a transport mean that any application can communicate with any other application using Web services. Thus, the client only requires the WSDL definition to exchange message with the service. However, in the WSDL language, the elementary Web services are conceptually limited to relatively simple operations. In fact, for certains types of applications it is necessary to combine a set of elementary Web services into composite Web services. These services are generally invoked in parallel, using the flow constructor. Thus, in this section, we are focused on the mean response time of a composite Web service S which is composed by n elementary services invoked in parallel. In [START_REF] Menascé | Response-time analysis of composite Web services[END_REF], the author give an analytical formula for the response time of flow constructor but he supposes that n is fixed and elementary Web services are exponential service time distribution. Our contribution is to consider that n is random and Web services are heterogenous.

In the following, we give an analytical expression for the mean response time:

E(T f low ) = n i=1 ∞ 0 tf i (t) n j =i F j (t)dt (3)
where:

T f low = M ax{T i , i = 1, n}
As we assume that the random variables T i are independents, the cumulative function of random variable T f low is given by:

F (T f low ) = P (T f low ≤ t) = n i=1 F i (t)
Thus the probability density of T f low is:

f T f low (t) = n i=1 f i (t) n j =i F j (t) (4)
Thus E(T f low ) can be easily derived.

Case of Pareto distributions. We give in the following the mean response time analytical formula where the random variables T i , i ∈ {1, ..., n} are Pareto distributed with parameters

(α i , k i ), i ∈ {1, ..., n}. E(T f low par ) = n i=1 αik α i i X∈P(En\{i}) (-1) X β -( j∈X α j +α i -1 ) j∈X αj + αi -1 j∈X αj kj (5)
Where:

β = max(k i , i ∈ {1...n}
) and E n = {1, ..., n} and P(E n \ {i}) the sub -set of E n without {i}.

Proof: From equation 4, the probability density of random variable T f low par is given by:

f T f low par (t) = 0 if t ≤ max{k i , i = 1...n} ; n i=1 αik α i i t α i +1 n j =i (1 -( ki t ) αi ) else.,
As we have:

n j =i (1 -( k i t ) αi ) = X∈P(En\{i}) (-1) |X| j∈X k j t αj
Thus, the average response time is:

E(T f low par ) = n i=1 α i k α i i X∈P(En\{i}) (-1) |X| ∞ β t -j∈X α j -α i j∈X α j k j dt
As we have:

∞ β t -j∈X αj -αi dt = β -( j∈X αj +αi-1) j∈X α j + α i -1
Thus we obtain that the mean response time for a composite Web service S is given by the following formula:

E(T f low par ) = n i=1 αik α i i X∈P(En\{i}) (-1) X β -( j∈X α j +α i -1 ) j∈X αj + αi -1 j∈X αj kj
Case of homogeneous servers. In the case of all elementary service times are Pareto distributed with same rates (α i , k i ) = (α, k) (i.e ∀i ∈ {1, ..., n}), α i = α, k i = k). In this case the response time for S is given by:

E(T f low par ) = nαk α n-1 m=0 (-1) m k (-(m+1)α-1) (k α ) m (m + 1)α -1 C m n-1 (6) Where: C m n-1 = (n -1)! m!(n -1 -m)!
Case of heterogeneous servers. In the case where n -k elementary service times follow a Pareto distribution with parameters α 1 , k 1 and k elementary service times follow a Pareto distribution with rates α 2 , k 2 . Let factor g which is the slowdown factor such that k2α2

1-α2 = ( k1α1 1-α1 )g. With these assumptions, the response time of S is as follows:

E(T f low par ) = R 1 + R 2 (7)              R1 = (n -k)α1k α 1 1 n-1 m=0 m j=0 (-1) m k -((j+1)α 1 +(m-j)α 2 -1) 1
((j+1)α 1 +(m-j)α 2 -1) R2 = kα2k α 2 2 n-1 m=0 m j=0 (-1) m k -(jα 1 +(m-j+1)α 2 -1) 2 (jα 1 +(m-j+1)α 2 -1)
This equation ( 7) is easily derived by the equation ( 5) by considering that (α i , k i ) = (α 1 , k 1 ), ∀i ∈ {1, ..., n -k} and (α i , k i ) = (α 2 , k 2 ), ∀i ∈ {n -k + 1, ..., n}.

C. Computation for the switch constructor

In this case, we consider that we have one choice of n elementary Web services. Let P (Y = i) the invocation probability of elementary Web service i, with n i=1 P (Y = i) = 1. The response time of switch constructor is then given by the following analytic formula:

E(T switch ) = n i=1 P (Y = i)E(T i ) (8)
with E(T i ) the mean response time of service i.

Proof: First we calculate the probability density of the random variable T switch . The cumulative distribution function of the variable T switch is defined as: F T switch (t) = P (T switch ≤ t). According to the total probability theorem, we have:

F T switch (t) = n i=1 P (T switch ≤ t | Y = i)P (Y = i)
Thus, probability density function of random variable T switch is given by:

f T switch (t) = n i=1 f Ti (t)P (Y = i)
The definition of the average of T switch allow to deduce the result given in equation [START_REF] Nelson | Approximate Analysis of Fork/Join Synchronization in Parallel Queues[END_REF].

Case of Pareto distribution.

As in this paper, we consider the case of exponential distribution time for each elementary service time, thus the formula for mean response time is given by:

E(T switch par ) = n i=1 α i k i α i -1 P (Y = i) (9)
Case of heterogeneous servers. As well as in the case of the previous presented constructor, we give in the following the response time for the case that the execution times of elementary services are not the same:

E(T switch par ) = n-k i=1 P (Y = i) α 1 k 1 α 1 -1 + n i=n-k+1 P (Y = i) α 2 k 2 α 2 -1 (10
) In the next section, we are interested to multi-choice pattern which is not supported directly by BPEL, but it can be implemented using the links controls inherited from WSFL.

V. COMPUTATION FOR THE multi-choice PATTERN

The difference with the previous pattern where only one Web service is chosen, the multi-choice pattern allows the invocation of a subset of elementary services among the n possible. Take for example the case of a booking flights operated as follows: Web services invoked depend on two criteria namely the city of departure and destination. Next, according to these cities, agencies providing this trip are invoked on parallel. The number of services, and relied on is random. Let N the random variable for the number of invoked services and P (N = i) the probability that the number of invoked service is equal to i, with n maximum number of the invoked services. In this case, the response time of composite web service S is given by the following formula:

E(T multichoice ) = n i=1 [P (N = i)E(T S i )] (11)
Where E(T S i ) is the mean response time for composite Web service S when i elementary services are invoked.

Proof:

First, we give the cumulative function F T multichoice (t) of random variable T multichoice . F T multichoice (t) = P (T multichoice ≤ t). From totaly probability theorem, we can obtain:

F T multichoice (t) = P ( n i=1 {P (T multichoice ≤ t) ∧ N = i})
The events (N = i, i ∈ {1, ..., n}) are incompatible, so:

F T multichoice (t) = n i=1 P (T multichoice ≤ t ∧ N = i) thus, F T multichoice (t) = n i=1 P (T multichoice ≤ t | N = i)P (N = i) So: F T multichoice (t) = n i=1 P (T S i ≤ t)P (N = i)
The cumulative function of T multichoice is:

F T multichoice (t) = n i=1 F T S i (t)P (N = i)
We can derive the probability density f T multichoice of T multichoice and we obtain:

f T multichoice (t) = n i=1 f T S i P (N = i)
Case of homogenous servers. As, we consider the case that the elementary service execution times are Pareto distributed with (α, k) parameters and the invocation probability of elementary service s i is p, thus the mean response time for composite Web service S can be easily derived from equation [START_REF] Kiczales | Aspect-oriented programming[END_REF] and is given as follows:

E(T multichoice par ) = n λ n i=1 C i n p i (1 -p) n-i γ(i) (12)
Where:

γ(i) = iαk α i-1 m=0 (-1) m k (-(m+1)α-1) (k α ) m (m + 1)α -1 C m i-1
Case of heterogeneous servers. We give also the analytical formula for composite Web service response time where we consider two classes of elementary services. The execution time in each class is the same. N 1 (resp. N 2 ) is the random variable which defined the number of elementary services in class 1 (resp. class 2). The mean response time formula is also derived from equation [START_REF] Kiczales | Aspect-oriented programming[END_REF] and is given by:

E(T multichoice par ) = n i=1 P (N 1 = i) k j=0 E(T multichoise (i, j))P (N 2 = j | N 1 = i) (13)

VI. EXPERIMENTAL RESULTS AND DISCUSSIONS

In this section, we present some numerical computation and results that we have obtained. When two class of services are considered, let first define a heterogenous coefficient noted g, such as k2α2 1-α2 = g k1α1 1-α1 (the mean response time of elementary Web services belong respectively to class one and two). It is clear that if g = 1, then all of elementary Web services belong to the same class (i.e. the elementary Web services are homogeneous). However, if g > 1 means that Web services belong to the second class are slower than services belong to the first class. For simplicity, we assume that the probability of elementary Web services invocation is p for all services. The synchronization time, when g = 1, is the same for any value for the number of elementary Web services belong to the second class denoted N 2 . In figure 1, we give the response times by varying the slowdown factor g and where we consider different values of the number of elementary services for second class which takes these values N 2 = 20, N 2 = 60, N 2 = 80 and N 2 = 100. In figure 2, we give the response times by varying the the number of elementary services for second class and we consider the case of g = 2, g = 3, g = 4 and g = 5. From figure 1, we can conclude two things. First, for any value of N 2 , the synchronization response time increases linearly with the heterogeneous coefficient g. Second, when g = 1 the response time of the composite Web service is the same for any value of the elementary Web services belong to the second class. From figure 2, we Slowdown factor (g)

N 2 =100 N 2 =80 N 2 =60 N 2 =20
Fig. 1. Response times for composite Web service versus slowdown factor g can notice that the waiting time increase logarithmicaly with invocation probability p. It is clear that the response time increases logarithmicaly with the number of invoked Web services (see figure 3). So, we can conclude that the choice of elementary Web services must be made on their physical characteristics and not on their number.

In the figure 4, we shown the evolution of Texp Tpar , where T exp and T par is the response time of a composite Web services when respectively the response time of elementary Web services is exponential and heavy-tailed. The results

VII. CONCLUSION

Web Services are based on a set of standards and protocols, that allow us to make processing requests to remote systems by exchanging with a common language, and using common transport protocols. Once deployed, Web services provided can be combined (or inter-connected) in order to implement business collaborations, leading to composite web services. With the proliferation of Web Services as a business solution to enterprise application integration, the quality of service offered by Web Services is becoming the utmost priority for service provider and their partners. The QoS is defined as a combination of the different attributes of the Web services such as availability, response time, throughput, etc. In this paper, we have focused in the response time of composite Web services. We have proposed analytical formulas for the mean response In this paper, we have studied the Pareto distribution. It is justified by the fact that experimental studies shown that Web services response time is typically heavy-tailed. However, the methodology can be applied to other service response time distributions.

We plan to consider the dynamic composition of Web services and we will give the analytical formulas for BPEL constructors as a perspective study.

  the composite Web service (S)

Fig. 2 .Fig. 3 .

 23 Fig. 2. Response time for composite Web service versus slowdowns Web services

Fig. 4 .

 4 Fig. 4. Application slowdown factor Texp Tpar versus Web services number

* This work is supported by French research projects CheckBound ANR-06-SETI-002 and Perso ANR-07-JCJC-0155-01


Prof Sonal Kulkarni-Joshi

Discussant -Shahzaman Haque

Shahzaman Haque
email: shahzaman.haque@inalco.fr

Titre : Language, Culture and Identity among Internally Displaced Tribals in Nandurbar (Maharastra): A sociolinguistic perspective

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

First of all, I want to thank Michel Boivin for having invited me here as a discussant. I am also very thankful to Sonal Kulkarni-Joshi and I am really honored to comment on your text. This text is devoted to a very important issue concerning the sociolinguistic and socio-cultural dimensions of displacement and resettlement of two tribes due to the construction of dams in Western India, notably in the state of Maharashtra. As Kulkarni-Joshi pointed out, this paper is about the sociolinguistic consequences of the migration in terms of retention of /change in patterns of language use and socio-cultural practices. The methodology dwells on sociolinguistic and ethnographic tools. Data were collected from the original village and the resettled villages of the tribes. The objective of the project is to find the patterns of continuity and change in language use and sociolinguistic practices among the tribal communities in their original and resettled villages.

Let us first start from the river Narmada. This river starts from Amarkantak in the Shahdol district of Madhya Pradesh and it travels around 1312 km before it falls into the Gulf of Cambay near Gujarat. The Narmada Valley Development Project was the mastermind of the Gujarat government. While only 70 km of river stretches into Gujarat and the rest accross the two other states Gujarat has claimed that it is a drought-prone area and portrayed the Narmada Project as its lifeline. However, one can understand very well the drought-prone problem of Gujarat as it is a coastal part of India and the problem is not as severe as it is represented. According to Jashbai [START_REF] Patel | Is national interest being served by Narmada project?[END_REF], the Gujarat government declares some region as drought-prone to score some political capital in order to gain some welfare schemes to please its people. Gujarat's dam building policies have earlier damaged the Maharashtrian adivasis and later have also affected the Rajasthani tribes by building a dam at Kadana. Internal displacements for the sake of development projects is a big issue in India as we can see in other cases when looking at dam-building politics around the world such as Mekong Delta Dam Project in Vietnam. Few studies, particularly from a sociolinguistic viewpoint have been taken to comprehend the consequences on the language practices of the individuals affected. Undoubtedly, there is also a cultural and linguistic loss which are at stake. In this regard, I find your work highly stimulating and challenging. I find that your contribution is very significative not only in the field of sociolinguistics but also for policy makers particularly concerning tribal groups.

According to GOI (1985), around 40% of the tribals are affected because of development projects and one of the major reasons for such displacements is dam building projects because vast chunks of land are absorbed in the process. The Land Acquisition Act 1894 was the central act empowering the government to acquire land. The Act was amended first in 1984, later in 2013 and now that is hugely controversial because the current BJP government wants to amend the bill, which seems that it is very much in favour of the corporate sector. The Land Acquisition Bill in India gives very few powers to the people, because, once the government decides to take away the land for any public project, there are few chances to fight the decision. One can imagine the plight of tribal groups who have been subjected to forced displacements due to the Land Acquisition Act. The foundation of the Sardar Sarovar Project was laid in 1961. [START_REF] Dhagamwar | The Sardar Sarovar Project: A study in sustainable development[END_REF] indicate that in the initial phase of the Sardar Sarovar Project, land was acquired by «mutual consent» as the landless and powerless knew that they could not stand up effectively against the government's decision.

Bhils and Pawras are two distinct tribal groups and for both their main occupations are as daily wage labourers, hunters or land cultivators. Despite this commonality of working life, it has been noticed that in Lakkadot (Madhya Pradesh), Pawras regard Bhils as inferior because the Pawras are financially better off. Basu (1992: 197) wrote that in Shahda Taluka, Udaspur village which comes under Nandurbar Headquarter, Pawras consider themselves from Rajput clans and they remain politically inactive. Bhils are low waged poor peasants and they often borrow money from Pawras which may lead to disputes between the two groups.

Remarks and questions

I didn't understand the use of the term «sociolinguistic methodology», perhaps you meant to use the term sociolinguistic tools instead ? I would like to know : What are the other tools apart from questionnaires or interviews you have used in order to elicit your data ? Which ethnographic tools and observations have been most beneficial to you ? Have you relied upon «Outcropping», an ethnographic tool coined by David Fetterman, which helps to give information on the landscape, with things like burned-out buildings, graffiti etcetera? Perhaps you have noticed linguistic markers inside households during your fieldtrip which might have helped you to refine your data. What was the the language of communication between you and informants? Were you perceived as «outsider», as we say in the ethnographic jargon? Are you also considered as «researchwalla from Pune» as you were referred to in the Kupwar region?

The construction of the dams started in 1979. I wonder : Was there any sociolinguistic study conducted about the displacement between 1979 and 1994 in this region ? If we consider it started in 1961, when the foundation of the Sardar Sarovar was laid, it has been around 33 years, and that's about one generation. It means then that the families displaced since 1961 are now in their second generation of resettlement. The resettled villages are Narmadanagar and Rewanagar, both of them are found in Madhya Pardesh where the main official language is Hindi and other dialects of Hindi such as Nimari are spoken over there. Rozwa is the village found in Gujarat. What are the languages of communication among the two tribes in the resettled villages who are affected by the Sardar Sarovar Project? Are the languages of the parents transmitted to the children? What are the languages spoken by the second generation or by the children? What is the status of parental languages vs the status of prestigious official languages like Marathi or Hindi or Gujarati inside the household?

If some of you are familiar with my work, which also covers the intergenerational transmission of parental languages among the Indian diaspora in Europe, it has been found that the role of women were instrumental [START_REF] Haque | Transmission des langues natives aux deuxièmes générations : le cas de la diaspora indienne en Europe nordique et occidentale[END_REF]. They have imbibed the traditional values with pride and took the necessary steps in order to transmit the heritage language and culture in some families. I am interested in knowing the role of women in Bhils and Pawara tribal groups in the retention of heritage language.

Concerning the linguistic attrition and gain : In what language have you noticed losses and gains in the lexicon? As the story-telling practices have ceased to exist, has it also meant that there is a significant loss of cultural and linguistic transmission ? Does the impact on socio-cultural practices have consequences for the tribal languages? Can you illustrate examples of folkloric items that «got lost» in the migration process and on the contrary of some that have been retained ? And, your hypothesis or observations on why it is so? Did you have any information about the belief-system of these two groups? Is there any particular sacred language to perform the rites? The deities for Pawara tribe are mainly animals, nature, hills, forests etc. Do they use the Pawri language during their prayers? How does the tribal identity articulate with the religion and cope with the sudden rise in e economic status? What were your observations about the changes in identity? Do Bhils and Pawras benefit from any reservation in terms of jobs and education?

Conclusion

I find the study fascinating. The interplay between place, language, culture, identity, migration in your research work shows a complex phenomenon of societal dynamics. The gales of development projects, based on national capitalism, have uprooted the tribal groups. There is an attrition of heritage language besides significant loss in cultural practices under the overarching status of Marathi language entwined with urban culture's influence.


Sébastien Larrue
email: sebastien.larrue@uca.fr

Jean-Luc Baray

Julien Chadeyron

Jean-Yves Meyer

Lucas Mazal

Curtis C Daehler

Boris Fumanal

Modeling long-distance seed dispersal of the invasive tree Spathodea campanulata in the Society Islands

Keywords: atmospheric transport model, barrier effect, biological invasion, tropical oceanic islands

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Due to their small land area, geographic isolation, and high level of endemism, the remote oceanic islands of the Pacific Ocean are particularly susceptible to biological invasions [START_REF] Keppel | Isolated and vulnerable: the history and future of Pacific Island terrestrial biodiversity[END_REF]Larrue, 2013;[START_REF] Loope | Characteristics of invaded islands, with special reference to Hawaii[END_REF][START_REF] Meyer | Threat of invasive alien plants to native flora and forest vegetation of Eastern Polynesia[END_REF][START_REF] Russell | Invasive alien species on islands: impacts, distribution, interactions and management[END_REF]. The distribution of alien species on the Society Islands has been well documented (e.g., [START_REF] Fosberg | Vegetation of the Society Islands[END_REF][START_REF] Fourdrigniez | Guide Protection des îles contre les espèces envahissantes en Polynésie française. Guide de reconnaissance et de gestion des espèces[END_REF][START_REF] Meyer | Threat of invasive alien plants to native flora and forest vegetation of Eastern Polynesia[END_REF][START_REF] Meyer | Critical issues and new challenges for research and management of invasive plants in the Pacific islands[END_REF][START_REF] Meyer | Tahiti's native flora endangered by the invasion of Miconia calvescens DC. (Melastomataceae)[END_REF][START_REF] Pouteau | Using range filling rather than prevalence of invasive plant species for management prioritisation: the case of Spathodea campanulata in the Society Islands (South Pacific)[END_REF], but our knowledge about long-distance seed dispersal of invasive plants between neighbouring islands is still very limited, although it is crucial for understanding plant invasions and the potential for a 'bridgehead effect' [START_REF] Ricciardi | Invasion science: a horizon scan of emerging challenges and opportunities[END_REF][START_REF] Trakhtenbrot | The importance of longdistance dispersal in biodiversity conservation: LDD in conservation[END_REF]. A bridgehead effect is said to occur when one population of an invasive species serves as the source of origin for many geographically distant populations of that invasive species [START_REF] Lombaert | Bridgehead effect in the worldwide invasion of the biocontrol harlequin ladybird[END_REF], but assessing the possibility of a bridgehead effect requires identifying sources of geographically distant invasive populations and their pathways of movement.

The invasiveness of introduced plants in new geographic areas may be related to longdistance seed dispersal, and some invasive plants have natural modes of seed dispersal that potentially allow them to be dispersed over long distances (e.g., [START_REF] Egawa | Wind dispersal of alien plant species into remnant natural vegetation from adjacent agricultural fields[END_REF][START_REF] Higgins | Predicting plant migration rates in a changing world: the role of long-distance dispersal[END_REF][START_REF] Soons | Non-random seed abscission, long-distance wind dispersal and plant migration rates[END_REF]. What constitutes a long-distance seed dispersal event from a source population may depend on the context of the study, and no consensus definition exists for what distance qualifies as long-distance dispersal [START_REF] Jordano | What is long-distance dispersal? And a taxonomy of dispersal events[END_REF]. Some researchers consider a seed dispersal event to be of long-distance if it is over 80-100 m [START_REF] Bullock | Long distance seed dispersal by wind: measuring and modelling the tail of the curve[END_REF][START_REF] Cain | Long-distance seed dispersal in plant populations[END_REF][START_REF] Tackenberg | Modeling long distance dispersal of plant diaspores by wind[END_REF] or several kilometers [START_REF] Jordano | Frugivores, seeds, and genes: analysing the key components of seed shadows[END_REF] up to thousands of kilometers [START_REF] Muñoz | Wind as a longdistance dispersal vehicle in the southern hemisphere[END_REF]. Two approaches are generally used to define long-distance dispersal: it can be based (1) on the probability distribution of dispersal distances for the species under study, corresponding to the farthest distances reached by a small proportion of all dispersed seeds, or (2) being greater than a fixed distance [START_REF] Nathan | Mechanisms of Long-distance Seed Dispersal[END_REF].

Field measurements of the seed dispersal trajectories and distances are generally feasible only within the vicinity of a source tree (e.g., using seed traps), while projections of long-distance seed dispersal are needed over the scale of several kilometres to predict plant invasion patterns [START_REF] Kuparinen | Modeling air-mediated dispersal of spores, pollen and seeds in forested areas[END_REF], since long-distance seed dispersal and initial establishment may promote secondary establishment in other remote geographic areas, thus increasing global rates of invasions [START_REF] Bertelsmeier | Recurrent bridgehead effects accelerate global alien ant spread[END_REF][START_REF] Garnas | Complex patterns of global spread in invasive insects: eco-evolutionary and management consequences[END_REF].

For wind-dispersed seeds, it is well known that wind velocity is an important determinant of seed dispersal distance [START_REF] Cousens | Dispersal in Plants: A Population Perspective[END_REF]. Wind dispersal distance is also related to seed traits such as seed mass, shape and terminal velocity, as well as plant life form (e.g., [START_REF] Einzmann | Dispersal and establishment of vascular epiphytes in human-modified landscapes[END_REF]Green & Johnson, 1989[START_REF] Schupp | Seed-seedling conflicts, habitat choice, and patterns of plant recruitment[END_REF][START_REF] Pasquill | Atmospheric Diffusion[END_REF][START_REF] Tackenberg | Modeling long distance dispersal of plant diaspores by wind[END_REF][START_REF] Tamme | Predicting species' maximum dispersal distances from simple plant traits[END_REF][START_REF] Zotz | Measuring the terminal velocity of tiny diaspores[END_REF].

Models that consider a combination of plant height, seed traits and horizontal wind speed may be most useful to estimate the potential long-distance dispersal and invasion range for winddispersed plants [START_REF] Thomson | Seed dispersal distance is more strongly correlated with plant height than with seed mass[END_REF]. However, recent studies showed that the maximum dispersal distances predicted by models based on key plant traits (e.g., growth form, dispersal syndrome, seed terminal velocity) were underestimated compared to those measured under field conditions [START_REF] Egawa | Wind dispersal of alien plant species into remnant natural vegetation from adjacent agricultural fields[END_REF][START_REF] Herrmann | Connectivity from a different perspective: comparing seed dispersal kernels in connected vs. unfragmented landscapes[END_REF]. Simulations indicate that expected dispersal distances increase with decreasing terminal velocity, and this change in dispersal distance is particularly dramatic between terminal velocities of 0.4 m s -1 and 0.2 m s -1 [START_REF] Kuparinen | Modeling air-mediated dispersal of spores, pollen and seeds in forested areas[END_REF]; this range of terminal velocity is associated with a transition towards greater influence of atmospheric disturbances on particle dispersal and reduced influence of gravity. These discrepancies between modelled dispersal distances based on plant traits and actual field dispersal distances, may highlight the importance of including wind behaviours (i.e., vertical, horizontal and swirling wind) together with wind-speed data when predicting dispersal distances. Thus, for plants with wind-dispersed seeds, models assessing the potential for airborne seed dispersal across long-distances based on atmospheric mechanisms affecting particle movement are needed, even though they cannot be directly verified with field observations [START_REF] Kuparinen | Modeling air-mediated dispersal of spores, pollen and seeds in forested areas[END_REF].

Atmospheric models have been used to predict the long-distance dispersal of various organisms, including weeds or invasive species. For example, the Hybrid Single-Particle Lagrangian Integrated Trajectory model (HYSPLIT) of the National Oceanic and Atmospheric Administration (NOAA), which was first created to observe the atmospheric dispersal of pollution [START_REF] Draxler | HYSPLIT (HYbrid Single-Particle Lagrangian Integrated Trajectory) Model access via NOAA ARL READY website[END_REF] has been used to predict wind dispersal of some invasive insects, such as the cotton boll weevil in Texas [START_REF] Kim | Multidisciplinary fingerprints: forensic reconstruction of an insect reinvasion[END_REF], and to confirm the passive long-distance dispersal of insects vectoring pathogens in Australia [START_REF] Eagles | Modelling spatio-temporal patterns of long-distance Culicoides dispersal into northern Australia[END_REF] and invasive Hymenoptera in France [START_REF] Lander | Reconstruction of a windborne insect invasion using a particle dispersal model, historical wind data, and Bayesian analysis of genetic data[END_REF]. The model used in these studies was based on a digital elevation model and meteorological data at relatively low spatial resolution and did not incorporate the dispersing organism's terminal velocity during aerial transport. These limitations are likely to affect model predictions of an invader's atmospheric dispersion [START_REF] Egawa | Wind dispersal of alien plant species into remnant natural vegetation from adjacent agricultural fields[END_REF][START_REF] Liu | Long-distance and dynamic seed dispersal from horseweed (Conyza canadensis)[END_REF].

In this paper, we examine the wind seed dispersal potential of an invasive alien tree across Pacific Islands by using a recent atmospheric model. This model considers trees at different elevations above sea level, the terminal velocity of the seed, and climatic conditions that seeds may experience during their flight. Specifically, we focus on assessing the potential for longdistance seed dispersal of the alien invasive evergreen tree Spathodea campanulata P. Beauv., 1865 [Bignoniaceae] in the Society Islands (French Polynesia, South Pacific Ocean).

S. campanulata was first introduced to the island of Tahiti as a garden ornamental tree in 1932 and has since spread into natural environments across Tahiti, mainly through wind dispersal [START_REF] Meyer | Mécanismes et gestion des invasions par des plantes introduites dans des forêts naturelles à Hawaii et en Polynésie française : une étude de cas[END_REF]. This invasive tree has also been reported on five other high volcanic islands of the Society archipelago: Bora Bora, Huahine, Moorea, Raiatea, and Tahaa [START_REF] Fosberg | Handwritten and unpublished notebook field of F.R. Fosberg[END_REF][START_REF] Fourdrigniez | Guide Protection des îles contre les espèces envahissantes en Polynésie française. Guide de reconnaissance et de gestion des espèces[END_REF]. It is not known whether S. campanulata reached these remote islands by means of human transportation or wind dispersal from the island of Tahiti. A previous study using a simple model with terminal velocity and typical trade wind speeds suggested long-distance seed dispersal of 42 km [START_REF] Larrue | Seed rain, dispersal distance and germination of the invasive tree Spathodea campanulata on the island of Tahiti, French Polynesia (South Pacific)[END_REF]. However, because this projection did not consider patterns of wind variation or advection, the natural dispersal distance of S. campanulata could have been dramatically underestimated.

We hypothesize that the wind dispersed seeds of the alien invasive tree S. campanulata can travel long distances naturally from the island source of Tahiti to other remote Society Islands, and thus the Tahiti population serves as a source for invading populations discovered in other geographically isolated islands. We also examined the potential for a "barrier effect" (i.e., interception of seeds by island topography during aerial transport from Tahiti) that may be caused by combined effects of island elevation and spatial geography.

MATERIAL AND METHODS

Study species

Commonly called African tulip tree, S. campanulata (here after Spathodea) is a large tropical tree native to the wide Equatorial region of Africa [START_REF] Smith | Impact of alien plants on Hawaii's native biota. In Hawaii's terrestrial ecosystems: preservation and management[END_REF]. Spathodea trees introduced in the Pacific Islands originated from West Africa [START_REF] Sutton | Genetic matching of invasive populations of the African tulip tree, Spathodea campanulata Beauv. (Bignoniaceae), to their native distribution: Maximising the likelihood of selecting host-compatible biological control agents[END_REF]. In 1998, Spathodea was designated to be a species threatening native biodiversity by the Government of French Polynesia (decree 244 CM of the 12 February). Since that date, the planting and transportation of Spathodea have been forbidden in the Society Islands, as well as in every island of French Polynesia. This invasive tree is mainly propagated by wind-dispersed seeds contained in pods produced near the top of the canopy; each pod contains about 500 papery winged seeds [START_REF] Fosberg | Flora of Micronesia." Part 5. Bignoniaceae-Rubiaceae[END_REF][START_REF] Staples | Survey of invasive or potentially invasive cultivated plants in Hawai'i[END_REF]. Generally, species with seed structures that promote wind dispersal, such as pappi, have low terminal velocities leading to potential for long dispersal distances [START_REF] Cousens | Dispersal in Plants: A Population Perspective[END_REF].

Atmospheric transport model

The Computing Atmospheric Trajectory tool (CAT) model is a 3-D kinematic trajectory model using initialization wind fields from the ECMWF ERA-5 Reanalysis [START_REF] Baray | Cézeaux-Aulnat-Opme-Puy De Dôme: a multi-site for the long-term survey of the tropospheric composition and climate change[END_REF]. A cluster of starting forward trajectory points is defined by the user. The advection of air masses between two grid points is estimated by the CAT model by using time and space interpolation of ECMWF ERA-5 wind fields, including the integration of topography at a resolution of around 10 km [START_REF] Bezdek | MATLAB script for 3D visualizing geodata on a rotating globe[END_REF]. The ECMWF ERA-5 Reanalysis includes updates to the physical model, core dynamics and 4D-Var data assimilation [START_REF] Hersbach | ERA5 hourly data on single levels from 1959 to present[END_REF][START_REF] Hoffmann | From ERA-Interim to ERA5: the considerable impact of ECMWF's next-generation reanalysis on Lagrangian transport simulations[END_REF]. [START_REF] Hoffmann | From ERA-Interim to ERA5: the considerable impact of ECMWF's next-generation reanalysis on Lagrangian transport simulations[END_REF] have quantified the differences between transport simulations using the recent ERA5 ECMWF reanalysis and the previous ERA-Interim reanalysis, showing an improvement of ECMWF's new-generation reanalysis on Lagrangian transport simulations. In the framework of the present study, forward trajectories were calculated with a modified version of CAT by including the Spathodea seed terminal velocity and atmospheric vertical wind to simulate the uplift and falling of the seeds during aerial transport. The falling terminal velocity of Spathodea seeds ranges from 0.241-0.642 m s -1 with SD 0.069 and a mean terminal velocity of 0.378 m s -1 (n=250 seeds dropped at 3.65 m elevation in a closed environment, i.e., under windless conditions; [START_REF] Larrue | Seed rain, dispersal distance and germination of the invasive tree Spathodea campanulata on the island of Tahiti, French Polynesia (South Pacific)[END_REF]. This terminal velocity is in the range associated with an important influence of atmospheric disturbances on long-distance dispersal [START_REF] Kuparinen | Modeling air-mediated dispersal of spores, pollen and seeds in forested areas[END_REF].

Targeted islands

The Society Islands is one of the five archipelagos forming the territory of French Polynesia in the South Pacific Ocean, lying between 7°-28°S and 134°-155°W. This archipelago consists of 14 tropical oceanic islands including five coral atolls (Manuae, Maupihaa, Motu One, Tetiaroa, Tupai), and nine high volcanic islands, namely Bora Bora, Huahine, Maiao, Maupiti, Mehetia, Moorea, Raiatea, Tahaa, and Tahiti (Fig. 1). The oceanic tropical climate of the Society Islands is dominated by a cooler season (May to October) with lower rainfall, an average monthly temperature of 25.1°C, and a warm wet season (November to April) with high rainfall, and average monthly temperature of 26.7°C [START_REF] Laurent | Atlas climatologique de la Polynésie française[END_REF]. The region is characterized by the persistence of southeastern trade winds blowing between 0.036 km h -1 and 40.6 km h -1 [START_REF] Laurent | Atlas climatologique de la Polynésie française[END_REF], with a mean annual wind-speed at ca. 23 km h -1 .

With an island area of 1,045 km² and a summit at 2,241 m above sea level (asl), Tahiti is the largest and highest island of the Society Islands [START_REF] Brousse | La géologie des îles hautes[END_REF]. The main island of Tahiti is also a stepping-stone island for native plants in the Society Islands [START_REF] Larrue | Cyclones influence native plant diversity on 22 remote high islands of French Polynesia and Pitcairn (eastern Polynesia)[END_REF] and in the Tuamotu archipelago of French Polynesia [START_REF] Larrue | Native plant species richness on Eastern Polynesia's remote atolls: Which abiotic factors influence its spatial pattern?[END_REF]. The earliest and now densest population of Spathodea is found on Tahiti, ranging from sea level up to 1,200 m elevation, with some scattered adults up to 1,415 m asl [START_REF] Meyer | Threat of invasive alien plants to native flora and forest vegetation of Eastern Polynesia[END_REF].

The seven targeted Society Islands included the closest island and the most remote island from Tahiti, and included islands with and without an observed population of Spathodea. One of the Society Island's nine high islands (Tahaa) was excluded from modeling because of its proximity to another island already included in the model (Table 1). <Figure 1 near here> <Table 1 near here>

Source island of Tahiti

A field area of 143 km² (11×13 km) was delineated on the island source of Tahiti by using Google Earth Pro Software. The field area (17.58-17.68°S; 149.48-149.60°W) was chosen according to densest population of Spathodea on Tahiti, including mature Spathodea near sea level and mature Spathodea on steep precipices at high elevation (Larrue and Meyer, pers. obs.). The field area ranged from 5 m to 1,200 m elevation. Geographic coordinates of the field area were imported into the atmospheric trajectory model as the starting domain for long-distance dispersal simulations. Long-distance dispersal from the field area was modeled using climate data for 4 months from September to December 2019. This time window corresponds to the fruiting season of Spathodea and potential release of wind dispersed seeds from the population on Tahiti [START_REF] Larrue | Seed rain, dispersal distance and germination of the invasive tree Spathodea campanulata on the island of Tahiti, French Polynesia (South Pacific)[END_REF].

Long-distance seed dispersal

For the purposes of this study, a potential long-distance seed dispersal event (LDD) corresponds to the distance between the island source of Tahiti and the nearest Society Island, namely the island of Moorea 20 km away (Table 1). We also recorded the longest wind seed dispersal distance (km) observed in each simulation, even if the associated seed trajectory settled in the ocean.

Long-distance transport estimation

Atmospheric parameters used to calculate the forward trajectories were extracted from the ECMWF ERA-5 meteorological reanalysis data [START_REF] Hersbach | ERA5 hourly data on single levels from 1959 to present[END_REF] with a grid resolution of 0.25° in latitude and longitude, comprising 20 vertical atmospheric levels between 1,000 hPa (sea level) and 300 hPa (around 9 km altitude), and a temporal resolution of 3 hours.

Simulation was done inside a large domain stretching from 5° to 30° South and 120° to 160° West, encompassing the Society Islands and the surrounding ocean.

Clusters of 138 seed release points were regularly distributed in the 143 km² field area of Tahiti. The starting altitude of the 138 points ranged from 30 m to 1,225 m, corresponding to the altitude of the topography plus 25 meters to consider the average height of mature trees in this region. From each release point, starting seed trajectories were calculated every 3 hours from 1 September 2019 0h UT to 31 December 2019 21h UT with: 138 (number of clusters in the field area) × 8 (number of starting seed trajectories per day and cluster) ×122 days (duration of analysis). Thus, a total of 134,688 starting seed trajectories were simulated from Tahiti.

Every seed trajectory was then monitored inside the large domain for 168 hours (7 days) with a temporal resolution of 15 minutes (time between two successive trajectory points). In order to check whether extreme temperatures were encountered by the seeds during aerial transport, atmospheric temperature was extracted from ECMWF ERA5 and interpolated on each trajectory point during transport. To assess potential LDD, we then examined the spatial distribution of seed trajectory endpoints, determined by the number of trajectory points reaching the ground (terrestrial area or oceanic surface) per square of 0.1° size across the Society Islands and in the surrounding ocean.

For the purpose of tracking seed dispersal potential from Tahiti, the seven islands were modelled in seven surveyed island-zones of 400 km² (20×20 km). The size of the surveyed island-zone was chosen to enclose the largest island of the sample (namely Raiatea; Table 1).

Each island-zone of 400 km² included the real island area and topography, plus a part of the surrounding ocean (as a "buffer") to also account for seeds settled in the vicinity of island (Table 1). Measurements are reported for the island-zone, in addition to the island alone, because our simulation was done during 4 months of one specific year, and atmospheric conditions may slightly differ from one year to another. Thus, we assessed seeds settling in the vicinity of an island as a general measure of feasibility of dispersal to specific islands.

Impact of rainfall

Additionally, the role of precipitation on LDD is unknown and rainfall could reduce the percentage of Spathodea seeds reaching an island-zone from Tahiti. Thus, we incorporated an estimate of the impact of rainfall on seed dispersal in each island-zone. Whenever a seed spatial and temporal trajectory point corresponded to a zone of precipitation (as extracted from ECMWF ERA5) it was assumed that the seed would drop to the ground (or to the ocean) at the point when the precipitation was encountered. Different effects of precipitation on seed drop were used, ranging from a weak influence of rain (the seed falls to the ground or ocean only when it encounters a zone of precipitation greater than 1.2 mm h -1 , corresponding to the 90 th decile of precipitation values in the region and period of study) to a strong influence of rain (the seed falls to the ground or ocean when it encounters a zone of precipitation greater than 0.017 mm h -1 , corresponding to the 10 th decile of precipitation values).

Barrier effect of islands

A barrier effect of high volcanic islands could help wind-dispersed seeds colonize some islands, while also reducing the feasibility of seeds reaching some remote island-zones beyond a "barrier island". To simulate the barrier effect, a Geographic Information System (ArcGIS Pro 2.8 software, Intersect 3D-line with surface tool) with a Digital Elevation Model of the Society Islands (DEM 5 m resolution) was used to identify seed trajectories derived from CAT that would have been intercepted by the main "barrier island" of Moorea, which lies immediately downwind from Tahiti during the predominant trade winds, as well as trajectories that would have been intercepted from elevated areas of the other six islands.

Here, note that the resolution of the DEM was higher than the resolution of ECMWF ERA 5 data. Consequently, the local effects of the elevated land mass on wind currents along the slopes of islands were not included in the CAT simulation. Thus, when the seed trajectory met an elevated terrestrial island area, the seed was immediately settled at that location. These results constitute the realized LDD (Table 2).

Successful connectivity

For the purposes of this study, we refer to arrival of a seed from Tahiti to another island as 'successful connectivity'. In addition to qualitatively assessing the potential for successful connectivity, we quantified the strength of the connection between Tahiti and the other islands by considering the number of seeds settled on the terrestrial island area relative to the entire number of seed trajectories simulated. Thus, the "strength of connectivity" (B) was estimated as:

B=(Ndp/Nr)×1,000
where Ndp is the number of seeds deposited on each terrestrial island area and Nr the total number of simulated trajectories from Tahiti (n=134,688). This fraction was multiplied by 1,000 to allow reporting with fewer decimal places, expressing B per ‰ simulated seed trajectories.

Because we did not have direct field observations of Spathodea seeds aerially transported from the island of Tahiti to the terrestrial area of remote islands, it was not possible to directly validate our model; however, dispersal potential from Tahiti to the seven target islands, as predicted by the model, was compared to the documented presence of Spathodea on the seven targeted islands.

RESULTS

Long-distance seed dispersal

The distribution of the total seeds settled inside the large domain showed that 56.7% of all seeds settled beyond the arbitrary LDD threshold of 20 km while 43.3% of seeds settled in the first 20 km (Fig. 2), thereby indicating the potential for seeds to settle across the entire island of Tahiti. The furthest seed trajectory settled on the oceanic surface at 10.4257° South and 159.8966° West, indicating a dispersal distance of 1,364 km from Tahiti (Fig. 2). Most seed trajectories (69%) settled in the domain were found in the region surrounding Tahiti shown in Figure 3. Our simulation suggests that Spathodea seeds can reach most of the Society Islands from Tahiti. The maximum altitude among trajectories reaching an island-zone was 2,068 m (not shown), while lowest atmospheric temperature encountered during a trajectory reaching an island zone was 11.3°C (Appendix S1: Figure S1). <Figure 2 near here> <Figure 3 near here>

Impact of rainfall

When we accounted for rainfall's potential impact on seed dispersal, we found that including a precipitation threshold for seed settling generally resulted in fewer Spathodea seeds settling in an island-zone (Fig. 4). Conversely, the number of settled seeds on the island-zone of Moorea increased with assumptions of seed drop in response to precipitation, and any level of precipitation increased seed drop over Moorea (Fig. 4). <Figure 4 near here>

Barrier effect

The barrier effect of the high volcanic island of Moorea was very important in reducing the number of seeds that reached the more remote islands (Table 2). Based on the CAT simulation (i.e., 134,688 trajectories) and the barrier effect, the percentage of total seed trajectories associated with settlement on the studied islands was 2.9%. The realized LDD ranged from 0% (Mehetia) to 90.3% (Moorea) of total island settlement (Table 2). Thus, the island of Moorea received most of the simulated seeds that settled on the studied islands (Table 2). <Table 2 near here>

Successful connectivity

No simulated seed was found on the terrestrial area of Mehetia (Table 2), although some seeds were observed in the surrounding ocean (Fig. 5), but simulated seeds were observed on the terrestrial areas for the other surveyed islands. The simulation demonstrated the potential for successful connectivity because seeds originating from Tahiti arrived at six out of seven distant islands, potentially accounting for invasion of those islands. Most seeds settled on the windward coast of the islands (Fig. 5), i.e., the coast exposed to the dominant humid eastern trade winds.

The relative "strength of connectivity" with Tahiti was nonexistent for Mehetia (0 ‰), very low for Bora Bora, Maiao, and Maupiti (< 0.5 ‰); it was low for Huahine and Raiatea (< 1.5 ‰) and high for the closest island of Moorea (> 25 ‰) (Fig. 6). As a validation, Spathodea trees were reported on the island of Bora Bora, Huahine, Moorea and Raiatea, while no Spathodea were reported on the island of Maiao, Maupiti and Mehetia (Table 1

Long-distance seed dispersal

According to our simulation, Spathodea seeds can be dispersed and advected by wind from the island of Tahiti to most of the Society Islands, even to the remote island of Maupiti (300 km from Tahiti). Spathodea was expected to exhibit LDD based on its plant traits (growth form, plant height, seed terminal velocity; [START_REF] Tamme | Predicting species' maximum dispersal distances from simple plant traits[END_REF]; however, our study, coupling trait information with an atmospheric model, suggests that Spathodea has a surprisingly longdistance dispersal potential (> 1,000 km). Coupling plant traits with an atmospheric model also allowed us to explore how a range of scenarios (e.g., response of airborne seeds to rainfall, temperatures experienced during dispersal) can be expected to influence the spread of invasive plants from a source population to new islands via natural processes.

Our simulation showed substantial variation in the quantity of deposited Spathodea seeds among islands. Seed deposition was affected by the geographic location of islands relative to the source population and the southeast dominant trade winds. For example, the island of Raiatea (198 km northwest from Tahiti) received 4.4% of all seeds that landed on islands across all iterations while the island of Mehetia (180 km east from Tahiti) had no deposited seeds. Thus, the quantity of deposited seeds on an island is not only related to the distance from Tahiti but also to the geographic location of the island and dominant direction of trade winds (included in the CAT model). Mehetia, which lies east of Tahiti, was the only island that was largely protected from seed dispersal by the tradewinds that blow east to west (Appendix S1: Figure S2).

Our results showed that the barrier effect of some high islands can be an important phenomenon decreasing the number of seeds reaching more remote islands from Tahiti. For example, realized LDD showed that the high island of Moorea (20 km northwest from Tahiti) received more than 3,600 seeds, representing 90% of the total Spathodea seeds settled within the islands.

Finally, our findings showed that precipitation may decrease the number of seeds reaching the remote island-zones from the island source of Tahiti, thus reducing the chance for wind dispersed seed to be settled on an island. Conversely, rainfall increased the number of Spathodea seeds that settled on the closest island-zone of Moorea, increasing the chance for seed to be deposited on this island. However, some simulated trajectories never encountered rainfall, so rainfall does not continuously limit dispersal.

Successful connectivity

Our simulations suggest that substantial numbers of Spathodea seeds can reach the remote islands of the Society Islands, supporting a possible connection from Tahiti. However, it is well known that "realized dispersal" depends also on successful germination and seedling establishment [START_REF] Schupp | Seed-seedling conflicts, habitat choice, and patterns of plant recruitment[END_REF]. There is no doubt that successful germination depends on seed viability, which could potentially be decreased by very cold atmospheric temperatures during wind dispersal. Our simulations indicated that atmospheric temperature decreased to as low as around 11°C during Spathodea seed dispersal events. Since this temperature is not lethal for the embryo of seed, germination remains possible after LDD. Additionally, Spathodea seedlings and adult trees were observed in natural environments with extreme low temperature reaching less than 10°C [START_REF] Larrue | Elevational distribution and photosynthetic characteristics of the invasive tree Spathodea campanulata on the island of Tahiti (South Pacific Ocean)[END_REF]. Furthermore, our simulation indicated that most seeds settle on the east, humid side of the islands (windward coast), and the high humidity at these sites is a preferred condition for seed germination of Spathodea [START_REF] Larrue | Seed rain, dispersal distance and germination of the invasive tree Spathodea campanulata on the island of Tahiti, French Polynesia (South Pacific)[END_REF].

Regarding seedling establishment upon arrival, Spathodea seedlings are known to successfully establish in various environments including human-disturbed forests, abandoned agricultural land, as well as native forests on tropical oceanic islands [START_REF] Anderson | Distribution and Spread of Alien Plants in Kipahulu Valley, Haleakala National Park, above 2,300 ft Elevation[END_REF][START_REF] Smith | Impact of alien plants on Hawaii's native biota. In Hawaii's terrestrial ecosystems: preservation and management[END_REF][START_REF] Staples | Hawaii's Invasive Species: a Guide to the Invasive Alien Animals and Plants of the Hawaiian Islands[END_REF]. On the island of Cuba, it was reported that the greatest abundance of Spathodea saplings was recorded in areas of abandoned coffee plantations (Labrada & DiazMedina, 2009), supporting that shaded or semi-shaded conditions provide a suitable habitat for Spathodea seedling establishment and growth. Spathodea seedlings were reported growing in different light environments of Hawaiian Islands, with an estimated mean compensation point below 10 µmol photons m -2 s -1 photosynthetically active radiation (PAR) and a positive net carbon gain at 50 µmol photons m -2 •s -1 PAR, allowing seedling establishment in the understory of island rainforests [START_REF] Larrue | Forest invasion by the African tulip tree (Spathodea campanulata) in the Hawaiian Islands: are seedlings shadetolerant?[END_REF]. Thus, previous research suggests that seeds settling in a variety of environments, both natural and humanmodified, will have a chance of germinating and establishing, although some environments, such as sandy beaches and zones with high salt exposure, are likely to be unsuitable for germination or seedling establishment.

Presence of Spathodea across the Society Islands

The CAT simulation shows that Spathodea seeds can be transported from the main island of Tahiti to the islands of Bora Bora, Huahine, Moorea, and Raiatea. These results are consistent with the documented presence of Spathodea trees on these islands. On the other hand, our simulation also showed an expected connection that extends to the terrestrial island areas of Maupiti and Maiao, two islands where Spathodea has not yet been observed [START_REF] Fourdrigniez | Guide Protection des îles contre les espèces envahissantes en Polynésie française. Guide de reconnaissance et de gestion des espèces[END_REF]. This could be explained by failure of Spathodea seedling establishment, as this depends on environmental conditions at the drop points. Additionally, establishment may not yet have occurred for stochastic reasons. The low simulated seed counts being settled on the island of Maupiti and Maiao these islands are likely proportional to the probabilities of establishment [START_REF] Lockwood | The role of propagule pressure in explaining species invasions[END_REF], which were very low for these islands.

We limited our examination to natural wind dispersal of seeds, though Spathodea is a popular ornamental tree in many tropical islands worldwide, where it has been introduced intentionally. Its seeds also have the potential to be accidentally dispersed via inter-island movements of local people and tourists. However, we have no evidence for human introduction (intentional or accidental) in the Society Islands other than to Tahiti. Moreover, note that the observed distribution of Spathodea does not coincide well with areas that receive substantial air and tourist traffic, such as the North of the island of Huahine [START_REF] Meyer | Islander perceptions of invasive alien species: the role of socio economy and culture in small isolated islands of French Polynesia (South Pacific)[END_REF]. Likewise, human movement appears unable to explain the isolated Spathodea trees recently observed in a more remote region in the South of Huahine (M. Fourdrigniez, pers. com). Thus, in the case of Spathodea, we feel that model of wind movement can provide additional insights that cannot be explained by human movements.

Strength of connectivity

The percentage of seeds reaching every island area was estimated for a given fruiting season based on a CAT simulation with 134,688 seed trajectories. Although the entire number of available Spathodea seeds per season is unknown on Tahiti, this number is certainly greater than our simulation, as there are at least several thousand mature trees on Tahiti, each producing more than 50,000 seeds per season (Larrue, pers. obs). Our finding suggests that early detection surveys on Huahine, Maupiti and Maiao could be warranted to prevent Spathodea establishment on these islands, with survey priority given to Huahine and Maiao, as our simulation indicates that Mehetia is at much lower risk of colonization by wind-dispersed seeds of Spathodea. Here, relative strength of connectivity (‰) allows us to provide relative probabilities of invading each island by wind dispersal. Additionally, our results support a possible "bridgehead effect" with the island of Tahiti as the source of origin for geographically distant populations of Spathodea, but further study of alternative invasion pathways in this system is warranted.

Our results suggest that Spathodea seeds can be dispersed at very long distance, up to 1,364 km, reaching most of the Society Islands from the main island source of Tahiti. Thus, a connection from Tahiti is possible, even if some stochastic precipitation events may decrease the number of seeds reaching the remote islands. Overall, our findings suggest that studies of LDD in wind-dispersed invasive species, using atmospheric models with other physical parameters such as topography and rainfall, can help anticipate island invasions and provide new insights into spatial patterns of invasion.

Table 1. Geographic characteristics of the nine volcanic islands of the Society Islands (French Polynesia). Seven island-zones (square with cross) were monitored for long-distance seed dispersal by Spathodea seeds using a simulation with CAT. Note: The island of Tahaa was not selected due to the very short distance between it and Raiatea Island (⁓5 km). (1) adult Spathodea was mentioned in the handwritten and unpublished notebook field of F.R. [START_REF] Fosberg | Handwritten and unpublished notebook field of F.R. Fosberg[END_REF] as "it is less common on Moorea and still less on Huahine" (available at the Smithsonian Institution of Washington, Meyer, pers. Com) but it was not reported on the island of Huahine by [START_REF] Fourdrigniez | Guide Protection des îles contre les espèces envahissantes en Polynésie française. Guide de reconnaissance et de gestion des espèces[END_REF]. Recently, some Spathodea were observed in the South of the island (M. Fourdrigniez, pers. Com). Figure 6

Figure captions

Figure 1 .Figure 2 .

 12 Figure 1. Study area. Location of the Society Islands in the French Polynesia territory (Pacific

Figure 3 .

 3 Figure 3. Spatial density of settled Spathodea seeds (spatial resolution 0.1°

Figure 4 .

 4 Figure 4. Effect of assuming that differing levels of rainfall cause seed drop in Spathodea in

Figure 5 .

 5 Figure 5. Realized LDD of Spathodea seeds in the seven 400 km² island-zones of the Society

Figure 6 .

 6 Figure 6. Relative strength of connectivity (‰) from the main island source of Tahiti to the

  ).

	<Figure 5 near here>
	<Figure 6 near here>
	DISCUSSION AND CONCLUSION

Table 2 .

 2 Potential and realized LDD (n=134,688 simulations) in 400 km² island-zones including the real island area and the surrounding ocean. For each island, we report the number of settled Spathodea seeds on both the island area and surrounding ocean within the island-zone. The actual presence of Spathodea trees on each island is also reported (Society Islands, French Polynesia). Distribution of Spathodea refers to a qualitative index of distribution across the island: (1) sparse, (2) moderate, or (3) widespread.

	High volcanic islands	Highest	Area	Distance	Human	Targeted
	(n=9)	elevation	(km²)	from Tahiti	Population	island-zone
		(m)		(km)	(date) 1
	Windward Islands
	Maiao	154	8	100	335 (2012)	
	Maupiti	380	13.5	300	1,234 (2012)	
	Mehetia	435	2.3	180	0	
	Moorea	1,207	142	20	17,718 (2017)	
	Tahiti (island source of			0	192,760 (2017)
	Spathodea seeds)	2,241	1,045
	Leeward Islands
	Bora Bora	727	29	248	10,605 (2017)	
	Huahine	669	74	170	6,313 (2012)	
	Raiatea	1,017	175	198	12,245 (2012)	
	Tahaa	590	88	220	5,234 (2017)
	1 last available population census (Gauchenot & Breuilh, 2017)

Acknowledgments

This project was funded by a grant (PEEPS ECOMOB 2019-2020) provided by the Institut Écologie et Environnement (INEE-CNRS) with additional funding support from the Maison des Sciences de l'Homme du Pacifique (MSHP-USR 2003, University of French Polynesia).

The ERA5 reanalysis data used in this study were provided by the ECMWF organization (https://doi.org/10.24381/cds.adbb2d47 and https://doi.org/10.24381/cds.bd0915c6) and generated using Copernicus Climate Change Service information (C3S). Neither the European Commission nor ECMWF is responsible for any use that may be made of the Copernicus information or data it contains.

data] of the surveyed islands were downloaded from https://www.data.gouv.fr/fr/datasets/modeles-numeriques-de

Conflict of Interest statement

The authors declare no conflict of interest.