Sabah Al-Fedaghi
email: salfedaghi@yahoo.com

"Change" in Conceptual Modeling and Systems Reconfiguration

Keywords: Conceptual modeling, change, thinging machine model, Reconfiguration, Zeno's paradox

In this paper, we explore the notion of change in systems and software engineering, emphasizing its philosophical elucidation. Generally, it has been claimed that change is so pervasive in systems that it almost defeats description and analysis. In this article, we analyze change using the conceptual modeling technique called a thinging machine (TM), which reflects change in terms of the actions of creating, processing, releasing, transferring, and receiving things. We illustrated change in TM modeling with an example of a system's reconfiguration of business product handling designed using business process modeling notation (BPMN). Then we analyze the notion of change and compare its various definitions in philosophy. Specifically, we examine Zeno's paradox that involves how to account for change and continuity together in moving things. The problem is that we cannot assert that an arrow is actually moving when it has been shot from a bow because the arrow needs to be at a certain place at each point in time, which by definition cannot contain any duration at all. In our analysis of this problem, we convert the arrow trajectory into space units called thimacs. In the TM generic actions, two types of change are identified: state and progression (PROCESS) changes. Therefore, when an arrow flows to a TM machine that represents a trajectory space unit, it is rejected, causing it to bounce away to the outside. That is, the arrow is transferred, arrives, and is transferred back; therefore, the arrow is never accepted into a thimac in the trajectory at any moment. The result of such analysis seems to introduce a logical explanation for the notion of movement discussed in Zeno's puzzles.

Introduction

In software and systems engineering, adaptation to future user requirements or changing domain-imposed requirements is an essential consideration in the system's development and operating environment [START_REF] Karsai | An Approach to Self-Adaptive Software Based on Supervisory Control[END_REF]. Systems are expected to operate in dynamic environments and to deal with the new problems and arbitrary changes. To cope with these changes, a reconfiguration process may be applied to rearrange the system components concerned with deliberate modifications to technical and organizational subsystems. Frequent changes are made to update hardware and software components, fix software flaws and other errors, address security threats, and adapt to changing business objectives [START_REF] Magalhaes | The Organizational Implementation of Information Systems: Towards a New Theory[END_REF]. This paper focuses on schematic changes involving structural changes resulting from altering requirements and bringing a system into compliance with those requirements. Such changes necessitate modifying the conceptual specification of the involved system. System specifications can be developed at various levels of abstraction, with transformations ranging from high-to low-level specifications. A high-level specification describes the overall configuration of a system.

Change is a central concept for software and systems engineering. According to Idris [START_REF] Idris | The Concept of Change in the Philosophy of Mulla Sadra and Hegel: A Comparative Analysis[END_REF], "The meaning of change is one of the fundamental subjects of inquiry of philosophy. It plays a substantial role in providing our understanding of reality." Such issues as what change is, how it happens, and how we can know it has happened are essential to our understanding of systems. Examining the paradoxical nature of change, we can gain new insights into theory and practice in many scientific fields [START_REF] Thornley | Information Retrieval (IR) and the Paradox of Change: An Analysis Using the Philosophy of Parmenides[END_REF].

We further explore the notion of change utilizing our thinging machine (TM) model. Our aim is to develop a better understanding of the notion of change to appreciate the nature of the field of software and systems engineering. Such a field of inquiry, despite considerable technical developments, has yet to form a coherent and theoretical framework for its key notions. Accordingly, we attempt to offer a conceptual framework to study theoretical and trans-disciplinary foundations of the notion of change. According to Uysal [START_REF] Uysal | In Search of Software Engineering Foundations: A Theoretical and Trans-disciplinary Perspective[END_REF], "Investigating the trans-disciplinary aspects of [software engineering] may pave the way of some solutions while it may shed light on building theoretical background of possible empirical studies. However, the review of [software engineering] literature shows the little effort given to this research gap."

The next section provides a brief description of the TM model. Section 3 gives a sample TM application in software engineering in the form of a conceptual model of a business orders system. The example involves modification of an ordering conceptual schema as an instance of changes in requirements in the original description of the system. In section 4, we focus on reviewing the notion of change. In section 5, we apply the TM model to change in the philosophical sense with the problem of an arrow's movement in Zeno's paradox.

Thinging Machine (TM) Modeling

The traditional ontology divides entities into objects, which are extended in space, and processes, which are extended in time. TM modeling introduces a drastically different conceptualization, which consists of a lower (static) characterization of entities as things that are simultaneously machines, and both merge into a complex of interrelated entities called thimacs [START_REF] Al-Fedaghi | Conceptual Modeling of Events Based on One-Category Ontology[END_REF]. At the upper level (dynamics), a time thimac combines with the static thimac to initiate events (See Fig. 1).

The thing and the corresponding machine "exist" as one thimac; the thing reflects the unity, and the machine shows the structural components, including potential (static: outside of time) actions of behavior. The static "thing" does not actually exist, change, or move, but it has potentialities for these actions when combined with time. Such a view reminds us of the wave particle dualism of quantum mechanics.

A thimac is a thing. The thing is what can be created (appear, observed), processed (changed), released, transferred, and/or received. As we will discuss later, a thing is manifested (can be recognized as a unity) and related to the whole TM or as a static (timeless) phenomenon. This whole TM occupies a conceptual "space" that forms a network of co-existing thimacs. The whole is a grand thing/machine. Thimacs can be "located" only via flow connections among thimacs. Later, when we discuss dynamism, this thing becomes an "instance" when supplemented with time (which is also a thing) to form a dynamic unity of a thing called an event. Therefore, things are part of the TM static description (model) and are part of the dynamic model when merged with time.

The thimac is also a machine that creates, processes, releases, transfers, and/or receives. Fig. 2 shows a general picture of a machine. The figure indicates five "seeds" of potentialities of dynamism: creation, processing, release, transfer, and receive.

All things are created, processed, and transported (acted on), and all machines (thimacs) create, process, and transport other things. Things "flow through" (denoted by a solid arrow in Fig. 2) other machines. The thing in a TM diagram is a presentation of any "existing" (appearing) entity that can be "counted as one" and is coherent as a unity. Fig. 2 can be described in terms of the following generic (has no more primitive action) actions: Arrive: A thing moves to a machine. Accept: A thing enters the machine. For simplification, we assume that all arriving things are accepted; thus, we can combine the arrive and accept stages into one stage: the receive stage. Release: A thing is ready for transfer outside the machine. Process: A thing is changed, handled, and examined, but no new thing results. Create: A new thing is born (found/manifested) in the machine and is realized from the moment it arises (emergence) in a thimac. Things come into being in the model by "being found." Transfer: A thing is input into or output from a machine.

Additionally, the TM model includes the triggering mechanism (denoted by a dashed arrow in this article's figures), which initiates a flow from one machine to another. Multiple machines can interact with each other through the movement of things or through triggering. Triggering is a transformation from one series of movements to another.

Example of TM Modeling

According to Zhou [START_REF] Zhou | A Case Study of Workflow Reconfiguration: Design and Implementation[END_REF], systems are increasingly expected to operate in dynamic environments to deal with the new problems and tasks, and the system's flexibility requires dynamic reconfiguration. "Reconfiguration" refers to changes such as adding actions or deleting components, changing links between systems, and modifying component configuration. Zhou [START_REF] Zhou | A Case Study of Workflow Reconfiguration: Design and Implementation[END_REF] emphasized that systems have to face problems caused by continually developing new web services and modifying or terminating existing web services. The area of service reconfiguration requires more work on the modeling and verification of dynamic reconfiguration of dependable services, including the problem of interface between old configuration activities, new configuration activities, and reconfiguration activities [START_REF] Zhou | A Case Study of Workflow Reconfiguration: Design and Implementation[END_REF].

For example, Zhou [START_REF] Zhou | A Case Study of Workflow Reconfiguration: Design and Implementation[END_REF] designed a system using business process modeling notation (BPMN). This case study was conducted on an organization that handles product orders from customers. When the organization receives an order from a customer, a form is filled out. Then this form is sent to credit check and passes to inventory check. After this evaluation, the order is rejected, or it is processed and passed on to billing and shipping. The billing procedure bills for the total cost of ordered items plus their shipping costs. Afterward, the order is archived and a confirmation notification is sent to the customer. Fig. 3 shows a partial view of the BPMN model of the given case study.

Time

Reconfiguration

According to Zhou [START_REF] Zhou | A Case Study of Workflow Reconfiguration: Design and Implementation[END_REF], the company decides to reconfigure the order of billing and shipping activities, moving the billing activity to occur before the shipping activity and keeping the old configuration process and new configuration process simultaneously available. This reconfiguration requires change only in the system's main lane while the rest of the workflow remains the same. Fig. 4 shows the modified part of the new configuration's BPMN diagram. Comparing this BPMN to the old BPMN diagram in Fig. 3, the two parallel gateways in the main lane have been removed, and the two activities are now called synchronously to keep the old and new configuration processes simultaneously available. Accordingly, Zhou [START_REF] Zhou | A Case Study of Workflow Reconfiguration: Design and Implementation[END_REF] defines a default flow that is identical to the old configuration. This default flow can be altered by an interrupting message event contained in the "determine configuration" activity included in a separate reconfigure region pool. This activity determines which configuration should be used when the system is called. The modified part of new configuration BPMN diagram is shown in Fig. 4.

TM Static Model

Fig. 5 shows the corresponding TM static model. The figure can be described as follows. First, a customer request arrives at the office (circle 1). It is sent to the order generator, ( 2) where an order is created (3) and sent to the office, where it is processed (4). If it is OK, a credit check is created ( 5) that flows to the credit check unit, ( 6) where the result of checking is created [START_REF] Zhou | A Case Study of Workflow Reconfiguration: Design and Implementation[END_REF] and flows to the office [START_REF] Mortensen | Change and Inconsistency[END_REF]. If the result is not OK (9), a rejection is sent to the customer (10 and 11). If the result is OK, (12) an inventory check is created and sent to inventory (13). The result of the inventory check is sent to the office (14 and 15), where it is processed. If the result is negative, a rejection is sent to the customer (16 and 17). If the inventory result is positive (18), a Bill&Ship request is sent to Bill&Ship main (19). There, requests for a call bill (20) and call ship (21) are sent to the billing and shipping units. When the billing details ( 22) and shipping details are received (22 and 23), an invoice with billing and shipping details is created (24) and flows to the archive (25). When an acknowledgement is received from the archive (26), a notification of success is sent to the customer (27 and 28).

TM Events Model

A TM event is defined as a subdiagram of the static diagram (called a region of the event) plus time. Fig. 6 shows a sample of two events: calculating the billing details and calculating the shipping details. Accordingly, we can specify events on the static TM diagram assuming that regions represent events. Each generic event can be converted to a generic event; however, models usually specify larger events.

The set of events defined over the static description can be listed as follows.

….

Office workflow

Process

Order generator

Region of Event

Release

Region of Event

Time

Receive

Bill&Ship Main

To save space, we will not list all nineteen events that Fig. 7 shows.

From the chronology of these events, we can construct the behavioral model of the system of handling product orders from customers, as Fig. 8 shows. Accordingly, the behavioral model is structured as Fig. 9 shows. The change involves the control system, which activates various modules of events. Imagine Zhou's configuration problem involves n>2 series of alternatives. This situation requires an extensive additional modification to the original schema. A TM events-level solution is a more effective solution.

Office workflow

Process

Order generator

A Glimpse of the Change Notion

The remaining part of this paper will focus on exploring the notion of change. Because the philosophical field of the topic is very broad, we will concentrate on a specific track of study, namely Zeno paradoxes.

Generally, "change" is used to refer to an object changing its ordinary properties over time. An object undergoes change whenever it gains or loses some of its properties. According to Mortensen [START_REF] Mortensen | Change and Inconsistency[END_REF], "Change is so pervasive in our lives that it almost defeats description and analysis." Change is problematic because it requires something becoming something out of something that it is not. Also, as change is a fluid process, how can we accurately determine when it has happened or to what extent? [START_REF] Thornley | Information Retrieval (IR) and the Paradox of Change: An Analysis Using the Philosophy of Parmenides[END_REF].

In ancient Greece, Heraclitus was famous for his insistence that "the only thing that is constant is change." Heraclitus claimed that everything changes all the time. Aristotle claimed that "time is the measure of change" and that "there is no time apart from change…." (Physics) of things. According to Aristotle, "time is not change [itself]" because a change "may be faster or slower, but not time…." (Physics). In a modern context, Einstein's theory of relativity implies a moving clock can tick more quickly or slowly than another clock, but time itself isn't faster or slower [START_REF] Dowden | Time. In: The Internet Encyclopedia of Philosophy[END_REF].

Zeno argued that change cannot exist; it is all an illusion. The argument in this context is that things cannot exist and not exist simultaneously. Reality is an unchanging unity. Zeno developed a series of paradoxes to demonstrate logically that change is an illusion. Motion, for example, is an illusion. To reach a destination, one must first reach a halfway point. When one reaches that halfway point, they have yet another one to reach, and this process is logically infinite. Movement does exist, but how can we possibly determine exactly when and how it happens without involving Zeno-type paradoxes [START_REF] Thornley | Information Retrieval (IR) and the Paradox of Change: An Analysis Using the Philosophy of Parmenides[END_REF]?

In the next section, we apply one of the Zeno-type paradoxes in the context of TM where space is conceptualized as thimacs. Accordingly, we will visualize "space units" as thimacs with their five action potentialities (no speculation about the nature of these thimacs).

A thimac can be viewed as having interior (create, process, and receive (accept)) and boundary (release, transfer, and receive (arrive)) posts. A moving thing may reach the boundary of this space thimac (arrive) but not necessarily "enter" it (accepted). Some factor (e.g., movement) leads the arriving thing to be ejected to the outside (transfer: output) of the space thimac. Fig. 10 illustrates this scenario. Therefore, we have two disjoint cases: inside the space thimac, where settlement and continuity occurs, and the thimac boundary posts, where moving things collide with the space thimac but never succeed in penetrating to the inside. Accordingly, a motion is possible among these space thimacs similar to a child walking inside a container filled with plastic balls. However, we assume that such bouncing of things among space thimacs is applied to things in motion. Stable things can settle inside these space thimacs. The following section elaborates on such speculative analysis and applies it to Zeno's puzzle of an arrow's movement. We explore the notion of change by analyzing Zeno's paradox of motion using the TM model. A paradox is a proclamation that holds conflicting concepts. The discussion is pure speculation and may contribute to logical analysis of the concept of space.

Change and Zeno's Paradox

One philosophical approach claims that space (and time) exist always and everywhere regardless of what else exists and that space (and time) provide a container within which matter exists and moves independently of the container [START_REF] Dowden | Time. In: The Internet Encyclopedia of Philosophy[END_REF]. Newton argued that space is an absolute entity and that everything moves in relation to it. This concept led to the distinction between "relative" and "absolute" motion. Leibniz maintained that space is the spatial relations between things. Space cannot exist independently of the things it connects. If nothing existed, then space would not exist. This statement implies that there is no container; space is only a set of relationships among existing physical material, and time is a set of relationships among the events of that material [START_REF] Dowden | Time. In: The Internet Encyclopedia of Philosophy[END_REF].

Current thinking is that space is quantized; therefore, when we move across space, we are actually jumping from small locations to other small locations [START_REF] Cham | What Is Space? Nautilus. Science Connected[END_REF]. As Cham and Whiteson [START_REF] Cham | What Is Space? Nautilus. Science Connected[END_REF] stated, in this view, space is a network of connected nodes, like the stations in a subway system. Each node represents a location, and the connections between nodes represent the relationships between these locations (i.e., which one is next to which other one).

These nodes of space can be empty and still exist. A field just means there is a number, or a value, associated with every point in that space. In this view, particles are just excited states of these fields [START_REF] Cham | What Is Space? Nautilus. Science Connected[END_REF].

Space and Motion

Zeno's paradox under consideration deals with the problem of how to account for change and continuity together.

We cannot assert that an arrow is actually moving after it has been shot from a bow because the arrow needs to be at a certain place at each point of time, which by definition cannot contain any duration at all [START_REF] Hongladarom | Metaphysics of Change and Continuity: Exactly What is Changing and What Gets Continued?[END_REF]. The arrow is not moving because all of its trajectories consist of a series of these moments, and at each moment, it is not moving. So if it is not moving at one moment, then it is not moving at all [START_REF] Hongladarom | Metaphysics of Change and Continuity: Exactly What is Changing and What Gets Continued?[END_REF]. According to Hongladarom [START_REF] Hongladarom | Metaphysics of Change and Continuity: Exactly What is Changing and What Gets Continued?[END_REF], One might, for example, argue against Zeno that points of time containing no duration at all do not actually exist and what do exist are only chunks of time which contain a length of time however small. Hence there is not such a thing as a point in the line of time, and what does exist in the line are smaller sections of the line which can be divided and further divided, but no absolute point can be reached. The arrow, then, moves in these smaller chunks of time, and since these chunks are not points the arrow can move within those chunks. This argument does not seem to work, however, because one would then need to find an account of how the arrow moves from the beginning of the chunk to the end.

The basic problem, according to Hongladarom [START_REF] Hongladarom | Metaphysics of Change and Continuity: Exactly What is Changing and What Gets Continued?[END_REF] is the simultaneous existence of continuity and change in the case of the moving arrow. Mortensen [START_REF] Mortensen | Change and Inconsistency[END_REF] described the arrow puzzle as follows:

An arrow in flight could not really be moving because at any given instant it would be at a place identical with itself (and not another place); something at just one (self-identical) place could not be described as moving, and an arrow which is motionless at every instant in a temporal interval must be motionless throughout the interval.

Following the view that space is a network of connected nodes, we propose that these nodes are thimacs. Therefore, we have a net of thimacs, as Fig. 11 shows, illustrated as connected machines in two-dimensional background. Two connected machines denote connectedness that permits flow of things between the thimacs.

Boundary Boundary Boundary

Events (changes) propagate between the two connected thimacs through the transfer stages that form their "borders." For example, Fig. 12 shows the propagation of change (events) between two machines in terms of sequence of events, assuming that each machine represents a unit of space. Next, we distinguish between two types of phenomena in a TM: states and progressions. The idea is that progression is unstable change that does not need to be the thing to be in a fixed place. For example, suppose that a ball hit a player and bounced away. In this case, we can say, using TM terminology, that the ball has been transferred, arrived to the player, then transferred away without being received by the player. Similarly, an arrow can "touch" the space thimac without being received into the corresponding space.

A TM stage can be viewed as either a state or progression (typically called PROCESS). When understood as a state, a stage is a complete potentiality ready to be actualized. Understood as a progression, it is an accumulated PROCESS. A transfer event between two thimacs is a pure progression stage. For example, when an arrow in the Zeno puzzle is in the transfer event between two space thimacs, this does not mean that it is located in the transfer stage. Transfer itself is a pure change; therefore, change cannot be captured as a stable phenomenon. In contrast, a process event is a change and a state. For example, changing the color of a car from blue to white involves the process of "whiting" the car and the result: the car is now a white car. Transferring an arrow between two adjacent spaces (e.g., through a door between them) involves movement but no location where the arrow can be in the transfer state. Creation also involves a location, e.g., the arrow is created and ready to be released or processed.

In TM, a change happens in the model when a generic event occurs, e.g., creation, processing, releasing, transferring, and receiving. A generic event can be understood in term of states and/or a progression -When understood as a state of a thing (such as being created), as in physics, a state of matter is one of the distinct forms in which matter can exist, i.e., solid, liquid, gas, or plasma. Accordingly, states of things in a TM machine are created, processed, released, transferred, and received. For example, the state created indicates existence, which may be declared initially as in "there is" or appears as a result or effect of processing, e.g., salt (NaCl) appears from processing its chemical components, sodium (Na) and chlorine (Cl).

-Understood as a progression, the event is the rising stretch of flux. A thing is subjected to alteration to reach the state of being processed, e.g., a car is exposed to damaging before being labeled as a damaged car; a patient needs to be anesthetized to be in the state of unconsciousness.

Accordingly, we can redefine a thinging machine to emphasize the internal states and progression actions, as Fig. 13 shows.

The machine is described as follows:

-Create: a thing is created initially (given) by a previous process in the machine (circle 1), e.g., processing Na and Cl creates NaCl. As a result of the creation event, a thing is in the created state. A state will be denoted by a thick horizontal bar, as the figure shows. There may be a queue of created things in this state. The thing in the creation state may flow to either the process stage or the releasing stage.

Fig. -If a created thing flows to the process stage (2), then the first phase of the processing includes a progression to change the thing (3). This progressing is denoted by an upward thick arrow, as the figure shows. Thus, the thing first starts changing, half changing, etc. until it reaches the changed (processed) state, which is indicated by the horizontal thick bar (4). It may stay in this state for a while, or it may flow to either the released state or progression (released immediately) (4).

-If a created thing flows to the release stage [START_REF] Al-Fedaghi | Conceptual Modeling of Events Based on One-Category Ontology[END_REF], it may stay in the released state [START_REF] Zhou | A Case Study of Workflow Reconfiguration: Design and Implementation[END_REF], waiting for a while to be actually released, or it may be subjected to releasing (progression) immediately ( 8). This progression event is denoted by a downward thick arrow. It involves continuous motion of a thing to the thimac's boundary, or "periphery."

-A good example of the release state is an output buffer filled with data waiting to be released to the outside. The progression starts with bits leaving the buffer and racing to reach the output port. This "race" is a progression.

-Transfer -Output ( 9): This is a progression represented by "jumping" to the outside. The jump itself is not a state and involves time. No stable state exists between racing to the edge (release progression) and jumping to the outside (output progression). It is a continuous change.

-Arrival (10): This is a progression of a thing reaching a machine's boundary from the outside. At this point, the thing is not in the machine but only arriving and interacting with this boundary to be accepted or castoff to the outside. It is a progression analogous to an ocean wave reaching upward by a push of air to reach a high point and then collapse downward. The wave is never in a recognizable state. Similarly, at the thing's arrival, it evolves and collapses in being judged to be accepted or pushed back to the outside (we denote this progression with two thick arrows in a reverse form of a wave).

A thing being subjected to progression means that it is never "motionless" in the involved stage. Fig. 14 shows an analogy for this scenario, in which a bed frame is moved through various floors without actually being on any one floor before reaching its destination. Another analogy is a traveler who arrives at several transit countries before reaching their destination.

Applying this concept to Zeno's arrow, the moving arrow is never in two successive place units at one time, and no diverse states of the arrow exist within one time. Fig. 15 illustrates this situation in which the arrow flows to input, arrival, and output. See also Fig. 16. The arrow "squeezes" through the space units, bouncing back at the entrances, as Fig. 17 shows. As soon as it loses its motion, its momentum is "absorbed" inside a space unit.

Conclusion

In this paper and several previous papers, we have explored the TM model and its application in several notions, such as change, event, and systems behavior. This type of study enhances the software and systems engineering community's philosophical foundations. In this article, we aimed to reflect on philosophical concepts, specifically the concept of change, and attempted to introduce conceptual modeling in the philosophical context. We started by giving a sample TM application in software engineering in the form of a conceptual model of a business orders system. The example involves modification of an ordering conceptual schema as an instance of requirements change in the original description of the system. This case study of change in a system led to application of the same modeling tool, the TM model, of change in the philosophical sense, as in the problem of an arrow's movement in Zeno's paradox. Although the general idea of dividing space into connected nodes is not a new concept, applying thimacs as space units seems to introduce a logical explanation for the movement discussed in Zeno's puzzles. This direction of study needs further scrutiny and examination, but it seems to be a promising exercise that ties together problems in several fields of study.

  Fig. 1 Static and dynamic thimacs

Fig. 4 Fig. 5

 45 Fig. 4 The modified part of new configuration BPMN diagram

Fig. 7

 7 Fig. 7 TM events model of the case study

Fig. 10 A

 10 Fig.10A thing flows across space thimacs where each thimac does not accept it until it loses its movement energy and settles in the last thimac

Fig. 14 A 7 Fig. 15

 14715 Fig.14A bed frame moves between floors; however, at no particular point in time it is at a place that is part of any floor.

Bill Bill details Process Ship details Ship

									Customer 11	Transfer Rejection	28 0	Archive
								10					Release	Acknowledge
	Request								Process		Create	Create 14	17	Create Release	Process Receive
										Receive		Inventory Result	Release	Transfer	Transfer
										Transfer		Transfer	Transfer	Transfer
	2	Transfer Receive Process Transfer Transfer Release		Process 4 Transfer Transfer Receive	Create Transfer 5 Request Credit check OK Release	NO	9	Create Release Transfer YES Process	13 Request Inventory check 12	Transfer Receive 15	NO 16	Receive 26 0	Create Release Process 0 25 Call Archive
		Receive	Order	Release Create						Transfer Receive		YES 18	Process	Transfer Receive
				3		6	Transfer Receive	Credit check Result 8	Transfer Release	Bill&Ship request Create Release	Transfer Release Success 27 0
							Process				Create	7	Transfer	Create
				Call Ship		Bill&Ship Main		Receive Transfer	19	Release Transfer
				Create Transfer Release	0 21	Call bill 0 20	Create Transfer Release			Process 0 22	Receive Transfer	Receive Transfer	0 23	Create Bill & ship 24 details 0
									Transfer			Transfer
									Receive			Release
									Process			Create
				Transfer								Transfer
				Receive								Release
				Process								Create
							Create	Event: Calculate the billing details
							Transfer	Receive	Process	Release	Transfer
							Call bill		Create
										Release			Receive	Receive
									Transfer			Transfer	Transfer
										Transfer Receive Process			Bill	Bill details	Transfer Release Create
													Ship	Transfer
													Ship details	Create
								Transfer	Receive		Process	Release	Transfer
							Create
							Fig. 6 Two events of the case study

Time

Event: Calculate the shipping details

bill Bill Bill details Process Ship details Ship

  's[START_REF] Zhou | A Case Study of Workflow Reconfiguration: Design and Implementation[END_REF] reconfiguration of the order of billing and shipping activities involves moving the billing activity to occur before the shipping activity and keeping the old and new configuration processes simultaneously available. From the TM modeling prospect, it is clear that the required reconfiguration aims at change in the behavioral model. This change can be accomplished without changing the original static TM description. In contrast, Zhou's BPMN model involves a single static-level description; therefore, it is necessary to change the original BPMN diagram. In the TM, we can introduce two additional events as follows:E 20 : Configuration of behavior 1, where the billing activity and the shipping activity are simultaneously activated. E 21 : Configuration of behavior 1, where the billing activity occurs before the shipping activity and bookkeeping.

	3.4 Reconfiguration
										Customer
											Rejection
											Transfer	Archive
		E 1								Create Release	Create Acknowledge	Process
	Request								Process	Create	Release	Receive
										Receive	Inventory Result	Release	Transfer	Transfer
										Transfer	Transfer	Transfer	Transfer
	E 2	Transfer Receive Process Transfer Release Transfer Receive	Process Release Create Transfer Transfer Receive Create Request Credit check OK Call Ship Transfer Release E 3 E 4 Order E 6 Create Process Transfer Receive E 5 Bill&Ship Main Credit check Create Result Transfer Receive Create Transfer Create Release Release Transfer Release Transfer Release YES NO Process E 9 E 10 Request Inventory check YES Process Bill&Ship Process Transfer Receive request Transfer Receive Release Receive Transfer Create E 8 E 11 E 12 NO Transfer Transfer Receive Release Success Receive E 13 E 14 E 17 Call Transfer Transfer Create E 7 E 19	Release Transfer Release Create Transfer Receive Process Bill & ship details Create Call Archive E 18
										Transfer Receive	E 16	Transfer Release
										Process	Create
						Transfer Receive			E 15		Transfer Release
						Process					Create
										E9
		E1	E2	E3	E4	E5	E6	E7	E8	E12	E15
										E10	E11
											E13	E14	E17	E18	E19
											E16
								Fig. 8 TM behavioral model of the case study

Zhou

  [START_REF] Hongladarom | Metaphysics of Change and Continuity: Exactly What is Changing and What Gets Continued?[END_REF] Thinging machines adjacent to each other

	Process	Accept	Receive Arrive		Arrive	Receive	Accept	Process
			Transfer	Transfer							Space				Space
	Create	Release	Output Input	Output	Input	Release	Create	Transfer		Receive	Release	Transfer	Transfer	Receive	Release	Transfer
	Create	Release	Transfer Output Input	Transfer Output Input	Release		Create
									Fig. 12 Propagation of change between machines in terms of sequence of
	Process		Receive				Receive	Process		events, assuming that each machine represents a unit of space
		Accept	Arrive	Arrive	Accept
								5			6		7	8	Output 9	Input
									1	Create		Release		Transfer
											2
															Arrive
								4	Process	3		Accept	Receive
										Fig. 13 States and progressions in a thinging machine


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Joel Labat

PRESENTATION OF A REAL-TIME HIGH DATA RATE ACOUSTIC LINK BASED ON A SPATIO-TEMPORAL BLIND EQUALIZATION The TRIDENT acoustic system

There is no doubt about the growing interest in underwater acoustic communications. Among all existing applications, the objective of the Groupe d'Etudes Sous-Marines de l'Atlantique (GESMA) is to develop a sufficiently robust high data rate acoustic link, named TRIDENT. For that purpose, different kinds of information (text, images…) could be periodically emitted through the acoustic channel. A real-time receiver, based on a spatio-temporal blind adaptive decision feedback equalizer, developed and patented by ENST Bretagne was designed to cope with all perturbations induced by such harsh channels. Some sea trials were realized on June 2002. The first results are clearly convincing since most of the 48 sequences of 5 minutes are successfully demodulated by the DSP in realtime. This acoustic system allows the transmission to data rate from 8 to 25 kbps in horizontal configuration.

I-INTRODUCTION.

and for the feedback filter Q(z):

A real-time high data rate acoustic link is currently developed by GESMA. The objective of this project is to develop a solution allowing wireless communications since a vehicle towards surface. This acoustic link must be sufficiently robust to equip the mine hunting vehicles. Indeed, the evolving roles of underwater vehicles are currently constrained by the lack of reliable underwater communications.

The last years of this project were dedicated to up-stream studies. The aim was to choose the best receiver able to cope with multi-path and variability of the acoustic channel. A patented equalizer developed by ENST Bretagne was clearly well-suited for desired applications [START_REF] Lapierre | Evaluation of high data rate acoustic link: contribution of blind spatio-temporal equalization[END_REF].

As a consequence, an acoustic link was developed in order to test the whole communication from the acquisition of useful data to the restitution. The emission part was realized by ORCA Instrumentation, a French company specialized in acoustic modems. The receiver was realized by ENST Bretagne. The heart of this receiver is a spatio-temporal decision feedback equalizer (DFE) able to identify and follow strong variations of underwater acoustic channel (UWA). The last edition of OCEANS gave some information about the integration of this receiver on a platform DSP (Digital Signal Processor) [START_REF] Trubuil | Development of a real-time high dated rate acoustic link[END_REF].

This paper is organized as follows. The second part gives some recalls about the SOC MI DFE. The two running modes of this receiver are described. The simplicity and modularity of such an equalizer are also presented. The third part presents an overview of this equipment called TRIDENT.

] : 1 [ ] [ ] [ . ] [ 0 K i k n l h d k s N l i i l k i + = =
The expression of the optimal linear receiver which minimizes the mean squared error (MSE) is given by:

2 1 * * 2 * * 2 ) / 1 ( ). ( . ) / 1 ( . ) ( n K i i i d i d i z H z H z H z C + = =
The spectral factorization of the denominator of this expression gives then:

{ 1 ) z ( A ) z ( B * * K * * i 2 d i ) z ( G 1 . ) z / 1 ( G . S ) z / 1 ( H . ) z ( C i + = 43 42 1
where G(z) stands for the minimum phase polynomial Usually, this linear equalizer (LE) is implemented as a transversal filter (FIR) in order to avoid instabilities. The optimal linear receiver thus consists of a filter A(z) common to each branch and a dedicated filter B i (z). A(z) is the reverse of a minimal phase filter. It is thus stable and realizable in recursive form. The separation of these two stages allows the LE equalizer to easily evolve towards the conventional DFE.

The expression of the optimal nonlinear receiver gives: For the forward filters P i (z): One can realize that the two structures are relatively similar. The only difference is given by the position of feedback filter either in front of the transversal filters B i for the linear structure or around the decision device for the non-linear structure. Whatever the used structure, each stage is driven by a specific adaptive algorithm (blind in the starting mode and decision directed in the running mode). This receiver is then characterized by a great flexibility in use and an increased robustness. The various used algorithms are detailed in [START_REF] Labat | Blind adaptive multiple input decision feedback equalizer with a self optimized configuration[END_REF]. In this context, the bound of reachable performances of a DFE are:

) / 1 ( . ) / 1 ( . ) ( * * * * 2 z G S z H z P K i d i = 1 ) ( ) ( = z G z Q Starting mode s 1 (k) A(z) + - B 1 (z) u 1 (k) v 1 (k) A(z) + - B 2 (z) u 2 (k) v 2 (
d h T S w T T K k d k K ) . ) ( log( . ) log( 2 2 / 1 2 / 1 1 2 2 = + = It appears since ) 1 ( min ) ( min 1 1 2 2 / 1 2 / 1 1 1 2 2 2 2 / 1 2 / 1 1 2 2 ) ( ) . ) ( ( . ) . ) ( ( . ) ( = = < > > + > + = K DFE K DFE K K K w T T K k d k w T T K k d k K EQM EQM S S S log d h log T d h log T S log
Consequently, the more sensors are used, the more theoretical performances are improved. From a practical point of view, adaptive algorithms impose a maximum limit on the number of used sensors. For example, the rhythm recovery can be hard to achieve when delay between too distant sensors exceed several symbol duration. A trade-off has to be found.

The main idea of this receiver is to combine the advantages of these two structures to define a decision feedback equalizer with an adaptive configuration. Thus, in period of convergence, the linear structure is selected in order to benefit from the stability and speed of convergence. When trust in decided data is sufficient, the structure turns into DFE by the evolution of the position of the recursive filter and all stages are then decision-directed. Usually, a measurement of the MSE is used to define the mode of the SOC MI DFE.

III-

SYNOPTIC OF THE ACOUSTIC LINK. Fig. 3 depicts a conceptual schematic of the acoustic system TRIDENT. A low-rate mode is first used to fix all parameters of the expected high data rate communication. Moreover, this low data rate acoustic link is able to evaluate the quality of the channel, to give an estimation of signal to noise ratio (SNR) and to draw a snapshot of the impulse response. A graphical user interface (GUI) was developed especially for this application. Among parameters which could be fixed, one can select:

The kind of information. TRIDENT is able to transmit some useful data (CCD camera), text, recorded pictures, MLBS 1 and voice soon; The kind of transmission. Digital information could be scrambled, and differential encoded. Resulting information are then modulated with 2, 4 or 8-PSK. The data rate up to 25 kbps chosen by the number of samples per symbol duration (from 2 to 16). Two bandwidths will be available in the next version of TRIDENT. The first one goes from 30 to 40 kHz with an emitted level of approximately 185 dB@1LPa\1m. The second one will cover frequencies from 10 to 30 kHz. Emitted signal is received on a 4-sensors antenna, each of them placed wherever on the antenna.

The core of the receiver platform is an acquisition card with a Texas Instruments DSP (TMS320C3201). Most of the processing is written in assembler language in order to reduce the processing time. One can save more than 90 % of time between a same function written either in C-language, either in assembler.

Only amplification is realized in an analogical way. After that, each input signal is synchronously sampled. Demodulation, rhythm recovery and equalization are then performed using digital processing. Demodulation are made easily by sampling every signal at a clock frequency 4fo, fo denoting the carrier frequency. That is why symbol duration T was chosen in such a way that the product fo.T is integer. Timing recovery is performed with the GARDNER algorithm [START_REF] Gardner | A BPSK, QPSK timing-error detector for sampled receivers[END_REF].

After that, T-spaced equalization can be realized. Decided data are then decoded and displayed into the GUI.

IV-

RESULTS OF THE FIRST SEA-TRIALS.

The first sea-trials were realized in the bay of Brest during June 2002. Acoustic transmissions were performed on two ranges, 300 and 1000 meters. 300 meters long stand for a distance where UWA channel is characterized by a harsh structure of multipath. 1000 meters long correspond to the nominal range for desired applications. Fig. 5 illustrates the procedure of sea trials on two stations, respectively 300 and 1000m on the bay of Brest. The system TRIDENT is buried at sea and recovered once a day. The emission part is placed approximately at 7 m depth. The antenna is deployed since the BEE Langevin. The space between hydrophones is 2m (around 50 acoustic wavelengths). The first hydrophone is deployed at 7m depth (approximately 3m below the ship's draught).

1 Maximum Length Binary Sequence The first example shows some results about a transmission of recorded pictures. Symbols (differential coded and scrambled) are transmitted using a Q-PSK modulation and a bit rate of 14 kbps. The distance between transmitter and receiver was about 1000m and the depth around 22m. The different parameters of the SOC MI DFE equalizer are the following: transversal filters had 17 taps among which 5 are reserved for the casual part. The recursive filter is filled with 35 coefficients. This length has to fit with the duration of estimated impulse response. Fig. 6 shows the evolution of the estimated mean square error (MSE) of the SOC MI DFE for 1 sensor (either with sensor 1 or sensor 3), 2 sensors and 4 sensors. 4 minutes (more than one and a half million of symbols) of transmission are also successfully demodulated which proves once again the robustness of this receiver. Even if estimated MSE are relatively low whatever the number of sensors used, one can note that performances of the SOC MI DFE with one sensor (named in that case SADFE) can greatly fluctuate according to the position of the sensor. This variation is drawing with sensor 1 (dash line) and sensor 3 (dash dot line). The interest of using multiple sensors clearly appears in that case providing more stability and sufficient safety margin. The gain brought by 4 sensors can reach more than 7 dB. This figure illustrates in the same way the gain brought by multiple sensors judging by the output constellations. The main interest of this figure is to show the evolution of input constellation according to samples of different symbols selected by the rhythm algorithm. Samples are clearly chosen in order to minimize a MSE of Gardner error. As a consequence, a sample kept in SADFE equalization could be rejected in SOCMIDFE equalization. That is why a ring structure as the input constellation of the sensor 3 in 1-sensor equalization can be relatively different in the 4-sensors processing. One can note some usual structures of input constellations typical of inter-symbol interference (ISI) in the 4 sensors processing.

Finally, with 4-sensors equalization, data are decoded and send to the GUI which displays received picture. Fig. 8 illustrates one example of an emitted and received picture respectively on the left and right side. Available recorded pictures are representative of sonar processing picture, or drawings. Decoded picture present some errors during JPEG packet decoding. This result could be improved with some channel coding. From a general point of view, this equipment is clearly able to transmit high data rate information over a long duration.

The second example correspond to a transmission of Q-PSK modulation with a bit rate of 17.5 kbps. The kind of information are MLBS without coding and scrambling. This type of information is useful to draw estimated impulse response. The distance between transmitter and receiver was about 300m and the depth around 20m.

The different parameters of the SOC MI DFE equalizer are the following: Transversal filters had 17 taps among which 13 are reserved for the casual part. The recursive filter is filled with 35 coefficients.

The plots in Fig. 9 and Fig. 10 display the evolution of magnitude of different taps every 800 symbols and for a file duration around 3 minutes. The length of the recursive filter is representative of the length of the impulse response as mentioned in part II-. In that case, three main paths appear on the first twenty taps. Fading could explain the variation of magnitude of the main path during the second minute of transmission.

different levels of the transversal filters show some tap values of the first filter twice greater than those of the last two sensors filters. Transmission loss and acoustic propagation could explain this variation of power. As mentioned above, the structure of multipath seem to be more difficult at the range of 300m than at 1000m. The ring structure of the constellations in the previous example could be representative of a relatively simple structure (one or two main paths) even though the blurred constellations are more representative of a very harsh UWA channel.

V-CONCLUSION.

In this paper, a real time acoustic link developed by GESMA, ENST Bretagne and ORCA Instrumentation is presented. Based on a patented blind equalizer, this system, named TRIDENT, showed some interesting performances in terms of MSE, Bit Error Ratio (BER) and convergence speed. Most of the transmitted sequences were successfully demodulated during several minutes. The robustness and adaptability of its receiver is clearly shown. Interest of spatial diversity is confirmed. Even if mono sensor equalization exhibits a good behavior, spatio-temporal equalization offers a safety margin and an improved stability. As a result, evolution of this system could be either the integration of channel coding or iterative procedure. For that purpose, some theoretical points needs further works.

These first sea trials will be followed by other evaluations whose aim will be the evaluation of Doppler immunity. The TRIDENT equipment will be carried out by a ROV in order to test a typical mine hunting mission.

Fig. 1 :

 1 Fig. 1 : SOC MI DFE in its starting mode.

Fig. 2 :

 2 Fig. 2 : SOC MI DFE in its tracking mode.

=

  By using the spectral factorization, one can show without difficulty the following relation :

Fig. 3 :

 3 Fig. 3 : Description of the acoustic system TRIDENT.

Fig. 4 :

 4 Fig. 4 : TRIDENT sub-surface equipment.

Fig. 5 :

 5 Fig. 5 : Illustration of the sea-trials.

Fig. 6 :

 6 Fig. 6 : Evolution of the MSE for 1, 2 and 4 sensors.

Fig. 7

 7 Fig. 7 depicts constellations taken from 150 to 153 seconds of the different signals processed in real-time by the DSP (after digital demodulation and rhythm recovery). The first line corresponds to the SADFE equalization on sensor 3. The second line shows input constellations of sensors 2 and 3. The third line presents constellations given by 4-sensors equalization. The right column draws output constellations given in the different cases (respectively with 1, 2 and 4 sensors).

Fig. 7 :

 7 Fig. 7 : I-Q constellations of the SOCMIDFE for 1, 2 and 4 sensors (DSP processing).

Fig. 8 :

 8 Fig. 8 : Example of an emitted (left side) and a received (right side) picture.

Fig. 9 :Fig. 10 :

 910 Fig. 9 : Evolution of the magnitude of recursive filter taps during transmission.

Fig. 11

 11 Fig.11shows the evolution of the estimated mean square error (MSE) of the SOC MI DFE for 1 sensor (dash line), 2 sensors (dot line) and 4 sensors. 3 minutes (more than one and a half million of symbols) are successfully demodulated. Estimated MSE are more stable than in the previous example. MSE bound goes from 10 dB in the 1 sensor case to 16 dB in the 4 sensors case. As a consequence; the gain brought by 4 sensors can reach more than 6 dB. Performances seem to be less good even if the range was reduced. Once again, spatial diversity provides a safety margin.

Fig. 11 :

 11 Fig. 11 : Evolution of the MSE for 1, 2 and 4 sensors.

Fig. 12

 12 Fig. 12 depicts constellations taken from 70 to 73 seconds. As Fig. 7, the first line corresponds to the SADFE equalization (on sensor 1 in that case). The second line shows input constellations of the first two sensors. The third line presents constellations given by 4 sensors equalization. The right column draws output constellations given in the different cases (respectively with 1, 2 and 4 sensors).As mentioned above, the structure of multipath seem to be more difficult at the range of 300m than at 1000m. The ring structure of the constellations in the previous example

Fig. 12 :

 12 Fig. 12 : I-Q constellations of the SOCMIDFE for 1, 2 and 4 sensors (DSP processing).

  Finally, two examples of the first results of the last sea-trials realized in June 2002 are presented. These data are transmitted through K channels h i. . In addition to the corruption of the channel, the received signals are sullied with Gaussian noise n i [k] with variance

	II-	SOME RECALLS ABOUT THE SOC-MI-DFE.
	Let d[k] denote a zero-mean, with unit power d ²,
	independent and identically distributed (i.i.d) sequence of
	discrete data.

n ². The received signals s i [k] in this context SIMO (Single Input Multiple Outputs) can be written as:


Valentin De Mazancourt
email: valentin.demazancourt@laposte.net

Magalie Castelin

Clementine Renneville

Musa C Mlambo

Gerard Marquet

Philippe Keith

Brevidactyla Roux

C Gracilipes De Man

C Longirostris

H Milne Edwards

REVALIDATION OF CARIDINA NATALENSIS

Keywords: Caridina, Integrative taxonomy, 16S, Morphology, South Africa, Seychelles, Comoros, Madagascar, Mayotte

Numerous specimens of a freshwater shrimp with small eggs belonging to the Caridina nilotica complex collected in the South Western Indian Ocean were studied and compared with recent and old collection specimens genetically (16S mitochondrial analysis for recent and type specimens) and morphologically. The results revealed that, in the Indian Ocean, what has been identified by several authors under various species names of the complex C. nilotica, was in fact C. natalensis De Man, 1908. This valid species is re-described and compared with closely related species, often confused with it in this area: C.

Introduction

From 1991 to 2010, several South West Indian Ocean islands were prospected by field trips conducted by the Muséum national d'Histoire naturelle (MNHN) in Mascarenes archipelago (Reunion, Mauritius and Rodrigues; see [START_REF] Keith | Atlas des poissons et des crustacés d'eau douce de la Réunion[END_REF][START_REF] Keith | Atlas des poissons et des crustacés d'eau douce des Comores, Mascareignes et Seychelles[END_REF], in Comoros (Anjouan, Mohéli) and Mayotte (see [START_REF] Keith | Atlas des poissons et des crustacés d'eau douce des Comores, Mascareignes et Seychelles[END_REF] and in Seychelles (La Digue, Mahé, Praslin and Silhouette; see [START_REF] Keith | Atlas des poissons et des crustacés d'eau douce des Comores, Mascareignes et Seychelles[END_REF]. In 2008 and2010 the MNHN conducted also freshwater inventories in the Northeastern rivers of Madagascar, for the DIAMSOI (Diversité des AMphihalins du Sud-Ouest de l'Océan Indien) program. Recently two of us (GM and MM, in February 2018) collected various Caridina from South Africa. During these prospections, numerous specimens of freshwater shrimps with small eggs belonging to the "Caridina nilotica complex" were collected.

De [START_REF] De Man | On Caridina nilotica and its varieties[END_REF] compared all the specimens he received from all the Indo-Pacific area, related to the C. nilotica complex with type material and recognized nine varieties. Four of those with small eggs were then reported as occurring in the Indian Ocean: C. nilotica brachydactyla, C. n. longirostris, C. n. gracilipes and C. n. natalensis. Later, Roux (1920) described C. n. brevidactyla and reported it from the Indian Ocean (1929). The first three are considered valid species (Cai & Shokita2006 Cai & Ng, 2001;[START_REF] Richard | Decapoda: Caridea: Atyoidea: Atyidae) and the synonymy by Johnson[END_REF]), respectively C. brachydactyla De Man, 1908, C. longirostris H. Milne Edwards, 1837and C. gracilipes De Man, 1892, whereas C. n. natalensis and C. n. brevidactyla are currently junior synonyms of C. brachydactyla [START_REF] Richard | Decapoda: Caridea: Atyoidea: Atyidae) freshwater shrimps from eastern and southern Africa[END_REF].

Caridina brachydactyla was originally described from Mbawa (Flores) and from Palopo, (Celebes) [START_REF] De Man | On Caridina nilotica and its varieties[END_REF]. According to [START_REF] Lenz | Crustaceen von Madagaskar, Ostafrika and Ceylon[END_REF] C. brachydactyla occurs in Madagascar, Mohéli and Mayotte (Comoros Islands). [START_REF] Costa | Results of the Austrian-Indian Hydrobiological Mission 1974 to the Seychelles-,Comores and Mascarene-Archipelagos: Part III: The Ecology and the Distribution of Decapoda Caridea in the Indian Ocean Islands of Seychelles, Mauritius, Comores & Réunion[END_REF] identified C. brachydactyla brachydactyla from Seychelles, Mauritius, Comoros and Reunion islands. More recently, [START_REF] Richard | Decapoda: Caridea: Atyoidea: Atyidae) freshwater shrimps from eastern and southern Africa[END_REF] have identified C. brachydactyla, for the first time, from Africa (Tanzania, South Africa).

Caridina longirostris was originally described supposedly from the river Macta, near Oran, Algeria, however, authors like [START_REF] Bouvier | Recherches sur la morphologie, les variations, la distribution géographique des crevettes de la famille des Atyidae[END_REF] have suggested that this locality indication is erroneous. The types would more likely be coming from Egypt (unpublished data). [START_REF] Richters | Beträge zur Meeresfauna der Insel Mauritius und der Seychellen[END_REF] identified C. longirostris from Seychelles; [START_REF] Holthuis | The Atyidae of Madagascar[END_REF] identified C. longirostris from Madagascar, so did [START_REF] Gurney | Freshwater shrimps genera Caridina and Parisia (Decapoda: Caridea: Atyidae) from Madagascar, with descriptions of four new species[END_REF] and [START_REF] Short | Atyidae and Palaemonidae, freshwater shrimps[END_REF]. [START_REF] Keith | Atlas des poissons et des crustacés d'eau douce des Comores, Mascareignes et Seychelles[END_REF] reported C. longirostris from Comoros, Mascarenes archipelago and Seychelles.

Caridina gracilipes was originally described from Maros (Celebes). According to [START_REF] Lenz | Crustaceen von Madagaskar, Ostafrika and Ceylon[END_REF] C. gracilipes occurs in Mohéli and Madagascar.

Caridina n. natalensis De Man, 1908 was described from specimens collected in the river Umgeni, Natal (South Africa) in November 1894. They were wrongly referred by [START_REF] Weber | Beiträge zur Kenntniss der Fauna von Süd-Afrika. I. Zur Kenntniss der Süsswasser-Fauna von Süd-Afrika[END_REF] to C. wyckii (Hickson, 1888) and considered by De Man (1908) as a distinct variety of C. nilotica, C. nilotica natalensis. [START_REF] Lenz | Afrikanische Crustaceen aus schwedischen sammlungen[END_REF] also identified C. nilotica var. natalensis near Amawzentoti (Natal, correct spelling: Amanzimtoti) and [START_REF] Bouvier | Recherches sur la morphologie, les variations, la distribution géographique des crevettes de la famille des Atyidae[END_REF] in the river Tiwi, 20km south of Mombasa (Kenya) and in the river Imanambo in Madagascar. In his key for the South African species and varieties, [START_REF] Barnard | Descriptive Catalogue of South African Decapod Crustacea[END_REF] listed C. nilotica var. natalensis with small eggs (0.42-0.46 mm major axis). Recently, according to [START_REF] Richard | Decapoda: Caridea: Atyoidea: Atyidae) freshwater shrimps from eastern and southern Africa[END_REF], C. n. natalensis was not considered as a valid species but as a junior synonym of C. brachydactyla. However, [START_REF] Klotz | Elephantis jaggeri, a replacement name for Elephantis natalensis (Bouvier, 1925), a junior primary homonym of Caridina nilotica var. natalensis De Man[END_REF] predicted that C. n. natalensis should be resurrected for certain African populations, but they were lacking data to effectively do it.

Caridina n. brevidactyla [START_REF] Roux | Süßwasserdekapoden von den Aru-und Kei-Inseln[END_REF] described from the Aru Islands, Indonesia, occurs also in Madagascar according to [START_REF] Roux | Crustacea. III. Atyidae. In G. Petit, Contribution à l'étude de la faune de Madagascar[END_REF]. [START_REF] Richard | Decapoda: Caridea: Atyoidea: Atyidae) freshwater shrimps from eastern and southern Africa[END_REF] considered that C. nilotica brevidactyla was also a junior synonym of C. brachydactyla in contrast of [START_REF] Cai | The freshwater decapod crustaceans of Halmahera, Indonesia[END_REF] who considered it as a valid species.

Comparing the new material collected by the MNHN in the South West Indian Ocean to the old collections, the first aim of the present work is to review the status of C. n. natalensis, currently a junior synonym of C. brachydactyla, and provide additional taxonomic information about their respective morphologies and distributions. The second aim of this study is to re-examine existing material and descriptions related to all the species of the C. nilotica complex that have historically been reported as occurring in the Western Indian Ocean.

Material and Methods

Field collection data

All specimens were collected in Indian Ocean islands by electrofishing (portable Dekka 3,000 electric device, Germany) and by hand nets in South Africa. In the field, caught specimens were fixed in 75%. All material has been deposited in the collections of the Muséum national d'Histoire naturelle (MNHN) or Albany Museum in Grahamstown (South Africa). P2: second pereiopod. P3: third pereiopod. P5: fifth pereiopod. Pl1: first pleopod. PlI2: second pleopod.

Abbreviations

Morphological comparison.

The rostrum, the general cephalon, the pereiopods 1, 2, 3 and 5 and the abdomen were observed using a stereoscopic microscope. The proportions of the various joints of the appendages were measured using microphotographs and the AnalySIS Works software (Olympus). Drawings were made using the "Digital Inking" method [START_REF] Coleman | Digital inking": How to make perfect line drawings on computers[END_REF][START_REF] Coleman | Substituting time-consuming pencil drawings in arthropod taxonomy using stacks of digital photographs[END_REF]) by tracing vectorial paths on high-resolution photographs using Adobe Illustrator (CS6) and a WACOM MPTZ-1230 graphic tablet.

DNA extraction, amplification and sequencing.

For recent specimens, DNA was extracted from abdominal tissues using the semi-automatic Ependorf ep-Motion 5075 robot. Fragments of the mitochondrial 16S rRNA (~ 520 bp) were amplified using the newly designed primers 16Sar-Lmod (TACTTCTGCCTGTTTATCAAAAA) and 16Sbmod (GGTCTGAACTCAAATCATGTAAA). DNA amplification was performed in 20µl PCR reactions, containing approximately 3 ng of template DNA, 2.5 mM MgCl2, 0.26 mM of each nucleotide, 0.3 µM of each primer, 5% DMSO, 1 ng of BSA and 1.5 units of QBIOTAQ polymerase (MPBiomedicals). Amplification products were generated by an initial denaturation step of 4 min at 94°C followed by 35 cycles of denaturation at 94°C for 30 sec, annealing at 52°C for 40 sec, extension at 72°C for 60 sec and a final extension step at 72°C for 7 min.

For old collection specimens (Type and non-type specimens of C. brachydactyla, C. brevidactyla, C. gracilipes, C. longirostris and C. natalensis), a CTAB protocol was used to extract DNA from pleopods. A shorter fragment of the 16S rRNA (332 bp) was amplified using the newly designed primers 16S-Car-81F (AGGTAGCATAATAAATAGTC) and 16S-Car-413R (CTGTTATCCCTAAAGTAAC). If these primers could not amplify successfully, another Reverse primer was designed and used to try amplifying a shorter fragment (141 bp): 16S-Car-222R (CTTTATAGGGTCTTATCGT). DNA amplification was performed in 20µl PCR reactions, containing 2.5 mM MgCl2, 0.26 mM of each nucleotide, 0.3 µM of each primer, 1 ng of BSA and 1.5 units of QBIOTAQ polymerase (MPBiomedicals). Amplification products were generated by an initial denaturation step of 4 min at 94°C followed by 45 cycles of denaturation at 94°C for 30 sec, annealing at 55°C for 30 sec, extension at 72°C for 40 sec and a final extension step at 72°C for 7 min.

PCR products were sequenced using the same primers and in both directions to insure the accuracy of base calls.

Chromatograms were edited using Geneious v.8 software (http://www.geneious.com/ [START_REF] Kearse | Geneious Basic: an integrated and extendable desktop software platform for the organization and analysis of sequence data[END_REF]. All new sequences were deposited in GenBank (Table 1, Numbers MH644413 to MH644429).

(Table 1) Molecular analyses DNA sequences were aligned using MEGA7 software [START_REF] Kumar | MEGA7: molecular evolutionary genetics analysis version 7.0 for bigger datasets[END_REF] with Muscle algorithm [START_REF] Edgar | MUSCLE: multiple sequence alignment with high accuracy and high throughput[END_REF]. Using Bayesian information criterion in jModelTest [START_REF] Darriba | jModelTest 2: more models, new heuristics and parallel computing[END_REF][START_REF] Guindon | A simple, fast and accurate method to estimate large phylogenies by maximum-likelihood[END_REF] we retained the GTR + G model. Best-scoring ML trees were estimated using RAxML HPC2 v.8.2.10 (Stamatakis, 2014) and best-scoring Bayesian Inference trees were estimated using MrBayes v.3.2.6 [START_REF] Ronquist | MRBAYES 3: Bayesian phylogenetic inference under mixed models[END_REF], both methods implemented in the Cyber Infrastructure for Phylogenetic Research (CIPRES) portal v.3.1. [START_REF] Miller | Creating the CIPRES Science Gateway for inference of large phylogenetic trees[END_REF]) (https://www.phylo.org/) with the previously determined model, running for 10,000,000 generations, a sampling frequency of 2,000 and a burn in of 25%. Support for nodes was determined using posterior probabilities calculated by MrBayes implemented in CIPRES. One hundred independent searches, each starting from distinct random trees, were conducted. Robustness of the nodes was assessed using non-parametric bootstrapping [START_REF] Felsenstein | Confidence limits on phylogenies: an approach using the bootstrap[END_REF] with 1,000 bootstrap replicates. We considered a group to be 'moderately supported' if it had a bootstrap support value (B) between 75 and 89% or a posterior probability (PP) between 0.80 and 0.94 and 'highly supported' when B ≥ 90% or PP ≥ 0.95.

Results

Molecular results

Due to their old age, no DNA in sufficient quantity and quality could be extracted using our method for the type specimens of C. brachydactyla, C. brevidactyla, C. longirostris and C. natalensis, thus, no 16S sequence was amplified for these specimens. However, the approach was successful for type specimens of C. gracilipes and non-type specimen of C. brachydactyla. Furthermore, we tried to obtain recent specimens as close as possible to the type locality for C. brachydactyla (Palopo, Sulawesi, Indonesia) and C. natalensis (Durban, South Africa).

Four major clades can be separated in the 16S tree. The first one (A in Fig. 1 , 1908: 262-263 pl.20, fig.3, 3a, 3b;Lenz, 1912: 5;Bouvier, 1925: 154-155 fig. 320;Barnard, 1950: 655 (key).

Caridina longirostris Richters, 1880:162-163 ;Holthuis, 1965: 20-23 fig. 6 ; Keith et al. 2006: 50-51.

Caridina nilotica var. brachydactyla Lenz, 1910: 568;Roux, 1929: 303-304 First pereiopod (Fig. 2a): Stout, chela about 1.8-2.4 times as long as wide, dactylus 2.5-6.0 times as long as wide, 0.8-1.6 length of palm; carpus 1.7-3.3 times as long as wide with shallow excavation on anterior margin.

Second pereiopod (Fig. 2b): More slender and longer than first pereiopod. Chela 1.9-3.0 times as long as wide, dactylus 3.5-7.0 times as long as wide, 1.1-1.9 times length of palm; carpus 4.3-6.0 times as long as wide.

Third pereiopod (Fig. 2c): Dactylus (Fig. 2d): 2.9-4.0 times as long as wide (terminal spine included) with 6-9 spineson flexor margin in addition to the terminal one; propodus 12.7-18.6 times as long as wide, 4.1-6.6 times as long as dactylus.

Fifth pereiopod (Fig. 2e): Dactylus (Fig. 2f): 3.0-6.01 times as long as wide with 31-61 spiniform setae on flexor margin; propodus 15.2-22.0 times as long as wide, 4.3-5.7 as long as dactylus.

First male pleopod (Fig. 2k): Endopod leaf-like with a developped appendix interna in males.

Second male pleopod (Fig. 2l): Appendix masculina on second pleopod reaching 0.52 times length of endopod; appendix interna reaching about 0.84 times length of appendix masculina.

Egg size (Fig. 2j): 0.35-0.46 × 0.22-0.29 mm.

Preanal carina (Fig. 2h): with a strong spine.

Telson (Fig. 2i): ending triangular with a posteromedian projection; 1 pair of longer lateral simple setae and 2 to 3 pairs of shorter intermediate simple setae shorter or slightly longer.

Uropodal diaeresis (Fig. 2g): with 9-14 short spinules.

Colour pattern. Colours (Fig. 3) vary and tend to match the substrate the shrimp lives on. The body can vary from hyaline to brownish with red dots, with sometimes a large red border on the ventral side of the rostrum. An oblique brown or carmine red band on the cephalothorax is very characteristic. The coloration is lost on preserved animals.

(Figure 3)

Habitat. All specimens were collected in the lower course of rivers, (altitude 5-25 m), among macrophytes in running water.

Distribution. C. natalensis occurs in Comoros (Anjouan, Mohéli), Mayotte, Seychelles (La Digue, Mahé, Praslin and Silhouette), Mauritius, in Madagascar and South Africa. Present before in Reunion Island [START_REF] Costa | Results of the Austrian-Indian Hydrobiological Mission 1974 to the Seychelles-,Comores and Mascarene-Archipelagos: Part III: The Ecology and the Distribution of Decapoda Caridea in the Indian Ocean Islands of Seychelles, Mauritius, Comores & Réunion[END_REF][START_REF] Kiener | Etude des problèmes piscicoles des eaux intérieures de la Réunion[END_REF] this species seems now absent despite extensive propspections made there since (Fig. 4).

(Figure 4)

Key

Discussion

Caridina natalensis, not a junior synonym of C. brachydactyla

The molecular and morphological analyses of specimens collected from a large geographic range, covering the entire known distribution of C. brachydactyla (sensu [START_REF] Richard | Decapoda: Caridea: Atyoidea: Atyidae) freshwater shrimps from eastern and southern Africa[END_REF]) in the Indian Ocean and including localities close to most of the type localities of its synonyms, suggest that C. n. natalensis is a valid species. These results disprove [START_REF] Richard | Decapoda: Caridea: Atyoidea: Atyidae) freshwater shrimps from eastern and southern Africa[END_REF] study, which based on old collection specimens (from which molecular studies are difficult to do), thus using morphology only, recognized C. n. natalensis and C. n. brevidactyla as junior synonyms of C. brachydactyla. Indeed, [START_REF] Richard | Decapoda: Caridea: Atyoidea: Atyidae) freshwater shrimps from eastern and southern Africa[END_REF] found that the dactylus to propodus ratios of the first and second pereiopods in C. n. natalensis fell into the range calculated for C. brachydactyla. They also showed that the Natal specimens differed from topotypical specimens of C. brachydactyla in having the appendix interna slightly turned down towards the exopod, whereas it was straight in the Indonesian material. This was regarded by the authors as a non-significant character for the separation of species.

Here, the molecular results show that the specimens from the Southwestern Indian Ocean (here attributed to C. natalensis -type locality: Umgeni River, Durban, South Africa) are genetically highly distinct from the specimens collected in Indonesia (here attributed to C. brachydactyla -type locality: Sulawesi, Indonesia) and to specimens from Melanesia (here attributed to C. brevidactyla -type locality: Aru Island, Indonesia). The morphological examination of the specimens used in the molecular tree allowed finding new characters that are stable within genetic clusters but clearly different among clusters. Having examined the type specimens of C. brachydactyla, we show that it can be separated from C. natalensis by P1 chela greater than 2.1 times as long as wide (vs mostly 1.8-2.1) and P3 dactylus with mostly 5-6 spines on flexor margin in addition to the terminal one (vs 6-9).

Having also examined the type specimens of C. n. brevidactyla, we show that it can be separated from C. natalensis by the tooth on the preanal carina that is present in C. natalensis but absent in C. brevidactyla. Indeed, in a not yet published work, we show based on many specimens from the Pacific Ocean that C. brevidactyla is also a valid species (see de Mazancourt et al. unpublished).

Taxonomy of Caridina nilotica complex in the Indian Ocean

Of the 298 known species of Caridina (WoRMs database as of May 2018), the complex C. nilotica, which includes 22 described varieties and/or species [START_REF] Karge | Süßwassergarnelen aus aller Welt[END_REF]) has a very confuse systematic [START_REF] Johnson | Distribution and other notes on some freshwater prawns (Atyidae and Palaemonidae) mainly from the Indo-West Pacific region[END_REF]. Although, assumed to be broadly distributed across the Indo-West Pacific (from Africa to Fiji), C. nilotica complex remains ill defined and subject to many confusions. In this study, we focussed on the Indian Ocean members of the C. nilotica complex. Since the studies of De [START_REF] De Man | On Caridina nilotica and its varieties[END_REF] and [START_REF] Roux | Süßwasserdekapoden von den Aru-und Kei-Inseln[END_REF], six varieties were generally reported in the Western Indian Ocean: C. n. brachydactyla; C. n. longirostris; C. n. gracilipes; C. n. natalensis and C. n. brevidactyla. Here, based on a large geographic range, covering the entire known distribution of C. nilotica complex in the Indian Ocean and including localities close to most of the type localities of its varieties, molecular and morphological analyses suggest that the only variety of C. nilotica that occurs in the Indian Ocean is C. n. natalensis, that we here resurrect as a valid species.

As demonstrated above, the 16S molecular tree showed that C. brachydactyla only occurs in Indonesia, and C. brevidactyla only occurs in the West Pacific. Moreover, the inclusion of the paralectotypes of C. gracilipes in the molecular tree also suggested that this species is absent from the Western Indian Ocean. Indeed, in this study, none of the specimens collected in the Indian Ocean and In this study, we have compared the specimens of C. natalensis with all the species of the C. nilotica complex that have been historically reported as occurring in the Western Indian Ocean, namely: C. n. gracilipes, C. n. brevidactyla, C. n. brachydactyla and C. n. longirostris. These comparisons showed that not only these species do not occur in the Western Indian Ocean, but they also are distinguishable from C. natalensis. Morphologically, C. gracilipes, can be separated from C. natalensis by the P5 propodus mostly 3.3-4.1 as long as dactylus (vs 4.3-5.7). As mentioned earlier, C. brevidactyla and C. brachydactyla can be morphologically separated from C. natalensis. Finally, although the type specimens of C. n. longirostris could not be genetically analyzed, they were morphologically easy to separate from C. natalensis (or from other variants of C. nilotica complex) because of their P1 and P2 carpus respectively 1. 7-2.3 (vs 1.4-1.8) and 4.3-8.0 (vs 3.9-4.7), P3 dactylus stouter, dactylus 2.9-4.0 (vs 4.0-4.8) times as long as wide, with propodus 4.1-6.6 (vs 3.4-4.0) times as long as dactylus, and P5 dactylus stouter with propodus 4. 3-5.7 (vs 3.2-3.7) times as long as dactylus.

Conclusion

Further studies should be led on a larger geographic coverage in the Indian Ocean to determine more precisely the northern limit of C. natalensis distribution range. This species is abundant in lower course of rivers from South Africa, Madagascar, Comoros, Mayotte and Seychelles, however, it has a critical status in Mascarene archipelago. Indeed C. natalensis seems to have now disappeared from Reunion Island [START_REF] Keith | Atlas des poissons et des crustacés d'eau douce des Comores, Mascareignes et Seychelles[END_REF]

  Abbreviations for museums. Muséum national d'Histoire naturelle, Paris: MNHN; Naturhistorisches Museum Basel, Basel: NMB; Rijksmuseum van Natuurlijke Historie (now in the Naturalis Biodiversity Center, Leiden): RMNH; Zoological Museum Amsterdam (now in the Naturalis Biodiversity Center, Leiden): ZMA.

  ), highly supported (B = 95% PP = 0.99) comprises the specimens of C. brevidactyla and is separated from all the others grouped in a moderately supported clade (PP = 0.89). Within this clade, the specimens of C. brachydactyla (B) cluster together in a highly supported clade (B = 99% PP = 1) away from the others grouped in a moderately supported clade (PP = 0.84). This clade is split in two, the first one (C), highly supported (B = 100% PP = 1), comprises the type and non-type specimens of C. gracilipes and the other one (D), moderately supported (PP = 0.84) with all the specimens of C. natalensis from different Indian Ocean localities. (Figure 1) Morphological comparison Our morphological study, confirming the molecular study results, reveals that what has been attributed by several authors to various species names is in fact C. natalensis De Man, 1908. Until now, C. natalensis was considered a synonym of C. brachydactyla. Caridina nilotica var. natalensis De Man

  cl 4.8mm; Near Reo, Flores, coll. M. Weber. Paralectotypes. RMNH.CRUS.D.2552, 2♀ ovig. cl 5.3-5.4mm; river near Palopo Luwu, Sulawesi, coll. M. Weber.. Caridina brevidactyla Roux, 1920: INDONESIA. Lectotype. NMB 4.VI.b 1, 1♂ cl 4,8mm; Sungi Manumbai,Wokam Island, Aru, April 14-15,1908. Paralectotypes. NMB 4.VI.a, 1♂ cl 3.3mm; Aru, Udjir Island, April 15, 1908, NMB 4.VI.b, 2♀ cl 5.8-6.4mm; Sungi Manumbai, Wokam Island, Aru, April 14-15,1908. NMB 00004 VIc, Wokamar, Wokam Island, Aru, April 17, 1908, 1♀ ovig. 5,7mm; NMB 4.VI.d; 2♀ ovig. cl 5.7mm, Seltutti, Kobroor Island, Aru, May 2, 1908.Caridina gracilipesDe Man, 1892: INDONESIA. Paralectotypes. ZMA.CRUS.D.102635, 1♂ cl 4.1mm (DNA: CA025), 1♀ ovig. cl 5.9mm (DNA: CA023), 3♀ cl 5.1mm (DNA: CA027), 5.2mm (DNA:CA024) and 5.6mm; in a rice field, Makassar, Sulawesi, coll. M. Weber, 1888. NMB 1061e, 1♂ 3.8mm; 2♀ cl 5.8-5.9mm; same data. Caridina longirostris H. Milne Edwards, 1837: ALGERIA. Paralectotypes. MNHN-IU-2013-19419, 3♂ cl 2.9-3.1mm; from the river Macta, near Oran. MNHN IU-2013-19418, 2♂ 3.2-3.6mm; same data. Non-types : Caridina natalensis KENYA. MNHN-IU-2015-1854, Tiwi river, 20km south of Mombasa. TANZANIA. NHM 1982.576, 3♀ ovig. cl 5.5-7.2mm, Ruo Lukuledi, Tanganyika. SOUTH AFRICA. MNHN-IU-2018-61, 1♂ cl 3.3mm (DNA: CA2079) and MNHN-IU-2018-62, 1♀ ovig. cl 6.0mm, River Mbanyana, 32°13.123'S Forested lake, saline, near Camp Poorun, altitude 11m, 20°10.517'S 57°45.767'E, coll. C. R. Turner, December 11, 2005. Diagnosis. Carapace (Fig. 2m, n, o) smooth, glabrous, with sharp antennal spine placed at lower orbital angle. Pterygostomian margin rounded. Rostrum rather constantly long, 0.8-1.3 of cl, straight or curved up distally, reaching well beyond scaphocerite. 15-26 dorsal teeth, leaving distally unarmed part of rostrum 0.4-1.2 times that of armed part, except for one to three subapical tooth, 1 to 2 post-orbital teeth present. 7-23 teeth present on the ventral margin extending from highest part of the rostrum either to tip or with short distal part unarmed. Number of dorsal teeth on the rostrum before the most proximal ventral tooth 10-14. Rostral formula: (1-2) 15-26 + 1-3 / 7-23.

  for studied species 1.1 Preanal carina with spine....................................................................................................................................2 1.2 Preanal carina unarmed................................................................................................................C. brevidactyla 2.1 P1 carpus greater than 1.9 times as long as wide and P2 carpus mostly than 4.3..............................................................................................................................................................................3 2.2 P1 carpus less than 1.8 (1.4-1.8) times as long as wide and P2 carpus than 4.2.........................................................................................................................................................C. longirostris 3.1 P1 Chela greater than 2.1 times (2.1-2.3) as long as wide; P3 dactylus with mostly 5-6 spines (5-7) on flexor margin in addition to the terminal one............................................................................................C. brachydactyla P1 Chela less than 2.1 times as long; P3 dactylus with mostly 6-9 spines on flexor margin in addition to the terminal one.............................................................................................................................................................. 4 4.1 P5 propodus 4.3-5.7 as long as dactylus..........................................................................................C. natalensis 4.2 P5 propodus mostly 3.4-4.1 (3.4-5.8) as long as dactylus..............................................................C. gracilipes

  morphologically resembling C. brachydactyla, C. brevidactyla or C. gracilipes, fell into the genetic clusters containing specimens of each of these three species. On the contrary, all of these specimens collected in the Indian Ocean formed a single clade, genetically highly differentiated from C. brachydactyla, C. brevidactyla and C. gracilipes, and morphologically close to the type specimen of C. natalensis.

  Figure1

  Figure 3

Figure 4

 4 Figure 4

  tab.1 no.15. Caridina brachydactyla brachydactyla Costa 1980: 673-700. Caridina nilotica natalensis De Man, 1908: SOUTH AFRICA. Lectotype. ZMA.CRUS.D.102886, 1♀ ovig. cl 6.4mm; Umgeni River, Durban, Natal, coll. M. Weber, 1898, det. J.G. De Man. Paralectotypes. ZMA.CRUS.D.102886, 2♀ ovig. cl 5.7-6.4mm; same data. Caridina nilotica var. brachydactyla De Man, 1908: INDONESIA. Lectotype. RMNH.CRUS.D.977, 1♀ ovig.

	Caridina nilotica var. gracilipes Lenz, 1910: 568.
	Material examined
	Type material:

Table 1 :

 1 like Macrobrachium hirtimanus (Olivier, 1811). Bayesian 16S rRNA phylogenetic tree showing the relationships of some of the species discussed in this study. Numbers above branches indicate bayesian posterior probabilities; numbers under branches indicate Maximum Likelihood bootstrap values. Views of living specimens of Caridina natalensis showing their coloration; a. Specimen from Madagascar (G. Marquet); b. Specimen from Seychelles (P. Keith); c, d. Specimen from South Africa (G. Marquet). e: Example of habitat where C. natalensis lives; Iharaka river, Madagascar (G. Marquet).. -FIGURE4: Distribution of Caridina natalensis with sampling localities of the specimens of this species examined for the study (black circles) and its type locality (white star). List of the specimens used in the genetic study

	Legends to figures:
	. -FIGURE 1: . -FIGURE 2: Caridina natalensis; a. first pereiopod; b. second pereiopod; c. third pereiopod; d. fifth
	pereiopod; e. dactylus of fifth pereiopod; f. dactylus of third pereiopod; g. uropodal diaeresis; h. pre-anal carina;
	i. telson; j. eggs; k. second male pleopod; l. first male pleopod; m. anterior region of cephalothorax: n, o. rostrum
	variations.
	. -FIGURE 3: a, b, c, d:

Acknowledgements

The authors wish to thank Dr Urs Wuest and Edi Stöckli (NMB), Paula Martin-Lefèvre and Dr Laure Corbari (MNHN), Dr Charles Fransen and Karen van Dorp (ZMA) for providing the specimens used in this study Comoros archipelago: thanks to Yaya, Abdallah Ahmed Soilihi and Halidi Ahmed Ben Ali. We are also grateful to Conservation International (CI) and particularly to F. Hawkins and CI Madagascar.

Mayotte: Thanks to DAF (Direction de l'agriculture et de la forêt) and ARDA (Association Réunionaise de Développement de l'Aquaculture).

Seychelles: We thank P. Grondin of ARDA (Association Réunionaise de Développement de l'Aquaculture) in Reunion Island for giving us specimens from this archipelago.

Magagascar: We thank the DIAMSOI team (The IH-SM from Tuléar with Dr Man-Wai Rabenevanana and the MNHN from Paris with E. Feunteun, P. Keith and T. Robinet) and the ARDA team (P. Bosc, H. Grondin and P.

Valade). We are grateful to Joe Aride from Madagascar National Parcs (MNP-ANGAP) and to the manager of Masoala National Parc at Maroantsetra. Lastly, we want to thank all the Responsible Chiefs of the areas concerned for their kind permission, and the villages and communities who have always heartily received us and helped us in our prospecting of rivers. This research was financed by the Institut Français de la Biodiversité (IFB) for the DIAMSOI program (2007DIAMSOI program ( -2010)).

South Africa: We are grateful to Patrick Kubheka and Helen James for facilitating collecting permits for us with provincial conservation urgencies in KwaZulu-Natal and Eastern Cape (permit no. CRO69/17CR), respectively.

We thank Nick and Tim McClurg, Patrick Kubheka, Lazola Maliwa and Pascal Tiberghien for their help in the field and Albert Chakona (SAIAB) for lending us his electric fishing gear.