Paula Dias Souza

Fabio Campos De Oliveira

Anna Carla Araujo

Anna Carla

EXTERNAL THREAD MILLING ON BOVINE CORTICAL BONE

Keywords: Thread Milling, Bone Machining, Biomechanics, Dynamometry

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

INTRODUCTION

There are two different basic types of thread bones: cortical threads and spongy threads. Spongy threads have deep depth and large pitch, which increase the surface contact of the device with the bone and, consequently, its strength against pull off. Screws with this type of thread can have thread on all the length of the shank (fully threaded screws) or just on its tip (partially threaded screws). Cortical threads have less deep depth and smaller pitch than spongy thread. Moreover, they are fully threaded and, generally, blind end. This type of bone screw is also used to fix plates to the bone. In Figure 1, can be viewed the difference between the geometry of the two types of thread.

Figure 1: Metalic threads used on bones [START_REF] Bretas | Avaliac ¸ão radiológica dos dispositivos de fixac ¸ão de fraturas. parte i: fios e parafusos[END_REF] Currently, the most used implants on the treatment of a fracture are the metallic ones, specially, the ones made of titanium. Such material, besides having great mechanical resistance, it does not deteriorate and it stays chemically inert, that is, it does not react with other substances. Sometimes, it is also used screws manufactured from bioabsorbable polymers. These polymers are a type of plastic especially developed to allow the body to absorb the material after some time. The absorption of this material happens because it is identified by the organism as a dead bone tissue and needs to be substituted. Therewith, the polymeric screw is slowly absorbed and substituted for alive bone tissue. Although widely applied, metallic implants are not bio-absorbables and can cause a series of problems, such as: biological rejection; damage in the biomechanical performance in the repaired area; loss of bone mass near the implant; displacements in the bone-implant interface caused by the difference of rigidity; and the necessity of a second surgery to remove the screw after the consolidation of the fracture [START_REF] Bento | Análise de resistência mecânica em implantes de osso -um enfoque numérico e experimental[END_REF]. This additional surgery can cause damages to the patient bone as the screw use to be wrapped by an amount of tissue that is formed around it as a defensive mechanism of the organism.

A lot of studies of bone implants used to odontologic applications verified that the overload in the bone-implant interface is a decisive factor in the bone loss that is observed around the implants. In the case of orthopedic implants to the repair of fractures, the bone adaptation to the mechanical load can result on an adverse redistribution of the stresses and, consequently, the bone reabsorption. This phenomenon is the result of the interaction of mechanical and biological processes and happens the following way: after the implantation, the prosthesis, having greater rigidity than the bone, protects it from the loads making the adjacent amount of bone to atrophy and be reabsorbed in response to the reduced load that it bears now. In extreme cases, the liberation of the implant and the increase of the incidence of fractures can happen [START_REF] Oesler | Algumas aplicac ¸ões de simulac ¸ão numérica em biomecânica óssea[END_REF].

In vivo studies have showed that a reduction of 1.2 to 1.6 times on the resistance to the extraction of the screw happens in the twelfth week after the implant placement, because of the bone reabsorption phenomenon [START_REF] Neto | Experimental determination of bone cortex holding power of orthopedic screw[END_REF]. Even the polymeric materials also have inconveniences: they can be toxic and can cause an inflammatory process in the region they were inserted, besides having an extremely high cost [START_REF] Bento | Análise de resistência mecânica em implantes de osso -um enfoque numérico e experimental[END_REF]. A third alternative that would eliminate all these unwanted complications would be the utilization of screws made of bone. These devices, still in experimental phase, are capable of acting as structural element during the treatment and are, later, absorbed by the organism, avoiding, this way, a new surgical intervention to their removal. Additionally, when integrated to the receptor bone, the bone screw causes a more uniform distribution of the deformations and of the loads borne. If the incorporation is well succeeded, there is a reduction of the interface of prosthesis-bone contact with the treatment and the material becomes more homogeneous, once the dead bone -the prosthesis -is substituted for newly formed bone. As a result, there is a behavior that comes near of the one bones without implant have and the response of the bone-implant system to external loads becomes more homogeneous. Besides, the removal and deposition cellular activities of bone mass take the bone tissue to a constant remodeling, that varies according to the mechanical solicitations. In the implantation region of the bone screw, contrary to the metallic one, these cellular activities continue to happen and the implanted dead bone is substituted by a new alive bone.

However, it is important to highlight that the application of bone screws must be restrict to some specific conditions that do not demand high resistance like maxillofacial and periodontal surgeries. The bone to be utilized in the manufacturing of these implants does not need to be originated from humans. The bovine bone tissue, according to the results obtained in [START_REF] Bento | Análise de resistência mecânica em implantes de osso -um enfoque numérico e experimental[END_REF], is capable to induce the bone integration even when it is inserted in bones of other species. Moreover, bovine bone has superior structural properties in comparison to human bone [START_REF] Cowin | Bone Mechanics Handbook[END_REF].

Considering the described technologies, thread milling process is adapted to the machining of cortical bovine bones. This technique allows dry cutting, cutting velocities that are not connected directly to feed velocity and good quality surface workpieces. Those characteristics are essential when a brittle material needs to be machined, as a bone which could not support high feed velocities as the thread pitch per revolution.

The objective of this article is to contribute to the manufacturing process of thread in bovine bone and the development of implants in biocompatible materials to medical and dentisthic applications. The workpiece consists in a cortical part of bovine femur and, as per its reduced information of knowledge on machining proprieties, values from drilling bones were used. The machined parameters are shown and the experiment is described in the next sections.

BONE PROPERTIES

The bone tissue is a very rigid connective tissue found in the skeleton of the vertebrates. It is mainly functions are: support the organism, serving as a base for the body; allow the performing of movements; protect vital structures as the heart, lungs and brain; hold mineral salts; produce cellular elements of the blood; besides of serving as mechanical base for the movement. The bone composition, in weight, consists of 65% of mineral, 20% of organic matrix and cells and 15% of water [START_REF] Cowin | Bone Mechanics Handbook[END_REF]. The mineral part is constituted, basically, of hydroxyapatite (calcium phosphate) which, despite its rigidity and fragility, gives the bone enough resistance to compression, thanks to the way it is attached to the collagen. The bone tissue can be divided in two types: spongy (or trabecular) and compact (or cortical). The difference between these two forms is associated to their porosity and, consequently, their density.

The spongy bone tissue has larger medullar spaces, being formed by several trabeculas that give a porous aspect to the tissue. The spongy bone is the one with minor weight and has grind shape, with bone spaces where it is found the [START_REF] Cowin | Bone Mechanics Handbook[END_REF] medullary bone. Generally, this kind of bone tissue is localized in the extremities of the long bones where is required high distributed resistance as shown on Figure 2.

The compact bone tissue has almost none medullar space, but a conjunct of canals where nerves and blood vessels go through. Inside the cylindrical cavity of the long bones is found the medullary bone. Generally, the cortical bone is found in regions of very high stresses. In long bones it is possible to identify three distinct regions: the epiphyses that corresponds to the extremities of the bones and is composed by trabecular bone tissue; the diaphysis which is located between the extremities and is composed, primordially, by cortical bone; and the metaphysis, located between the epiphysis and the diaphysis. The thickness of the layer of bone tissue and the resistance to rupture increase progressively going from the metaphysis to the diaphysis [START_REF] Neto | Experimental determination of bone cortex holding power of orthopedic screw[END_REF].

In biomaterials area, the knowledge of the mechanical properties of the bone is extremely important, specially, in the development of prosthesis more adequate to human conditions. The bone is considered a material with great mechanical resistance at the same time that shows elasticity and lightness. it is a dynamic structure, alive and continually renewed through the life of the person, according to the type and intensity of the load. The cortical bone is frequently considered an orthotropic material. Orthotropic materials are a class of anisotropic materials characterized by three Young modulus according to the direction of the load, three shear modulus and six Poisson coefficients.

Besides the anisotropy, another important characteristic of the bone is the viscoelasticity. The viscoelasticity is the property of the materials that have both characteristics, viscous and elastic, when under deformation. Viscous materials resist to shear rate and stress linearly with time when a stress is applied. Elastic materials deform instantly when under tension and compression and return equally fast to the original state when the load is removed. Viscoelastic materials have elements of both properties. As such, exhibit stresses dependent of the strain and the strain rate. [START_REF] Holanda | Efeitos da orientac ¸ão das fibras de colageno nas propriedades mecanicas de flexao e impacto dos ossos[END_REF] indicated that the collagen is the bigger responsible for the bone viscoelastic behavior. Contrary to the elastic materials, viscoelastic materials lose energy in a cycle of loading by thermal dissipation. Additionally, they are characterized for the capacity of having viscous strain under constant loads and relaxing under constant displacements. The different structures of the cortical and trabecular bone result in different mechanical properties that are highly variable with the species, age, anatomy, liquid content, among other factors.

The high anisotropic nature of the bone combined with its viscoelasticity and dynamic change of properties with time make the value of the mechanical properties vary from bone to bone. Even thought, Table 1 presents an average value of mechanical proprierties of human bone. Machining bones is not a usual topic of research because medical procedures are quite simple and well known during orthopedic surgery. When it concerns manufacturing of threads made of bones to be used later on surgery, the situation changes and there is a need of knownledge in order to make a proper workpiece.

THREAD MANUFACTURING

Thread manufacturing is the operation in charge to make internal or external threads, with normalized shapes and dimensions, on cylindrical or revolved conical surfaces. Threads can be produced by foundry, injection, mechanical forming and machining. When produced by forming, the thread has a higher resistance because of the strain hardening. Additionally, the absence of chip formation and long life of the tool are other advantages of the forming process [START_REF] Bretas | Avaliac ¸ão radiológica dos dispositivos de fixac ¸ão de fraturas. parte i: fios e parafusos[END_REF]. In opposite, the precision achieved by this technique is not capable of outdoing the one achieved by machining operations. There are a lot of different machining processes that can be used to manufacture the thread: turning, taps and dies machining, thread whirling, grinding and milling. The choice of the proper process takes into consideration several factors, such as: dimensional tolerance of the thread, geometry of the part and, mainly, the diameter of the thread [START_REF] Bretas | Avaliac ¸ão radiológica dos dispositivos de fixac ¸ão de fraturas. parte i: fios e parafusos[END_REF].

Thread Milling

Thread milling has becoming very popular in the last years as an alternative to other forms of manufacturing thread. Threads manufactured by this process can be done with single cutting edge or multiple cutting edges as in thread milling (Araujo et al., 2005a).

Thread milling tools are similar to taps, but its operation is completely different. Contrary to tap, thread milling tools do not have chamfer and are capable to manufacture the whole length of the thread, even in materials that were hardened, without sacrificing its profile, finishing and precision. Moreover, the feed per tooth speed of the tool does not depend of the thread pitch [START_REF] Smith | Cutting tool technology: Industrial Handbook[END_REF]. This method requires a CNC machine able to perform helical interpolations. In comparison to the conventional thread manufacturing processes, thread milling has the following advantages: provides good surface finish and precision; generates smaller chips; allows tolerance adjustments through exact calculations; allows full thread until the bottom of the hole; provides prolonged tool life; it is adequate for most materials; the same milling tool can be used to different diameters, as long as the pitch is the same; the same tool can be used to both left and right thread and both internal and external thread; and allows dry cutting.

The thread manufacturing in holes with thread milling tools can be divided in five stages. The first stage consists in the positioning of the tool from the start position to the central axis of the hole. Then, the tool is dislocated to the position where will start the cutting. Once in place and rotating at the selected spindle speed, the tool moves axially with a determined feed velocity until an appropriate cutting radial depth. In the third stage, the tool executes an up helical movement in the hole to a complete revolution of the tool axis. The number of threads made in one revolution of tool axis matches the number of threads initially engaged in the wall of the part. If the creation of threads to the total depth of the hole is not achieved in one round, the stages 1to 3 must be repeated until all the threads are completed. Once the thread is manufactured, the tool moves back to the center (fourth stage) and out of the hole (fifth stage) Araujo et al. (2005b).

Thread Milling Penetration Strategies

There are different methods of milling tools approximation to start the thread cutting, named thread penetration strategies [START_REF] Fromentin | Modeling of interferences during thread milling operation[END_REF]. Some CNC machines can be equipped with the specific cycles for this operation, however, machines with simpler commands demand different programming strategies.

The simple form of radial positioning of the tool is the linear entrance. According to [START_REF] Smith | Cutting tool technology: Industrial Handbook[END_REF], this strategy is characterized for generating a high contact angle between the material and the peripheral diameter of the tool. As a result, there is a high load situation on the tool which, depending on the material, can lead to long chips. Besides, the linear entrance is not advisable to precision threads because it leaves marks on the entrance point of the tool and it produces interferences and over machining of parts.

Most used penetration strategies are half penetration and quarter circle penetration. On those cases the tool axis moves with circular trajectory to the initial point of the full circle revolution that will machine the complete thread. A full study of interference on thread penetration was developed by [START_REF] Vishal | Modeling of interferences during thread milling operation[END_REF].

EXPERIMENTAL PROCEDURE

At this work it was verified the viability of manufacturing a thread on a piece of bone removed from a bovine femur. The experiment (Figure 3(a)) consisted of the manufacturing of the thread in a CNC machining center, using a thread milling tool. Moreover, were performed the measurement of the cutting forces involved in the process.

The knowledge of the cutting forces and the studying of their components are of great importance to the evaluation of the potency required to execute the cutting. Besides, it is an important criterion for the determination of the machinability of a given material.

In the specific case treated at this work, it is important to observe the behavior of the specific cutting pressure when cutting a material as an insert of bovine bone. The forces which act on the cutting edge strongly depend on the condition of the chip-tool interface. The principal factors which influence the cutting forces are: the workpiece material, the material and the geometry of the tool, cutting area, cutting speed, chisel angle and cutting fluid condition.

Experimental Stages

The experiment is divided in five steps, as described:

I -Preparing the Workpiece: Extraction of a piece of material from the bovine femur to be milled, cleaning and cutting of the bone.

II -Fixation of the sample: Manufacturing of a fixture device that allowed the attachment of the bone insert to the dynamometer.

III -Circular milling.

IV -Thread milling with the measurement of the cutting forces.

Stage I -Preparing the Workpiece

Before the start of the milling process, the bone had to pass through some preliminary procedures of cleaning and whitening. First, the bone was cut to remove the epiphysis (cutting the longitudinal edges) that is mostly made of trabecular bone tissue. Next, it was done the removal of the medulla that stays inside of it in a place called medullar cavity. After these two stages, the bone was boiled in water and bar soap for about two hours. This procedure facilitates the removal of all the residues which still are stuck on the surface. Then, the bone passed through alternate baths of sodium hypochlorite (bleach), water, hydrogen peroxide (oxygenated water) and water again. Last, the bone was exposed to sunlight for a couple of days. After this procedure, it got properly cleaned and bleached. [START_REF] Souza | Dynamic controlled milling process for bone machining[END_REF] In Figure 4, there is the illustration of each of the stages made on the preparation of the bone to be milled: (1) bone in its original state; (2) removal of the extremities; (3) boiling in water and soap; (4) bath in sodium hypochlorite solution and (5) bath in hydrogen peroxide.

The final shape of the sample was obtained using a hacksaw with a Bi-Metal blade. Despite the extremely irregular shape of the bone, it was tried to obtain a shape close to a parallelepiped with a base of 10 mm X 10 mm and height of 35 mm.

An observation can be made concerning possible alterations that the cleaning procedure and bone preparation may cause in its mechanical property. Previous works about bone machining used ungreased or freeze-died bone tissue. Freeze dying or cryodesiccation is a process of dehydration used to preservation where the material in question is frozen and the water is removed by sublimation, that is, not passing for the liquid phase. According to [START_REF] Bento | Análise de resistência mecânica em implantes de osso -um enfoque numérico e experimental[END_REF], in terms of mechanical behavior the cortical bone is more affected by the freeze-dying than the trabecular bone. [START_REF] Cowin | Bone Mechanics Handbook[END_REF] cites experiments that confirm a reduction of the elasticity modulus, of the deformation and of the rupture energy, in cortical bone freeze-died at -30 0 C and, later rehydrated in salty solution for two hours at temperature of 20 0 C. Furthermore, according to [START_REF] Bento | Análise de resistência mecânica em implantes de osso -um enfoque numérico e experimental[END_REF], a sample of bone, when removed from a living organism will inevitably suffer alteration of its mechanical properties. With the death of the cells of the bone tissue, will be observed temperature variation and, principally, humidity alteration. If the bone is kept in a humidity and temperature state compatible with the one of the body, will be produced enzymes that can deteriorate the organic and mineral matrix of the bone. An alternative that would avoid this problem would be the freezing of the bone. At last, it is worth pointing that the method of cleaning of the material used in the present work is very simple, but it satisfies the objective of the experiment which is the studying of the machining of an insert of a bovine bone. In the case of the manufacturing of implants, more sophisticated techniques would be necessaries, like, for an example, the irradiation of gamma rays to eliminate infectious organisms.

Stage II -Fixture Design

The fixture manufactured in the stage B was made from an inox steel 304 plate with dimensions of 300 mm X 100 mm and thickness of 1/2 in. The base of the fixture had four holes which allowed attach it to the dynamometer using four Allen M8 screws. The efficient fixation of the bone was harder because of its very irregular shape. The fixture was composed of a base and two vertical plaques, between which had a space reserved for the positioning of the bone. The fixation of the bone insert was given by the squeezing of one plaque against the other through two Allen M8 screws.

Stage III -Circular End Milling

Machining of a cylinder from piece of material extracted from the bone Before the performance of the threading, it was necessary to mill the material in order to obtain a cylinder with the diameter equal to the external diameter of the thread. The process was done in the ROMI Polaris V400 CNC machining center, using as tool an end milling tool. It was not applied any working fluid during the process. Basically, the tool performed a circular interpolation in the XY plane in counterclockwise direction. The machining happened in several passes. To each pass, the program was executed once making the correction of the radius.

In order to manufacture a cylinder with 10 mm of diameter, it was used an end milling tool with 10 mm of diameter, (INDAC ¸O model 1501). The geometric characteristics of the tool are showed in Table 2. On this stage, the Mmanufacturing of a right handed type thread on the workpiece is done by the milling process using a thread milling tool. The operation was performed by the same machine tool of the previous stage. Again, it was not used any working fluid. Also at this stage, it was measured cutting forces with a piezoelectric dynamometer.

As the machine tool used to execute the experiment did not have helical interpolation, the operator used small circular counterclockwise interpolations on the XY plane, alternated with linear displacements on the Z axis upwards. At each 12 0 arch made by the tool, it went up vertically 0.05 mm. With that, it was possible to make the tool to perform an approximated helical trajectory.

A radial penetration method with quarter circle was chosen. Such technique avoids that marks are left on the entrance point of the tool. The assembled experimental set-up is showed in Figure 3(a) and 3(b). For the manufacturing of the thread was used a Vargus M10 X 1.5 mm thread milling tool and the parameters shown on Table 3. For the selection of the cutting parameters (cutting speed and feed), [START_REF] Sandoval | Fabricación de tornillos em cortical de tbia. diseno para uma aplicación en fijación de fracturas de mano[END_REF] was taken as reference. The experiment executed by [START_REF] Sandoval | Fabricación de tornillos em cortical de tbia. diseno para uma aplicación en fijación de fracturas de mano[END_REF] was the one the used the smaller cutting speed comparing to the other references. The experiment showed that there the operation can be done without working fluid in this range.

For the measurement of the forces involved in the manufacturing of the thread was used a Kistler dynamometer, model 9257 AB, connected to a signal conditioner and amplifier, also from Kistler, model 5233A1. This set gives the cutting force components in X, Y and Z directions. A digital oscilloscope helped on the definition of the output value and on the behavior of the signal of the three components before the acquisition. The acquisition of the signals was performed connecting the signal conditioner to a data acquisition board. This board transmitted the signals of the force components to a microcomputer using the software LabVIEW with acquisition rate of 1 KHz.

EXPERIMENTAL RESULTS

Experimental Forces

During the manufacturing experiment of the thread, it was measured the cutting forces involved in the process. The dynamometer acquire forces F X , F Y and F Z in table referential R 0 . R 1 , the cylindrical surface referential, and R 2 , which follows the spindle movement, are presented in Figure 5a. In order to transfer to the machined surface referential R 1 , a rotation matrix is applied as a function of θ 1 , the position angle related to the tool axis position and the table referential, as shown in Figure 5a. Note that θ 1 is a function of tool positions X and Y .

F r =   F rad F tan F Z   =   cos(2π -θ 1 ) -sin(2π -θ 1 ) 0 sin(2π -θ 1 ) cos(2π -θ 1 ) 0 0 0 1     F X F Y F Z   (1)
All signal was taken during complete machining process but only steady state and full engagement during machining is considered in all data experiments, using the θ 1 range from 180 o < θ 1 < 340 o . The steady state range is displaced in Figure 6a.

It is possible to verified force spikes (negative) in the Z direction that coincide with a fall of the modulus of the forces in X and Y. This behavior is the consequence of the machining procedure adopted in the experiment: alternated linear interpolations with linear movements in Z. In order to be precise and disregard the linear movements in Z, thread milling data was extracted. Althought the peaks in Z were important to extract θ 1 calculation from CNC code. Forces in one revolution in R 0 are presented in Figure 6b.

Using θ 1 angles, force components in R 1 were calculated using Eq. 1and it is displayed in Figure 7 in different tool positions. In the range (180 o < θ 1 < 340 o ), 14 revolutions were taken for the statistical analysis considering the three maximums related to each thread flute. Those revolutions were equally spaced to guarantee independence of axial depth of cut a doc variation. The average of all maximum resultant forces for each flute Fres is presented in Table 4. Using the R 1 componentes Frad and Ftan were calculated.

It is also computed values of forces in those different θ 1 positions divided by the local a doc and the average of these relations are presented in Table 4 as F res /a doc , F rad /a doc and F tan /a doc .

Thread Quality

There are not enough studies today to determine the ideal roughness that a bone implant must have. However, it is known that this roughness must insomuch that it favors the bone integration process. According to [START_REF] Mora | Fabricac ¸ão de implantes ortopédicos a partir de usinagem de osso humano[END_REF], a rough surface, probably, facilitates the structural and functional connection between the alive bone and the surface of the implant. A picture of the profile of a manufactured thread can be viewed in the Figure 8. The image was obtained amplifying the thread on a microscope. From this profile, it was calculated the average roughness Ra. The result was 43 µm. With the help of a caliper with 0.05 mm resolution, was measured the external diameter of the machined thread. The value that was verified was 9.90 mm.

CONCLUSIONS

The experiment presented that is possible to manufacture a thread in a piece of bovine cortical bone using as threading technique the thread milling with a tool with multiple cutting edges. Through the experiment, was noted that the behavior of the bovine bone during the machining does not differ much from the one showed by fragile materials, with the formation of short loose chips. It must be emphasized that the piece of bone selected to the operation was extracted from the cortical (compact) bone, with no vestiges of trabecular bone tissue which has a porous structure, that could result in a damaged part.

It is especially important to control the cutting temperature when it is machining bones of live organisms, so that there is not the necrosis of the bone tissue and cells. The cellular necrosis of the bone starts at a temperature of 50 0 C and irreparable damages occur at temperatures bigger than 70 0 C. Thermal effects lead to the denaturing of the enzymes and proteins of the cellular membrane, resulting on the dead of the cell. Besides, the thermal damages to the bone can be attributed to both the magnitude of the temperature and to the time of exposure to high temperature [START_REF] Sugita | A cutting temperature study of bone machining for orthopaedic robotic surgery[END_REF]. To obtain lower cutting temperatures and, consequently, smaller possibilities of thermal damages, it must be selected cutting speed as smaller as possible and use salty solutions as working fluid. For the applied cutting conditions, the bone showed to be a material of easy machining and it was not verified as excessive heating that could damage the material. [START_REF] Sugita | A cutting temperature study of bone machining for orthopaedic robotic surgery[END_REF], in their study on cutting temperature of bone machining, verified a very small influence of the cutting condition, as speed cutting and feed per tooth, in the temperature. Also, it was verified that raising substantially the cutting speed, the variation of the cutting forces was very small (Sugita et al., 2009b,a). It is important to point out that in the case of the present work, the cutting temperature and the possible necrosis of the tissue are not critical aspects, once the material machined is a piece of dead bone.

The bone machined showed good machinability and, for the cutting parameters selected, it was not verified over heating that could damage the material or the tool. Also, it was verified that is possible to manufacture a normalized thread in a piece of bovine cortical bone. In the performed experiment, it was produced a metric thread ISO M10 with pitch of 1.5 mm. The cutting forces involved in the process were measured using a dynamometer and the maximum forces in each flute is analyzed and presented in the article. Bending component force in the tool showed to be very low comparing to the resultant force. Forces Tangential to the thread surface have values around 50 N while resultant force achieved 57N. The force profile is the analogous other metallic materials.

Regarding the quality of the machined surface, the result obtained is closely linked to the method used to get the tool to perform the trajectory. As claimed, the machining center is not prepared to perform helical interpolations and alternating small circular interpolations with small upwards movements was used. This alternate movement introduced on the part little marks that would not exists if it was used helical interpolation.

Figure 2 :

 2 Figure 2: Trabecular and Cortical Bone[START_REF] Cowin | Bone Mechanics Handbook[END_REF]

Figure 3 :

 3 Figure3: Experiments for measuring the cutting forces[START_REF] Souza | Dynamic controlled milling process for bone machining[END_REF]

Figure 4 :

 4 Figure 4: Preliminary Bone Preparation[START_REF] Souza | Dynamic controlled milling process for bone machining[END_REF]

Figure 5 :

 5 Figure 5: Forces decomposed in three Referential Frames: R 0 , R 1 and R 2 .

  (a) Forces in Range 180 o < θ 1 < 340 o (b) Forces in one Revolution

Figure 6 :

 6 Figure 6: Experimental Thread Milling Forces in R 0

Figure 7 :

 7 Figure 7: Forces in One Revolution Forces for different θ 1

Figure 8 :

 8 Figure 8: Microscopic Picture of one Manufactured Thread[START_REF] Souza | Dynamic controlled milling process for bone machining[END_REF]

Table 1 :

 1 Mechanical Proprieties of Human Bone

	Cortical Bone	Trabecular Bone

Table 2 :

 2 Parameters of the end milling process Milling tool diameter Total length Number of tooth

	Helix angle

Table 3 :

 3 Parameters of the Thread milling process

	Milling tool diameter	Thread	Number of tooth	Helix angle
	8.2 mm	M10 X 1.5 mm x 15.0 mm	3	30 0
	Spindle speed	Feed per tooth	Cutting speed	Working fluid
	240 RPM	0.02 mm	7.5 m/min	Dry Cutting

Table 4 :

 4 Results for average maximum of data from 14 θ 1 locations Fres F res /a doc

	Fres ādoc .a doc

ACKNOWLEDGEMENTS

The authors thanks the laboratories LTM and CEFCON where is was possible to run the experiments and manufacture the device. The authors thanks to the Mechanical and Materials Master degree Program from CEFET/RJ by its friendship and to make the dynamometer available whenever it was necessary for running tests.


S J Holbrook

A Rassweiler

R J Schmitt

Hedonic evaluation of coral reef fish prices on a direct sale market

Introduction

World-wide, coral reefs support small-scale subsistence fisheries [START_REF] Cinner | Coral Reef Livelihoods[END_REF]. These are particularly important in the South Pacific, where coastal communities are strongly dependent on reef fisheries [START_REF] Leenhardt | Complexities and Uncertainties in Transitioning Small-Scale Coral Reef Fisheries[END_REF]Rassweiler et al. 2020). The subsistence nature of these fisheries has often led to the assumption that, with the exception of export-oriented fisheries, their dynamics and the associated trade in fish products cannot be fully explained by standard market behavior [START_REF] Léopold | The Dynamics of Institutional Innovation: Crafting Co-Management in Small-Scale Fisheries through Action Research[END_REF]. Indeed, the existing social science research on coral reef fin-fish fisheries in the Pacific is largely focused on their ethnographical and sociological characteristics and non-market determinants of their evolution [START_REF] Johannes | Words of the Lagoon: Fishing and Marine Lore in the Palau District of Micronesia[END_REF][START_REF] Lauer | Indigenous Ecological Knowledge as Situated Practices: Understanding Fishers' Knowledge in the Western Solomon Islands[END_REF][START_REF] Audras | La République, le Pays et le Tavana[END_REF]. (but see Cinner et al. 2007).

Here, we will show how an economic analysis can help explain the patterns of fish sales and fish prices in a coral reef fin-fish fishery without centralized market. We assess the extent to which different taxa of reef fish attract different prices, reflecting relative supply and demand characteristics. In order to highlight such pricing strategies, we use data from a survey of fish sales on the island of Moorea, French Polynesia. Fishing plays an important role on Moorea, as a source of food for the local population, of income for fishers, and as an important aspect of Polynesian cultural identity [START_REF] Mcmanus | Tropical marine fisheries and the future of coral reefs: a brief review with emphasis on Southeast Asia[END_REF]Rassweiler et al. 2020). The majority (58%) of the fish landed are taken from the lagoon [START_REF] Yonger | Approche de la pêcherie récifo-lagonaire de Moorea (Polynésie française) : évaluation de la production halieutique et de la population de pêcheurs[END_REF], and a fraction of these are sold in lots called tuis. Each tui is composed of individuals of one or several different species of fish, tied together in strings of varying length. This local market is composed of multiple outlets along the island's coastal road, where fishers present their landings (tuis hanging from a rack) and consumers come to buy fresh fish [START_REF] Leenhardt | Quel est le rendement de la pêche récifolagonaire à Moorea ? Synthèse des différentes données obtenues[END_REF][START_REF] Moussa | Estimation de la taille des poissons lagonaires vendus sous la forme de tui1 en bord de route sur l'île de Moorea (Polynésie française) par analyse de clichés numériques[END_REF]Rassweiler et al. 2020). Both fish buyers and sellers are sensitive to the quality of the fish offered for sale. They also have a good knowledge of the value of each species, and of the value of tuis composed of different species as well as the distribution of prices across outlets. Therefore, the willingness of buyers to pay for an additional quantity or quality of a species of fish is likely to be equivalent to the costs that a fisher would incur to provide it, which should also equal the value that they expect to derive from the market.

To identify fish pricing strategies, we apply a hedonic modelling approach which accounts for different sources of price heterogeneity. With the required precautions, using the principle of revealed preferences [START_REF] Rosen | Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition[END_REF], this method enables estimation of the implicit price of a non-marginal variation in the length (taken as a measure of the quantity) of individual groups of fish species, based on the price of the tui composed of these species groups. Indeed, fish buyers pay a price based on their knowledge of the species groups that compose the tui: their preference for each species group is thus expressed as a monetary amount equivalent to their willingness to pay to acquire an additional quantity of this species group.

Our analysis demonstrates how applied economic methods can be used to elicit the relative economic value of different species of reef fish landed in a small-scale fishery. Estimates of the market value of species groups frequently observed in tuis in Moorea reveal that implicit prices of fish may vary by a factor of four to five across species groups. These prices are affected by the origin of the catch and fishing techniques used. The results, derived from the fraction of catch that is sold, may be used as a guide to assessing the economic stakes associated with changes in the composition of catches in the broader, subsistence-oriented and non-market components of the fishery. The results may also help inform the design of management strategies for the fishery, taking into account economic drivers of fishing pressure on this local market. Beyond the fishery under study, the results also highlight the relevance of empirical economic analysis to improve the understanding of small-scale coral-reef fisheries in the Pacific, and demonstrate a methodology to investigate the economic stakes associated with changes in the structure of their production, which could be applied across a broad range of contexts.

Context and Data: Tui Sales on the Island of Moorea, French

Polynesia

Coral reef fishing is a key activity for the coastal communities of French Polynesia. On the island of Moorea, fishing is strongly embedded in the livelihood and lifestyle of the local population, with most households engaged in a fishery-related activity [START_REF] Leenhardt | Complexities and Uncertainties in Transitioning Small-Scale Coral Reef Fisheries[END_REF]Rassweiler et al. 2020;[START_REF] Thiault | Combining Participatory and Socioeconomic Approaches to Map Fishing Effort in Small-Scale Fisheries ». Édité par Sebastian C. A. Ferse[END_REF]. A fraction of the landings of Moorea's small-scale fishery is sold along the roadside, generally close to the fisher's home in the form of strings of fish called tuis. The prices of individual tuis are observed through direct surveying of the sellers.

Tui composition varies significantly, being made up of the same species or a mix of species, and of variable numbers of fishes of different sizes.

Tui prices and composition were surveyed on Moorea during 2014 and 2015 along the 60 km ring road. The survey documented the price of tuis sold. The species composition and sizes of fish on each tui were determined from photographs taken of each seller's rack at the time of the survey, with fish lengths calculated based on comparison with a scale bar of known size (see Rassweiler et al. 2020). Over the two years, 12 002 individual fishes were measured, of which there were 8 568 records with complete information, incorporated in 742 tuis sold by 164 sellers 1 and the majority of these (79.88%) are the fishers themselves. The mean number of tuis observed 2 per seller on a given day was 4 to 5, with a maximum of 23, and half of the sellers were selling 3 tuis or more. Fish on each tui were identified taxonomically from the photographs with variable levels of precision (usually to genus or species). The identified taxa were aggregated into 37 functional groups (here called species groups). Parrotfish that had been noted as potentially belonging to two or more taxa (e.g., Scarus/Chlorurus) were assumed to belong 1 559 tuis sold by 123 fishers in 2014, and 183 tuis sold by 41 fishers in 2015. 2 This was the number observed at the moment of sampling, so in certain cases, may be an underestimate of the total number of tuis offered for sale by a seller each day, as some tuis may already have been sold.

to the first group listed. A range of non-reef taxa were aggregated within a group designated "pelagic" (Cheilopogon, Coryphaena, Cypselurus, Katsuwonus, Sarda, Scombridae, Thunnus).

A large number of the observed tuis were composed of single-species groups: 360 out of 742.

Multi-species group tuis were composed on average of 3 different species groups, and rarely contained more than 7.

The resulting database contains three dimensions: the tui t of seller i composed of several species groups j. Table 1 provides summary statistics on the composition of the observed tuis.

The data reveal that some species groups are commonly encountered in a majority of the recorded tuis with consistent lengths offered across multiple sellers. Indeed, the total length of fish offered with the first fourteen species groups (in grey) in Table 1 represents the vast majority (95.85%, 4 th column) of the total length of available fish across all the recorded tuis.

Other species groups are more rarely encountered, and they appear in a limited number of tuis presented by some sellers. Within the same tui, the number and size of the fish pieces are negatively correlated (-37.3% being the correlation coefficient) and the species groups most frequently encountered consist of smaller fish. The median length is about 22 cm for the four most frequent species groups and 26 cm for the others.

According to these observations, the prices of the 742 tuis vary by 482 3a CFP 4 around an average of 1773 3b CFP and their lengths by 106 3a cm around an average length of 249 3b cm. These tuis are characterized by substantial heterogeneity along several dimensions, particularly with respect to their species-group composition. Almost half of the sample (361 tuis out of 742) is composed of single-species groups, corresponding to 42% of the total length of fish sold on this market by three quarters of the sellers (118 out of 164). These single-species tuis are composed of 21 of the 37 species groups recorded in roadside sales. The survey of 742 tuis includes both species groups characterized by smaller-(Acanthurus, Siganus and Myripristis) and larger-bodied (Epinephelus and Naso) fish, between 16 and 39 cm each. The prices of these tuis vary across species groups and sellers from 850 CFP to 2000 CFP, around an average price of 1620 CFP (Standard deviation, SD=594 CFP). The lengths of all fish offered on individual tuis also vary greatly with a 107 cm standard deviation around an average length of 216 cm. It should be noted that price and length variations are positively correlated, but these correlations are weak between tuis (27.37%) as well as between species groups5 (13.75% the correlation coefficient). Therefore, price variations among tuis and among species groups are not a simple function of the number or total length of fish on each tui. 1 and2: 14 a sellers have 311 b tuis containing Scarus (S) and 78 c sellers have 140 d tuis containing Chlorurus (C), which corresponds respectively to 42% e and 19% f of the total number 742 g tuis of the survey (100% h ). Tuis do not contain only one species group. Among the 311 b tuis, 90 i contain exclusively Scarus (Table 2) and, by subtraction, 221 tuis may contain up to 27 j different species groups (Table 1). Note that 122 tuis are composed of the two species groups, Scarus and Chlorurus (for brevity this information is not included in the table). So there are 329 tuis that contain one, the other or both species groups according to the counting rules: 𝐶𝑎𝑟𝑑(𝑆 ∪ 𝐶) = 𝐶𝑎𝑟𝑑(𝑆) + 𝐶𝑎𝑟𝑑(𝐶) -𝐶𝑎𝑟𝑑(𝑆 ∩ 𝐶) = 311 + 140 -122 = 329. The total number of the tuis is equal to 742 g , 100% h of the survey, and not the sum of all the elements of the third column. The same is true for the columns 3 and 4 in Table 1 and the number of sellers in Table 2.

In the sample, more than 90% of tuis containing Selar or Pelagic taxa are single-species tuis, meaning that these species are rarely mixed. By contrast, the proportion of tuis containing only Parupeneus, Epinephelus, Chlorurus or Mulloidichthys does not exceed 6%, indicating that these species groups are frequently mixed with others. The large number of single-species tuis and their broad taxonomic representation allowed calculation of average prices of a number of individual species groups. Table 2 provides statistics regarding the characteristics of these tuis, including average and standard deviation of prices per species group for the 11 species groups observed in the survey among the 14 most frequent.

Tables 1 and2 highlight the strong heterogeneity of tuis in terms of length, price and species group composition. Using a benchmark length of 10 cm to calculate species-group prices, we observe that the price of the 11 most frequent species groups varies considerably: the species group with the lowest average price, Epinephelus (49 CFP/10 cm) is more than four times less expensive than the species group with the highest price (Naso, 233 CFP/10 cm).

Not unexpectedly, prices of single-species group tuis differ from one species group to another.

But strikingly, they also differ within each species group, both among sellers and among tuis for the same quantity (length) of fish. Measured by the standard deviation (SD in Tables 1 and2), these deviations range from 34 CFP for an average price of 84 CFP for Scarus to 119 CFP for an average price of 107 CFP for Chlorurus, which are the two most frequently encountered species groups in the sample. For Chlorurus and two other species groups, Siganus and Selar (making up a total of 17% of single species group tuis), the deviations are even greater than average prices: by 11%, 175% and 156% respectively. Such price disparities for the same species group between tuis and sellers may relate to the length of the individual fish (consumers may prefer fish pieces of shorter or longer lengths depending on the species groups) and thus to the number of pieces included in the tuis.

Overall, however, the observed price disparities imply the existence of a wide variety of quality attributes of the fish being sold. These attributes may relate to the tuis, their composition in terms of variety of species groups and length of fish offered, but also to the sellers, the fishing techniques used to catch the fish and other determinants of their quality, such as fishing location. Indeed, in addition to the composition and price of tuis, the roadside surveys also collected information regarding the sellers, particularly where and how the fish composing the tuis had been caught, which may directly affect their quality, and hence the price. Table 3 presents the qualitative variables measuring these quality attributes.

Among quality attributes of fish, freshness is a key factor. Local buyers have a keen sense of how long a fish has been out of the water based on the color of the gills, opacity of the eyes, texture of the skin, flesh and fins, and smell of the entrails, with the key indicators of freshness differing across species groups. Many of these factors, however, are subtle and difficult to generalize. In order to control for these factors involving freshness, roadside sellers were asked in the survey when the fish being sold were caught. However, the time when fish were caught had low variability and a skewed distribution. 83.98% of fishers declared departure time was between 6 pm and midnight, which corresponds to 85.21% of the quantity of fish sold. Most fish were thus taken at night and sold the next morning to ensure freshness at the time of sale.

In addition, the low variability of the time when fish were caught is closely linked to many other factors in our empirical model such as "Habitat" and "Boat". Because of these problems of low variability and collinearity with other factors, we do not introduce the time variable in our estimation. Fish offered on the tuis came from several different reef habitats. However, the vast majority of landings originated from the lagoon or coral reef areas: 76% of tuis (offered by 73% of sellers) came from the lagoon, and 14% of tuis (offered by 17% of sellers) came from reef areas and the remaining 10% from the pass and open ocean. A total of 38% of sellers had been fishing alone, and were offering 29% of tuis. A large majority of the fish offered had been caught with an average crew of 2 people, but some crews were as large as 7. The two most widely used fishing methods were speargun and polyvalent fishing methods including harpoon and line fishing techniques from motorboats called poti marara, often with powerful motors. Spearguns6 had been used by 136 sellers (82.93%) to land 83% of the fish offered on tuis; and poti marara fishing had been used by 7% of the sellers to land 10% of the tuis. These are both fairly selective fishing methods. Sellers (80 out of the 164) also used vaas (outrigger canoes), without motors or with very small motors, to catch the fish on offer in 45% of the tuis. In addition, a significant part of the fish sold was caught without a boat: about 16% of tuis consisted of fish caught while swimming from shore by 17% of the sellers. Finally, the survey showed that sellers had only rarely used multiple techniques to catch the fish offered on their tuis.

Additional information regarding the fishing trips was obtained during the surveys of sellers.

Table 4 summarizes quantitative attributes of fish catches. A total of 42% of sellers used motor boats with an average engine power of 39 HP. Trip length varied, with an average duration of 6 hours. This trip length did not change when sellers used more powerful boats, although it did vary across fishing locations (with shorter trips when fishing in the lagoon and longer (1-2 hour) trips when going to the reef and beyond). Only 28 sellers (17%) retained a fraction of their catch before composing their tuis. Their retained catch averaged about one fourth of their total catch (22%), with a maximum value of 62%. The empirical observations of tui sales derived from the roadside survey summarized in Tables 1-4 highlight a wide heterogeneity in the characteristics of tuis. A modelling approach is thus needed to address these different sources of heterogeneity in order to assess the extent to which changes in the quantities (lengths) of fish of different species groups offered on tuis are likely to affect their price, all else being equal.

Hedonic Modeling Approach

Hedonic modeling approaches are beginning to be applied in seafood studies as for health goods [START_REF] Jensen | Group Health Insurance: A Hedonic Price Approach[END_REF], real estate [START_REF] Farber | Undesirable Facilities and Property Values: A Summary of Empirical Studies[END_REF], computers (Karamti, s. d.), and agricultural [START_REF] Roka | Examining the Use of National Databases in a Hedonic Analysis of Regional Farmland Values[END_REF] or environmental goods [START_REF] Freeman | The measurement of environmental and resource values: theory and methods[END_REF]. This development has been driven by new evaluation questions, relating to the identification of attributes impacting the quality of seafood, as well as their associated monetary value [START_REF] Carroll | Pricing U.S. North Atlantic Bluefin Tuna and Implications for Management: North Atlantic Bluefin Tuna[END_REF][START_REF] Larkin | Intrinsic Fish Characteristics and Intraseason Production Efficiency: A Management-Level Bioeconomic Analysis of a Commercial Fishery[END_REF][START_REF] Mcconnell | Hedonic Prices for Fish: Tuna Prices in Hawaii[END_REF][START_REF] Shimose | Influence of the Flesh Quality and Body Size on the Auction Price of Parrotfishes (Scaridae) at Tropical Island, Southern Japan: Implications for Fisheries Management[END_REF]. The approach builds on the observation that on a market, the price of a good is dependent on several attributes that are intrinsic or extrinsic to it, and that measure the level of good quality in its different dimensions. Applications of the approach have thus also relied on the increasing availability of adequate data sets of good quality.

In the case of the Moorea market for fish, since sales are based on the catch of the day and a direct interaction between fishers and fish consumers, demand and supply adjustments can be considered to be very short-term. This is a small-scale subsistence fishery and a closely connected island market of a basic consumption good. Hence it is not surprising to assume in this study that sellers as well as consumers have all and the same information at the moment of the sale 7 . However, demand is expected to be more sensitive to market changes, while supply is constrained by environmental conditions determining access to fishing grounds as well as the productivity of fishing effort, which is in turn related to fish abundance. Given this, the 7 Some authors introduce more adequate econometric methods to deal with asymmetric information with seller overestimating and consumer underestimating price [START_REF] Kumbhakar | Estimation of Hedonic Price Functions with Incomplete Information[END_REF][START_REF] Bonanno | Credence Attributes and the Quest for a Higher Pricea Hedonic Stochastic Frontier Approach[END_REF]).

willingness to pay to dispose of an additional quantity of fish of a given species group is expected to be equivalent to observed marginal variations in the (hedonic) price of tuis.

Contrary to demand, in the context of Moorea reef fisheries, the supply of fish is considered not flexible enough to follow market variations so that the (marginal) cost of fishing an additional quantity could be equivalent to the variations of (hedonic) prices of tuis. Fishers who sell part of their catch are aware of this and are compelled to compose their tuis and set the tui price taking into account the preferences of local consumers.

Following [START_REF] Rosen | Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition[END_REF], we estimate the implicit price of individual species groups of fish encountered on tuis using the two-step hedonic price approach. First we estimate the hedonic price model of tuis and, second, the implicit price model of the fourteen most abundant species groups in our sample. For the purpose of our analysis, we consider a set of intrinsic and extrinsic attributes that have been shown to determine seafood quality in previous studies [START_REF] Hammarlund | The Big, the Bad, and the Average: Hedonic Prices and Inverse Demand for Baltic Cod[END_REF][START_REF] Larkin | Intrinsic Fish Characteristics and Intraseason Production Efficiency: A Management-Level Bioeconomic Analysis of a Commercial Fishery[END_REF][START_REF] Mcconnell | Hedonic Prices for Fish: Tuna Prices in Hawaii[END_REF].

We also considered factors that might affect the quality of the fish of each species group.

Ciguatera fish poisoning is an important health and safety issue in coral reef fisheries, including in Moorea [START_REF] Morin | Ciguatera Fish Poisoning: Incidence, Health Costs and Risk Perception on Moorea Island (Society Archipelago, French Polynesia)[END_REF]. Caused by a toxin that is produced by dinoflagellates and contained in fish tissues, the risk of contamination varies greatly among different taxa of fish.

We thus included a qualitative score capturing the absence of risk associated with Ciguatera for a species group j, noted W j , varying from 40 (high risk of Ciguatera) to 100 (no Ciguatera risk)

for each of the 37 species groups ( ⁄ depending on whether the species group is or is not present in the tui.

According to different studies of seafood products [START_REF] Aubanel | Evaluation socio-économique de la pêche en milieu corallien dans l'île de Moorea[END_REF][START_REF] Leenhardt | Quel est le rendement de la pêche récifolagonaire à Moorea ? Synthèse des différentes données obtenues[END_REF][START_REF] Mcconnell | Hedonic Prices for Fish: Tuna Prices in Hawaii[END_REF][START_REF] Moussa | Estimation de la taille des poissons lagonaires vendus sous la forme de tui1 en bord de route sur l'île de Moorea (Polynésie française) par analyse de clichés numériques[END_REF][START_REF] Vignes | Price Formation on the Marseille Fish Market: Evidence from a Network Analysis[END_REF], the quality of fish products strongly depends on the fishing techniques used to catch the fish. These are considered by both sellers and buyers of fish as indicators of the quality of seafood. In the context of Moorea, as shown in Table 3, fish are largely caught with a speargun. This technique is likely to be perceived as producing high quality fish as it is selective and preserves the fish flesh [START_REF] Nielsen | Eating Quality' of Fish-A Review[END_REF]. The location of the catch, whether from the lagoon or the reef, can also be an additional quality indicator. Tables 3 and4 summarize the available data regarding these quality attributes of the fish sold.

Using these attributes (represented by the matrix Z), we estimate the following log-quadratic specification of the hedonic tui price equation:

𝒍𝒏(𝑷) = 𝜶 𝟎 + 𝜶 𝒎 + 𝒁𝜽 + ∑ 𝝆 𝒋 𝑰 𝒋 + 𝜷 𝟏 𝑳𝑷 + 𝜷 𝟐 𝑳𝑷 𝟐 + 𝜺 𝒋 (1)
This specification enables measuring 𝜌 𝑗 , the equivalent of a lump sum payment incorporated in the price of tui containing the individual species group j, provided it is present in the tui (𝐼 𝑖𝑡 𝑗 = 1 𝑖𝑓 𝐿 𝑖𝑡 𝑗 > 0; 0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒) regardless of the quantity available. Fixed effects are also introduced when estimating the model in order to account for the potential existence of temporal trends 𝛼 𝑚 , or other sources of unobservable heterogeneity between tuis or sellers9 .

The Rosen two-step evaluation procedure consists of deriving the purchaser willingness to pay 𝑃𝑊𝑃 ̂𝑖𝑡 𝑗 for a marginal increase in length of each species group j from the derivative of the tui's hedonic price, as follows:

𝑷𝑾𝑷 ̂𝒊𝒕 𝒋 = 𝑷 ̂𝒊𝒕 𝝎 𝒊𝒕 𝒋 (𝜷 ̂𝟏 + 𝟐𝜷 ̂𝟐𝑳𝑷 𝒊𝒕 ) (2)
Following standard recommendations of [START_REF] Heckman | NONPARAMETRIC IDENTIFICATION AND ESTIMATION OF NONADDITIVE HEDONIC MODELS[END_REF] and the pioneering studies of Griliches ( 2013), [START_REF] Freeman | The measurement of environmental and resource values: theory and methods[END_REF] and [START_REF] Mäler | Handbook of Environmental Economics[END_REF], three methods are used to identify such demand functions for each species group j in the Rosen two-stage model.

First, the estimation relies on flexible non-linear specifications with changes in the functional form of the hedonic tui price and the demand functions of each species group. The hedonic price of the tui is assumed to be a log-quadratic function of its aggregated length (Equation 1)

while the demand function of the j th species group is a translogarithmic function [START_REF] Berndt | The Translog Function and the Substitution of Equipment, Structures, and Labor in U.S. Manufacturing 1929-68[END_REF] of the length of all the species group present in the tui (Equation 3):

𝑙𝑛(𝑃𝑊𝑃 ̂𝑗) =
where X is the matrix summarizing the available demand factors (see below).

Second, the species group demand function (Equation 3) is estimated in the second-stage with a stratified sample database containing the species group under consideration while the firststage model is estimated using the entire data set. The third column of Table 1 shows that all species groups are not present in all tuis. The first fourteen species groups in the table occurred most frequently in this market, such as Scarus which is present in 42% of the tuis (see next section).

Third, identification is based on geographical demand factors (named X in Equation ( 3) and described in Table 5) characterizing the demand for fish in the different locations based on where each tui was sold. We distinguish the five municipalities of Moorea using a municipality fixed effect 10 and a set of instrumental variables to measure purchasing power in each municipality, such as unemployment rate, population density and population change [START_REF] Bellwood | Human Activity Selectively Impacts the Ecosystem Roles of Parrotfishes on Coral Reefs[END_REF]. Indeed, these instrumental variables show that the five municipalities differ in some characteristics, which may directly affect the local demand for fish 11 . Other instruments are also used to account for the impact of the fish supply differentiation operated by sellers in this market. Three instruments are calculated from the database (Table 6), which correspond to the number of tuis (NTUIS) and the total number of species groups (NSPECV) offered by each seller, as well as the total number of species groups in each tui (NSPECT). The two first instruments vary in one dimension, between fishers, and the third in two dimensions, between fishers and tuis. Indeed, 50% of fishers offer more than 3 tuis (some of them up to 23 tuis) while the number of species groups varies from 5 to 14 between sellers and from 2 to 9 among the tuis of individual sellers. 10 Each municipality is represented by a dummy variable. One of the five municipalities is excluded in the estimation as a reference modality. This statistical precaution is respected for all the other binary variables.

11 Equations 1 and 3 are estimated with Stata16 software. All available factors are introduced using a stepwise estimation approach with backward selection, only the variables with statistically significant parameters at the 90% confidence level are retained in the final model.

As for the hedonic price of tuis, species group pricing strategies have a quantitative dimension in the demand function (i.e., the price and length of fish offered), as well as a qualitative dimension: sellers can combine species groups j in variable proportions. To capture this, the binary indicator 𝐼 𝑖𝑡 𝑘 = (1,0) is included in the model, specifying that the k th species group (k=1,...,J ; 𝑘 ≠ 𝑗 ) is present in the tui with the j th species group, in addition to its length 𝐿 𝑖𝑡 𝑘 .

The final step in Rosen's model is a monetary evaluation of the additional length (quantity) ∆𝐿 of individual species group j in the tui using the estimated demand function. This amount is equivalent to the sum of the purchaser's willingness to pay for this additional quantity using the estimated Equation 3. Represented by 𝒑 𝑗 (𝑳 * ), this is the price in CFP of an additional length ∆𝐿 taken to be 10 cm, or one extra piece of fish, as follows:

𝒑 𝒋 (𝑳 * ) = ∫ 𝑷𝑾𝑷 ̂𝒋(𝒙)𝒅𝒙 𝑳 * +∆𝑳 𝑳 * (4)
This price is not a fixed amount but varies according to the length of the tui because of the flexibility of the estimated demand function (Equation 3). We calculate this price for a fixed reference length of each species group j, L*=100 cm, which is the per tui median length encountered for the fourteen most frequent species groups in this market.

Results

Applying least square estimation of Equation 1 and the backward stepwise selection procedure of significant variables, we find that several factors have decisive effects on tui prices that seem consistent with the reality of the market (Table 7 and commentary below). The overall level of reliability of the results is relatively high: the empirical model offers significant explanatory power of tui price variations, with an overall coefficient of determination between 64% and 76%, and its level of reliability exceeds 99.9% based on the Fisher test.

However, there is reason to doubt the exogeneity of two of the explanatory variables. These relate to the fraction of the catch retained by the seller for his personal use (KEPT_UN, a binary variable which identifies sellers who keep part of their catch for themselves, and FRAQ_KEPT, the share-in percentage of this fraction). It is possible that this fraction is kept because of the value of the fish and the species group landed. These variables therefore relate to decisions that are specific to sellers (to retain part of the catch, and how much), and may not be independent of the price of the tuis offered for sale. Carrying out the Hausman test (using its Nakamura and Nakamura version) confirms this. To correct the ensuing endogeneity bias, we use a 2SLS method retaining four instrumental variables in addition to the significant explanatory variables.

These instruments provide information on the standard of living in the geographical areas where sellers sell the tuis (usually close to their home), measured via levels of unemployment as well as the demographic weight of the municipality (respectively UNEMPL and POIDEMOG in Table 5) and variables capturing the diversity of catches measured by the number of species groups available from each seller (Table 6) and whether or not the seller is the fisher who caught the fish being sold (79.88% of sellers are the fisher). The estimated auxiliary equation using a

2SLS method shows that most of these instruments have significant impact on the endogenous factor FRAQ-KEPT. In addition, performing the Sargan over-identification test confirms the validity of these instruments12 .

Results from the estimation of Equation 3with OLS and 2SLS are presented in Table 7. Given the endogeneity problem mentioned above, only the 2SLS estimation is considered hereafter.

The Price Index column of the table gives the value of the tui price index for each category of the binary variables and the marginal/elasticity effect for the quantitative explanatory variables.

After correcting the endogeneity bias, we note that the price of tuis is 175% higher on average for sellers who retain a share of their catch for their consumption. However, this price drops as the retained share increases, which may be related to the fact that the most highly priced fish are those that are retained by the sellers first.

The price of a tui is an increasing function of its length. This function is quadratic: the price increase is steeper for longer tuis. The price elasticity is 7.16% for a tui of average length (252 cm), but varies according to the different factors introduced in the model.

Our results indicate that of the 37 species groups that compose tuis, the presence of four13 has a fixed effect on tui prices. Based on parameter values, the price of a tui is lower if it contains Chanos, Mulloidichthys, Pelagic taxa and Tylosurus; the tui price index decreases on average to 59%, 92%, 55% and 54% respectively in these cases (last column in Table 7). Two of these species groups (Chanos and Tylosurus) are rare in this market, representing only 0.4% of the total length of all of the 37 species groups (Table 1).

The results also reveal the existence of monthly fixed effects with lower prices of tuis in the months of February, July, and the last four months of the year. As reported by Graddy ( 2006), these seasonal variations may highlight a strong dependency of the fresh seafood market on the suitability of sea conditions for fishing as well as temporal differences in the amount of time available for fishers to participate in the fishery (relative to other activities).

In addition, fishers who sell fish they caught on their own or with smaller crew have tuis with higher prices (price index up to 118%). The price of tuis increases with crew size, up to a point (crew of 3) after which it decreases. Tui prices appear to be higher if they are composed of fish caught with selective fishing gear such as line (price index up to 115%) and motorized boats such as poti marara (price index up to 142%). The price of tuis also depends on the power of the motors on boats, in the shape of a convex polynomial function with a minimum of 83 HP 15 .

Hence, tui prices are higher when the fish have been caught either with small or unmotorized Tuis can contain up to nine different species groups and half of the sampled tuis (51.28%) contain at least two species groups. Table 8 shows the structure of species group combinations on the tuis. Some species groups are more often combined for sale than others. Two species groups, Pelagic taxa and Selar, are crossed with very few other species groups: Selar, present in only 30 tuis is combined with two other species groups only (Lutjanus and Pelagic); Pelagic taxa are sold with four other groups (Myripristis, Selar, Siganus and the unidentified species group). The other 12 species groups (in grey in Table 8) are often combined with a large number of other species groups (between 20 and 28 of the 37 species groups present in the market). For example, the most abundant species group, Scarus, is combined with 27 other species groups, while Myripristis is with 28 (Table 8, Line 3). The second most frequent species group, Chlorurus, is pooled on 122 tuis together with Scarus, but only on 4 tuis together with Myripristis. Note that Naso is combined with Cephalopholis only on one tui. This structure of species group combinations provides information on the degree of dependence between different groups in the composition of tuis.

To account for cross-species group elasticities within the same tui, we introduce in the model of each of these fourteen species groups, the lengths of the other species groups, as well as a binary indicator of their presence in individual tuis. However, the tuis in each sample do not contain all possible combinations with the other 37 species groups in the database. The most frequent combinations are only between the fourteen most frequent species groups and between a subset of these for some species groups. In the subsample of tuis of the most frequent species group, Scarus is combined with Chlorurus, Parupeneus, Mulloidichthys, Epinephelus, Acanthurus, Cephalopholis and Siganus in respectively 39% , 21%, 17%, 8%, 8%, 7% and 7% of the 311 tuis. In estimating the model of the implicit price of Scarus, we only introduce these seven species groups in order to identify the corresponding parameters. We do the same for each of the other 14 species groups. Table 9 gives cross-elasticities for only those combinations of species groups that are observable and frequent enough among the tuis. Using Rosen's second stage (Equation 3), we estimate the demand functions for the fourteen most abundant species groups (Table A1 in the supplementary material). We limit this analysis to these fourteen species groups, because they are the only ones with sufficient sample size.

Additionally, the demand factors needed to identify these functions only have a discriminating strategies to enhance the value of the fish sold: where cross price elasticities exist, the species groups on offer value gain in the presence of other species groups, except in the case of Pelagic species (which are caught outside the lagoon and reef areas). Using the estimated demand function of the fourteen most abundant species groups, we calculated their prices according to Equation 4. The results are illustrated in Figure 2, for eleven of the reef-associated species groups 18 .

Figure 1a shows the price-index of these species groups relative to the price of the most frequent taxon encountered in the survey (Scarus). The results highlight strong heterogeneity in the market value across species groups, which varies between 133 and 137 per cent of the market value of Scarus. The next most abundant species groups in this market (Parupeneus, Myripristis and Mulloidichtys) have high market value, with a price index varying between 120 and 135 per cent. Acanthurus and Sargocentron display high price indices (respectively 137 and 133 per cent), but are encountered less frequently in the tuis. 18 Excluding Chlorurus which appeared as an outlier in the price distribution with a price index of 479%. This may have been due to the heterogeneity of the species group, and observation biases.

When applied to the average size of individuals encountered in each species group 19 , prices derived from Equation 4 provide an estimation of the minimum, mean and maximum price one would pay for a single fish of each species group (Figure 1b). The four species groups appear to be the more valuable (with prices/fish of between 184 and 237 CFP for an additional medium-sized fish measuring between 35.42 and 48.25 cm). Naso display the highest prices per fish (274 CFP for a medium-sized fish of 68.50 cm), and is not frequently encountered in the tuis (Table 1). All the other species groups, which are less frequently encountered on this 19 See Table A2 in the Appendix for data regarding average fish sizes of each species. The medium size of individual fish across all species groups varies between 27.17 and 68.50 cm. market, present lower prices/fish piece (under 184 CFP/fish of medium size varying between 27.17 and 53 cm). Selar and Pelagic taxa present very low prices, in addition to being rare in the composition of tuis.

Discussion and Conclusion

This research examines the extent to which economic analysis can help explain the patterns of fish sales and fish prices observed in the coral reef fin-fish fishery of Moorea, French Polynesia.

We used the data collected in a survey of roadside tui sales around the island to assess the factors contributing to the price at which the tuis are sold, and to deduce the implicit price of different species groups entering in their composition. Our results show that different groups of reef fish attract implicit prices that may vary by a factor of four to five across species groups.

In addition to certain species groups, factors that entail higher prices for tuis include a seasonal dimension (higher prices being fetched during the first half of the calendar year), as well as the fishing techniques and other characteristics of the fishing trips such as the size of the crew.

Ciguatera risk, by contrast, did not seem to account for price differences between species groups. Furthermore, our results highlight positive cross-price elasticities between many coral reef species groups. In other words, this means that sellers develop strategies to enhance the value of their daily catches through the species mix (except in the case of Pelagic taxa, that are caught outside the lagoon and reef areas).

This fish market can be considered transparent, since the sellers catch the fish they offer close to sale outlets, using local fishing techniques. However, the quality of the fish and therefore their price can also depend on other criteria (that were not measured in the survey). For example, the appearance of fish was not documented in the survey. Data on the physical quality of fish sold, such as traces of handling or state of freshness, are notoriously difficult to observe and measure. Attributes such as the presence of marks due to the fishing method could affect the perception of the quality of fish offered on tuis, leading to bias in the measurement of their implicit prices [START_REF] Pope | Fear of Crime and Housing Prices: Household Reactions to Sex Offender Registries[END_REF].

Despite these limitations, the results of this analysis illustrate that market processes can help explain the composition and relative prices of tuis offered in roadside sales in coral reef fishery.

Taking the observed price differences as a reflection of the preferences of local consumers and associated demand for fish, the results can also be used to assess the economic implications of changes in the supply of the different species groups, such as would result from changes in the abundance and accessibility of these groups to fishers around the island. In particular, Moorea In addition, the results provide important information on the status of the market for fish on the island. Fish buyers are willing to pay more for extra quantities of fish. This implies that the demand is not completely met by the supply of fish from the local fishery. Besides, the fish demand is expected to grow with an increasing number of new inhabitants less involved in fishing activities themselves (Thiault et al. 2018b). Provided the local fish resources enable additional catch and landings, this market would be expected to expand over time.

Finally, our results show how these fishers value their coral reef fish species on a local and direct sale market. This should be complemented by an analysis of the costs of fishing to gain a comprehensive economic perspective of small-scale fishing activities in Moorea. Beyond this case study, the research also illustrates how empirical economic research can help improve the understanding of small-scale coral-reef fisheries, and demonstrates a methodology which can be applied to a broad range of contexts in the Pacific, where these fisheries have particularly strong social and cultural value, provided similar data on fish sales is available.

  data: 311 a tuis contain Scarus (2nd line). Scarus is combined with 27 b other species groups (3rd line). Scarus is combined with Chlorurus in 122 c tuis, which corresponds to 39% of the subsample of 311 tuis of Scarus (the matrix).

  (a) Price index of coral reef fish species groups (based on Scarus) (b) Price in CFP of mean (min and max)-size fish per species group Figure 1. Price estimation results for most frequent coral-reef fish species groups (Species groups are ranked left to right from most to less frequently encountered in the survey) most frequently encountered on tuis (Scarus, Parupeneus, Myripristis and Mulloidichthys) still

  has undergone strong environmental disturbance in its recent past due to the detrimental impacts of blooms of a coral predator sea star and cyclones (Lamy et al. 2016). Although most of the effects on fish resulted in biomass transfer within functional groups (Lamy et al. 2015), the marine ecosystems presented a recovery debt (Dubois et al. 2019) and understanding how fishermen respond and adapt, and how this translate into changes into how fish are sold remain unresolved..

Table 1 . Characteristics of the tuis observed in the survey Species group j (by decreasing number of tuis) Num. of. sellers Num. of tuis % of tuis in sample containing each species group Num. of other species groups present in tuis sold by seller Total Length of each species group (cm) % of Total Length in sample Average Length of species group j in single tuis (cm) SD Length of species group j in single tuis (cm) Average Price of a tui (CFP) SD Price of a tui (CFP) Average Length of fish of species group j (cm) SD Length of fish of species group j (cm) CIG (Index of ciguatera risk absence)

 1

	Scarus	114 a	311 b	42% e	27 j	57734	31.2%	186	109	1926	246	5	100
	Chlorurus	78 c	140 d	19% f	21	9813	5.30%	70	66	1900	301	6	100
	Parupeneus	81	130	18%	25	11121	6.01%	86	67	1919	247	4	100
	Myripristis	59	115	15%	28	18924	10.2%	165	117	1939	249	3	100
	Mulloidichthys	75	108	15%	27	11737	6.34%	109	88	1898	296	4	100
	Siganus	55	104	14%	24	15609	8.43%	150	104	1952	215	3	100
	Pelagic	20	90	12%	4	15739	8.51%	175	76	864	549	13	100
	Naso	49	85	11%	21	6760	3.65%	80	71	1929	269	13	100
	Epinephelus	53	73	10%	22	8698	4.70%	119	136	1986	117	5	75
	Acanthurus	43	58	8%	21	6427	3.47%	111	108	1922	226	4	100
	Cephalopholis	46	55	7%	21	2567	1.39%	47	29	2000	0	5	67
	Sargocentron	37	52	7%	24	2355	1.27%	45	31	1885	307	3	100
	Lutjanus	24	30	4%	20	1968	1.06%	66	68	1967	183	5	40
	Selar	7	30	4%	2	7798	4.21%	260	91	1350	494	4	100
	Monotaxis	14	17	2.29%	17	675	0.36%	40	23	2000	0	9	40
	Cheilinus	13	16	2.16%	15	730	0.39%	46	25	1906	272	6	75
	NI (Non Identified)	10	16	2.16%	16	604	0.33%	38	21	1813	512	6	40
	Kyphosus	6	15	2.02%	13	830	0.45%	55	35	2000	0	7	100
	Lethrinus	13	15	2.02%	12	566	0.31%	38	23	1933	258	12	40
	Calotomus	14	14	1.89%	12	603	0.33%	43	28	1893	289	4	100
	Gnathodentex	10	11	1.48%	15	542	0.29%	49	24	1955	151	3	100
	Carangoides	6	7	0.94%	9	383	0.21%	55	29	1857	244	23	100
	Epibulus	7	7	0.94%	11	228	0.12%	33	9	2000	0	8	100
	Tylosurus	4	7	0.94%	3	478	0.26%	68	35	714	567	36	100
	Caranx	4	6	0.81%	5	333	0.18%	55	33	2000	0	17	40
	Crenimugil	4	6	0.81%	12	333	0.18%	55	44	2000	0	2	40
	Albula	2	4	0.54%	1	288	0.16%	72	14	1750	289	19	100
	Ctenochaetus	3	3	0.40%	8	94	0.05%	31	26	1833	289	3	75
	Pseudobalistes	3	3	0.40%	0	188	0.10%	63	10	2000	0	10	100
	Sphyraena	3	3	0.40%	6	275	0.15%	92	76	1833	289	21	100
	Chanos	2	2	0.27%	3	254	0.14%	127	28	1250	1061	6	100
	Heteropriacanth.	2	2	0.27%	5	159	0.09%	80	86	2000	0	4	100
	Liza	2	2	0.27%	8	85	0.05%	42	3	1750	354	20	100
	Priacanthus	2	2	0.27%	4	44	0.02%	22	2	2000	0	1	100
	Balistapus	1	1	0.13%	5	24	0.01%	24		1500			100
	Cantherhines	1	1	0.13%	1	67	0.04%	67		2000			100
	Coris	1	1	0.13%	8	21	0.01%	21		2000			100
	All the survey a	164	742 g	100% h		185054	100%	249	106	1773	482	11
	a Note for Tables

Table 2 . Characteristics of the single species group tuis observed in the survey

 2

	Species group j	Num. of	Num.	% of	Num. of	%	Average	SD	Average	SD Price	Average	SD
	(by decreasing	sellers	of tuis	single	tuis	Length	Length	Length	Price of	of a tui	Price of	Price of
	number of tuis)			species	Single/Al	of Single	of	of	a tui	(CFP)	species	species
				group	l tuis (%)	Species	species	species	(CFP)		group j	group j
				tuis		group	group j	group j			(CFP/10	(CFP/1
						tuis/ all	in single-	in			cm)	0 cm)
						tuis	species	single-
							group	species
							tuis (cm)	group
								tuis
								(cm)
	Scarus	55	90 i 25%	29%	41%	262	82 1961	154	84	34
	Chlorurus	5	6	2%	4%	16%	264 108 1833	408	107	119
	Parupeneus	4	5	1%	4%	10%	224	91 2000	0	109	64
	Myripristis	18	43 12%	37%	57%	252 106 1977	152	107	88
	Mulloidichthys	6	7	2%	6%	17%	293	90 1857	378	69	27
	Siganus	19	34	9%	33%	52%	239	91 1971	171	160	280
	Pelagic	19	85 24%	94%	91%	169	69	850	533	62	62
	Naso	14	30	8%	35%	53%	120	86 1933	254	233	121
	Epinephelus	2	3	1%	4%	17%	506 233 2000	0	49	30
	Acanthurus	4	7	2%	12%	34%	309	28 2000	0	65	5
	Selar	5	27	7%	90%	94%	271	90 1333	460	76	120
	All the single
	species groups	118	361 100% 49% 42.12%	216	107	1620	594
	of the survey a

Table 3 . Qualitative attributes characterizing the sellers and fish sold

 3

		Variable	164 SELLERS n %	n	742 TUIS %
	HABITAT	LAGOON	119	73%	561	76%
		REEF	28	17%	104	14%
		PASS	9	5%	29	4%
		OPEN OCEAN	8	5%	48	6%
	CREW	FISH WITH CREW	101	62%	525	71%
		FISH ALONE	63	38%	217	29%
	FISHING	SPEARGUN	136	83%	618	83%
	GEAR	 with un-motorized boat	72	44%	264	36%
		 with motorized boat	38	23%	244	33%
		 without boat	26	16%	110	15%
		POTI MARARA Fishing	11	7%	72	10%
		LINE	10	6%	26	4%
		 with motorized boat	9	5%	24	3%
		NET	7	4%	26	4%
		 with un-motorized boat	4	2%	18	2%
	BOAT	WITH MOTOR	69	42%	379	51%
		WITHOUT MOTOR	67	41%	246	33%
	BOAT TYPE VAA	80	49%	334	45%
		 un-motorized	67	41%	246	33%
		 low power (<40 HP) motorized	13	8%	88	12%
		POTI MARARA	56	34%	291	39%
		 high power (>40 HP) motorized	53	32%	286	39%
		NONE (without boat)	28	17%	117	16%

Table 4 . Quantitative attributes characterizing the sellers Variable Definition % of non- zero Average (SD) Max

 4

	HP	Engine power (HP)	42%	39	(21)	125
	CREW	Number of crew	61.59%	1.87	(1.25)	7
	HOUR FISH Hours fishing	100%	6	(3)	17
	FRAQ KEPT Fraction of catch kept for family and friends (not	17%	22%	(13)	62%
		sold)

  Table1)8 . The length of the j th species group was weighted 𝐿 𝑖𝑡 𝑗 in the tui t of the seller i (𝐿 𝑖𝑡 𝑙 is the length in cm of each l th species group present in this tui). The hedonic price of a tui 𝑃 𝑖𝑡 is assumed to depend on the aggregate length of fish 𝐿𝑃 𝑖𝑡 = 𝑛 𝑖𝑡 ∑ 𝐿 𝑖𝑡 𝑗 𝜔 𝑖𝑡 𝑗 37 𝑗=1 of all species groups 𝑗 = {1, … , 𝑛 𝑖𝑡 } composing the tui t of the seller i, weighted by its relative Ciguatera absence score 𝜔 𝑖𝑡 𝑗 = 𝑊 𝑗 ∑ 𝑊 𝑙

	by its relative absence of Ciguatera risk 𝑊 𝑖𝑡 𝑗 = 𝐿 𝑖𝑡 𝑗 𝑊 𝑗 ∑ 𝐿 𝑖𝑡 𝑙 𝑊 𝑙 𝐽 𝑙=1 ⁄ importance of its length 𝑛 𝑖𝑡 combined with the 𝑙=1

Table 5 . Geographical demand factors

 5

	Municipal.		Sellers		Tuis	POP POPVAR SURFACE DENSITY POIDEMOG UNEMPL
		n	(%)	n	(%)	Populat	Population	Area in km²	Population	% of	Unemploym
						ion in	growth		density per	municipality in	ent rate in
						2012	between		km²	total population	2012
							1977 and			2017
							2012
	Afareaitu	229 (30.86%)	69 (42.07%)	3455	277.50	23.80	145.20	21.04	33.80
	Paopao	305 (41.11%)	40 (24.39%)	4580	271.00	30.00	152.70	26.56	15.60
	Haapiti	106 (14.29%)	32 (19.51%)	4062	352.30	38.80	104.70	24.36	21.60
	Papetoai	80 (10.78%)	16	(9.76%)	2318	339.90	25.10	92.40	13.34	26.80
	Teavaro	22	(2.96%)	7	(4.27%)	2484	311.30	15.80	157.20	14.70	21.80
	TOTAL	742	(100%) 164	(100%) 31199	80139	27,99 132,4993		23,47

Table 6 . Definition and descriptive statistics of supply differentiation instruments

 6

	Variable	Signification	Mean (SD)	Median	Max
	NTUIS	Number of tuis of each seller	4.52 (3.60)	3	23
	NSPECV	Number of species groups of each seller	5.29 (3.44)	5	14
	NSPECT	Number of species groups in each tui of each seller	2.08 (1.41)	2	9

Table 7 . Estimated hedonic price function of tuis (Equation 3): 2SLS method vs OLS

 7

			Statistics	OLS				2SLS
										Price Index
		VARIABLES	Mean	SD	𝛽: Param.	(p value)	𝛽: Param.	(p value)	𝑒 𝛽 or Elasticity*
		L	249.4	106.0
	Length	LP	252.6	109.9	N.S.		N.S.	14 .
		LP²	75,877	65,450	4.32e-07	(0.000)	4.83e-07	(0.004)	7.16%*
		Chanos
	Species	(1 vs. 0)	0.00270	0.0519	-0.515	(0.000)	-0.535	(0.005)	59%
	group	Monotaxis
		(1 vs. 0)	0.0229	0.150	0.0930	(0.077)	N.S..

  boats, or with boats with powerful motors. Tui prices are lower for fish caught with boats of intermediate horsepower (80 HP).Implicit Price of the Most Frequent Species GroupsTo estimate the demand function with Equation 3, we first stratify our database to form subsamples of tuis containing each species group. This stratification shows that the first fourteen species groups in Table1(Scarus followed by Chlorurus, Parupeneus, Myripristis, Mulloidichthys, Siganus, Pelagic taxa, Naso, Epinephelus, Acanthurus, Cephalopholis, Sargocentron, Lutjanus and Selar) are the most abundant, representing 95.85% of the total length of all the fish present on the 742 tuis. Only these species groups have large enough subsamples to obtain reliable estimates. These fourteen species groups are ranked in Table8from right to left in descending order of the number of tuis in which they are encountered. The size of these subsamples varies from 311 to 30 tuis. The most abundant species group is Scarus (in 311 tuis) followed by Chlorurus (in 140 tuis) and Parupeneus (in 130 tuis), while Lutjanus and Selar are rare (in 30 tuis only).

15 ln (𝑃) ̂= 7.524 -0.0403 𝐻𝑃 + 0.000243 𝐻𝑃 2

Table 8 . Species groups combinations on tuis

 8

		Scarus Chlor. Paru. Myri. Mull.	Siga.	Naso. Epine. Acan. Ceph. Sarg.	Lutj.	Pela. Sela.
	Number of tuis	311 a	140	130	115	108	104	85	73	58	55	52	30	90	30
	Number of species groups	27 b	21	25	28	27	24	21	22	21	21	24	20	4	2
	Scarus		122 (0.87)	64 (0.49)	18 (0.16)	53 (0.49)	22 (0.21)	16 (0.19)	26 (0.36)	25 (0.43)	23 (0.42)	18 (0.35)	12 (0.4)	0 (0.00)	0 (0.00)
	Chlorurus	122 c (0.39 d )		22 (0.17)	4 (0.03)	15 (0.14)	12 (0.12)	8 (0.09)	10 (0.14)	10 (0.17)	7 (0.13)	4 (0.08)	6 (0.2)	0 (0.00)	0 (0.00)
	Parupeneus	64 (0.21)	22 (0.16)		19 (0.17)	72 (0.67)	20 (0.19)	20 (0.24)	26 (0.36)	20 (0.34)	20 (0.36)	15 (0.29)	10 (0.33)	0 (0.00)	0 (0.00)
	Mulloidichthys	53 (0.17)	15 (0.11)	72 (0.55)	14 (0.12)		13 (0.13)	10 (0.12)	24 (0.33)	16 (0.28)	17 (0.31)	13 (0.25)	7 (0.23)	0 (0.00)	0 (0.00)
	Epinephelus	26 (0.08)	10 (0.07)	26 (0.2)	22 (0.19)	24 (0.22)	12 (0.12)	8 (0.09)		14 (0.24)	40 (0.73)	16 (0.31)	12 (0.4)	0 (0.00)	0 (0.00)
	Acanthurus	25 (0.08)	10 (0.07)	20 (0.15)	13 (0.11)	16 (0.15)	16 (0.15)	14 (0.16)	14 (0.19)		10 (0.18)	7 (0.13)	4 (0.13)	0 (0.00)	0 (0.00)
	Cephalopholis	23 (0.07)	7 (0.05)	20 (0.15)	14 (0.12)	17 (0.16)	9 (0.09)	1 (0.01)	40 (0.55)	10 (0.17)		13 (0.25)	5 (0.17)	0 (0.00)	0 (0.00)
	Siganus	22 (0.07)	12 (0.09)	20 (0.15)	21 (0.18)	13 (0.12)		17 (0.2)	12 (0.16)	16 (0.28)	9 (0.16)	14 (0.27)	3 (0.1)	2 (0.02)	0 (0.00)
	Myripristis	18 (0.06)	4 (0.03)	19 (0.15)		14 (0.13)	21 (0.2)	17 (0.2)	22 (0.3)	13 (0.22)	14 (0.25)	27 (0.52)	9 (0.3)	1 (0.01)	0 (0.00)
	Sargocentron	18 (0.06)	4 (0.03)	15 (0.12)	27 (0.23)	13 (0.12)	14 (0.13)	5 (0.06)	16 (0.22)	7 (0.12)	13 (0.24)		3 (0.1)	0 (0.00)	0 (0.00)
	Naso	16 (0.05)	8 (0.06)	20 (0.15)	17 (0.15)	10 (0.09)	17 (0.16)		8 (0.11)	14 (0.24)	1 (0.02)	5 (0.1)	6 (0.2)	0 (0.00)	0 (0.00)
	Lutjanus	12 (0.04)	6 (0.04)	10 (0.08)	9 (0.08)	7 (0.06)	3 (0.03)	6 (0.07)	12 (0.16)

Table 9 . Signs of cross-price elasticities between the 14 species groups Species groups Sca. Chl. Par. Myr. Mul. Sig. Pel. Nas. Epi. Acan. Cep. Sar. Lut. Sel. NI

 9

	Scarus		+	+	+	+	+	+	+	+		+	+
	Chlorurus	+				+				+
	Parupeneus	+			+	+	+	+		+	+	+
	Myripristis	+		+			+	+	+	+		+	+
	Mulloidichthys	+	+	+					+
	Siganus	+		+	+		-			+
	Pelagic						-					-
	Naso	+		+	+
	Epinephelus	+			+	+				+	+	+
	Acanthurus	+	+	+	+		+		+
	Cephalopholis			+					+
	Sargocentron	+			+				+
	Lutjanus			+	+
	Selar						-

a=Standard deviation and b=Average

The local currency is the Pacific Franc, Compagnie Française du Franc: 1 CFP= 0.008380 Euro as of March 2021.

Correlation is calculated with the length and the price of the 118 single-species groups (Table2).

A skilled spearfisher will shoot fish in particular spots to maintain the fish's aesthetics.

The scores were established based on expert knowledge of researchers from CRIOBE (Centre de Recherches Insulaires et Observatoire de l'Environnement, www.criobe.pf). Although ciguatera risk can vary spatially somewhat around the island, for our analyses we applied the same risk factor to a species regardless of where it was caught because finer-scale risk patterns have not been quantified for Moorea.

Other fixed effects parameters were tested during the estimation process, in order to take into account disparities between tuis of each fisher, including the location of sales considered at different scales, but these proved not statistically significant.

The significance level of this test is 24.30%, for the null hypothesis not to be rejected.

There is a fifth species group (Monotaxis) present in 2.29% of our sample, which seems to be the only species increasing the value of tuis (it increases prices by 106%) but the estimated parameter is not statistically reliable after correcting for endogeneity.

p value of bilateral Student test exceeding 10%.

effect for these fourteen species groups, with their parameters having statistically significant and reliable values. In estimating the demand functions, we also correct for the endogeneity problem of the explanatory variable FREQ_KEP, by the use of a double least squares estimation procedure (as in the hedonic price estimation), and for the problem of collinearity between the explanatory variables by stepwise elimination of variables with the highest VIF (all the factors in the estimated models have VIF values below the theoretical reference threshold of 5).

The length combinations of the fourteen species groups whose implicit price models are estimated allow us to identify the signs 16 of cross-price elasticities between these groups (Table 9). These elasticities specify whether the species groups enter into the composition of tuis as complements (+) or substitutes (-). Results show that all the elasticities are positive between all reef species and negative between Pelagic taxa and two reef species, Selar and Siganus. except for two species groups: Pelagic taxa and Selar. Selar appear as a substitute group for Pelagic taxa only; This means that, except for Pelagic taxa which appear as a substitute group 17 for Selar and Siganus, The other twelve all the reef species groups enter as complements in the composition of tuis: some with more species groups than others. Scarus is combined with ten other species groups; Parupeneus and Myripristis with eight; Epinephelus and Acanthurus with six; Mulloidichthys and Siganus with four; Chlorurus, Naso and Sargocentron with three;

Lutjanus and Cephalopholis with two. Other interaction parameters are not statistically significant (according to Student's bilateral test): the underlying elasticities are therefore not important and the corresponding species groups appear to enter independently in the composition of tuis. Scarus, for example, is present independently of Lutjanus, Selar and Cephalopholis, which are rare species groups in our sample. These interactions reflect seller 16 Price elasticity of species group j with respect to a variation in the length of species group k available on the tui is 𝑒 𝑗/𝑘 = 𝛽 𝑘 𝑗 + 2𝛽 𝑘𝑘 𝑗 𝑙𝑛(𝐿 𝑘 ) + ∑ 𝛽 𝑘𝑙 𝑗 𝑙𝑛(𝐿 𝑙 ) 37 𝑙≠𝑘

. Given the flexible form of the implicit price equation, this elasticity is not constant, but its sign is easy to determine: it is equivalent to the sign of the parameters. 17 We note in Tables 1 and2 that Pelagic taxa are often sold alone: 24% of single species group tuis and only 12% of all the survey.