Bruno Richard

Jean-Francois F Le Page

Pierre Schuck

Christophe André

Romain Jeantet

Guillaume Delaplace
email: guillaume.delaplace@lille.inra.fr

C Andre

Towards a better control of dairy powder rehydration processes

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

Introduction

Today, dairy ingredients are increasingly used throughout the food industry. One of the approaches used to facilitate transport and storage is to convert dairy liquids into powders by spray drying [START_REF] Schuck | Spray drying of dairy products: state of the art[END_REF]. In a further step, the powders are reconstituted to supplement fresh milk in dairy manufacture and then transformed with various processing equipment to obtain milk products with different functional properties (e.g., gelling, foaming or nutritional properties; [START_REF] Aneja | Equipment for recombination[END_REF].

Reconstitution is usually realised in mechanically agitated tanks. Ideally, the process should be as fast as possible and should require a minimum input of energy. The resultant reconstituted product should be devoid of lumps [START_REF] Jensen | Reviews of the progress of dairy science: milk powder and recombination of milk and milk products[END_REF]. These requirements are common to both industry and consumers, but difficult to fully satisfy [START_REF] Cayot | Les propriétés d'hydratation des protéines[END_REF][START_REF] King | Dispersibility and reconstitutability of dried milk[END_REF][START_REF] Schubert | Instantization of powdered food products[END_REF].

With regard to process complexity, knowledge of powder rehydration is still insufficient. Many models exist on the kinetics of dissolution, sometimes semi-empirical, sometimes mechanistically realistic (diffusion, swelling, erosion/degradation), but the analysis of particle hydration shows significant differences between theory and experimental values [START_REF] Jeantet | The influence of stirring speed, temperature and solid concentration on the rehydration time of micellar casein powder[END_REF]. Potentially, influencing parameters are too numerous to consider [START_REF] Siepmann | Review: mathematical modelling of drug delivery[END_REF].

In this work, an attempt has been made to better understand the mechanisms of hydration; namely the effect of stirring speed, of geometry of the mixing device, of temperature of the solvent, of composition and of structure (granulated or not) of the powder, were investigated.

Many observations have been made on the structure of the ingredients that compose a powder, but knowledge of these structural arrangements is not yet sufficient to properly explain the different rehydration kinetics observed. [START_REF] Jeantet | The influence of stirring speed, temperature and solid concentration on the rehydration time of micellar casein powder[END_REF] established a relationship between the number of impeller revolutions in agitated vessels and the degree of rehydration of the powder. This correlation was ascertained for one micellar casein powder only and a limited range of process conditions (one mixing system and a range of impeller rotational speeds). The generic feature of this relationship and its domain of validity needed to be better defined by investigating possible extension to a larger process parameters range (mixing equipment and agitator speed) and applicability to other powders. In addition, there is a lack of in situ information on the successive steps occurring during the powder rehydration process; in previous publications, the rehydration process was usually monitored through the reduction in the size of powder particles measured on samples by laser granulometry (static light scattering, SLS), without visual observation of the morphological aspect of dispersed and continuous phases during the course of rehydration.

The aim of this contribution was to begin to fill this gap, by first determining the influence of rehydration conditions (stirrer speed and mixing systems, temperature of the agitated suspension) on dairy powder dissolution time. The influence of the composition and structure (granulation or not) of the powder on rehydration kinetics were also studied. Powders with slow and fast dissolution kinetics were used for this purpose, using various ingredients (lactose, whey protein, native phosphocaseinate). The time to achieve a certain degree of size reduction was determined through SLS analysis of samples during the course of the rehydration process.

Simultaneously, digital images of powder during dissolution were obtained using a commercial granulomorphometer. Digital image analyses were performed to visualise solvent penetration inside powders and to better understand the associated fragmentation mechanisms.

Rehydration times, solvent penetration mechanisms and fragmentation are discussed with regard to rehydration conditions and dairy powder type.

Materials and methods

Powders

Dairy powders

Four different dairy concentrates were prepared specifically for this study by spray drying, so as to obtain various powders with different rehydration properties. A pilot plant spray dryer (GEA, Niro Atomizer, Montigny le Bretonneux, France) was used for this purpose. The atomiser was equipped with a pressure nozzle (0.73 mm diameter orifice) and a 4-slot core (0.51 mm nominal width), providing a 60 spray angle; the pressure pump (16 MPa) was supplied by Gea-Niro-Soavi (Copenhaguen, Denmark). The evaporation capacity of the plant was 70e120 kg h À1 .

To obtain granulated powder (G), fine particles were recycled within the spraying cone according to [START_REF] Jeantet | Residence time distribution: a tool to improve spray-drying control and product quality[END_REF]. Agglomeration occurred between particles so as to form a larger diameter than that of the nongranulated powder (NG).

Two types of concentrate were used: a native phosphocaseinate (NPC) concentrate that is slow to rehydrate after spray drying [START_REF] Gaiani | The dissolution behaviour of native phosphocaseinate as a function of concentration and temperature using a rheological approach[END_REF][START_REF] Gaiani | Dairy powder rehydration: influence of protein state, incorporation mode, and agglomeration[END_REF][START_REF] Schuck | Déshydratation par atomisation de phosphocaséinate natif obtenu par microfiltration sur membrane[END_REF]; and a whey protein isolate concentrate with fast rehydration kinetics. The term 'native' is used to indicate undenatured phosphocaseinate, very close to initial state. In this study, evidence was provided that spray drying induces a very rapid heating, inducing only slight protein denaturing, as seen by the absence of insoluble aggregates during powder rehydration.

The initial NPC (Promilk 872 B1) was provided by Ingredia (Arras, France) and obtained from 0.1 mm membrane tangential microfiltration of skimmed milk followed by spray drying [START_REF] Pierre | Préparation de phosphocaséinate natif par microfiltration sur membrane[END_REF][START_REF] Schuck | Déshydratation par atomisation de phosphocaséinate natif obtenu par microfiltration sur membrane[END_REF].

The whey protein isolate (WPI), Prolacta, was provided by Lactalis Ingrédient (Bourgbarré, France) and obtained by ultrafiltration and diafiltration of the microfiltration permeate ("ideal whey") collected during NPC production.

Apart from the NPC and WPI, the two other concentrates resulted from a mixture of lactose or WPI with NPC. Precisely, the 2 concentrates were: NPC/lactose powder (70/30; w/w) and NPC/WPI powder (80/20; w/w). The pure monohydrated a-lactose was provided by Lactalis (Lactosérum France, Baleycourt, France).

The powders obtained were stored at 4 C in hermetic bags. One hour before the rehydration test, the necessary amount was equilibrated at room temperature.

Physico-chemical analysis

Various physico-chemical analyses were performed on the 8 powders resulting from the spray drying of the 4 concentrates under different operating conditions (with or without recycling of fine particles). Ash, casein, whey protein and non protein nitrogen, noncasein Nitrogen, lactose content, dry total solids, powder particle size and true density were determined for each powder.

The total solids amount was calculated by weight loss after drying a sample of the powder mixed with sand in a forced air oven at 105 C for 5 h. Casein, whey protein and non protein nitrogen contents were determined according to [START_REF] Aschaffenburg | New procedure for routine determination of the various non casein proteins of milk[END_REF] and [START_REF] Rowland | The determination of nitrogen distribution in milk[END_REF]. The lactose content was determined by enzymatic reactions (Boehringer, Ingelheim am Rhein, Germany). The ash content was measured after incineration at 550 C for 5 h. True density was measured using gas pycnometry with both helium and nitrogen, on a Pycnometry ATC (Thermo Fisher Scientific, Courtaboeuf, France). The chemical composition of the powders (NPC, WPI, NPC/lactose and NPC/WPI) in their granulated or non-granulated form (G, NG) is reported in Table 1. Dry particle sizes were measured by laser granulometry.

Powder particle analysis

In this work, two complementary techniques were used to follow the morphological parameters of dispersed particles all along the rehydration process: SLS (determination of mean particle size) and granulomorphometry (particles number, solvent penetration into the core of particle, shape of particle).

Granulomorphometry

Digital images of powder particles were obtained during the course of rehydration, using a granulomorphometer, which here refers to the commercial name of the apparatus developed by Occhio (Angleur, Belgium) to acquire high quality pictures of particles dispersed in solvent using a microscopic technique, and the associated image analysis software (Fig. 1).

The microscopic technique consists of pumping a sample of the solid/liquid suspension into a flow-cell of prescribed width and obtaining digital high resolution pictures. In the following part, the use of the granulomorphometer is detailed; complementary information concerning this device is given in [START_REF] Petit | Granulomorphometry: a suitable tool for identifying hydrophobic and disulfide bonds in b-lactoglobulin aggregates. Application to the study of b-lactoglobulin aggregation mechanism between 70 and 95 C[END_REF].

In this work, both particle number and size of the samples were analysed using the Flow-Cell 200 S-M. The width of the flow-cell was 300 mm, and magnification was 6Â corresponding to 0.58 mm per pixel. Moreover, sample pictures were acquired when the flow was completely stopped so as to avoid blur on the obtained digital pictures. Since the powder concentration used in the rehydration test was too high for direct measurement, it was necessary to dilute before analysis. The dilution was made automatically and was the same for all the rehydration tests.

The digital images obtained were analysed with Callisto Ò software (Angleur, Belgium) to count the number of particles per picture, to measure their size distribution by using greyscale level differences between the particle and the background and to deduce the morphological characteristics of the powder particles (area, perimeter or circularity). Light calibration was realised on the solvent, with an associated grey level of 200 (being the value 0 for black). Powder particles were not fully black, as a homogenous mineral powder, but appeared generally with white to grey shade: the periphery was well defined in grey (more or less dark) and the inner was marbled, making it difficult to adjust the threshold at initial state. Each pixel on the pictures taken, with a value less than the threshold defined on the greyscale, was analysed by the software. It used the greyscale to pinpoint particles, then calculated various morphological parameters (inner diameter, area diameter, circularity, length, bluntness). The most accurate measurements were obtained with a 165 threshold for particle detection as seen in numerous preliminary tests, by comparison with SLS analysis.

The principal morphological parameter of this study is the inner diameter. The inner diameter was defined as the equivalent diameter of a sphere circumscribed by the analysed particle. This was preferred to the area diameter, i.e., the diameter of an equivalent sphere having the same apparent area as the particle, which overestimates diameter. The mean particle diameter (Dv50) was calculated by averaging the inner diameter of all analysed particles.

Particle number and size distribution were determined by processing at least ten pictures, which corresponded to approximately 10,000 particles, depending on the powder and operating parameters (i.e., initial mean size of dry powder particles that influences the number of particles per gram). Each analysis during rehydration was controlled by the two analysis technique (granulomorphometer and SLS analysis).

Static light scattering

The granulometric distribution was determined by laser light scattering using a MasterSizer 2000 (Malvern Instruments, Malvern, Worcestershire, UK) equipped with a 5 mW HeeNe laser operating at a wavelength of 633 nm. Samples were diluted into the Malvern cell (volume: 100 mL) with distilled water to reach appropriate obscuration (25%). Refractive indexes for solvent, particle and adsorption were respectively 1.33, 1.3 and 0.1. These indexes are recommended by manufacturer (Malvern).

The class size limits were 0.02e2000 mm Dv50 was used to estimate size reduction during rehydration.

Rehydration test

The rehydration experiments were carried out using a 3.5 L jacketed glass vessel (16 cm diameter) equipped with one baffle to limit vortex formation (Fig. 2A), as described by [START_REF] Jeantet | The influence of stirring speed, temperature and solid concentration on the rehydration time of micellar casein powder[END_REF]. Two impellers were studied, the first agitator (impeller 1; 8 cm diameter, Fig. 2B) was a 6-pitched-blade impeller, the second (impeller 2; 8 cm diameter, Fig. 2C) consisted of two propellers (airscrew) distant from 5 cm with two blades arranged at right angles; both impellers were vertically, centrally mounted. The influence of impeller rotational speed (N; rpm) was studied within the range of 500e900 rpm; and temperature range (25 C and 30 C AE 0.5 C, depending on the experiments). The solid/liquid concentration was set at 8% (w/w).

T 0 corresponds to the powder insertion. The impeller speed was set at 1200 rpm during the first 45 s of insertion to reduce insertion time and to establish a constant wetting time for all powders, and then it was put back to the desired speed. The monitoring of granulometric distribution started immediately after by sampling 0.5 mL of powder suspension for SLS analysis and by an automatic dilution for granulomorphometrics. The automatic dilution loop included two peristaltic pumps (one for the sample, one for distilled water). It was checked that these pumps did not affect particle features (shape, appearance, fragmentation, number). The manual sampling was carried out with a 16 mm diameter syringe, type BD Discardit II (Becton Dickinson, Le Pont de Claix, France), located halfway between the liquid surface and the vessel bottom and about halfway between the vessel wall and the paddle shaft to limit the presence of foam in samples. The size measurements were made initially every 3 min, increasing to 5 min and then 15 min, respectively, after 25 min and 45 min of rehydration. It was then reduced again to 3 min when the Dv50 fell below 15 mm, the decrease in size becoming faster after that threshold. The time between two measurements depended on the speed of powder rehydration powder: the faster the kinetics, the more frequent the measurements. The reproducibility of the results was estimated by repeating experiments. An example is given in Fig. 3: white squares show the kinetics of rehydration of the NPC/WPI non-granulated powder (in triplicate), at 700 rpm, 25 C with impeller 1.

On average, size measurements were accurate to about 1 mm.

The accuracy on the rehydration time total was less than 10% (measured on different replicates of rehydration). Given the limited amount of powder and the significant amount used for each rehydration, for each parameter studied, the repetition is usually done in case of doubt on the values obtained. However, most of the data were measured twice.

Size reduction kinetics are described by evolution of Dv50 with time and kinetics performed of other parameters. The images obtained with the granulomorphometer provide insight into the phenomena observed. The powders are fairly comparable, given the parameters considered (mainly speed and temperature), the resulting images were quite similar.

Systematically, a post manual processing was performed to eliminate scatters contained in the digital images (as presence of air bubbles or particles superposition). This was done to make sure the automatic image analysis process, and the Dv50 computation.

Dissolution time determination: total rehydration time

Particle size distribution measured by SLS was used to determine rehydration time for each test. Dv50, extracted from the particle size distributions, was plotted as a function of time. Fig. 3 shows a typical rehydration curve obtained by the SLS method.

As expected, Dv50 decreased with time and reached an asymptotic value close to the mean diameter of casein micelles, 0.2 mm. The powder size reduction just before reaching this value was quite marked and consequently the criterion of achieving micellar size was appropriate to define total powder rehydration time. Consequently, total rehydration time was defined as the time required after powder incorporation for Dv50 to reach 0.2 mm (Fig. 3, the cross symbol at 260 min corresponds to micellar size). Note that although a decrease in particle size with time is also observed in granulomorphometry analysis, the asymptotic value obtained at the end of rehydration process is not the same as that obtained by the SLS method: approximately 10 mm. This can be explained by the fact that the detection limits of the two devices were not similar. For the granulomorphometer, the detection limit was 0.58 mm (the size of one pixel defined on the device), slightly greater than the micelle size, whereas for the SLS method the detection limit was 0.05 mm. This means that only particles above 0.58 mm were visible when using the granulomorphometer; all the particles inferior to this size are not taken into account in the particle population balance. Thus, the particle population balance became more and more inexact as the amount of fine particles increased. Indeed the digital image processing analysis delivered a Dv50 based only on the volume of larger particles, without taking into account all the finer particles (under the size detection limit). Unfortunately when the fine particles are numerous, they have a strong impact on the final value of Dv50.

These scatters are well known; the total rehydration time was evaluated by the SLS method. Digital images obtained by granulomorphometer are best used to discuss the solvent penetration and fragmentation process.

In addition to size, the granulomorphometer gave a particle distribution of the solution through recorded images: all the particles seen on acquisition were counted and the total number of particles in the sample calculated. This information was used to track the number of particles and provides information on the kinetics of fragmentation of the particles versus erosion. Since the detection limit of granulomorphometer was greater than the casein micelles mean diameter, only particles with several agglomerated micelles could be analysed. The number of particles, combined with the Dv50, provided information on the state of fragmentation of particles and their kinetics of reduction in size.

Thus, the total number of particles increased at the beginning of rehydration as a result of fragmentation of larger particles. This number reached a maximum, balanced between fragmentation and release of single casein micelles, prior to decreasing until only partially soluble or insoluble particles remain.

Results and discussion

3.1. Qualitative analysis of rehydration curves: effects of dairy powders chemical composition, structure and stirring speeds on rehydration kinetics Typical evolution of mean powder diameter (Dv50) over time after dispersion of the dairy powders in liquid is presented in Fig. 4.

Curves obtained at 25 C under constant stirring conditions induced by the impeller 1 were similar to those of impeller 2 and at 30 C. The three curves (square symbols) on the right side show the effect of stirring speed on rehydration kinetics and the two curves on the left (cross and triangular symbols) show the effect of granulation on rehydration kinetics at a given impeller rotational speed.

Irrespective of stirring speed, it can be observed that the rehydration curves obtained with NPC powders (square symbols) present all three stages, revealing that at least three successive mechanisms in milk powder reconstitution. The three stages are as follows.

Initially, mean particle size decreases sharply for a period of 10e15 min for NPC powder (generally, this step last 5e10% of the total rehydration time of the powder). This first stage mainly corresponds to the wetting and dispersing of fragile particles, from Dv50 55e60 mm to 35e40 mm (AE5 mm, depending on the composition of powders). [START_REF] Fitzpatrick | Effect of vortex formation on powder sinkability for reconstituting milk powders in water to high solids content in a stirred-tank[END_REF] discussed in depth wettability, sinkability and relation to stirring speed. The next stage corresponds to a more gradual decrease in mean particle Fig. 4. Follow-up of the particle size (SLS analysis) over time, for the native phosphocaseinate (NPC) powder, non-granulated, at 25 C, with the impeller 1, at: -, 900 rpm; , 700 rpm; ,, 500 rpm and also the follow-up of the particle size (SLS analysis) over time, for NPC-lactosepowder: Â, non-granulated and 6, granulated, at 700 rpm, impeller 1. Fig. 3. A typical follow-up of the particle size over time, during a powder rehydration (NPC powder, non-granulated, impeller 1900 rpm, 30 C). :, granulomorphometer analysis; Â, SLS analysis; ,, native phosphocaseinate/whey protein ingredient powder SLS analysis, non-granulated, impeller 1700 rpm, 25 C, with statistical analysis.

size through dissolution of the external layer of the solid by the liquid. This step was first observed by [START_REF] Hixon | Dependence of reaction velocity upon surface and agitation: I e theoretical consideration[END_REF]. This has also been observed more recently for mineral powders such as sodium hydroxide pellets [START_REF] André | Influence of mixing system design and operating parameters on dissolution process[END_REF]. The last step deals with final reduction of particle size. During this period, the rehydration kinetics are marked by a prompt acceleration, and mean particle size falls sharply from about 10 to 15 mm (AE5 mm) to a particle size of 0.2 mm.

The final part of rehydration suggests a sudden increase in fragmentation, as a fast decrease in cohesion between micelles is observed: forces are no longer sufficient to maintain particle shape. This differs from mineral powders where cohesion remains high enough to avoid particle fragmentation. Indeed for milk powder, the particle structure is an agglomerate of micelles and dissolution also includes fragmentation.

Analysis of Fig. 4 for a given powder (square symbols) shows that the higher the stirring speed the lower the processing time required to reach ultimate particle size. At 500 rpm, 290 min is needed to reach a Dv50 of 0.2 mm, whereas 220 min is needed at 900 rpm. This phenomenon was observed for all the powders tested clearly revealing the effect of impeller rotational speed on dissolution rate. The positive influence of stirring speed on rehydration speed was observed throughout this study. On average (rehydration times of the different powders are reported in Table 2), when the stirring speed increases from 700 rpm to 900 rpm, the total rehydration time is reduced by 25%.

Irrespective of the powders and operating conditions (mixing system design, solvent and temperature), an increase in stirring speed implied an inversely proportional reduction of the total rehydration time.

The decrease in rehydration time with increasing stirring speed is well known [START_REF] Hixon | Dependence of reaction velocity upon surface and agitation: I e theoretical consideration[END_REF]. Increasing mechanical agitation contributes to better dispersion of solids in liquids, by promoting turbulence around solid particle, favouring mass transfer and consequently rehydration and dissolution processes. In this study, the beneficial effect of agitation was linked directly to total rehydration time deduced from mean particle size distribution rather than through a mass transfer coefficient, as more commonly encountered in mixing scientific community.

Fig. 4 and Table 2 show that total dissolution times are very different in magnitude depending on the chemical composition of a given structure (Granulated or not). The cross and square symbols coloured in grey in Fig. 4 compare rehydration kinetics obtained for two non-granulated powders differing in chemical composition (NPC/lactose powder versus NPC powder) under the same stirring conditions (700 rpm). The addition of lactose to NPC powders decreases the total rehydration time by a factor of 5.2 (260 min for the NPC powder and 50 min for the NPC/lactose powder).

This factor can increase to as much as 10 (For example, for granulated powders, rehydration time decreases from 750 min to 38 min when lactose is added to NPC, Table 2).

By comparing total rehydration time at similar stirring speed for different powders having the same structure, it can be seen that the addition of a compound with rapid dissolving properties (WPI, lactose) to a slow dissolving powder (NPC) accelerated the dissolution of the latter. One hypothesis may be that the creation of porosity with dissolution of the first compound facilitates the deconstruction of the casein micelle network by the created pores. The presence of lactose, which is a simple fast-dissolving sugar, helps water penetrate the core of the particle and dissolution is accelerated. [START_REF] Gaiani | How surface composition of high milk proteins powders is influenced by spray-drying temperature[END_REF] reported that the presence of some ingredients (WPI, lactose) strongly affects the spacial distribution of chemical compounds at the surface of the powder, thus modifying rehydration time according to the dissolving behaviour of the latter. For example, the addition of WPI to NPC slightly increased the amount of fat on the surface of the particles. When lactose is added, half was located at the periphery and half in the core of particles.

Table 2 and Fig. 4 show total dissolution times are also strongly dependent on the structure (granulated or not) of powders. The comparison of cross symbols and triangles in Fig. 4 shows that for a given chemical composition under the same stirring conditions (700 rpm), different rehydration behaviours can be observed. Dissolution time is decreased by a factor of 1.6 when NPC/lactose powder is granulated: for the non-granulated powder the total rehydration time is 50 min rather than 32 min. Analysis of rehydration curves obtained for all the powders (Table 2) reveals that the granulation of the powder can modify total rehydration time by over 60%.

It is generally considered that the granulation of powders facilitates the immersion stage since it decreases the surface to mass ratio. The granular structure also allows for rapid wetting of the particles and an easy dispersion in water. Non-granulated powders tend to stay on the free surface of the agitated liquid [START_REF] Hall | Drying of milk and milk products[END_REF]. When the powder was granulated, the total rehydration time decreased for NPC and NPC/lactose powders but the effect of granulation is highly dependent on chemical composition. Depending on ingredients, it is shown here that granulation does not systematically improve rehydration. Indeed, when WPI is added to NPC, total rehydration time was 2e5 times longer than for the corresponding non-granulated powder (60 min versus 280 min when the NPC/WPI powder is granulated; Table 2). This trend is somewhat expected in that the spray drying operation also strongly affects particle structure. Namely the number of path in the spray drying tower is radically different between granulated and nongranulated particles. The powders are subjected to a more or less severe thermal treatment that induces powder surface property changes. The principle of granulation is to recycle a part of the fine particles obtained to induce agglomeration. During this process path, the initial non-granulated particles are partially rehydrated and then re-dried several times.

It should be noticed that although the granulated particles size obtained by spray drying was about 200e250 mm, 2 min after the beginning of the rehydration process, granulated powders had already achieved a size equivalent to that of the corresponding nongranulated powder: Fig. 4 shows that at 2 min, the sizes are similar between the two structures. Consequently, the time required for granulated particles to split apart and reach the size of nongranulated particles was negligible compared with the change in total rehydration time (greater than 200 min in the case of NPC/WPI powder). This reinforces the fact that the time required for the separation of the grain does not alone explain the slower rehydration time, only a surface structure change would lead to such an important change [START_REF] Mimouni | Rehydration process of milk protein concentrate powder monitored by static light scattering[END_REF]. Granulation should best be considered only if the wetting stage is limiting and the surface properties are not strongly modified by spray drying.

Quantitative analysis of rehydration curves: total rehydration time data obtained in various operating conditions and resulting processing relationship

The total dissolution time for the rehydration kinetics of different powders and impellers is given in Table 2. For each powder and impeller, the rehydration test was carried out at three stirring speeds (500, 700 and 900 rpm). In addition, the total revolution number Ntr reached by each impeller to achieve total rehydration was also calculated and reported in Table 2. The results show that for a given powder and agitation system, Ntr is fairly constant, regardless of impeller speed. This indicates that for the range of Re numbers tested and solid/liquid fractions (for 50,000 < Re < 100,000 and 8%, w/w), the number of revolutions made by the agitator govern the rehydration curve. For the powders tested, the average variation in the total revolution number is 10.6% of Ntr (calculated from the variation with each powder, for three speeds obtained with a given configuration, Table 2), which is acceptable for process engineering purpose.

The fact that the rehydration time for various dairy powders was inversely proportional to impeller rotational speed is in agreement with the work of [START_REF] Jeantet | The influence of stirring speed, temperature and solid concentration on the rehydration time of micellar casein powder[END_REF], which was validated for one powder and one mixing system. In spite of using a mixing system similar to that of [START_REF] Jeantet | The influence of stirring speed, temperature and solid concentration on the rehydration time of micellar casein powder[END_REF], the rehydration times Ntr obtained with NPC powder were much higher than those obtained with the NPC powder tested. This is due to differences in spray drying conditions, chemical composition and ageing time of the powder.

In this work, such a process relationships were shown to be valid for other dairy powders (NPC, NPC/WPI, NPC/lactose) and mixing systems. Recently, [START_REF] André | Influence of mixing system design and operating parameters on dissolution process[END_REF] measured dissolution time for non-food powder (highly soluble particles of sodium hydroxide) dispersed in aqueous solution, using similar approach. For another mixing system, the revolution number achieved by the agitator governed the rehydration time and was almost independent of Reynolds number (range 5000e100,000). For the mineral powders used, of course the number of agitator revolution required to achieve dissolution was largely inferior to those observed for our dairy powder due to the use of fast-dissolving mineral particles instead of organic ones.

So this work shows that the number of revolutions made by the agitator is a generic law to ensure that a rehydration process is completed. It seems applicable to food and non-food particles which could be dissolute in water and various mixing systems.

Fig. 5 illustrates for an NPC/WPI powder the effect of temperature on reconstitution kinetics. Analysis of Fig. 5 reveals that from 25 C to 35 C the reconstitution process is faster with increasing temperature but at 37 C, and above, aggregation occurs, disturbing the rehydration process. To avoid aggregation the reconstitution process should be carried out below 30 C for all the powders. In parallel, preliminary results of reconstitution process (not shown here) with NPC non-granulated powder revealed that the dissolution process was extremely long at 20 C (more than 6 h were required to reduce the mean particle diameter from 50 mm to 30 mm). So, it was decided to investigate only temperature effect between 25 C and 30 C.

The experimental impeller revolution number obtained for achieving total rehydration at 25 C and 30 C, for the two mixing systems used is shown in Table 3 demonstrating that temperature influences dissolution time to a greater extent than stirring speed. It could be also observed. The process relationships (consistency of Ntr) remained valid at 25 C and 30 C.

Consumption measurements made on the laboratory equipment during a rehydration test (for the electric motor of the agitator and the heating system) are presented in Table 4. The results shows that the total energy consumption for rehydration could be divided by a factor of 2 and total rehydration time by a factor of 4.7 by increasing temperature to 30 C and stirring speed to 900 rpm. In this case, a small increase in temperature and faster stirring speed have a positive impact on rehydration time and energy consumption. More knowledge is necessary on this topic to enable a manufacturer to adjust these parameters (temperature and stirring speed) and so reduce operating costs and increase process efficiency.

3.3. Visualisation of solvent penetration and importance of impeller effect and energy dissipation on fragmentation

Granulomorphometry provided online capture of powder dispersed in solvent and provided a tool for image processing. Thus, it was possible to track the evolution of powder appearance during rehydration and also provided observations on particle/solvent interactions and fragmentation.

Fig. 6 shows pictures obtained during rehydration of NG NPC with impellers 1 and 2 at 900 rpm and 25 C. The evolution of particles differed, depending on impeller type. With impeller 1, the background darkened much faster and appeared darker than with impeller 2 after a long time (here 180 min). This indicates that a larger amount of small particles were dispersed in water (less light passing through the cell); in addition, the average size was lower than the threshold of the granulomorphometer: 580 nm. The Dv50 at 55 min was to 25 mm for impeller 1 and 33 mm for impeller 2. These observations confirm that dissolution time was dependent on impeller type. Fig. 7 is a representation of the evolution of particle size distribution obtained at three processing time of rehydration carried out with the two different impellers (same diameter and same stirring speed). Analysis of Fig. 7 shows that there are only slight differences between particle size distributions for the two impellers at 5 min after powder insertion. Note that for sake of clarity, it was chosen not to use a scale of frequency for the ordinate axis. The presence of a symbol on the horizontal line means that one or several particles exist in corresponding class size. The different symbols stand for the particle size distribution obtained with the different agitators. This representation allows the mechanical effect of the impeller to be followed on particles and rehydration kinetics; that is to say to follow the impact of the impeller geometry on the fragmentation. The particle distribution contains only few larger particles with impeller 2 compared with impeller 1, showed by the presence of more symbols in the range 60e110 mm. On the contrary, 55 min after powder insertion the difference in particle size distribution is more pronounced. The presence of several larger particles is observed with impeller 2, while there are only smaller particles with impeller 1. The size distribution of impeller 1 varies from 0 to 15 mm with few particles around 25 mm and 35 mm whereas for impeller 2, the size distribution goes from 0 to 50 mm, with some particles around 75e80 mm. This means that impeller 1 provided better fragmentation and/or dissolution of large particles and favoured small sized particles. Note that 90% of the total particle number had a mean diameter of less than 6 mm (not represented to clarify the diagram).

This highlights the influence of the mixing equipment design on the dissolution process. Impeller 1 with its 6-pitched blades had an important local energy dissipation promoting the fragmentation of large particles, while the energy dissipation induced by impeller 2 concerned the whole liquid phase, favouring particle circulation in the tank on the detriment of fragmentation.

Impeller 2 provided a better insertion of the powder by suction phenomena (size lower at the beginning of the dissolution), but its overall energy dissipation decreases its fragmentation efficiency and thus increases the time required for complete dissolution.

Image analysis provided other observations: i.e., the entry or not of the solvent into the powder particles. Indeed, granulomorphometer light calibration was always realised on the solvent, with an associated grey level of 200. Consequently, whatever the solvent nature (pure water, pure ethanol or mixtures of water and ethanol) an important contrast exists at the first stage of dispersion between solvent and powder before solvent penetration in the particle. On the other hand, when solvent penetrates inside the particle all along the rehydration process, this contrast tends to decrease immediately.

Fig. 8 shows pictures captured by the granulomorphometer for the NPC non-granulated powder suspension in three different solvents (water, a 50/50 water/ethanol mix and absolute ethanol) 5 min after the powder insertion. In absolute ethanol, the particles stay very dark with no size reduction all along the rehydration process. Conversely, in pure water and in 50/50 water/ethanol the particles appear immediately clearer. In pure water, this phenomenon observed is of course more important.

The fact that contrast between particle and solvent is very pronounced during all the rehydration process when ethanol is used as solvent can be explained by the fact that ethanol does not succeed in penetrating inside the core of particle. However, when an amount of water is present in the solvent (pure water or mixture of water and ethanol), penetration of solvent inside the particles is allowed, explaining the contrast decrease with the advancement of rehydration process. This highlights the potential of the granulomorphometer in identifying solvent interactions with the particles. Rehydration of the particles occurs not only from the particle shell, but also from water transfer to the core and departure of casein micelles from the inside. Image analysis shows some particles at the end of rehydration with only a peripheral shell, the inside of the particle appearing empty [START_REF] Mimouni | Investigation of the microstructure of milk protein concentrate powders during rehydration: alterations during storage[END_REF]. This could explain the sharp drop in size below a threshold (generally 15 mm, observed on many size curves), and suggests a sudden fragmentation of the particles, emptied of their contents (arrow on Fig. 8C). The structure is no longer strong enough to maintain shape; the forces exercised by the agitator become higher leading to fragmentation.

Conclusions

This work illustrates that many parameters impact dairy powders rehydration: mixing equipment design, operating conditions (stirring, temperature) and chemical composition of powder.

Analysis of rehydration curves with regards to powder structure revealed that granulation is not always a pre-requisite to acceleration of the rehydration process, depending on wettability versus total rehydration time.

Analysis of rehydration curves shows that the presence of certain compounds such as lactose/and WPI facilitate rehydration process kinetics, by favouring solvent penetration.

In general the number of agitator revolutions required to achieve a desired degree of rehydration is constant and independent of impeller rotational speed. This work enlarged the domain of validity of relationships first proposed by [START_REF] Jeantet | The influence of stirring speed, temperature and solid concentration on the rehydration time of micellar casein powder[END_REF]. Comparison of rehydration times achieved at various impeller speeds and temperature conditions confirms that rehydration process is more sensitive to temperature, than impeller speed. Proper temperature minimises the mechanical energy necessary.

Granulomorphometer analysis was found to be an interesting tool to track solvent transport and to understand associated mechanisms of fragmentation, highlighting dynamic structure modifications.

Fig. 1 .

 1 Fig. 1. Operating diagram of granulomorphometer.

Fig. 2 .

 2 Fig. 2. Experimental rehydration device: A, 3.5 L jacketed glass vessel; B, six-pitchedblade impeller; C, two propellers with right angled arrangement.

Fig. 5 .

 5 Fig. 5. Follow-up of the particle size (SLS analysis) over time, for the granulated native phosphocaseinate/whey protein ingredient powder at different temperatures (-, 25 C; Â, 30 C; , 35 C; þ, 37 C; :, 40 C) with impeller 1, at 900 rpm; arrows indicate aggregation.

Fig. 6 .

 6 Fig. 6. Comparison of images obtained by the granulomorphometer, for the two types of impellers, at three different times: close to start (A and D), in the middle of the rehydration (B and E), and near the end of rehydration (C and F).

Fig. 7 .

 7 Fig. 7. Presence of particles of non-granulated native phosphocaseinate powder, at 30 C, in each class size diameter, for both impellers (6, impeller 1; C, impeller 2; 900 rpm), at different times after powder insertion: panel A, 5 min; panel B, 35 min; panel C, 55 min.

Fig. 8 .

 8 Fig. 8. Comparison of images obtained by the granulomorphometer for the solid/liquid suspension of non-granulated native phosphocaseinate powder 5 min after powder insertion (25 C, 900 rpm) in three types of solvent: A, ethanol; B, 50/50 ethanol/water mixture; C, water. Arrow indicates suggested sudden fragmentation of the particles.

Table 2

 2 Total dissolution time and revolution number of each impeller to achieve a given rehydration for different dairy powders with standard deviation (in percent of the mean Ntr of each group of speed; water temperature 25 C).

	Powder a	Impeller 1

a Abbreviations are: NG, non-granulated; G, granulated.

Table 3

 3 Number of revolutions of the impeller to achieve total rehydration, for different type of impeller, temperature, and type of (non-granulated) native phosphocaseinate (NPC) powder.

	Reynolds	Impeller 1,	Impeller 1,	Impeller 2,	Impeller 1,
		NPC, 25 C	NPC/lactose, 25 C	NPC, 30 C	NPC, 30 C
	54217	145,000	32,500	45,000		50,000
	75904	182,000	35,000	51,100		58,100
	9759	198,000	31,500	52,200		61,200
	Table 4
	Laboratory power consumption of the agitator motor and the heating system, for
	two stirring speeds and two temperatures for non-granulated native phosphoca-
	seinate powder.
	Temperature	Stirring	Rehydration	Power consumption (J)
	( C)	speed (rpm)	time (min)	Stirring	Heating	Total
	30	900	58	0.0182	0.263		0.281
	30	500	73	0.0140	0.306		0.320
	25	900	210	0.0660	0.447		0.513
	25	500	275	0.0527	0.586		0.638

B. Richard et al. / International Dairy Journal 31 (2013) 18e28

Acknowledgements

The authors are indebted to the scientific committee of CNIEL Recherche (Paris, France) for stimulating discussions and financial support. We wish to thank Dr David F. Perry for his proofreading and corrections of the English language.


Rogers Sm
email: srenaut@interchange.ubc.ca

Genome-wide patterns of divergence during speciation: the lake whitefish case study

Keywords: divergent selection, gene expression, QTL, reproductive isolation, speciation islands

The nature, size and distribution of the genomic regions underlying divergence and promoting reproductive isolation remain largely unknown. Here, we summarize ongoing efforts using young (12 000 yr bp) species pairs of lake whitefish (Coregonus clupeaformis) to expand our understanding of the initial genetic aspects of species boundaries. Our results confirmed the predictions that: 1) on average, phenotypic QTL show higher F ST values and are more likely to be outliers (and therefore candidates for being targets of divergent selection) than non-pQTL markers; 2) large islands of divergence rather than small independent regions under selection characterize the early stages of adaptive divergence of lake whitefish; 3) there is a general trend towards an increase in terms of numbers and size of genomic regions of divergence from the least (East L.) to the most differentiated species pair (Cliff L.). This is consistent with previous estimates of reproductive isolation between these species pairs being driven by the same selective forces responsible for environment specialization. Altogether, dwarf and normal whitefish species pairs represent a continuum of both morphological and genomic differentiation contributing to ecological speciation. Admittedly, much progress is still required to more finely map and circumscribe genomic islands of speciation. This will be achieved trough the use of next generation sequencing data but also through a better quantification of phenotypic traits molded by selection as organisms adapt to new environmental conditions.

Introduction

Dobzhansky [START_REF] Dobzhansky | Genetics and the Origin of Species[END_REF] initially proposed that the genotype of a species is an integrated system adapted to the environment or ecological niche in which the species lives, whereby recombination in hybrid offspring may lead to the formation of discordant gene patterns. Understanding how speciation can take place in the presence of the homogenizing effects of gene flow remains a major challenge in evolutionary biology. The ecological theory of adaptive radiation hypothesizes that shifts of organisms into novel habitats will be adaptive, whereby populations will diverge for specific phenotypes and genotypes influencing survival and reproduction when exposed to different environments [START_REF] Mayr | Animal Species and Evolution[END_REF][START_REF] Schluter | The Ecology of Adaptive Radiation[END_REF]. Under the genic view of speciation, divergent selection should create heterogeneous genomic differentiation by causing adaptive loci (and those physically linked to them) to flow between populations less readily than others. This will result in accentuated genetic divergence of regions affected by selection while the homogenizing effects of gene flow should preclude divergence in other regions [START_REF] Lewontin | Distribution of gene frequency as a test of the theory of selective neutrality of polymorphisms[END_REF][START_REF] Wu | The genic view of the process of speciation[END_REF][START_REF] Nosil | Divergent selection and heterogeneous genomic divergence[END_REF].

The nature of genomic islands of divergence

The nature, size and distribution of these genomic regions underlying divergence and promoting reproductive isolation are still a contentious and debated area of research. While extensive theoretical and empirical research has been conducted, the precise genetic processes that regulate and favor regions of genomic divergence promoting speciation remain largely unknown [START_REF] Wu | The genic view of the process of speciation[END_REF][START_REF] Rice | Laboratory experiments on speciation: what have we learned in 40 years?[END_REF][START_REF] Rieseberg | Chromosomal rearrangements and speciation[END_REF][START_REF] Feder | The efficacy of divergence hitchhiking in generating genomic islands during ecological speciation[END_REF][START_REF] Via | Hiding in plain sight: divergence hitchhiking and the dynamics of genomic isolation between incipient ecological species[END_REF]. How populations go from little evidence of phenotypic and genotypic divergence to fully incompatible and reproductively isolated entities remains one of the key unanswered questions in evolutionary biology.

There are two conceptually different ideas to explain how genetic differences between populations and species arise and are maintained in the presence of gene flow. First, genetic differences and thus isolation are predicted to accumulate in a few, but large genomic "islands" of reduce gene flow [START_REF] Wu | The genic view of the process of speciation[END_REF][START_REF] Wu | Genes and speciation[END_REF][START_REF] Turner | Genomic islands of speciation in Anopheles gambiae[END_REF][START_REF] Via | Hiding in plain sight: divergence hitchhiking and the dynamics of genomic isolation between incipient ecological species[END_REF]. Conversely, selection can also act simultaneously on many physically unlinked genomic regions. Under this view, genomes are highly porous and islands of speciation, as small as a single gene, are scattered throughout the genome [START_REF] Rice | Laboratory experiments on speciation: what have we learned in 40 years?[END_REF][START_REF] Feder | The efficacy of divergence hitchhiking in generating genomic islands during ecological speciation[END_REF][START_REF] Kane | Comparative genomic and population genetic analyses indicate highly porous genomes and high levels of gene flow between divergent Helianthus species[END_REF][START_REF] Noor | Islands of speciation or mirages in the desert? Examining the role of restricted recombination in maintaining species[END_REF]. Both scenarios may act concurrently, as large regions of differentiation are created while simultaneously, selection isolates single genes or mutations from the homogenizing effects of gene flow. If the process of speciation takes its course, these regions under the effect of divergent selection, originally expected to be rare, will tend to grow in both size and number until eventually genomic islands merge and the whole genome becomes fully incompatible [START_REF] Wu | The genic view of the process of speciation[END_REF][START_REF] Wu | Genes and speciation[END_REF]. Given that, with time, islands of speciation will become drowned in a sea of divergence, this process should also be studied in the early step of a speciation event.

Chromosomal rearrangements are one genetic mechanism that may promote the initial appearance and further spread of genomic islands of divergence [START_REF] Rieseberg | Chromosomal rearrangements and speciation[END_REF][START_REF] Noor | Islands of speciation or mirages in the desert? Examining the role of restricted recombination in maintaining species[END_REF][START_REF] Faria | Chromosomal speciation revisited: rearranging theory with pieces of evidence[END_REF]. These rearrangements are expected to impede gene flow through the suppression of recombination around chromosomal breakpoints, thus promoting the growth of diverging regions and ultimately facilitating speciation. While there is theoretically support for this idea, empirical evidence has been mixed [START_REF] Strasburg | What can patterns of differentiation across plant genomes tell us about adaptation and speciation?[END_REF][START_REF] Rieseberg | Major ecological transitions in wild sunflowers facilitated by hybridization[END_REF][START_REF] Noor | Divergence between the Drosophila pseudoobscura and D. persimilis genome sequences in relation to chromosomal inversions[END_REF][START_REF] Lowry | A widespread chromosomal inversion polymorphism contributes to a major life-history transition, local adaptation, and reproductive isolation[END_REF][START_REF] Stemshorn | Rapid formation of distinct hybrid lineages after secondary contact of two fish species (Cottus spec.)[END_REF]. In a manner analogous to the effect of chromosomal rearrangements, strong divergent selection at specific loci can also promote the accumulation Comment citer ce document : Renaut, S., Maillet, N., Normandeau, E., Sauvage, C., Derome, N., Rogers, S.M., Bernatchez, L.

(2012). Genome-wide patterns of divergence during speciation: the lake whitefish case study. [START_REF] Via | The genetic mosaic suggests a new role for hitchhiking in ecological speciation[END_REF] empirically showed that quantitative trait loci (QTL) for adaptive traits between pea aphid populations were linked to regions of higher genetic differentiation and that this effect extended far (> 10 centiMorgans) from the putative target of selection. Via [START_REF] Via | Hiding in plain sight: divergence hitchhiking and the dynamics of genomic isolation between incipient ecological species[END_REF] recently highlighted a similar scenario in three-spined sticklebacks [START_REF] Hohenlohe | Population genomics of parallel adaptation in threespine stickleback using sequenced RAD tags[END_REF] where divergence hitchhiking protected and isolated large genomic regions surrounding genes responsible for adaptation to freshwater. While attractive, this idea is again supported by mixed empirical evidence [START_REF] Strasburg | What can patterns of differentiation across plant genomes tell us about adaptation and speciation?[END_REF][START_REF] Hawthorne | Genetic linkage of ecological specialization and reproductive isolation in pea aphids[END_REF][START_REF] Emelianov | Genomic evidence for divergence with gene flow in host races of the larch budmoth[END_REF][START_REF] Harr | Genomic islands of differentiation between house mouse subspecies[END_REF][START_REF] Counterman | Genomic Hotspots for Adaptation: The Population Genetics of Mullerian Mimicry in Heliconius erato[END_REF][START_REF] Nadeau | Evidence for genomic islands of divergence among hybridizing Heliconius butterflies obtained by large-scale targeted sequencing[END_REF]. Moreover, theoretical modeling has shown that divergence hitchhiking will only create large regions of differentiation around selected loci under restrictive conditions [START_REF] Feder | The efficacy of divergence hitchhiking in generating genomic islands during ecological speciation[END_REF]. Thus, locally reduced effective recombination, low migration rates (m < 0.001), small effective population sizes (Ne < 1000) and strong selective pressures (s > 0.10) should promote the maintenance and subsequent growth of genomic islands of divergence.

The role of gene expression in the study of speciation

Initial attempts to identify regions of genomic divergence underlying adaptive traits has necessarily focused on easily measured morphological, and to a lesser degree, behavioral traits [START_REF] Schluter | Genetics and ecological speciation[END_REF]. However, focusing only on easily identifiable traits may bias our view about the number and nature of phenotypic traits involved in the process of ecological speciation. One way to circumvent these limits is to use gene expression data as a way to reveal otherwise hidden phenotypes of potential ecological relevance [START_REF] Pavey | The role of gene expression in ecological speciation[END_REF]. Moreover, in an analogous manner to traditional pQTL (phenotypic QTL) studies, eQTL (expression QTL) studies allow the identification of specific genomic regions responsible for gene expression differences [START_REF] Kammenga | Microarray challenges in ecology[END_REF]. These studies have revealed patterns of significant clustering of genes in regulations "hotspots" and hinted at the existence of localized genomic islands of expression divergence [START_REF] Pavey | The role of gene expression in ecological speciation[END_REF]. If these hotspots are studied in the context of a recent divergence event, they may be representative of regions involved in ecological speciation [START_REF] Pavey | The role of gene expression in ecological speciation[END_REF]. Expression QTL studies can potentially inform about the mechanisms of gene regulation, and provide insights into the process of speciation [START_REF] Bernatchez | On the origin of species: insights from the ecological genomics of lake whitefish[END_REF]. Thus, studying gene expression may improve our understanding of ecological speciation, particularly when integrative approaches are applied in the context of recent divergence.

The lake whitefish study system

Here, we investigated key issues pertaining to the nature, number and size of genomic regions underlying species divergence in lake whitefish by conducting novel analyses on previously published data [START_REF] Rogers | Linkage maps of the dwarf and normal lake whitefish (Coregonus clupeaformis) species complex and their hybrids reveal the genetic architecture of population divergence[END_REF][START_REF] Rogers | The Genetic architecture of ecological speciation and the association with signatures of selection in natural lake whitefish (Coregonus sp. Salmonidae) species pairs[END_REF][START_REF] Whiteley | The phenomics and expression quantitative trait locus mapping of brain transcriptomes regulating adaptive divergence in lake whitefish species pairs (Coregonus sp.)[END_REF][START_REF] Derome | Pervasive sex-linked effects on transcription regulation as revealed by eQTL mapping in lake whitefish species pairs (Coregonus sp, Salmonidae)[END_REF]. The lake whitefish species complex includes several sympatric populations inhabiting northern temperate lakes in Canada and Maine [START_REF] Fenderson | Evidence of subpopulations of lake whitefish, Coregonus clupeaformis, involving a dwarf form[END_REF]. These species pairs are characterized by two postglacial derived forms living in sympatry. A "dwarf" form, typically growing slower, maturing at a much earlier age and size, and living in limnetic zone of lakes, and a larger "normal" form, which grows faster, reaches a larger size, matures at a later age, and lives within the benthic zone of lakes. Their phenotypic divergence is recent (< 12 000 yr bp) and involved both a phase of allopatry (geographic isolation) and sympatry (secondary contact) [START_REF] Bernatchez | On the origin of species: insights from the ecological genomics of lake whitefish[END_REF][START_REF] Bernatchez | Allopatric origin of sympatric populations of lake whitefish (Coregonus clupeaformis) as revealed by mitochondrial DNA restriction analysis[END_REF]38]. This system is especially well suited to study the genetics of species boundaries for several reasons. First, lake whitefish represents a rare illustration of a continuum of both morphological and genetic differentiation within a given taxon. This [START_REF] Rogers | Linkage maps of the dwarf and normal lake whitefish (Coregonus clupeaformis) species complex and their hybrids reveal the genetic architecture of population divergence[END_REF][START_REF] Rogers | The Genetic architecture of ecological speciation and the association with signatures of selection in natural lake whitefish (Coregonus sp. Salmonidae) species pairs[END_REF] and gene expression differences (eQTL mapping) [START_REF] Whiteley | The phenomics and expression quantitative trait locus mapping of brain transcriptomes regulating adaptive divergence in lake whitefish species pairs (Coregonus sp.)[END_REF][START_REF] Derome | Pervasive sex-linked effects on transcription regulation as revealed by eQTL mapping in lake whitefish species pairs (Coregonus sp, Salmonidae)[END_REF]. Third, these genetic markers have also been characterized in natural populations, thus permitting to make inference about the effect of selection acting on phenotypic traits, including gene expression. Fourth, the repeated independent parallel evolution of normal and dwarf phenotypes imply that populations evolved under similar selective pressures [START_REF] Bernatchez | On the origin of species: insights from the ecological genomics of lake whitefish[END_REF]. Lastly, these lake whitefish populations have small effective population sizes (Ne < 1000), low migration rates (m varying between 0.0004 and 0.0019) [41, 44], as well as strong selection against hybrids [45][46][47]. Under these conditions, divergence hitchhiking is theoretically expected to facilitate the formation of large genomic islands of divergence [START_REF] Feder | The efficacy of divergence hitchhiking in generating genomic islands during ecological speciation[END_REF].

In this study, we pursued three objectives pertaining to the genome-wide patterns of divergence observed during speciation: 1) Test the prediction that genetic markers associated with potentially adaptive traits (identified through pQTL and eQTL mapping) will show stronger evidence of divergent selection in natural populations than non-QTL linked markers; 2) Assess the prevalence of a few large islands of divergence along the genome rather than small independent regions; 3) Test whether sympatric species pairs showing more pronounced ecological, phenotypic and genetic divergence are also characterized by sharper speciation boundaries in terms of number and sizes of genomic regions of divergence.

Methods

Genetic mapping

We used genetic linkage maps previously generated from two backcross hybrid families (F1 X limnetic dwarf: BC D map, F1 X benthic normal: BC N map). Briefly, hybrids were produced between parents representing two allopatric whitefish populations belonging to two different glacial races and permitted to genotype and position about 900 AFLP and microsatellite loci amongst 336 progeny [for details see, 32]. These particular populations were chosen because they overlap in reproductive schedule and showed strong parallel phenotypic differentiation with sympatric populations studied here. Nine different phenotypes characterizing normal and dwarf populations were measured on these progeny and 34 pQTL (phenotypic QTL) linked to eight of these traits were mapped over 13 linkage groups using interval mapping [START_REF] Rogers | The Genetic architecture of ecological speciation and the association with signatures of selection in natural lake whitefish (Coregonus sp. Salmonidae) species pairs[END_REF]. While using a single mapping population is a common practice, it must be noted that it leads to the possibility that pQTL from the crosses may not always correspond to pQTL in the populations under study here.

Gene expression and genome scan in natural populations

We used gene expression data obtained from the analysis of white muscle [START_REF] Derome | Pervasive sex-linked effects on transcription regulation as revealed by eQTL mapping in lake whitefish species pairs (Coregonus sp, Salmonidae)[END_REF] and whole brain [START_REF] Whiteley | The phenomics and expression quantitative trait locus mapping of brain transcriptomes regulating adaptive divergence in lake whitefish species pairs (Coregonus sp.)[END_REF] tissues. Briefly, these studies used microarrays and the linkage map of [START_REF] Rogers | Linkage maps of the dwarf and normal lake whitefish (Coregonus clupeaformis) species complex and their hybrids reveal the genetic architecture of population divergence[END_REF] to localize expression QTL (eQTL) of genes expressed in white muscle (262 transcripts localized) and brain (249 transcripts localized) for one of the backcross family (BC D map). The markers (AFLP) used for genetic mapping where also genotyped in four lakes containing dwarf and normal sympatric populations [START_REF] Rogers | The Genetic architecture of ecological speciation and the association with signatures of selection in natural lake whitefish (Coregonus sp. Salmonidae) species pairs[END_REF]. Combining both QTL and genome scan information revealed that a total of six eQTL regions co-localized with pQTL and were also outliers in a genome scan study [START_REF] Bernatchez | On the origin of species: insights from the ecological genomics of lake whitefish[END_REF][START_REF] Rogers | The Genetic architecture of ecological speciation and the association with signatures of selection in natural lake whitefish (Coregonus sp. Salmonidae) species pairs[END_REF]. Moreover, these genomic regions were nonrandomly distributed across the genome and hinted at the role of major regulatory hotspots controlling the expression of numerous genes [START_REF] Whiteley | The phenomics and expression quantitative trait locus mapping of brain transcriptomes regulating adaptive divergence in lake whitefish species pairs (Coregonus sp.)[END_REF][START_REF] Derome | Pervasive sex-linked effects on transcription regulation as revealed by eQTL mapping in lake whitefish species pairs (Coregonus sp, Salmonidae)[END_REF].

Association between F ST and pQTL, eQTL, eQTL hotspots.

T-tests were performed for each lake individually to test whether mean F ST was greater for genetic markers associated with pQTL, eQTL or eQTL hotspots (QTL associated with the expression of five or more (up to 52) genes; see details in [START_REF] Rogers | The Genetic architecture of ecological speciation and the association with signatures of selection in natural lake whitefish (Coregonus sp. Salmonidae) species pairs[END_REF]). In addition, chi-square tests were performed for each lake individually to test whether there were significantly more F ST outliers for markers associated with pQTL, eQTL or eQTL hotspots.

Spatial autocorrelation

Spatial autocorrelation analyses were run and Moran's I was quantified for each lake individually in order to assess whether F ST outlier loci were clustered together more than expected by chance, thus representing evidence of relatively large speciation islands. Moran's I is a measure of spatial autocorrelation where -1 indicates perfect dispersion and +1 perfect correlation among samples [48].

Distance from nearest outlier pQTL

First, we identified outlier markers (markers showing F ST value > 95% quantile of F ST distribution in natural populations) associated with an adaptive trait (hereafter referred as outlier pQTL). Then, we tested the correlation between genetic distance (in centiMorgans) from an outlier pQTL and F ST values for all other mapped markers on the same linkage group. This was done separately for all four lakes. A linear regression between F ST and genetic distance was fitted in order to test whether the effect of divergence extended far from the region under selection itself, thus suggesting the existence of relatively large speciation islands. This relationship could be tested only for pQTL given that neither eQTL nor eQTL hotspots were significantly associated with higher F ST values than non-eQTL markers (Table 1). A logistic regression was also fitted, however, relationships were not significant in any of the lakes. In addition, linear models always had lower Akaike Information Criterion (AIC) and thus represented a better fit for the data (i.e. the differences in AIC between the logistic and linear regressions were 47.4, 50.9, 24.4 and 23.5 for Indian, East, Webster and Cliff lakes respectively).

Among lake differences characterizing genomic islands of divergence.

In order to provide a relative basis to compare the extent of differences in the characteristics of genomic islands of divergence among lakes, the following parameters were quantified: 1) The number of islands: defined as the number of unlinked outliers detected in each sympatric whitefish species pairs; 2) The relative size of islands: defined by the xintercept at the lake specific mean F ST value for the relationship depicted in Figure 1 (F ST values vs. chromosomal distance to the nearest outlier pQTL). These values (in cM) were then divided by the value for the least divergent lake (East L.) in order get relative estimates among lakes; 3) The "sea level" was defined for each lake separately as the F ST outlier threshold value (95% quantile) above which markers were considered outliers, and 4) The "mean island height" was defined in each lake as the difference between the mean F ST value of all outliers minus the F ST outlier threshold value. Note that none of these parameters should be taken as an absolute quantification of the actual physical or genetic size of a region of divergence, but instead used purely as comparative measures.

Results

pQTL, eQTL, eQTL hotspot.

Results in table 1 indicate that pQTL are characterized on average both by higher F ST values (t-tests) and an outlier status (chi-square tests) relative to non-pQTL markers. In contrast, neither eQTL nor eQTL hotspots were significantly associated with either higher F ST or an outlier status in all four lakes individually or combined. However, the fact that all relationships were stronger and tended to be more significant when combining the data from the four lakes for either pQTL or eQTL suggests that the absence of significant correlation may be partly due to a lack of statistical power caused by the limited number of QTL in each category.

Spatial autocorrelation

In the BC D map, we found weak, yet significant autocorrelation between outliers in three of the four lakes studied; Indian (Moran's I = 0.044, p-value = 0.02), East (Moran's I = 0.09, p-value < 0.01) and Cliff (Moran's I = 0.051, p-value = 0.01). The significant autocorrelation values were mainly due to three regions where two linked markers were outliers (two Indian outliers in linkage group 7 (LG7) which were 16.6 cM apart; two East outliers in LG4, 12.1 cM apart and two Cliff outliers on LG8, 26.8 cM apart). No significant association was found in the BC N family (table 2). This is likely due to the much lower number of pQTL segregating in that family (10 pQTL for BC N vs. 24 for BC D ) possibly because the phenotypic differences between hybrid and normal individuals were less marked than between hybrid and dwarf [START_REF] Rogers | The Genetic architecture of ecological speciation and the association with signatures of selection in natural lake whitefish (Coregonus sp. Salmonidae) species pairs[END_REF].

Distance from nearest outlier pQTL

Figure 1 illustrates the relationship between the distance (in cM) from an outlier pQTL and F ST value for all markers on the same linkage group, in each lake separately. All outlier pQTL were found on different linkage groups. A significant negative linear relationship (pvalue < 0.05) was detected for three of the four lakes studied (East L. r 2 = 0.33, Indian L. r 2 = 0.18 and Cliff L. r 2 = 0.21), whereas a similar, albeit not significant trend was observed in Webster L. (r 2 = 0.14, p-value = 0.13). In the BC N map, the relationship could only be tested in Cliff L., given that the other lakes did not have any outlier QTL. In this case, the relationship was significant (p-value = 0.004, results not shown).

Among lakes differences in characteristics of genomic islands of divergence.

Table 3 illustrates that the four lakes differed in their parameters characterizing genomic islands of divergence. Lakes were ordered according to a gradient of the expected intensity of divergent natural selection [41][42][43]. We observed a general trend towards an increase in number, size and height of genomic islands of divergence from the least ) towards the most differentiated whitefish pair (Cliff L.). Roughly speaking, the three genomic island characteristics doubled from the least to the most differentiated lake. In particular, it is noteworthy that the relative size of islands of divergence increased from 1 (East L.), to 1.43 (Indian L.), 1.57 (Webster L.) and 1.95 (Cliff L.). Given that the threshold was much higher in the most differentiated lake, it should become increasingly difficult to observe islands of divergence above the global sea level. Despite this, the mean height of the islands above sea level (defined as the F ST outlier threshold) increased from the least to the most differentiated lake (table 3).

Discussion

Association between F ST and QTL.

The general goal of this study was to investigate key predictions pertaining to the nature of regions of genomic divergence among lake whitefish species pairs. Our results partly confirmed our first prediction given that in general, phenotypic QTL showed higher Fst values and were more likely to be outliers (and therefore candidates for being targets of divergent selection) than non-pQTL markers. The detection of a significant association between genetic divergence and pQTL would imply that the genetic bases of traits conferring adaptability are also under divergent natural selection. While this is perhaps a simplistic or self-evident assumption of ecological speciation, it has seldom been explicitly demonstrated [49]. This is in part because, even in an optimal experimental system, one may not expect this relationship to always hold true, such as in situation where adaptation results from incomplete selective sweeps [50] or if traits under selection are highly polygenic [51]. In the end, pQTL allow a limited view of an organism's genetic complexity; some phenotypes will never be measured and therefore QTL underlying these traits never be detected. This is part why gene expression and eQTL studies can have such great potential to survey all relevant molecular phenotypes in an unbiased manner.

In contrast to pQTL, neither eQTL nor eQTL hotspots were associated with high (outlier) divergence values. There are biological reasons explaining why gene expression differences (eQTL) are less prone to be associated with signs of divergent natural selection. For one, given the numerous levels of control that exist between the transcription of mRNA and the expression of a phenotype, it is plausible that gene expression differences do not always translate into meaningful phenotypic differences. Segregating genetic variation affecting expression level may also evolve neutrally, due to the redundancy of developmental and physiological systems, and therefore remain hidden from selection acting at the level of the phenotype [52]. In addition, compensatory mutations evolving in a neutral fashion can result in transgressive patterns of expression when recombined in hybrids. For these reasons, genes expression differences in hybrids are not necessarily correlated with difference in parental species and a significant proportion of gene regulation is expected to behave in a non-additive fashion [53][START_REF] Bougas | The transcriptional landscape of cross-specific hybrids and its possible link with growth in brook charr (Salvelinus fontinalis Mitchill)[END_REF][START_REF] Renaut | Gene expression divergence and hybrid misexpression between lake whitefish species pairs (Coregonus spp. Salmonidae)[END_REF].

The size of genomic islands of divergence

Here, we must clarify that our analyses and conclusions differ from the ones suggested by Via & West [START_REF] Via | The genetic mosaic suggests a new role for hitchhiking in ecological speciation[END_REF] and Via [49] who concluded that F ST outliers were separated from their [START_REF] Via | The genetic mosaic suggests a new role for hitchhiking in ecological speciation[END_REF] and Via [49] suggested that divergence hitchhiking created surprisingly large genomic regions (> 10cM) around divergently selected pQTL. Given that, as a rough rule of thumb, 1 cM corresponds to a physical distance of one megabase [START_REF] Allen-Brady | Genetic distance and markers used in linkage mapping[END_REF] this would indeed imply extremely large islands of genomic divergence. Because of the relatively low marker density of the studies by Rogers and Bernatchez [START_REF] Rogers | The Genetic architecture of ecological speciation and the association with signatures of selection in natural lake whitefish (Coregonus sp. Salmonidae) species pairs[END_REF] and Via & West [START_REF] Via | The genetic mosaic suggests a new role for hitchhiking in ecological speciation[END_REF], the hypothesis of linkage between a given F ST outlier and the closest pQTL has to be interpreted carefully. Indeed, F ST outlier could as well be in linkage disequilibrium with other loci targeted by natural selection and independent from the closest pQTL.

In the present analysis, the data were treated differently. Analyses were performed separately for each lake, because each environment represents an independent speciation event [40,[START_REF] Pigeon | Multiple modes of speciation involved in the parallel evolution of sympatric morphotypes of lake whitefish (Coregonus clupeaformis, Salmonidae)[END_REF]. Moreover, all QTL cannot be viewed as being implicitly under divergent natural selection and thus, should not necessarily be expected to show high (outlier) divergence values [START_REF] Rogers | Integrating QTL mapping and genomic scans towards the characterization of candidate loci under parallel directional selection in the lake whitefish (Coregonus clupeaformis)[END_REF]. Therefore, we restricted our analysis to outlier QTL, the genetic regions most likely to be directly responsible for adaptive traits and evolving under divergent natural selection. The linear regressions in figure 1 imply that selection influences relatively large regions of differentiation. The spatial autocorrelation analyses are also indicative that some outlier loci are clustered even if they are genetically far apart (table 3). As such, our results provided support for the second prediction; the occurrence of large islands of divergence rather than small independent regions under selection. This is also in concordance with the recent work of Hohenlohe and colleagues [START_REF] Hohenlohe | Population genomics of parallel adaptation in threespine stickleback using sequenced RAD tags[END_REF] and the interpretation of Via [START_REF] Via | Hiding in plain sight: divergence hitchhiking and the dynamics of genomic isolation between incipient ecological species[END_REF] which argue for large chromosomal regions around selected QTL. Yet, it does not rule out the existence of much smaller and localized regions of divergence. Namely, our small autocorrelation values suggest that outlier loci show limited clustering and mostly represent independent regions of divergence.

While the occurrence of both small regions under selection and large speciation islands may seem contradictory, we re-emphasize that the two opposing views on how genomic divergence spread throughout the genome are merely the end of a continuum. It then seems that, while strong selection can create relatively few and large islands of divergence, it may also act in a much more localized sense on several independent regions. This scenario is probably closer to reality than either extreme views of speciation under the presence of gene flow. Consider, for instance, the case of Anopheles gambiae regarding the recent divergence of several reproductively isolated populations. In fact, the expression 'islands of speciation' itself comes from Turner and colleagues [START_REF] Turner | Genomic islands of speciation in Anopheles gambiae[END_REF], who first identified three large regions of divergence along a sea of neutral divergence between M and S forms in A. gambiae. Recent whole genome sequencing and genotyping have revealed a more complex scenario with pervasive genomic divergence inconsistent with contemporary inter-form gene flow [START_REF] Neafsey | SNP genotyping defines complex gene-flow boundaries among African malaria vector mosquitoes[END_REF][START_REF] Lawniczak | Widespread divergence between incipient Anopheles gambiae species revealed by whole genome sequences[END_REF]. In another example, strongly selected Drosophila populations harboring standing genetic sweeps and on traits which are highly polygenic, then identifying genes critical to initiating the speciation process may become much more difficult than initially perceived.

Another confounding factor which could explain the observed wide spread of highly divergent loci is the effect of selective sweeps on mutations that are beneficial in all populations. In the traditional interpretation, loci with higher levels of population differentiation than the expected neutral level are seen as evidence of divergent natural selection acting between populations. However, unconditionally beneficial mutations are expected to appear often in nature. Therefore, depending on how far the selective sweep has progressed when populations are sampled, such mutations may appear highly divergent, even though they are merely incidental in explaining the maintenance of species boundaries [START_REF] Bierne | The distinctive footprints of local hitchhiking in a varied environment and global hitchhiking in a subdivided population[END_REF]. This alternative explanation has been largely overlooked and emphasizes that genetic data should not be interpreted without an understanding of the genotype-phenotype association.

Among environment differences in characteristics of genomic islands of divergence.

Cases of closely related species such as dwarf and normal whitefish permit evaluations of the effect of divergent selection according to a gradient of ongoing ecological speciation. Here, our third prediction of a general trend towards an increase in terms of numbers and sizes of genomic regions of divergence from the least differentiated (East L.) to the most diverged species pair (Cliff L.) was also confirmed.

Previously, Landry et al. [42] and Landry & Bernatchez [43] showed that sympatric lakes with the most divergent sympatric populations (Cliff, Webster and Indian Lakes) were characterized by less habitat availability, less zooplanktonic prey biomass, smaller prey size range and larger gap in prey size distribution between the limnetic and benthic niches compared to the least divergent populations (East, Témiscouata and Crescent Lakes). The authors concluded that resource limitation resulted in increased potential for competition and selective pressure towards optimal normal and dwarf adaptive peaks. In addition, Lu & Bernatchez [47] and Renaut et al. [46] also showed that there was a continuum of differentiation among lakes both from a phenotypic and genetic standpoint, from East Lake being the least differentiated to Indian, Webster and Cliff L., being the most differentiated. Here, East L. generally differed from the three more differentiated species pairs, being characterized by a smaller number of putative islands of divergence. These were also smaller in relative size, both in terms of the size of chromosomal regions being hitchhiked, as well as the height of the islands (table 3). On the contrary, the Cliff Lake species were the most distinct, showing the highest number of islands, which were also on average the largest. As such, our results confirm in whitefish one of the basic premises of the genic view of speciation [START_REF] Wu | The genic view of the process of speciation[END_REF], whereby populations that are more representative of the early steps of ecological speciation are also those characterized by a lower and generally smaller number of islands.

Comment citer ce document : Renaut, S., Maillet, N., Normandeau, E., Sauvage, C., Derome, N., Rogers, S.M., Bernatchez, L.

(2012). Genome-wide patterns of divergence during speciation: the lake whitefish case study. Admittedly, the criteria we used to define genomic islands characteristics were arbitrary and should be interpreted as qualitative and relative measures of divergence. Yet, they still provided a useful means to visualize the main differences observed between whitefish species pairs form different lakes. More rigorous confirmation of the nature and extent of genomic divergence among different species pairs will require a re-analysis of this system with a denser genomic coverage, both for the genetic map and the genomic scan of wild populations. Such endeavor is currently underway.

Outlook

As recently suggested, detection of widespread genomic divergence may support a very different speciation model where the identification of genetic changes responsible for ecological and behavioral divergence will be more difficult than initially hoped [START_REF] Neafsey | SNP genotyping defines complex gene-flow boundaries among African malaria vector mosquitoes[END_REF][START_REF] Lawniczak | Widespread divergence between incipient Anopheles gambiae species revealed by whole genome sequences[END_REF]. Certainly, from a technological standpoint, next generation sequencing technologies are rapidly revolutionizing the field of evolutionary biology, genetics and ecology [START_REF] Tautz | Next generation molecular ecology[END_REF]. However, there is also a marked lag in the development of analytical tools to take full advantage of this new type and sheer quantity of data [START_REF] Mcpherson | Next-generation gap[END_REF][START_REF] Gompert | A hierarchical Bayesian model for next-generation population genomics[END_REF]. Moreover, one has to keep in mind that merely identifying the genetic basis of phenotypic traits does not fulfill the conditions necessary to define a phenotype-environment association [START_REF] Schluter | The Ecology of Adaptive Radiation[END_REF]. Ultimately, phenotypes are what matter for organisms. Therefore, we indisputably maintain the importance of knowing the genotypephenotype-environment association [START_REF] Houle | Phenomics: the next challenge[END_REF]. One of the great advantages of gene expression studies lies in the fact that they allow to simultaneously measure thousands of different phenotypic traits and thus get a phenome-wide view of the extent of divergence [START_REF] Ranz | Uncovering evolutionary patterns of gene expression using microarrays[END_REF]. Unfortunately, while high-throughput sequencing, genotyping and gene expression studies have matured into widely available procedures, high throughput phenotyping remains in its infancy, and will be required to better quantify the phenotypic space occupied by diverging populations. The integrative approach developed in the lake whitefish study system certainly brings insights into the multidimensional nature of the genetic changes responsible for speciation.

Comment citer ce document : Renaut, S., Maillet, N., Normandeau, E., Sauvage, C., Derome, N., Rogers, S.M., Bernatchez

  Comment citer ce document : Renaut, S., Maillet, N., Normandeau, E., Sauvage, C., Derome, N., Rogers, S.M., Bernatchez, L.(2012). Genome-wide patterns of divergence during speciation: the lake whitefish case study. Philosophical transactions of the Royal Society of London. Series B, Biological sciences, 367, 354-363. DOI : 10.1098/rstb.2011.0197 Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript

Figure 1a- d .

 d Figure 1a-d. The relationship (linear regression) between distance from the nearest outlier pQTL and genetic divergence (F st ) for all four lakes.

  Author manuscript closest pQTL on average by 10.6 cM in pea aphids (Acyrthosiphon pisum pisum) and by 16.5cM in the lake whitefish species pairs discussed in the present study[START_REF] Rogers | The Genetic architecture of ecological speciation and the association with signatures of selection in natural lake whitefish (Coregonus sp. Salmonidae) species pairs[END_REF]. To this day, there is no consensus into what should be the best method to measure speciation islands and what are the expected patterns of genomic divergence under varying conditions of gene flow[START_REF] Via | Hiding in plain sight: divergence hitchhiking and the dynamics of genomic isolation between incipient ecological species[END_REF]49,[START_REF] Feder | Establishment of new mutations under divergence and genomic hitchhiking[END_REF]. Further theoretical work will be needed to objectively characterize genomic islands of speciation given that different approaches can lead to substantially variable conclusions.Via & West

Comment citer ce document : Renaut, S., Maillet, N., Normandeau, E., Sauvage, C., Derome, N., Rogers, S.M., Bernatchez, L.

(2012). Genome-wide patterns of divergence during speciation: the lake whitefish case study. Philosophical transactions of the Royal Society of London. Series B, Biological sciences, 367, 354-363. DOI : 10.1098/rstb.2011.0197 Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur /

  Author manuscript variation did not reveal large islands of divergence or complete selective sweep after 600 generations of selection, a scenario inconsistent with a large speciation island model[50]. If early in divergence, selection acts on standing genetic variation through soft or incomplete

Comment citer ce document : Renaut, S., Maillet, N., Normandeau, E., Sauvage, C., Derome, N., Rogers, S.M., Bernatchez, L.

(2012). Genome-wide patterns of divergence during speciation: the lake whitefish case study. Philosophical transactions of the Royal Society of London. Series B, Biological sciences, 367, 354-363. DOI : 10.1098/rstb.2011.0197 Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur /

Table 1 .

 1 , L. (2012). Genome-wide patterns of divergence during speciation: the lake whitefish case study.Philosophical transactions of the Royal Society of London. Series B, Biological sciences, 367, 354-363. DOI : 10.1098/rstb.2011.0197 Genetic divergence (mean F st and number of outliers observed and expected) for markers linked to pQTL, eQTL and eQTL hotspots for all four lakes containing sympatric dwarf and normal populations. BC D (a F1 hybrid parent backcrossed with a pure dwarf parent) and BC N (a F1 hybrid parent backcrossed with a pure normal parent) represent the two backcross families analyzed here. T-tests and χ 2 tests were performed to assess if, respectively, mean F ST and number of outliers deviated for markers associated with a phenotype.Comment citer ce document : Renaut, S., Maillet, N., Normandeau, E., Sauvage, C., Derome, N., Rogers, S.M., Bernatchez, L.(2012). Genome-wide patterns of divergence during speciation: the lake whitefish case study. Philosophical transactions of the Royal Society of London. Series B, Biological sciences, 367, 354-363. DOI : 10.1098/rstb.2011.0197

	Manuscrit d'auteur / Author manuscript	Lake East L.	markers pQTL no pQTL pQTL no pQTL eQTL no eQTL eQTL	genetic map BC D BC N BC D BC D	mean F ST 0.07 0.04 0.03 0.03 0.05 0.04 0.07	p-value (t-test) 0.05 -0.69 -0.43 -0.63	observed outliers 3 1 0 0 3 1 0	expected outliers 0.94 3.06 0 0 2.65 1.35 0.09	p-value (χ 2 -test) 0.02 ---0.71 -0.76
			hotspot
			no eQTL		0.05	-	4	3.91	-
			hotspot
	Manuscrit d'auteur / Author manuscript	Indian L.	pQTL no pQTL pQTL no pQTL eQTL no eQTL eQTL hotspot hotspot no eQTL	BC D BC N BC D BC D	0.04 0.04 0.01 0.03 0.04 0.05 0.05 0.04	0.96 -0.0003 -0.73 -0.81 -	4 4 0 1 6 2 0 8	1.89 6.11 0.11 0.89 5.30 2.70 0.18 7.82	0.08 -0.73 -0.60 -0.67 -
		Webster L.	pQTL	BC D	0.12	0.26	1	0.94	0.95
	Manuscrit d'auteur / Author manuscript		no pQTL pQTL no pQTL eQTL no eQTL eQTL hotspot no eQTL	BC N BC D BC D	0.10 0.07 0.09 0.10 0.10 0.07 0.10	-0.45 -0.60 -0.51 -	3 0 1 4 0 0 4	3.06 0.11 0.89 2.65 1.35 0.09 3.91	-0.73 -0.15 -0.76 -

Comment citer ce document : Renaut, S., Maillet, N., Normandeau, E., Sauvage, C., Derome, N., Rogers, S.M., Bernatchez, L.

(2012). Genome-wide patterns of divergence during speciation: the lake whitefish case study. Philosophical transactions of the Royal Society of London. Series B, Biological sciences, 367, 354-363. DOI : 10.1098/rstb.2011.0197

Table 2 .

 2 Spatial autocorrelation statistics for all four lakes. Moran's I ranges from -1 (perfect dispersion) to +1 (perfect correlation) among F ST outliers within each lake.

			Moran's	I
			statistics
		genetic map	observed	expected
	East L.	BC D	+0.09	0.00
		BC N	no mapped outliers
	Indian L.	BC D	+0.04	0.00
		BC N	0.00	0.00
	Webster L.	BC D	-0.01	0.00
		BC N	0.00	0.00
	Cliff L.	BC D	+0.05	0.00
		BC N	-0.01	0.00

Comment citer ce document : Renaut, S., Maillet, N., Normandeau, E., Sauvage, C., Derome, N., Rogers, S.M., Bernatchez, L.

(2012). Genome-wide patterns of divergence during speciation: the lake whitefish case study. Philosophical transactions of the Royal Society of London. Series B, Biological sciences, 367, 354-363. DOI : 10.1098/rstb.2011.0197

Table 3 .

 3 Characteristics of genomic islands of divergence for each of the four whitefish species pairs. See Material and Methods for detailed explanations of how each parameter was defined. Note that outliers are the sum of both BC D and BC N pQTL also outliers in natural populations. ***Sizes are based only on BC D map. They represent the x value where y is equal to the mean F ST value for a given species pair in Fig.1. Sizes are then divided by the value for the least divergent lake (East) in order get among lake relative estimates.Bernatchez, L. 2004 Ecological theory of adaptive radiation: an empirical assessment from coregonine fishes (Salmoniformes). Pages 175-207 in Hendry, A. P. & Stearns S. C., eds. Evolution illuminated: salmon and their relatives. Oxford Univ. Press, Oxford. 39. Lu, G., Basley, D.J. & Bernatchez, L. 2001 Contrasting patterns of mitochondrial DNA and microsatellite introgressive hybridization between lineages of lake whitefish (Coregonus clupeaformis): relevance for speciation. Mol. Ecol. 10, 965-985. 40. Renaut, S., Nolte, A.W., Rogers, S.M., Derome, N. & Bernatchez, L. 2011 SNP signatures of selection on standing genetic variation and their association with adaptive phenotypes along gradients of ecological speciation in lake whitefish species pairs (Coregonus spp.). Mol. Ecol. 20, 545-559. 41. Lu, G. & Bernatchez, L. 1999 Correlated trophic specialization and genetic divergence in sympatric lake whitefish ecotypes (Coregonus clupeaformis): support for the ecological speciation hypothesis. Evolution 53, 1491-1505. 42. Landry, L., Vincent, W.F. & Bernatchez, L. 2007 Parallelism between limnological features and phenotypic evolution of lake whitefish dwarf ecotypes. J. Evol. Biol. 20, 971-984. 43. Landry, L. & Bernatchez, L. 2010 Role of epibenthic resource opportunities in the parallel evolution of lake whitefish species pairs (Coregonus sp.). J. Evol. Biol. 23, 2602-2613. 44. Campbell, D. & Bernatchez, L. 2004 Generic scan using AFLP markers as a means to assess the role of directional selection in the divergence of sympatric whitefish ecotypes. Mol. Biol. Evol. 21, 945-956. 45. Rogers, S.M. & Bernatchez, L. 2006 The genetic basis of intrinsic and extrinsic postzygotic reproductive isolation jointly promoting speciation in the lake whitefish species complex (Coregonus clupeaformis). J. Evol. Biol. 19, 1979-1994. 46. Renaut, S. & Bernatchez, L. 2011 Transcriptome-wide signature of hybrid breakdown associated with intrinsic reproductive isolation in lake whitefish species pairs (Coregonus spp. Salmonidae). Heredity, 106, 1003-1011. 47. Lu, G. & Bernatchez, L. 1998 Experimental evidence for reduced hybrid viability between dwarf and normal ecotypes of lake whitefish (Coregonus clupeaformis Mitchill). Proc. R. Soc. Lond. B. 265, 1025-1030. 48. Moran, P.A.P. 1950 Notes on Continuous Stochastic Phenomena. Biometrika, 37, 17-33. 49. Via, S. 2009 Natural selection in action during speciation. Proc. Natl Acad. Sci. USA 106, 9939-9946. 50. Burke, M.K., Dunham, J.P., Shahrestani, P., Thornton, K.R., Rose, M.R. & Long, A.D. 2010 Genome-wide analysis of a long-term evolution experiment with Drosophila. Nature, 40, 587-590. 51. Storz, J.F. & Wheat, C.W. 2010 Integrating evolutionary and functional approaches to infer adaptation at specific loci. Evolution, 64, 2489-2509. 52. Gibson, G. & Dworkin, I. 2004 Uncovering cryptic genetic variation. Nat. Rev. Genet. 5, 681-690. 53. Ranz, J.M., Namgyal, K., Gibson, G., Hartl, D. 2004 Anomalies in the expression profile of interspecific hybrids of Drosophila melanogaster and Drosophila simulans. Genome Res. 14, 373-379.

		Mean	AFLP	QTL outliers**	Relative size of	Outlier threshold	Height of
		F st	outliers**	(number of islands)	islands ***	(sea level)	island
	East L.	0.05	4	4	1.00	0.25	0.08
	Indian L.	0.04	9	3	1.43	0.20	0.08
	Webster L.	0.10	5	1	1.57	0.37	0.18
	Cliff L.	0.14	14	7	1.95	0.46	0.29
	**

Comment citer ce document : Renaut, S., Maillet, N., Normandeau, E., Sauvage, C., Derome, N., Rogers, S.M., Bernatchez, L.

(2012). Genome-wide patterns of divergence during speciation: the lake whitefish case study. Philosophical transactions of the Royal Society of London. Series B, Biological sciences, 367, 354-363. DOI : 10.1098/rstb.2011.0197 Comment citer ce document : Renaut, S., Maillet, N., Normandeau, E., Sauvage, C., Derome, N., Rogers, S.M., Bernatchez, L. (2012). Genome-wide patterns of divergence during speciation: the lake whitefish case study. Philosophical transactions of the Royal Society of London. Series B, Biological sciences, 367, 354-363. DOI : 10.1098/rstb.2011.0197 Comment citer ce document : Renaut, S., Maillet, N., Normandeau, E., Sauvage, C., Derome, N., Rogers, S.M., Bernatchez, L. (2012). Genome-wide patterns of divergence during speciation: the lake whitefish case study. Philosophical transactions of the Royal Society of London. Series B, Biological sciences, 367, 354-363. DOI : 10.1098/rstb.2011.0197

Acknowledgments

We would like to thank the organizers Patrik Nosil and Jeffrey L. Feder for kindly inviting us to contribute to this special issue. In addition, we thank Loren H. Rieseberg for fruitful discussions on the genetics of speciation and are grateful to P. Nosil, S. Via and one anonymous referee for their constructive comments. This research program on whitefish ecological genomics was funded by a Natural Science and Engineering Research Council of Canada (NSERC) and Canadian Research Chair in Genomics and Conservation of Aquatic Resources to LB, a NSERC postgraduate scholarship to SR and NSERC discovery grant to SMR.