Kinematic analysis of swimming ontogeny in seabass ( Dicentrarchus labrax )

. Swimming has been investigated in multiple species, but few studies consider the establishment of swimming through ontogeny. This study describes the establishment of cyclical swimming in Dicentrachus labrax , a marine fish from cold, temperate waters. The data were compared with results from previous studies on two subtropical freshwater catfish species ( Clarias gariepinus and Corydoras aeneus ). The three species have different modes of locomotion each during their adult stage (anguilliform, subacarangiform and carangiform). The swimming of Dicentrarchus labrax was recorded with a high-speed video camera (500 fps) from 0 to 288 hours and from 960 to 2496 hours post-hatching. Three indices, i.e. coefficient of determination (r²), coefficient of variation (CV), and Strouhal number ( St ), were used to investigate the establishment and efficiency of swimming. Important differences in the timing of swimming establishment were observed between the seabass and the two catfish species. The two catfish species display a sine-shaped swimming mode immediately or soon after hatching, and the efficiency of movement substantially improves during the first days of life. For seabass, however, establishment of swimming is slower during the same developmental period. These differences may be related to a faster developmental rate in the catfishes that allows them to swim rapidly in an intermediate regime flow and to develop the required morphology to establish efficient movements earlier.


INTRODUCTION
In most fish, swimming corresponds to the propagation of a wave of increasing amplitude from head to tail (Gray, 1933), which is commonly named the body/caudal fin locomotion (BCF) (BREDER, 1926;Lindsey, 1978;Videler, 1993).Depending primarily on the parameter of size, undulatory movements generate thrust in a range of flow regimes, by exploiting viscous or inertial forces or both (Videler, 1993).The ratio between the viscous and inertial forces can be assessed by the Reynolds number (Re).At hatching, larvae are only a few millimeters long and the corresponding flow regime is dominated by viscous forces (Re values below 100) (McHenry & Lauder, 2005;VIDELER, 2011).This means that larvae must use large body wave amplitudes along their whole body to enable them to exploit the viscous force optimally (Webb & Weihs, 1986).This set of movements corresponds to the anguilliform swimming mode (Müller & van Leeuwen, 2004;Mauguit et al., 2010a,b).Experiments showed that an increase in the viscosity of the medium induced an increase in the amplitude of the movement in the anterior part of the body (HORNER & JAYNE, 2008;DANOS, 2012).During growth, fish experience a gradual change from a viscous to an intermediate regime (Re > 300) and then from the intermediate to an inertial flow regime (Re > 1000) (Müller & Videler, 1996; Osse & van den Boogaart, 2000;McHenry & Lauder, 2005).Simultaneously, skeletal, muscular and nervous systems develop while new structures (i.e.fins) are recruited, and other structures (i.e.yolk-sacs) are lost.These changes are important in setting physical limits to locomotor performance (Webb, 1984), and are expected to affect the ontogeny of swimming (Fuiman & Webb, 1988).However, the developmental process driving the swimming capacity has received little attention.The kinematics of swimming in fish larvae has been studied in zebrafish Danio rerio (Hamilton, 1822) (Fuiman & Webb, 1988;Müller & van Leeuwen, 2004;Fontaine et al., 2008;Müller et al., 2008), the common carp Cyprinus carpio (L., 1758) (Osse, 1990; Osse & van den Boogaart, 2000), the European plaice Pleuronectes platessa (L., 1758) (Batty, 1981) and the Atlantic herring Clupea harengus (L., 1758) (Batty, 1984).However, these studies only focused on a few larval stages (from 2 to 7) and did not provide a global view of the developmental cycle.
More recently, MAUGUIT et al. (2010a,b) more thoroughly examined the development of swimming by studying 21 and 23 larval stages in Clarias gariepinus (Burchell, 1822) and Corydoras aeneus (Gill, 1858), respectively.Both studies used a new kind of analysis that allows a better understanding of the changes in swimming during fish growth.This method is based on the work of VIDELER (1993).In theory, during one undulatory movement, each body part follows a pure sine-like trajectory when two conditions are observed: (1) the swimming speed is constant during the execution of one swimming movement and (2) the lateral amplitude of each body part is small (Videler, 1993).In practice, neither condition is met.First, the thrust oscillates during one tail-beat as the tail beats back and forth.Consequently, the swimming speed also fluctuates (Müller & van Leeuwen, 2004).Second, the body wave amplitude increases from the pivot point to the tail (Videler, 1981).The pivot point, located just behind the head, characterizes the position on the body where the smallest amplitude of lateral movement is usually observed.Consequently, the propulsive wave deviates moderately from a pure sine-like trajectory at this pivot point and more markedly at the tail, where the amplitude is maximal.
Variations in swimming speed during one tailbeat are stronger in the viscous flow regime of small, slow swimmers than in the inertial flow regime of large, fast swimmers (Müller & van Leeuwen, 2004).In a viscous flow regime, large amplitudes of each body part are required to better exploit forces of the medium while in an inertial flow regime, smaller amplitudes allow better penetration in the water (Batty, 1981).
Thus, we predict larvae may be unable to perform sine-shaped movements at hatching.During ontogeny, as body length and absolute swimming speed increase and morphological developments occur, we expect larvae to progressively improve their swimming ability towards sinusoidal movements.
Our aim is to use the method of MAUGUIT et al. (2010a) to describe the ontogeny of the swimming in Dicentrachus labrax (seabass) (L.1758) from hatching to 104 days post-hatching.The data will then facilitate more comprehensive comparisons with the two species studied by MAUGUIT et al. (2010a,b): Clarias gariepinus and Corydoras aeneus.The two catfish species live in subtropical regions in freshwater.Both stay generally in quiet waters near the bottom (TEUGELS, 1986;BURGESS, 1992).At adult stage, the two species differ in their swimming mode, one using the anguilliform mode (C.gariepinus) and the other the carangiform mode (C.aeneus) (MAUGUIT et al., 2010a,b).Dicentrachus labrax generally favours turbulent environments in cold and temperate seawaters.Larvae hatch in the open sea and, once juveniles, drift towards the coast and estuaries (PICKETT & PAWSON, 1994).At adult stage, seabass use a subcarangiform swimming mode (PALOMARES, 1991;HERSKIN & STEFFENSEN, 1998).The differences between habitats and way of life should affect the growth and the rate of morphological development of the species and in this way the establishment of swimming behaviour.Being a marine fish living in cold/temperate water, the seabass should have slower growth and rate of morphological development than the two catfish species.We expect that the establishment of swimming in D. Swimming ontogeny in the seabass labrax will take more time than in C. gariepinus and in C. aeneus.

MATERIALS AND METHODS
In this study the larval period was determined as the period between hatching and the ossification of the caudal fin.Once the caudal fin was ossified, fish were considered as juveniles.Larvae of D. labrax were bred at Aquanord hatchery (Gravelines, France) in a community tank filled with running seawater at a temperature of 15°C.Larvae were kept in the darkness until 216 hours post-hatching (hPH).Then, light was turned on with a photoperiod of 12h and larvae were fed with brine shrimps three times a day (Artemia salina L., 1758).Juveniles (whose caudal fin is ossified) were also bred in a community tank at a temperature of 20°C.Fish were sampled at different stages: 0,4,8,12,16,20,24,32,40,48,60,72,96,120,144,168,192,216,240,264 and 288 hPH for larvae and 960, 1896 and 2496 hPH (respectively 40, 79 and 104 days post-hatching) for juveniles.For each stage, 15 individuals were sampled and were separated into three batches of five fish.In each batch, swimming was recorded at 500 frames s -1 with a high-speed digital video camera (RedLake MotionPro 2000; RedLake, San Diego, California, USA) from a dorsal view.Swimming sequence was recorded only once per batch to avoid studying the same individual twice.A total of three independent replicates was collected for each stage.Note that a sequence suitable for further analysis was defined when fish performed one complete undulatory movement in a straight direction and at a constant speed.For each swimming movement, the first three tail strokes were not recorded to avoid inclusion of acceleration movements.
Three tanks of variable dimensions were used: 7.5 cm × 2.5 cm, 14.5 × 8 cm, 123 × 8.5 cm respectively for larvae (3 to 5.6 mm TL), small juveniles (<20 mm TL) and large juveniles (>20 mm TL).The water level was always five times the fish height.Fish were free to move in all directions and at variable swimming speeds.The camera was mounted on a Stereozoom Microscope (Leica M10; Leica, Wetzlar, Germany) for larvae and equipped with a lens (Linos Mevis 25 mm, 1.6: 16; Linos; Munich, Germany) for juveniles.The two smallest tanks were lit from the top and the bottom (light reflected by a mirror) with two 240W Volpi 6000-1 cold light sources (Volpi, Schlieren, Switzerland) and optical fibers.The largest tank was lit from the top with two 1000W spotlights (IFF Q1250).
The analyses of sequences of the swimming movements were carried out with Midas software (RedLake, version 2.1.1).For larvae and juveniles, a total of 63 and nine sequences respectively were analyzed in an earth-bound frame of reference.The fish midline was divided into seven equal segments by selecting eight landmarks between the snout and the tail tip, i.e. at 0, 0.14, 0.29, 0.43, 0.57, 0.71, 0.86 and 1 TL (respectively LM1 to LM8, Fig. 1).A preliminary study determined the useful number of landmarks.The use of eight landmarks allowed placing the second one near the pivot point (where the amplitude of the movement is the weakest along the body).The x-axis was defined as the direction of fish displacement and the y-axis was perpendicular to the x-axis.A transformation was done to move the first point of the trajectory of each landmark to the x-axis origin (x = 0).The aim of this transformation was to use the same referential for analyzing the motions of each landmark independently of its position on the fish.
For each sequence, direct and indirect parameters were selected to describe the swimming movement.The direct parameters were total fish length (TL; mm), relative swimming speed (U; TLs -1 ), tail-beat frequency (f; s -1 ), the wavelength of the propulsive wave (λ) and the maximal amplitude movement of each landmark (A 1-8 ; %TL).
The indirect parameters were the three indices used by MAUGUIT et al. (2010b).The first index made it possible to assess the sinusoidal trajectories of the swimming movement.From a distribution of the observed values of x, and knowing the movement amplitude (A 1-8 ) and its wavelength, a theoretical sinusoid could be calculated for the various landmarks at each developmental stage.The sinusoidal function linking y th (theoretical y) and x is y th = A sin (ωx+φ), where A is the amplitude (in mm), ω the pulsation (in radian mm -1 ), and φ the initial phase (in radians).The amplitude (A) and the pulsation (ω) were determined from the observed coordinates: A = y max and ω = 2πT x -1 , where y max is the maximum amplitude observed during one tail-beat and T x is the period of motion.For each landmark, the y th values were calculated by varying φ between 0 and 2π by increments of 0.01 radian (this yields 628 theoretical sinusoids) to obtain the best fit between the observed and theoretical curves.The φ value of the theoretical sinusoid having the best fit (the highest r²) with the observed motion was then selected.These sinusoids correspond to the theoretical ideal trajectories that each landmark should follow during execution of a complete undulatory movement (i.e. to the situation that should be observed at the adult stage).The paths observed for the various landmarks throughout ontogeny were compared with these theoretical sinusoids by determining the coefficient of determination (r²) between the two curves.The coefficients of determination of LM1-LM8 (r² 1-8 ) provided an objective index of the similarity between this motion and the adult sinusoid motion for each landmark placed on a fish.The r² mean , the mean of the r² 1 to r² 6 , provided a global index of the body movement profile at a specific developmental stage.Swimming movements were considered to be sinusoidal when r² mean was ≥ 0.95.Landmarks 7 and 8 were not taken into account for the r² mean .Landmarks 7 and 8 were on the caudal region.This region is not yet developed in larvae (no ray-finned caudal fin and no intrinsic muscles), which therefore are unable to fully control their tail-tip movements.However the caudal fin follows a better sinusoidal path once developed (in juveniles); the caudal fin has intrinsic muscles that are able to alter the movement (Lauder, 1989(Lauder, , 2000)).In consequence, the caudal region does not behave the same way as the rest of the body.For this reason the corresponding r² were not taken into account for the r² mean .
The coefficient of variation of r² (CV), the second index, was calculated with the r² 1 -r² 6 values to gauge whether, at a given developmental stage, the movement appeared to have the same level of organization in different parts of the body.
The third index used was the Strouhal number: where f is the tail-beat frequency, A 8 the maximum amplitude of the caudal fin and U the swimming speed.Re values are very high, the swimming efficiency is optimal when the St values range from 0.25 to 0.45 (Borazjani & Sotiropoulos, 2008, 2009;Lauder & Tytell, 2006;Taylor et al., 2003).But for fish whose corresponding Re values are only 300, the optimal St values go down to 1.3 (Borazjani & Sotiropoulos, 2008, 2009).
Other parameters about fish morphology and flow regime were also calculated: yolk-sac volume (Vv) and Reynolds number (Re).The shape of the yolk-sac was assumed to be a prolate spheroid (Bagarinao, 1986), and the volume was calculated as follows: where L v and H are respectively the length and the height of the yolk-sac.This parameter was measured on photos using Vistametrix version 1.34 (SkillCrest LLC, Tucson, Arizona, USA).
The effects of size, swimming speed and yolksac volume (independent variables) on r² mean , CV, St and the amplitudes of LM1 to LM8, were investigated by multiple polynomial regressions of the third degree (the use of a higher degree did not improve the accuracy of the analysis).The best-fit model was identified in a stepwise forward-selection manner and was selected based on the lowest p-value.Only significant values were included in the models (Student's t test, p < 0.05) and presented in the results.In graphs showing effects of size and swimming speed on r² mean , CV and St values, data are presented in a surface plot where the size is on the x axis, the swimming speed is on the y axis, and the values of the dependent variable are provided by a color code.The surface that fitted best to the points of observation was determined by the weighted least squares method (McLain, 1974).Nonparametric correlation (Spearman) was also determined between Reynolds and Strouhal numbers.

RESULTS
Three movements from three different fish were Swimming ontogeny in the larval period (from hatching to 288 hPH) Larvae measured 3.3±0.2mm (n = 3) at hatching and were observed until they grew to 5.5±0.1mm(= 288 hPH; n = 3).The yolksac (initially 0.4±0.01mm³, n = 3) was totally resorbed between 96 and 120 hPH.Pectoral fins appeared at a size of 4.93±0.21mm (96 hPH; n = 3).Independent of age, size and morphology, the swimming bouts could be split into two groups swimming at different speeds.According to the terminology used in BLAXTER (1969), the first group used a steady swimming speed (1.31 to 4.88 TLs -1 ) (n = 50) while the second performed a burst of swimming (12.73 to 27.62 TLs -1 ) (n = 13).None of the larvae swam at the intermediate speed, between 4.9 and 12.73 TLs -1 .Tail-beat frequencies were 20.47±3.69Hz for the steady swimming group and 49.07±5.39Hz for the burst of swimming group.In burst of swimming larvae, the six fastest bouts (24 to 27.62 TLs -1 ) were in an intermediate regime (Re > 300).All the other recorded swimming bouts were in a viscous flow regime (Re ≤ 300).Swimming movements were observed at hatching.These movements were not completely sinusoidal (r² mean =0.77±0.17),but r² mean values continuously increased with growth (Fig. 2A; F [4,58] = 24.170,p < 0.001).At the size of 5.2 mm, all larvae were able to perform sinusoidal movements (r² mean ≥ 0.95) while swimming speed ranged from 1.9 to 23.23 TLs -1 (Fig. 2A).Moreover, independent of size, there was a strong correlation between a sinusoidal movement and swimming speed (Figure 2A; F [4,58] = 24.170,p < 0.001): all larvae with a burst of swimming (>12 TLs -1 ) performed sinusoidal movements independent of size (Fig. 2A).During ontogeny, the sinusoidal swimming motion was established first in the middle part of the body near the pivot point (LM3-LM4).The same acquisition was then observed along almost all the rest of the body (LM1-LM2; LM5).After larvae reached a size of 5.2 mm, all body landmarks (LM1 to LM6) exhibited sinusoidal paths (Fig. 3A).This variation in the time of acquisition of sinusoidal movement for different parts of the body induced high values of CV in larvae (ca 12%) (Fig. 2B).
Independent of size, fish swimming at least at 12 TLs -1 (= burst of swimming) show CV around 2% (Fig. 2B; F [3,59] = 7.6278, p<0.001), with all the body parts (LM1-LM6) exhibiting sinusoidal trajectories.Although the r² 7 and the r² 8 values increased regularly with growth and with speed (F 4,58 = 13.209,p < 0.001 for r² 7 and F 4,58 = Fig. 2. -Contour plot representing the changes in (A) mean coefficient of determination (r² mean ), (B) coefficient of variation of r² (CV of r²) and (C) Strouhal number (St) as a function of the total fish length (TL) and relative swimming speed (U) of larvae of seabass (Dicentrarchus labrax).The index values are given by the colour code.The white circles represent observations made during the present study.Each circle corresponds to one fish.These data were used to fit the isoclines by means of the weighted least square distance method.In A the yellow line represents the threshold value of 0.95.White circles located to the left of this line correspond to fish that did not execute fully sinusoidal swimming movements, whereas those to the right of this line correspond to fish with sinusoidal swimming movements.11.060, p < 0.001 for r² 8 ), sinusoidal movements were rarely observed at the level of the tail.
At hatching, larvae swam with high Strouhal numbers (> 2), and this index did not change significantly at the end of the larval period studied (Fig. 2C; F [3,59] = 27.527,p < 0.001).During the period studied, larvae did not grow very much and so Re values did not differ substantially: During growth, the relative amplitudes of the different body parts (LM1-6) decreased in parallel to a better sine-shaped swimming mode (Fig. 3B; F 1926) defined a subcarangiform mode as a swimming movement where the amplitude increases significantly in the posterior part of the body and where between 0.5 and 1 wavelength of propulsive wave (λ) is observed in the fish body.Despite the decrease in the amplitude movement of the LM1-6 during growth, all larvae swam with more than one λ on the body.So, the transition from an anguilliform to a subcarangiform mode was not yet complete.Except at the caudal tip (LM8), the amplitude of movement increased with swimming speed (F [2,60] = 51.144(LM1); 38.647 (LM2); 54.265 (LM3); 51.700 (LM4); 33.702 (LM5); 40.640 (LM6); 29.592 (LM7); p < 0.001).
The impact of yolk-sac resorption was also studied on the three indices and lateral displacements of the body during swimming movements (A 1 to A 8 ), but no significant relationship was found.

Swimming mode in juvenile stages (960-2496 hPH)
The size of the juveniles ranged from 14.3 to 34.2 mm, and all had a fully ossified caudal fin.Their swimming speed ranged from 2.32 to 23.4 TLs -1 with a tail-beat frequency of 14.8±10.72Hz.Juveniles between 14 and 19 mm swam in the intermediate flow regime with Re values The r² mean was always higher than 0.95 (0.98±0.01), and the CV was low (1.84±0.94%).Although the caudal fin followed better sinusoidal paths than in larvae, the threshold value of 0.95 was not always reached.The Strouhal numbers ranged from 0.48 to 1.58, with the lowest values being found for juveniles swimming in an inertial regime.Juveniles performed swimming movements with an important increase of the amplitude in the posterior part of the body and with a propulsive wave between 0.5 and 1 wavelength.Therefore, the transition to a subcarangiform mode occurred between the larval and juvenile stages.

DISCUSSION
All Dicentrarchus labrax larvae start their life swimming with an anguilliform motion that is functional in all types of hydrodynamic flow regimes (Gray & Hancock, 1955, Lighthill, 1969, Webb & Weihs, 1986).In addition, the anguilliform mode is used by all fish larvae, no matter what mode they eventually use as adults (Osse & van den Boogaart, 2000;Müller & van Leeuwen, 2004;Mauguit et al., 2010a,b).During growth, swimming movements become more sinusoidal, made up of movements having less relative amplitude.The St values do not change with size in larvae but are substantially reduced in juveniles that pass into the intermediate regime flow and have a subcarangiform swimming mode.However, it appears that swimming speed has a strong influence on all parameters studied, regardless of size and morphological development.
Previous studies on the ontogeny of swimming abilities in different fish species concerned only a few larval stages (Batty, 1981(Batty, , 1984;;Fuiman & Webb, 1988, Osse, 1990, Osse & van den Boogaart, 2000;Fontaine et al., 2008;Müller et al., 2008), restricting the accurate comparisons between taxa.The study on zebrafish by Müller et al. (2004) dealt with several larvae stages but none of the different indices used in our studies were used, so comparisons are difficult to make.For this reason, we can only compare our data to the data for Clarias gariepinus and Corydoras aeneus (Mauguit et al., 2010a,b) for which many developmental stages were also studied.
However, the biology of these three species differs in several points that can influence the establishment of swimming behaviour.Dicentrarchus labrax is a marine fish that lives in cold/temperate water.As a consequence, larval seabass were reared in seawater at 15°C.Being subtropical catfish species, larvae of C. gariepinus and C. aeneus were reared in freshwater at 28 and 25°C, respectively (MAUGUIT et al., 2010a,b).The time of hatching after fertilization differs between species; 24h only for C. gariepinus, 72h for C. aeneus (MAUGUIT et al., 2010a,b) and 96h for D. labrax.The temperature and the salinity are both ecological factors that act directly through receptors to increase or decrease growth (BOEUF et al., 2001), while the time between fertilization and hatching can have an effect on the morphological stage of larvae at hatching.The differences between these parameters can, probably, largely explain the differences observed in ontogeny of swimming development in the three species studied.
Figure 4 provides a panel contrasting the main modifications in swimming abilities between the three species that live in two different environments and have different modes of swimming in the adult stage.
At hatching, only C. aeneus has pectoral fins and is the only species to perform sinusoidal swimming (MAUGUIT et al, 2010b).Clarias gariepinus larvae hatch the earliest after fertilization and are unable to perform any swimming at this stage (MAUGUIT et al., 2010a).Dicentrarchus labrax larvae spend the longest time in the egg phase, but live in colder water with higher salinity, which should decrease their developmental, growth rate.At hatching, D. Swimming ontogeny in the seabass labrax cannot perform sinusoidal swimming (r² = 0.77±0.17)(Fig. 4).In various species it has been observed that oscillations in the anterior part of the body during swimming movements in larvae decrease once the pectorals fins appear (Batty, 1981, Osse, 1990, Thorsen et al., 2004).The present study confirms this statement.In D. labrax, pectoral fins appear at 4.93±0.21mm and almost all the body (LM1-LM5) follows a sinusoidal path from a size of 5 mm (Fig. 3A).
A common characteristic in the ontogeny of swimming in the three species is a progressive decrease in the amplitude of movement in the anterior part of the body.The amplitudes of LM1 to LM4 for catfishes and of LM1 to LM5 for the seabass decrease by 50% in the first days after hatching (Fig. 4).This amplitude reduction was earlier thought to explain the change in the St number (MAUGUIT et al. 2010a,b).However, this assumption is not verified in D. labrax (Fig. 4).The St number has mostly been studied in fish moving in an inertial regime (Taylor et al., 2003, Tytell, 2004;Lauder & Tytell, 2006).More recently, studies by BORAZJANI & SOTIROPOULOS (2008, 2009) showed the St number is inversely related to Re values: an Re of 300 (intermediate regime) corresponds to an optimal St number of 1.3, and an Re of 4000 (inertial regime) corresponds to an optimal St of 0.6.This correlation between Re and St is also observed in our results (Fig. 5).The fact that changes in St number are first of all related to changes in Re number could explain why catfish species reach a low St number faster than seabass (Fig. 4).Because catfish species For each species, all morphological changes cited were observed in the fish in the corresponding studies on ontogeny of swimming and not from the literature.The gradual transition between different swimming modes is indicated by bicolour arrows.grow faster, they are able to earlier reach high Re values and the intermediate regime at a cruise speed.Having slower growth, seabass larvae are restricted longer to a small size and to a viscous flow.In this flow, D. labrax larvae need to swim at high frequency (22.85±2.09Hz; n = 63), which decreases their efficiency.Consequently, the major decrease in St does not occur until the first juvenile stage studied (ca 15 mm TL: 960 hPH), corresponding to swimming in an intermediate regime at a cruising speed (Fig. 4).In this regime flow, the total drag decreases, the tail-beat frequency is slower (14.8±10.72Hz; n = 9) and the swimming efficiency improves (St = 0.095±0.04;n = 9).Additionally to the change in regime flow, the ossification of caudal fin rays corresponds to an important decrease in tail-beat frequency and in St number in all the species (Fig. 4).The ossification of the vertebral column and caudal fin increases the stiffness of the body and allows better force transmission (Batty, 1981;Long et al., 1994;McHenry et al., 1995;Hale, 1999).For C. aeneus and D. labrax, this ossification also occurs before the transition in swimming mode, demonstrating that a rigid axis is required for a subcarangiform and carangiform mode.
The swimming speed appears to strongly affect the values of r² mean , CV and St in D. labrax.All larvae swimming at high speed are able to perform a sinusoidal swimming motion (r² mean ≥ 0.95) with a constant motion along the length of the body (CV = 2.45±1.99;n = 13).According to the study by BUDICK & O'MALLEY (2000) on the fast swimming speed in Danio rerio, the ability in larvae to execute very fast movements could be due to a good synchronization of motoneurons firing along the body.This improved synchronization could partially explain the good coordination along the body during fast swimming movements.Larvae also show decreasing St number with increasing swimming speed, which is related to the way the Re number varies.At high speed, Re number increases considerably for swimming larvae.Consequently, total drag decreases and efficiency increases (St number decreases).

CONCLUSION
The gradual establishment of adult swimming movement is not the same between the three species studied, but varies according to morphological development and growth rate.However it does follow the same pattern: 1) they transition from a viscous to an intermediate and then to an inertial flow regime; 2) they begin with an anguilliform swimming mode; 3) for the three species the decrease in tail-beat frequency and in St correspond to an increase in Re and are correlated to ossification of caudal fin rays.
Being a marine fish, D. labrax growth rate is lower than that of the two catfishes.Therefore sea bass larvae stay in low Re values longer and have consequently high St values during their larval period.However the viscous flow regime does not impede the establishment of a sinusoidal movement since stabilization of r² mean and CV occur in this regime.

Fig. 1 .
Fig. 1. -Drawing of a swimming movement executed by a seabass larva (Dicentrarchus labrax).The eight paths made up of different markers represent the trajectory of each landmark (LM1-LM8) during the execution of a complete undulatory swimming movement.The larger symbol of each type indicates the placement of the landmarks on the fish body.
analyzed for each stage.The sample is similar to the ones of the two studies of MAUGUIT et al. (2010a,b) (72 sequences for D. labrax, 93 for C. gariepinus and 73 for C.aeneus).

Fig. 3 .
Fig. 3. -A.Representation of four stages: three larval and one juvenile.The eight landmarks used in the analysis of the swimming movement are indicated on the midline of each fish.White landmarks indicate that all fish from the size indicated reached at least a value of 0.95 for the corresponding r².B. Midline kinematics of seabass (Dicentrarchus labrax) larvae and juveniles during cyclic swimming at different stages of ontogeny.The superimposed midlines (time step 4 ms) of one tail-beat cycle show the amplitude envelope of the body wave.Each amplitude envelope corresponds to the fish represented by the black shape.The amplitude is expressed as a proportion of total fish length (TL), the x axis representing the total fish length in percentage.

Fig. 4 .
Fig. 4. -Major steps in the swimming ontogeny in Clarias gariepinus, in Corydoras aeneus and in Dicentrarchus labrax.The data on the catfishes are obtained from the studies of Mauguit et al; (2010a,b).The acquisition of sinusoidal swimming, the evolution of St values and the changes in swimming mode are expressed in relation to age, size, regime flow and morphological changes in the three species.For D. labrax, the transition between the viscous and the intermediate regime is lacking.For each species, all morphological changes cited were observed in the fish in the corresponding studies on ontogeny of swimming and not from the literature.The gradual transition between different swimming modes is indicated by bicolour arrows.

Fig. 5 .
Fig. 5. -Correlation between St and Re values in Clarias gariepinus (in white), Corydoras aeneus (in dark grey) and Dicentrarchus labrax (in light grey).The x axis is presented in log 10 .The values of the correlation (R) are indicated.
Damien Olivier, Quentin Mauguit, NicolasVandewalle & Eric Parmentier Swimming ontogeny in the seabass (Borazjani & Sotiropoulos, 2008, 2009)il is flapping relative to how fast the fish is swimming.The value of this index is dependent on the Re values(Borazjani & Sotiropoulos, 2008, 2009).For adult fish whose correspondingU -1