The Campeche Bank is located within the ecoregion of the Southern Gulf of Mexico and extends between 19˚23'N and 89˚93'W in the southern Gulf of Mexico. This region is the natural habitat of L. campechanus (Poey, 1860), being characterized by bottoms that have a bed suitable for the development of reef and rocky benthic communities, which are appropriate for the settlement of this species [23] (Figure 1).

Between January and February of 2015 (northerly winds season), a total of 194 specimens with sizes ranging from 3 to 30 cm in standard length (SL) were purchased from commercial fleet that holds commercial permits and follows the guidelines established by the Mexican Regulations Fisheries NOM-002-PESC-2013 and by the National Fisheries Chart (DOF 15/03/04) and (SNFA/034/12). These permits are issued every two years by SAGARPA (Secretaria de Agricultura, Ganadería, Desarrollo Rural, Pesca y Alimentación) (https://www.inapesca.gob.mx/), based on their commercial catch. Juvenile red snappers were collected by shrimp trawls, whereas adults (larger than 20 cm SL) were collected with hand lines; organisms were purchased dead, maintained horizontally and kept in containers with ice until their arrival to the laboratory, where they were maintained at -20^◦C for the subsequent analyses.

The specimens were separated into 6 size classes: CL0: 3.0 - 4.9 cm (20 organisms), CL1: 5.0 - 9.9 cm (35 organisms), CL2: 10.0 - 14.9 cm (31 organisms) CL3: 15.0 - 19.9 cm (32 organisms), CL4: 20.0 - 24.9 cm (40 organisms) and CL5: 25.0 - 29.9 cm (35 organisms). The CL0, CL1, and CL2 classes corresponded to pre-recruits and early juveniles, while CL3, CL4, and CL5 classes included juveniles larger than 15 cm, pre-adults and adults (individuals that had reached the size of their first sexual maturity) [21].

Each specimen was photographed from its left side using a digital Olympus camera, with a resolution of 12.4 megapixels and macro option. The tripod was 50 cm distant from the baseboard and the camera was attached to a sliding arm to control the distance. The baseboard was covered with black plastic (ethylene vinyl acetate), to avoid the light reflexion and the presence of shadows.

The morphometric analyses were carried out based on a series of landmarks (LM) and sliding reference points (i.e. semi-landmarks: SLM), defined as the whole fish and the dorsal head profile (DHP) respectively. The selection of the appropriate LM was carried out based on the typology proposed by Bookstein [24], these correspond to types 1 and 2 and the SML to type 3. The final points consisted of 18 homologous points arranged along the fish’s body (points 1 - 18), and 21 SML (points 19 - 39) along the curvature of the DHP (Figure 2(A) & Figure 2(B)).

The program MakeFan6 was used to position the semi-landmarks SML equidistantly along the DHP [25]. Homologous landmark 1, 2 and three were used supporting points to draw a fan on the cranial region; these corresponded to the most distal point of the upper jaw, from the first spine of the dorsal fin up to the most distal point of the operculum. TPS files were generated using the software tpsUtil 1.58 [26]. Landmarks and SML were digitalized using the program tpsDig 2.16 [27]. Analysis of the LM data allowed the quantification of the changes in

shape and direction throughout the development [8], for this, a non-parametric analysis and a morphometric-type exploratory analysis was performed.

The LM configurations were superimposed using the Generalized Procrustes Analysis (GPA) [28] [29]. The centroid and the effects due to the location, scale, and orientation of each of them were determined and removed using the Procrustes superimposition method of generalized least squares (GLS) [14]. These methods were used to record the LM configurations in a coordinate system that then is used as geometric variables [30]. The remaining differences in their location within the coordinate system were attributed to variation in shape. All data acquired were used as input data in the multivariate analysis.

The spline relaxation technique was also used to know if there was any change over the bowing on DHP at the same time of the development of the body: this procedure expands on the standard Procrustes superimposition method (GLS). The SML are slid along the curve of the profile until the positions of the corresponding points match as a reference configuration as closely as possible [31]. This analysis is called Relative Warp Analysis (RWA), and minimum Procrustes distance criterion was used. The Bookstein algorithm [24] was used, and then the points were slid along the tangent to the curve with 40 iterations. An alpha = 1 was used because the allometric effects tend to be large-scale [32]. After relaxation, the SLM were treated as if they were homologous reference points in the multivariate analysis [4].

After sliding, the Procrustes superimposition was recalculated to eliminate the information based on the original coordinates. This procedure was performed to standardize each specimen to a unit centroid size (CS: is a measure of geometric scale, defined as the square root of the sum of the squared distances of each reference point) [33]. The coordinates of all the aligned specimens were compared using the TPS function as a deformation method. In this way, the partial warps and their principal components or relative warps were calculated. The CS was obtained from this analysis, which represents a dispersion measure of LM around of the centroid. Further, a Principal Components Analysis (PCA) was performed on the weight matrix obtained from the RWA to examine the major trends of body shape variation.

Deformation grids were also obtained using a thin-plate spline analysis. This grid graphically described the variation between specimens by using the morphology of all the specimens to obtain an average shape where the position of the landmarks was compared, and the differences were represented as a deformed grid. Then changes in DHP shape were visualized to observe possible modifications in its curvature during fish development. These deformations were exaggerated three times to have a better perception of the morphological differences between classes. These analyses were performed in the tpsSpline 1.20 [34] and the tpsRelw 1.49 programs [35].

To evaluate the influence of size on shape, we performed a correlation analysis using the standard length against the CS (untransformed). The correlation value was r² = 0.999 (p < 0.001), and the centroid was used as a proxy in all the subsequent analyses.

The differences between classes as a possible consequence of the change in the coordinates set during fish growth were evaluated by a one-way PERMANCOVA (999 permutations) performed over a Euclidean distance matrix (after log-transformation of the CS data). The partial warp scores generated for the Relative Warp Analysis were considered as variables, the logarithm of the centroid (LogCS) and SL were included as covariates and the classes as fixed factor. The CS is often used as a covariate in the morphometric analysis to consider the possible allometric effect of a size that is not explained by the scaling function of Procrustes superimposition [36]. This analysis was performed in the R package.

The morphological integration between different regions of the body was evaluated using the “two-block Partial Least Square” (2B-PLS) analysis to establish the covariation of shape along the body among various modules. This procedure was performed using the tpsPLS program [37] creating pairs of variables, which are linear combinations of the original data of each block [18]. This test was also used to determine the combination of variables, in the two sets, that explained the highest covariation between them. The 2B-PLS analyses the variables of both modules symmetrically [i.e. it is not assumed that one set causes the other, that they are linearly related to one another, reflecting the responses of the underlying (unobserved) or latent variables] [4]. The correlation coefficient “r” can be used as a measure of integration between the sets [15] [38]. The statistical validation for the 2B-PLS analyses was performed through a bootstrap test of 9999 permutations to determine whether the unique values produced were consistent with the null hypothesis of no significant covariance in the patterns between sets.

Modularity was evaluated using the CR coefficient (the covariance ratio) to verify the consistency of the results of the analysis of integration achieved by the singular warps analysis [39]. The CR coefficient is not affected by the sample size, or the number of variables (LM). Before the analyses, data were aligned using the Generalized Procrustes Analysis (GPA).Both indices range between 0 to 1 value, where 0 indicates the independence between modules and, therefore, the presence of modularity; and 1 implies a process of integrated development. 999 iterations were used to evaluate the level of significance during the procedure of permutations. Both analyses were performed in the R package Geomorph [40].

During growth, fish evolve hydrodynamic skills to guarantee survival at every stage of their life. They swim either using the body and the caudal fin, or a combination of the dorsal-anal fins and the pelvic-pectoral fins [41]. The body shape grows from a slender shape in the larval stage into a streamlined adult to provide very little resistance to the flow of water and to optimize its performance [42]. Based on these premises; the body of L. campechanus were partitioned in three modules: head (HD), trunk (TR), and tail (TL) to assess their modularity by growth and by class (Table 1). Each block landmarks were selected based on the same homology criteria; all points should be observed in the distinct stages of development to describe the transition from juveniles to reproductive adults.

The outcomes of this study represented a quantitative assessment of the shape of L. campechanus that provide more information on their morphometrics analysis. The sliding semi land-marks technique was used to explain changes in homologous anatomical loci with emphasis on the processes that modify the DHP curve during growth as a way of explaining the streamlined swimming ability that they experience during the distinct stages of their cycle.

During growth, the juveniles must achieve a high survival rate, and this process requires compensatory allometric changes in size so that functional abilities can be maintained until fish reach adult size [43]. The increase in fish size influences dramatically the performance in certain fundamental aspects of the interaction between the individual and the environment. Without these changes, the ability of adults to perform certain tasks, such as swimming, may be affected unless the initial performance levels are high enough to absorb reductions in their size-related skills [47]. In L. campechanus, the RWA showed a continuous distribution of specimens along the two principal axes. Samples that were either very positive or very negative along RW2 have a strong influence on the allocation of the values of the evaluated traits and revealed contrasts in shape related to the length and depth of the body for the size classes. The negative values along both axes corresponded to smaller size classes (CL0, CL1, and CL2), whereas the positive values corresponded to classes with an SL that exceeded 15 cm. The specimens were equally distributed across the suggested size classes; hence the plot suggested that there was no clear size structuring in the populations from the catching site.

Lutjanidae family have both positive and negative allometric development [48] [49]. Mbaru et al. [48], Gómez et al. [50] and Manickchand-Heileman & Phillip [51] reported almost isometric growth in L. bohar, L. vivanus, and L. purpureus respectively. In its early larval stage, L. campechanus (Poey, 1860) has an allometric growth pattern, regarding to length of trunk on the standard length [52], allowing a faster development of the structures needed for feeding and locomotion [53] [54]. This could explain that the head showed great variations in the LM trajectories and tail of the smallest SL size classes (CL0, CL1, and CL2). In these groups, they are still growing, and their main functions are feeding and avoiding predation. The deformation grid of the thin plate analysis for each size class showed that the first three size classes had the most compelling changes in the head and caudal peduncle. It has been estimated that in larvae, the head can comprise up to 45% of the body length [55], a proportion that progressively decreases with growth.

All the variations experienced by L. campechanus (Poey, 1860) reflected a growth pattern like that found in the common carp [53]. These differential trends determine the size-shape relationship during ontogeny. When shape and size are linked by an allometric-type relationship, a change in size corresponds linearly to a change in shape [5]. An in theory, sizes larger than 50 cm SL of growth becomes almost isometric [56].

Some fish use distinct parts of the body during swimming related activities like predator evasion, prey capture and navigation in structurally complex environments [57]. The hydrodynamics of the environment influence partially the shape of fishes; for example, macro carnivores have kept fusiform shapes enabling them to have less friction with the water to have a greater and faster displacement, and the environment that fishes face depends on the individual size, the speed at which it moves, and the physical properties of the water itself (viscosity and density) [58] [59]. During ontogeny, fishes regime changes on the environment, because they get bigger and faster, and the relationship between inertia and viscosity change as they develop, altering their swimming behavior [42] [58] [59], which will affect the ability to escape predators [60].

The types of forces acting on a moving fish differ according to the hydrodynamic regime. The Reynolds number is used as an index to identify the hydrodynamic regimes experienced by the fish: Re = UL/v, where U and L are the velocity and length of the fish and v are the kinematic viscosity of the water [61]. The regime of inertial forces dominates when Re > 200 (inertial regime), however, viscous forces prevail when Re > 1 (viscous regime) and are significant for larvae up to Re = 30. At 30 < Re < 200 an intermediate zone is estimated, in which the balance between the two forces is gradually displaced from a viscous liquid to an inertial regime. Borazjani & Sotiropoulos [62] found that at low Re the larvae present greater fluctuations in swimming speed than adult fish; their results demonstrate that all fish swam more efficiently if they had a body shape or swimming style suitable to the speeds at which they swam. The fish swimming speed leads to rates of hydrodynamic forces that will influence the body shape and swimming style in subsequent stages favoring the balance between swimming bursts, needed for a rapid response to predation events during the youngest stage and the swimming sustained. These features are essential for activities such as foraging or searching for a mate in adult stages [36] [63] [64] [65].

In early stages (early juveniles and juveniles), L. campechanus (Poey, 1860) specimens had arge heads ending in a slightly pointed forehead and more sleek bodies when compared to adult shapes [21] [58]. This could explain the displacement paths observed in the thin plate analysis because the allometric growth influence over the variables of shape was detected with the PERMANCOVA analysis. In this case, the LogCS covariate explained a high percentage of variance on the effect of increase between classes. These changes in shape occurred mainly in the profile of the face and the structures of the head, in which the SLM undergo necessary changes in position on the anterior and dorsoventral axes of the body. The changes in shape reflected the transition from early juvenile to adult involving these regions, confirming the general findings reported in the RWA.

Modularity is the partitioning of the integration into evolutionarily or developmentally independent blocks of traits. Sizes and shapes of the body (or their parts) vary in a coordinated manner as a whole functional group [15]. This process is measured by statistical associations between traits [66]. The structure of these associations reflects the processes that affect certain traits but not others. These are covariance-generating processes that influence the patterns of morphological integration [67] that can be modified by mutations, by development dynamics or by environmental processes.

The study of ontogenetic morphological development in fish was based on the study of allometric models of three different regions detected along the anterior caudal axis: head, trunk, and tail [2] [53] [68]. According to our results and the configuration proposed herein, L. campechanus (Poey, 1860) has a modular conformation during growth. The greatest covariance between the modules was explained by SA1, although there were no significant differences between values, there were slight differences in growth outlines along the anteroposterior axis. The correlation value between the head and the trunk indicated that these modules maintained a slight synchrony in the development process; a large head corresponding to a deep trunk and this proportion is clearer in larger sizes.

In this study, a certain pattern of morphological integration between the head and trunk was observed, although this relationship was not strictly linear. The development of the tail was modular and independent from the other blocks. The head and the tail developed before the trunk of the body, and increases in depth quite late in development, this because of a possible adaptation to reduce transporting costs [54].

Genetic or environmental factors could also affect development of larvae but may have minor impact on trunk depth. Therefore, if development time explains integration, we could anticipate a greater correlation between parts that develop at the same time [4]. According to Klingenberg [16], the skull is designed to overcome mechanical forces produced during chewing, capture and processing of prey, respiration, and vocalization. In this sense, Osse et al. [53] demonstrated that during initial stages, feeding is a vital process that governs the speed of growth (positive allometric) of the head and all related structures.

The morphological development of larvae seems to be a process in which modularity and integration are two basic strategies [69]. The rate of development could contribute to the ontogenetic patterns detected by variance and integration; i.e. a high variance and low integration would be expected in smaller size classes, and a decrease in variance and increase in integration would be expected in mature individuals [67]. Pressure, friction, and resistance to movement are factors that highly depend on shape, because of isometric scaling and increase in mass. Acceleration during bursts and fast-starts may decrease due to an increase in size [70] [71]. However, Gibb et al. [59] found that escape performance improved with the development of adult morphology; hence, fish that enter the environment in an advanced development phase should have a greater ability to evade predators than those that enter during an early stage of development. Antonucci et al. [72] concluded that in adults the shape of apex predators is similar to the “BCF-transient” type proposed by Webb [73] since they can display a fast start, powerful turns, and powerful propulsion. Propulsion is provided by a long and narrow caudal peduncle. Evolution of uncoupled locomotive systems was an important factor underlying the adaptive radiation of teleosts [74].

The relative importance of the caudal module depth can depend on the context of the predator-prey interaction. The lutjanids are an opportunistic species that belongs to the mid- and top predator category focusing on slow-moving prey (crabs, shrimp & small fish). Adults L. campechanus (Poey, 1860) have few predators and their body are elevated depth, narrow caudal peduncle and small eyes [72]. The adult organisms are associated with depressions and high relief structures such as reefs and rocks [21]. During developmental stage, they do not move far from their settlement site [75]. This type of predatory behavior and lifestyle are the reason behind a body shape that is better adapted to sustained and prolonged swimming during its adult stage.

Finally, the size range used in this study was limited to the scale of the first sexual maturity, which is why the effects of variation between the last two classes were not observed. Morphological design for each stage of development reflects a correspondence where performance is optimized according to environmental conditions where they inhabit. In juveniles living in soft bottoms or low shallow areas of open water (<24 m), with moderate to strong currents, the structural complexity is minimal. Its fusiform shape could confer them certain ecological advantages, such as stability in swimming and fast-start performance that would increase their rate of survival in fast moving waters and high exposure to predators. The largest classes live associated with rocks or coral reefs in environments that are steadier; its body shape is deeper and robust designed for sustained swimming necessary for the switch to a more sedentary lifestyle. In future studies, it would be desirable to supplement this information including larger specimens (i.e. above 50 cm SL), a size at which this species continues to grow only isometrically [56].