Median fin function during the escape response of bluegill sunfish (Lepomis macrochirus). II: Fin-ray curvature

Ray-finned fishes (Actinopterygii) derive their name from the bony supports within each membranous paired or median fin. Each fin ray, or lepidotrich, is a segmented bilaminar structure capable of bending and twisting in response to external fluid forces or internal muscular actuation (Alben et al., 2007; Arita, 1971; Geerlink and Videler, 1986; Lauder et al., 2011). Although it is the fin rays that may be actively controlled by the fish, the fin rays by themselves do not define the fin; the membrane connecting the bony supports plays an integral role by providing both surface and tensile resistance that creates the ‘fan’ of the fin. Individual fin rays may curve, or move laterally or sagittally; such movements of the many fin rays within each fin interact with the flexible membrane, throwing the surface of the ‘fan’ into complex configurations. Actinopterygian fins are thus flexible structures that interact with the surrounding flow as dynamic curved surfaces (Lauder et al., 2006; Walker, 2004; Walker and Westneat, 2002). Understanding the complex interplay between fin shape and motion during locomotion will provide new insight into the hydrodynamic roles of the fins as control surfaces (Lauder and Drucker, 2004). Therefore, it is essential to quantify fin curvature as well as the motions of individual fin rays (Chadwell et al., 2012) to understand how fins may function.

Although the flexibility of the fins has been well documented (Blake, 1981; Breder, 1926; Lauder, 2006; Osburn, 1906), most recent studies have focused on experimental and computational analysis of fin hydrodynamics, with little emphasis on the individual fin-ray kinematics and curvature (Epps and Techet, 2007; Lauder et al., 2006; Mittal et al., 2006; Tytell and Lauder, 2008). Currently, we know of only two studies that have measured the curvature of individual fin rays during locomotion [dorsal and anal fins of bluegill sunfish (Standen and Lauder, 2005), pectoral fins of longhorn sculpin (Taft et al., 2008)]. However, in both of these studies, curvature was measured only along the length of the fin rays, irrespective of the fin surface. Additionally, the curvature was measured at a single time point of the swimming behavior, providing no information of how the curvature changed over time.

Based on morphological variation among the fin rays of the dorsal and anal fins (Chadwell and Ashley-Ross, 2012), we would expect variation in the potential for curvature as well. Curvature of an individual fin ray is the sum total of bending at the joints between segments of the hemitrichia, and sliding of the individual hemitrichs relative to their long axis (Alben et al., 2007; Geerlink and Videler, 1986; Lauder et al., 2011); therefore, rays with a greater proportion of their total length devoted to segments, and looser connection between the two hemitrichia, should be capable of greater maximum curvature. In both the soft dorsal and anal fins of bluegill, isolated posterior rays demonstrate more segmentation, and looser connection between hemitrichia, than isolated anterior rays (Chadwell and Ashley-Ross, 2012). Therefore, we expect greater capacity for curvature along the length of the rays in the posterior regions of the fins, because of both morphological differences in the rays themselves as well as less constraint (i.e. lack of connection with stiff spines) on movement of the posterior fin.

Three-dimensional (3-D) kinematic analysis of the rays and spines of the dorsal and anal fins revealed variation in movement and orientation based on position within the fin, suggesting that different regions of the fins were playing distinct roles during the escape response in bluegill (Chadwell et al., 2012). Visual analysis of videos shows that fin surface shape is influenced not just by the changing orientation of the fin rays through time, but also by the curvature within, among and between the fin rays (Fig. 1). This paper examines the spanwise and chordwise curvature of the soft dorsal and anal fin surfaces during the performance of the C-start escape response of bluegill sunfish (Lepomis macrochirus). We describe patterns of fin surface curvatures to address two specific questions. First, does fin-ray curvature vary based on position within the fin, as predicted by morphological variation (Chadwell and Ashley-Ross, 2012)? We expect the more flexible posterior rays of the fin to be more susceptible to curvature than the stiffer fin rays of the anterior region. Second, do the kinematic patterns of fin-ray curvature support the hypothesis that the fins are actively resisting opposing hydrodynamic forces during the C-start [as suggested by electromyographic (EMG) data on inclinator muscle activity (Jayne et al., 1996)] and contributing to the thrust forces generated by the fish? If so, we expect the fin surface to exhibit periods where it actively curves into the flow.

We show that the curvature patterns in both soft dorsal and anal fins conform to our expectations based on morphology. Further, the fin surface does behave in a manner consistent with resisting hydrodynamic forces. Complex undulations of the fin surface appear to accelerate water towards the tail, potentially increasing thrust generated during the C-start.

Bluegill sunfish, Lepomis macrochirus Rafinesque 1819, collected from seined ponds near Concord, MA, USA, were maintained in individual 40 liter aquaria on a 12 h:12 h light:dark photoperiod at a mean water temperature of 20°C (±1°C). The specimens (16–19 cm total length) used in the present study were the same as those examined in the companion paper on 3-D movements and orientation of the dorsal and anal fin spines and rays (Chadwell et al., 2012). In this paper, the term ‘fin ray’ is used to refer to all external skeletal fin supports when the distinction between spines and rays is disregarded.

Detailed analysis of fin ray curvatures was performed on the same video sequences as used in the companion paper (Chadwell et al., 2012). Three synchronized high-speed, high-resolution cameras at 500 frames s⁻¹ recorded the C-start escape response from a dorsal, ventral and lateral position as the fish maintained a position in the center of the flow tank. Video images from the three cameras were oriented and calibrated for 3-D digitization using a direct linear transformation algorithm (Reinschmidt and van den Bogert, 1997) following a previously described procedure (Standen and Lauder, 2005), and analyzed in the custom digitizing program DigiMat, written by Peter Madden.

Axial kinematics were used to determine the metrics of the C-start, e.g. onset of the C-start, timing of Stage 1 (S1) and Stage 2 (S2), turning rates of the body segments associated with the median fins [see fig. 1 in Chadwell et al. (Chadwell et al., 2012)] and the estimated stretched-straight center of mass (ssCOM) movement throughout the duration of the digitized sequences. In two of the nine sequences, the initial C-bend was to the left. To simplify the comparison between the sequences, these sequences were converted to right-handed C-starts by reversing the sign of the y-coordinates.

The surfaces of the two median fins at each time point of the escape response were reconstructed as in the companion paper (Chadwell et al., 2012). The four to six points digitized from the selected fin rays [see fig. 1 in Chadwell et al. (Chadwell et al., 2012)] were fit to a cubic smoothing spline with a mean square error of ca. 0.1 mm³ (Walker, 1998) and 21 equally spaced points along each fin ray were interpolated. The 21 interpolated points from all fin rays of a fin were fit to a bivariate tensor function (Kreyszig, 1991). From this function, we could determine at each point along the lengths of individual fin rays: (1) the orientation of the three axes of the fin ray – span, chord and lateral (Fig. 1C) [also see figs 1, 2 in Chadwell et al. (Chadwell et al., 2012)] – and (2) the absolute spanwise and chordwise curvature values, where absolute spanwise curvature is the fin surface curvature along the length of the fin ray, i.e. the span axis (synonymous with fin ray curvature reported in Standen and Lauder, 2005; Taft et al., 2008), and absolute chordwise curvature is fin surface curvature perpendicular to the long axis of the fin rays, i.e. the chord axis. It is important to note that because of the changing elevations of the fin rays with longitudinal position in the fins [see figs 1, 2 in Chadwell et al. (Chadwell et al., 2012)], spanwise and chordwise curvature are not aligned with the transverse (or longitudinal) axis of the fish's body. Details of the calculations and nomenclature are found in the  Appendix.

Previous studies that have examined fin-ray curvature (Standen and Lauder, 2005; Taft et al., 2008) have focused on the absolute spanwise curvature, i.e. bending along the axis of the skeletal supports of the fin. Although absolute spanwise curvature alone provides a measure of the configuration of the fin ray in 3-D space, it fails to provide important information about the direction of the curvature relative to the fin surface for several reasons. First, the values reported do not indicate to which side of the fin surface the curvature is oriented. Second, the spanwise curvature reveals nothing about the interaction among the neighboring rays and the resulting chordwise deformation of the fin surface. Third, these measures invariably include curvature of the rays parallel to, i.e. within, the fin surface, which would introduce confounding results. For example, if the fin were to lie completely flat with the entire surface confined to a single plane, the natural bending of a ray within the plane of the fin (i.e. within the fin membrane itself) would produce spanwise curvature values, though such curvature would not represent functionally meaningful deformation of the fin surface.

To address these issues in our analysis, the absolute spanwise and chordwise curvatures at each point of the fin rays were decomposed into their parallel and perpendicular components relative to the lateral axis, i.e. normal to the fin surface, analogous to decomposing 3-D velocity into its horizontal and vertical components. For the remainder of this paper, spanwise or chordwise curvatures (κ_span and κ_chord, respectively) will refer only to the components perpendicular to the fin surface. The sign of curvature denotes the direction, relative to the fin surface, with a positive value indicating the concavity faces towards the right of the fin (and the fish) and a negative value indicating left-facing concavity. This technique thus allows us to determine the magnitude and direction of κ_span and κ_chord along the length of a fin ray, and track changes in those values over time, as the fish performs all the stages of a C-start.

As the curvature of the spines of the spiny dorsal fin was negligible, only the fin-ray supports of the soft dorsal and anal fins were analyzed. The anterior-most support of the soft regions of the dorsal and anal fins are the last spines of the fins, DSp10 and ASp3, respectively [see fig. 1 in Chadwell et al. (Chadwell et al., 2012)], and were included in the analyses of the soft dorsal (sfD) and soft anal (sfA) fins. To simplify the incongruity of their numbering, the two spines will be referred to as DSp0 and ASp0. When referring to the fin rays of both dorsal and anal fins collectively, they will be referred to as Sp0, Ry2, Ry5, Ry8 and Ry12. When using a cubic spline, the curvature returned for the end points of a curve is zero; therefore, the final rays of sfD and sfA (DRy12 and ARy12) were excluded from the analysis of chordwise curvature as the chordwise curvature of those fin rays were zero at every position.

Each fin ray is capable of independent movement by its intrinsic musculature; however, the connection between neighboring fin rays by the fin membrane likely contributes to the resulting curvature of the fin ray. Therefore, position effects within sfD and sfA were tested using Friedman's method for randomized blocks (χ²), using each fish as a block and the fin rays within each group as the treatment levels (Sokal and Rohlf, 1981; Zar, 1984). Bias from pseudo-replication caused by the use of multiple C-start sequences from each fish was avoided by calculating the average values of each kinematic variable, which was ranked between fin rays for each group. Position effect was tested in the average timing and magnitude of the fin ray using the ranked averages from each of the three fish. Additionally, the position effect on the maximal curvature was tested using the ranked maximum curvature achieved by each fin ray (Chadwell et al., 2012). Kendall's coefficient of concordance (W) was calculated to evaluate the degree of concordance between fish (Sokal and Rohlf, 1981; Zar, 1984). Finally, for variables in which a significant position effect was found in both sfD and sfA, a multigroup coefficient of concordance () was calculated to test whether the position effect was conserved between the two groups (Zar, 1984).

Friedman's χ², Kendall's W and their associated P-values were calculated using SPSS v16.0 (IBM, Armonk, NY, USA). A custom program, based on the equations of Zar (Zar, 1984), was written in MATLAB (MathWorks, Natick, MA, USA) to calculate and its Z-score. To control for Type I errors resulting from multiple comparisons of the 15 variables of each fin group, P-values were compared with corrected α-levels using a sequential Bonferroni adjustment (Rice, 1989).

Axial movements during the C-start have been described in the companion paper and were shown to be consistent across the three fish analyzed (Chadwell et al., 2012). The curvature parameters of the five fin rays by fish for each fin group can be found in the supplemental material: data for sfD are in supplementary material Table S1 and data for sfA are in supplementary material Table S2.

Within 8–10 ms from the onset of the C-start (T₀) and rotation towards the right by the mid-trunk (Mid), a curvature towards the right, in the direction of the oncoming water flow, began to develop in the proximal region of the posterior fin rays that increased in magnitude as it moved distally along the ray over time (Figs 2, 3).

However, the curving of the fin into the flow of water was short lived; at 12–14 ms from T₀, the proximal regions of the rays began to bend to the left as the mid-trunk rotation to the right slowed down. The curvature also increased in magnitude as it moved distally along the ray over time. During the rotational transition from S1 to S2, a transient S-curve formed along the length of several rays, with ray curvature in the proximal region directed to the left at the same time as the distal region of the ray curved to the right (Figs 2, 3). This S-curve is observable in still images from the video sequence (Fig. 1A) and the digital reconstruction of the fins (supplementary material Movie 1).

A third spanwise curvature of the fin rays, directed to the right, occurred as the turning rate of the mid-trunk to the left increased during S2 (18–50 ms after T₀), as Mid rotated to the left. This curvature towards the right appeared first in the proximal region of the fin rays and traveled distally along the ray lengths, but magnitude of maximum curvature was approximately equal along the fin-ray lengths (Figs 2, 3).

The degree of curvature and variation between fin rays and along the ray lengths appeared greater during S1 and the S1/S2 transition than during S2 (Figs 2, 3 and 4). For both sfD and sfA, all three maximum κ_span values increased among the posterior fin rays (Fig. 4). In both fins, a significant position effect was found for mean and maximal κ_span0 but not for κ_span1; for mean κ_span2, a significant position effect was found only for sfA (sfD mean and max. κ_span0: both W=0.91, χ²=10.93, P=0.003; mean κ_span1: W=0.80, χ²=9.60, P=0.017; max. κ_span1: W=0.82, χ²=9.87, P=0.015; Table 1; sfA mean κ_span0: W=0.96, χ²=11.47, P=0.001; max. κ_span0: W=1.00, χ²=12.00, P=0.000; mean and max. κ_span1: W=0.82, χ²=9.87, P=0.015; Table 2). Δtκ_span0 was nearly synchronous with the time of maximum turning rate of the Mid-trunk, with Δtκ_span1 occurring shortly afterward (Fig. 4A,C). Δtκ_span2 occurred shortly before Mid reached its maximum turning rate to the left (Fig. 4E). Position effects were not found in any time parameter (sfD Δtκ_span0: W=0.56, χ²=6.67, P=0.163; Δtκ_span1: W=0.82, χ²=9.87, P=0.015; Δtκ_span2: W=0.47, χ²=5.60, P=0.253; Table 1; sfA Δtκ_span0: W=0.49, χ²=5.87, P=0.236; Δtκ_span1: W=0.56, χ²=6.67, P=0.163; Δtκ_span2: W=0.31, χ²=3.73, P=0.493; Table 2).

Over the course of the C-start, the greatest spanwise curvatures, in either direction, typically occurred during the rotational transition of the mid-trunk (14–26 ms), as the turning rate to the right decreased and changed direction to the left (Figs 2, 4). It is also during this time that many of the rays developed an S-curve as the proximal and distal regions curved in opposite directions (Fig. 1A, Figs 2, 3).

Unlike spanwise curvature, chordwise curvature along the length of the fin rays was generally uniform, with only an occasional change in direction (Figs 5, 6, supplementary material Movie 2). Instead, changes in the direction of chordwise curvature typically occurred between rays, particularly between Sp0 and Ry2. Alternating changes in chordwise curvature between fin rays indicates an S-curve in the chord length of the fins (Figs 5, 6), which can be seen in the still images from the video sequence (Fig. 1B) and the digital reconstruction (supplementary material Movie 2).

During S1 rotation of the Mid-trunk to the right, chordwise curvature of the anterior fin surface was directed towards the left. The time of maximum chordwise curvature towards the left (Δtκ_chord1) was nearly synchronous with the rotational transition of the mid-trunk, , with the greatest curvature occurring at Ry2 (Fig. 7A,B). A significant position effect was found only for maximal κ_chord1 of sfA (W=0.98, χ²=8.79, P=0.004; all other variables were non-significant after Bonferroni correction; Tables 1, 2).

As the mid-trunk rotated to the left during S2, the chord surface was curved to the right (Fig. 7C,D). The time of maximum chordwise curvature to the right (Δtκ_chord2) followed , as the Mid-trunk began its rotation to the left, with κ_chord2 more uniform among the fin rays (Fig. 7C,D). No significant position effects were found for either sfD or sfA (Tables 1, 2).

As with the spanwise curvature, the location of maximum chordwise curvature changed over time, moving posteriorly along the chord of the fin, indicating a traveling wave of chordwise curvature.

Of the 15 curvature parameters, significant position effects in both sfA and sfD were found only for mean and maximal κ_span0 (Tables 1, 2), both of which showed a significant degree of concordance between sfD and sfA (≥0.8, Z≥4.8, P<0.0001).

The dorsal and anal fins of bluegill are integral to the performance of the C-start, moving in patterns that suggest an active role in interacting with the surrounding fluid. Regions of the median fins differ in their mobility and flexibility, which we suggest affects their function in the escape response. Understanding how the median fins contribute to the C-start necessitates combining data regarding movements of the axial body and individual fin rays with measures of fin curvature. Detailed fin kinematics may be subsequently correlated with EMG and hydrodynamic data to suggest the function of median fins during the escape response.

The escape response is traditionally broken down into two consistent stages (S1 and S2) and one variable stage (S3), plus transitions between those stages, based on movements of the rostrum (Domenici and Blake, 1997; Wakeling, 2001). Changes in fin configuration follow the major kinematic events described for the body, with consistent patterns for S1, the S1/S2 transition and S2.

At T₀, the dorsal and anal fins are typically partially splayed and in line with the sagittal midline of the body. Curvature values are uniformly low in both span and chord axes (Figs 2, 3, 5, 6). Little movement of the fins occurs until approximately one-third of the way through S1, when the soft fin rays begin a sweep to the left [see fig. 9 in Chadwell et al. (Chadwell et al., 2012)], as if they were being moved passively by the resistance of the water. However, there is reason to suspect that the fin rays are not simply passive structures; spanwise curvature of the rays is to the right, into the flow, as if the fin ray musculature were contracting and causing the ray to bend through differential sliding of the hemitrichia (Alben et al., 2007; Lauder et al., 2011). These observations match the EMG patterns of the dorsal inclinators of bluegill sunfish during a C-start (Jayne et al., 1996), which have been shown to induce fin-ray curvature to the same side of activity (Arita, 1971; Geerlink and Videler, 1986). At the onset of the C-start, a brief period of activity in the dorsal inclinator muscles, ipsilateral to the initial C-bend, was synchronous with activity in the axial musculature. The initial spanwise curvature of the fin rays to the right coincides with this activity, and supports the hypothesis that the fins are actively resisting opposing forces. The little chordwise curvature that occurs, cupping the fin towards the right into the flow, may simply be the result of axial curvature of the body, rather than movement of the fins per se.

In the latter half of S1, as the Mid-trunk is slowing down (i.e. after ; Figs 2, 3, 5, 6), the rays of the soft fins sweep in the opposite direction, i.e. towards the right [see fig. 9 in Chadwell et al. (Chadwell et al., 2012)]. At the same time, magnitudes of both spanwise and chordwise curvature increased, but in complex ways. In general, the posterior regions of the soft fins (e.g. rays 8–12) are the least constrained by the connection both between hemitrichia and with neighboring rays, and thus tend to show more multidirectional curvature patterns. For example, examination of Figs 2, 3 and Fig.8C,D reveals that individual rays are thrown into S-curves [DRy8 and ARy12 are the most extreme examples; at 12–20 ms, they are curved strongly towards one side in the proximal portions, with (sometimes multiple) curves towards the other side in the distal regions]. Likewise, Fig. 5 shows that at the same time points, chordwise curvature undulates along the length of the fin as a whole (left curvature at DSp0, right at DRy2, left at DRy5, and then right again at DRy8), with the greatest magnitude at the distal ends of the rays. In both spanwise and chordwise directions, curvature of the fin surface propagates along the length of the rays (curvature along the axis of the individual rays; diagonal progression of color regions within panels in Figs 2, 3) and the chord of the fin (curvature normal to the span axis of the individual rays; diagonal progression of color regions between panels in Figs 5, 6), setting up the global undulation of the fin that will shed vortices during S2.

At the time of the rotational transition of the Mid-trunk, the fin rays continue sweeping to the right [see fig. 9 in Chadwell et al. (Chadwell et al., 2012)], while spanwise curvature is directed to the left of the fish (Figs 2, 3, Fig. 8E). As the Mid-trunk is now moving to the left, once again the spanwise curvature of the rays is directed into the flow. It is interesting to note that Jayne et al. reported that onset of EMG activity among the contralateral dorsal inclinators occurred prior to the end of trunk rotation to the right (Jayne et al., 1996), suggesting some active role in fin-ray position and curvature. However, it is unclear whether contraction of the fin musculature is sufficient to stiffen and curve the rays against the flow, or if the curvature direction is maintained at this time simply because the resistance of the water has not ‘caught up’ with the fin surface.

In the initial part of S2, the fin rays continue their sweep to the right, reaching maximum sweep angle prior to the time of maximum turning rate of Mid to the left [see fig. 9 in Chadwell et al. (Chadwell et al., 2012)]. At the same time, the wave of left-directed spanwise curvature is being shed from the distal ends of the rays, particularly in the posterior region of the fins (Figs 2, 3, Fig. 8F,G). A new spanwise curvature of the fin to the right, directed away from the flow, in the proximal portions of the rays develops soon after the rotational transition of the mid-trunk (Fig. 8G). The muscular activity of the dorsal inclinators found during S2 (Jayne et al., 1996) may be actively resisting the opposing hydrodynamic forces, but does not appear to be able to completely prevent fin-ray bending. Chordwise undulation of the fins in the anterior regions (Sp0, Ry2 and Ry5) propagates posteriorly and, because of the changing angle of the fin rays relative to the body axis (Fig. 8), is transformed to spanwise undulation of the fin rays in the posterior region (Ry8, Ry12; discussed further in Hydrodynamic implications, below).

During the final portion of S2, when the Mid-trunk is slowing (after ), the motions and curvature of the fin rays mirror those seen towards the end of S1. The rays begin to sweep towards the left, into the flow and towards the midline of the body [see fig. 9 in Chadwell et al. (Chadwell et al., 2012)], and both spanwise and chordwise curvature are directed towards the right, away from the flow, as if the tips of the fin rays lag behind the bases (Figs 2, 3, 5, 6). Jayne et al. reported activity in the contralateral dorsal inclinator muscles throughout S2 (Jayne et al., 1996); it is possible that the sweep of the rays to the left is driven by this contraction, which may be able to overcome hydrodynamic forces only as the trunk slows down.

Movements and curvature of the dorsal and anal fins during the S2/S3 transition and S3 are highly variable, reflecting the multitude of behaviors demonstrated by fish, e.g. braking, gliding to a stop, initiating a second propulsive stroke, etc. As a result, no consistent pattern in fin configuration exists for this portion of the C-start.

Previous studies that have examined the function of the dorsal and anal fins have demonstrated that their movement and conformation vary with the locomotor behavior (e.g. steady swimming, maneuvering, braking, etc.), with deformation being greatest in the posterior regions of the fins, i.e. the trailing edge (Drucker and Lauder, 2001b; Drucker and Lauder, 2005; Jayne et al., 1996; Lauder and Drucker, 2004; Standen and Lauder, 2005). Of these studies, most observations have comprised strictly qualitative remarks on fin shape; only one measured the absolute spanwise curvature of individual fin rays. Standen and Lauder examined dorsal and anal fin movement in bluegill during steady swimming at various speeds and during slow yaw maneuvers, measuring curvature at the point of maximum excursion by the fins (Standen and Lauder, 2005). Although they found that the average maximum curvature differed between fin rays within a single fin, no consistent pattern was observed in those differences among speeds or individuals. Rather, a significant difference in curvature was found when comparing different behaviors, with overall fin-ray curvature greater during slow turning maneuvers than in steady swimming at low speeds [≤1.0 TL s⁻¹ (Standen and Lauder, 2005)]. Similarly, our results show that patterns of maximum spanwise and chordwise curvature of the fin rays were statistically inconsistent (Figs 4, 7), though the posterior rays typically showed the greatest degree of spanwise curvature. Curvature magnitudes are strikingly different between the present study (mean maximum curvature ca. 0.28 mm⁻¹) and that of Standen and Lauder, where they reported mean maximum values of ca. 0.08 mm⁻¹ (Standen and Lauder, 2005). The nearly threefold increase in mean curvature magnitude between slow maneuvering and the fast-start escape response highlights the scope for deformation of fin rays in response to behavioral demands.

Studies of pectoral fin kinematics have also demonstrated the flexible nature of actinopterygian fins (Lauder et al., 2006; Lauder and Madden, 2007; Ramamurti et al., 2002; Taft et al., 2008). Curvature into the flow has been observed in the pectoral fin of the bluegill during turning maneuvers (Drucker and Lauder, 2001a), supporting the hypothesis that fin rays are under active control by their intrinsic musculature, as we have postulated for the median fins. Despite a number of hydrodynamic studies, to our knowledge only one paper has reported individual spanwise fin-ray curvature and shown that the degree of curvature differs not only between behaviors (steady swimming versus station holding) but among the individual rays (Taft et al., 2008). Despite the obvious differences in the shape and use of pectoral and median fins, both types of fins share a similar structure and act as control surfaces to modulate hydrodynamic forces.

Standen and Lauder suggested that the overall conformation, or fin shape, is achieved to some extent by the summation of spanwise curvature but also differences in the movements of individual fin rays (Standen and Lauder, 2005). The present results and those of the companion paper (Chadwell et al., 2012) support the hypothesis that differences in orientation of the fin rays, resulting from rotation at the fin-ray joint (sweep, span axis rotation and elevation), produce chordwise curvature of the fin; this combines with spanwise curvature of the fin rays to determine overall fin shape. Our studies have tracked both the timing and magnitude of both spanwise and chordwise curvatures throughout the entire C-start sequence to show the dynamic nature of fin shape over time (supplementary material Movies 1, 2). With such understanding, we can begin to connect how movement and conformation of the fin surfaces contributes to the hydrodynamic forces generated during the behavior.

During the C-start, both the soft dorsal and anal fins demonstrate undulatory waves that spread across their surfaces in a postero-distal direction (Fig. 8, supplementary material Movies 1, 2). The movement of the median fins coincides with the generation of a fluid jet (‘jet two’) by the body and fins that results in production of thrust forces that propel the fish away from the threat during the escape response (Borazjani et al., 2012; Tytell and Lauder, 2008).

Regional variation in curvature kinematics suggests functionally distinct roles in generating momentum. We propose that the initial chordwise curvature in the anterior region of the fins assists the body in initiating the movement of fluid, overcoming the inertia of the water during S1. In S2, as the fish is accelerating away from the threat, the volume of water must be moved posteriorly, towards the tail, if the fish is to gain thrust from the jet. Lateral undulation of the body moves the bulk of jet two towards the tail; the dorsal and anal fins contribute their own portions of jet two (Tytell and Lauder, 2008), and are responsible for moving the associated water. Therefore, the chordwise traveling wave of undulation begins the requisite movement. However, in the posterior region of both soft fins, the rays are directed more caudally than dorsally or ventrally. In these posterior regions, chordwise undulation would not act to continue moving the fluid towards the tail. Instead, spanwise undulation along the lengths of posterior rays allows the fluid to continue in its trajectory so that it may be finally shed from the trailing edge of the median fins and interact with the caudal fin, generating ca. 37% of the total momentum associated with the C-start (Tytell and Lauder, 2008).

Together, the present paper and its companion (Chadwell et al., 2012) comprise studies that are the first to reconstruct the orientation, movements and curvatures of individual fin rays, and the complete fin surface throughout the duration of the C-start escape response. The patterns observed provide evidence to support the hypothesis that fin rays are resisting opposing hydrodynamic forces by muscular activity and/or the intrinsic biomechanical properties derived from their morphology. Future comparative studies are needed to determine the active muscular control over the different regions of the median fins during the escape response, as are examinations of function of median fins that possess different underlying structure, shape or skeletal modifications (e.g. adipose dorsal fins of trout, sickle-shaped median fins in scombrids, unsegmented ceratotrich-supported median fins in elasmobranchs). By combining detailed kinematic analysis of the fin surface with morphological, EMG and hydrodynamics studies, we gain greater insight into the complex ways in which fish control a vitally important behavior.

We thank Peter Madden for writing DigiMat, the custom video analysis program used in this study. We also thank two anonymous reviewers for constructive comments that improved the manuscript.

For either fin (dorsal or anal), S_(a,b) is directed towards the distal end of the fin ray, L_(a,b) is directed towards the left side of the fin surface and C_(a,b) is directed towards the anterior edge of the fin ray (Fig. 4B,C). With the S-, L- and C-axes, the orientation of the fin rays, relative to the planes of the body segment to which the fin rays attach (i.e. anterior trunk for the spiny dorsal fin, and Mid-trunk for the soft dorsal and anal fins), were calculated [see fig. 2 in Chadwell et al. (Chadwell et al., 2012)]. At P_(a,b), sweep (ω, rotation about the chord axis) was calculated as the angle between S_(a,b) and the sagittal plane of the body segment. Span axis rotation (α) was calculated as the angle between C_(a,b) and the sagittal plane of the body segment. Elevation (ϕ, rotation about the lateral axis) was calculated as the angle between S_(a,b) and the frontal plane of the body segment.

LIST OF SYMBOLS AND ABBREVIATIONS
 
• ARy#

  anal ray, where # indicates its numbered position within the fin

 
• ASp#

  anal spine, where # indicates its numbered position within the fin

 
• C

  chord axis of the fin surface, perpendicular to the span axis

 
• cT

  tangent to the chordwise curve

 
• DRy#

  dorsal ray, where # indicates its numbered position within the fin

 
• DSp#

  dorsal spine, where # indicates its numbered position within the fin

 
• EMG

  electromyography

 
• L

  lateral axis, normal to the fin surface

 
• Mid

  middle trunk

 
• r

  fin-ray identifier

 
• S

  span axis of the fin surface

 
• S1

  stage 1 of the C-start

 
• S2

  stage 2 of the C-start

 
• sB

  binormal to the fin surface

 
• sfA

  soft region of the anal fin

 
• sfD

  soft dorsal fin

 
• ssCOM

  stretched-straight center of mass

 
• sT

  tangent to the spanwise curve

 
• t

  time point during a C-start sequence

 
• T₀

  time zero

 
• tr

  directional transition event, i.e. change in direction of rotation or orientation

 
• tX

  time of a given parameter, where X is the event of a given parameter

 
• ΔtX

  time difference between a given fin-ray parameter and its corresponding axial event, where X is the event of a given parameter

 
• κ_chord

  chordwise curvature, perpendicular to the fin surface and span axis

 
• κ_span

  spanwise curvature, perpendicular to the fin surface

 
• ϕ′

  turning rate, i.e. the first time derivative of yaw