The Contribution of the Pectoral Fins, Body, and the Ribbon Fin to Turning Maneuvers of a Gymnotiform Swimmer

Kennesaw State University DigitalCommons@Kennesaw State University

Department of Ecology, Evolution, and Master of Science in Integrative Biology Theses Organismal Biology

Spring 4-22-2021

The contribution of the pectoral fins, body, and the ribbon fin ot turning maneuvers of a gymnotiform swimmer

Olivia Hawkins

Follow this and additional works at: https://digitalcommons.kennesaw.edu/integrbiol_etd

Part of the Integrative Biology Commons

Recommended Citation Hawkins, Olivia, "The contribution of the pectoral fins, body, and the ribbon fin ot turning maneuvers of a gymnotiform swimmer" (2021). Master of Science in Integrative Biology Theses. 61. https://digitalcommons.kennesaw.edu/integrbiol_etd/61

This Thesis is brought to you for free and open access by the Department of Ecology, Evolution, and Organismal Biology at DigitalCommons@Kennesaw State University. It has been accepted for inclusion in Master of Science in Integrative Biology Theses by an authorized administrator of DigitalCommons@Kennesaw State University. For more information, please contact [email protected]. 1

The contribution of the pectoral fins, body, and the ribbon fin to turning maneuvers of a gymnotiform swimmer

Olivia H. Hawkins

Committee chair: Chris P. Sanford Committee members: Thomas McElroy, Lisa Ganser

Abstract

Turning is an ecologically important maneuver in fishes as it is used in prey detection, predator avoidance, and to navigate complex environments. Fishes with traditional control surfaces primarily use body bending and pectoral fins to turn. However, little is known about how fishes with atypical control surfaces facilitate turning. This study investigated the weakly electric Black ghost knifefish (Apteronotus albifrons: Apteronotidae) with an atypical control surface, namely a ribbon fin. To investigate how a fish with an atypical control surface performs turning maneuvers, A. albifrons was filmed performing small and large turns and during steady swimming using high speed videography. 3D kinematic analysis of the body, pectoral fins, and ribbon fin revealed that pitch angle, ribbon fin amplitude, and asynchronous movements of the pectoral fins dominated steady swimming while ribbon fin wavelength, frequency, wave speed, and pectoral fin flapping frequency contributed to both small and large turns. Digital particle image velocimetry (DPIV) showed that the ribbon fin generates larger counter rotating vortices during turning than is produced during steady swimming. All three control surfaces contributed to steady swimming and large turns while small turns relied mostly on movements of the pectoral and ribbon fins. Given the contribution of the ribbon fin during small and large turns in A. albifrons, the role of atypical control surfaces is likely more important than previously assumed.

Key words: maneuverability, knifefish, biomechanics, fluid dynamics

Table of contents

Integration of the Thesis Research…………………………………………………….…….…….3

Introduction……………………………………………………………………………….…….…4

Methods……………………………………………………………………………………………8

Animal care……………………………………………………………..…8

Experimental design……………………………………………………….9

Kinematic measurements……………………………………………...…10

Particle image velocimetry and analysis…………………………………12

Statistical analysis………………………………………………………..12

Results……………………………………………………………………………………………14

Body kinematics…………………………………………………….……14

Pectoral fin kinematics…………………………………………….……..14

Ribbon fin kinematics…………………………………………….……...15

Canonical discriminant analysis…………………………………………16

Particle image velocimetry……………………………………………....17

Discussion……..…………………………………….……..…………………………….………17

References……………………….……………………....…………………………………….…21

Tables……………………………………………....…………………………………….………26

Figures……………………………………………....………………………………….………...28

Integration of the Thesis Research

This study investigates how a fish with an atypical control surface performs turning maneuvers. The main aims of this study are to understand how the body, pectoral fins, and ribbon fin contribute to turning in the Black ghost knifefish (Apteronotus albifrons) as well as characterize the fluid dynamics of the ribbon fin during turning maneuvers. To standardize turning within and among individuals, we used an oscillating feeder consisting of an Arduino microcontroller and programmable digital servo motor. This part of the project relied on integrating mechanical engineering and computer science techniques with our experimental design to differentiate between treatments. Kinematic analysis of individuals allowed for the assessment of how specific control surfaces are used in turning maneuvers. This is a biomechanics approach which uses physics to quantify and describe biological behaviors of interest. To characterize flow patterns produced by the ribbon fin, we used digital particle image velocimetry (DPIV). This technique is traditionally used by engineers but has since been adapted by biologists to study the interaction between an organism and its fluid environment. Overall, this study relies on physics, engineering, and computer science to understand the roles of the control surfaces in contributing to turning maneuvers in A. albifrons, thus providing insights on how fish can navigate through complex environments using alternative means of propulsion, as well as additional selective pressures contributing to the evolution of fishes with ribbon fins.

Introduction

For the last 450 million years, aquatic propulsion stands out as an important selective pressure on fish evolution (Lighthill and Blake, 1990; Hurley et al., 2006). This has led to remarkable diversity in both fin and body morphology (Breder 1926; Drucker and Lauder, 2001).

Most bony and cartilaginous fishes have 6 control surfaces which include the body as well as the dorsal, caudal, anal, pelvic, and pectoral fins. These surfaces are important in aiding fishes to navigate complex flows and habitats, to maneuver, and to power swimming (Webb and Gerstner,

2000; Lauder and Drucker, 2004; Lauder et al., 2006). Given the morphological diversity of control surfaces, there is extensive variation in the mechanisms of propulsion used to power fish swimming.

Fish swimming is divided into two main groups: body and/or caudal fin (BCF) swimming and median paired fin (MPF) swimming (Breder 1926; Lindsey 1978; Webb and

Blake 1985). These two groups are further separated into modes categorized by both the type of control surface and the movement of the respective surface used to generate thrust. Among fishes that undulate their body and/or caudal fin (BCF swimming), modes are differentiated by the relative contribution of the body and the caudal fin (Blake, 1977). For fin undulators (MPF swimming), the modes are determined by the specific fins which are used. Fishes can undulate their pectoral fins (rajiform mode), dorsal fin (amiiform mode), anal fin (gymnotiform mode), or both the dorsal and anal fins (balistiform mode) (Blake, 1978; Blake 1983; Blake, 2004; Webb,

1984a).

The amiiform, gymnotiform, and balistiform modes are all representative of a broad category of swimming called ribbon-fin locomotion. This type of swimming is typically observed in fishes which have elongated anal and/or dorsal fins that are referred to as ribbon fins.

These modified control surfaces convergently evolved in multiple orders of both marine and freshwater actinopterygian fishes (Blake, 1980; Jagnandan and Sanford, 2013; Fig. 1). Fishes with dorsal ribbon fins include bowfin (Amia calva: Amiiformes) and the African aba aba

(Gymnarchus niloticus: Osteoglossiformes). Ventral ribbon fins are observed in the gymnotid knifefishes (Gymnotiformes) and the notopterid knifefishes (Osteoglossiformes). Fishes with both a dorsal and ventral ribbon fin include the filefishes and triggerfishes (Tetradontiformes) as well as seahorses and pipefish (Sygnathiformes) (Blake 1976; Blake, 1978). Although ribbon fin locomotion is used by basal and derived groups of bony fishes and is present in both marine and freshwater environments, the evolutionary drivers of ribbon fin locomotion and its role in shaping the ecology of these fishes is less understood.

Most of the literature on ribbon fin locomotion is limited to the gymnotiform mode- apart from Jagnandan and Sanford 2013, which investigated the wave properties of the dorsal ribbon fin in bowfin (A. calva), and several studies on triggerfish swimming (Blake, 1978; Korsmeyer et al., 2002; Sprinkle et al., 2017). It is important to note that gymnotiform swimmers are found in two orders: Gymnotiformes and Osteoglossiformes. Fishes within the gymnotiform order are often studied more than their osteoglossiform counterparts. For the gymnotid knifefishes, it was once suggested that ribbon fin propulsion allows the body to remain rigid during swimming, thus minimizing disruption of the electric field (Lissman 1958; Lissman, 1962; Lannoo and Lannoo,

1993). This hypothesis, however, does not extend to the gymnotiform swimmers in

Osteoglossiformes as they are not weakly electric fishes. Furthermore, mormyrid fishes are weakly electric but still swim using body undulation and do not possess a ribbon fin (Blake,

1983). While the electro-sensory system may serve as a possible selective pressure on the

6 evolution of the gymnotid knifefishes, it does not explain why many other families of non- weakly electric fishes evolved ribbon fins.

To understand additional selective pressures on the evolution of gymnotiform swimmers, researchers primarily focus on the weakly electric Black ghost knifefish, Apteronotus albifrons.

Investigations of A. albifrons consist of kinematic and morphological analysis, prey capture studies, and hydrodynamic analysis (Albert, 2001; MacIver et al., 2001; Shirgoankar et al., 2008;

Youngerman et al., 2014). A. albifrons also serves as bioinspiration for engineers designing efficient automated underwater vehicles (AUVs) which are used to further understand the mechanics of their locomotion (MacIver et al., 2004; Curet et al., 2011a; Neveln et al., 2013; Liu et al., 2018; English et al., 2019). Several of these studies suggest that the ribbon fin reduces the mechanical and hydrodynamic costs of swimming, therefore enhancing maneuverability

(Shirgoankar et al., 2008; Curet et al., 2011a; Nevelen et al., 2013; Youngerman et al., 2014).

Despite the diverse approaches used to study gymnotiform swimming, most investigations focus on forward swimming and minimally on other maneuvers such as turning.

Most of the foundational knowledge of fish turning comes from studies that focus on fish that use body undulation to power swimming, but it is suggested that the pectoral fins of most teleosts are integral to routine turning behaviors (Gerstner, 1999; Walker, 2000; Drucker and

Lauder, 2001; Drucker and Lauder, 2002a). In sunfish and trout, turning is powered by asynchronous movements of the pectoral fins which cause imbalanced forces pushing the fish in the direction opposite the fin producing the most thrust (Drucker and Lauder, 2002a; Drucker and Lauder, 2004). The unbalanced forces that are produced by pectoral fin asynchrony generate enough thrust on the side opposite to the direction of turning to complete the maneuver. While paired fins appear to contribute to turning maneuvers in most fishes, the median fins such as the

7 dorsal, anal, and pelvic fins is less clear. However, it has been shown that the dorsal fin of sunfish contributes to turning by counteracting torque caused by turning and therefore redirecting the heading of the fish (Drucker and Lauder, 2001). The contribution of the body to turning has mostly been addressed in the context of escape maneuvers (fast starts), but in the case of routine maneuvers, the role of the body is less well understood. It is suggested the body aids in stabilization during unsteady maneuvers by adjusting pitch angle and rolling (Webb, 2000;

Lauder and Drucker, 2003).

Turning maneuvers are ecologically important given they are used for prey capture, predator avoidance, and the navigation of complex environments. In fact, most of a fish’s time is spent actively making low speed turns to navigate its environment (Webb, 1981). Some environments, however, are more complex than others and may causally increase the amount of time a fish spends performing turning maneuvers. Environmental complexity is influenced by a habitat’s structural and hydrodynamic characteristics. Structural characteristics of a habitat include but are not limited to aquatic vegetation, inundated forests, corals, rocks, and narrow waterways. These structural components also introduce non-laminar flows into ecosystems, thus causing hydrodynamic complexity. Ribbon-finned swimmers are commonly found in complex environments. For instance, balistiform swimmers inhabit structurally and hydrodynamically complex coral reef systems, and notopterid knifefishes live in highly vegetated rivers (Sterba,

1962). Turning in the context of habitat navigation has not been investigated in these groups of fishes or the popularly studied gymnotiform swimmer A. albifrons.

A. albifrons is one of 170 species that swim using the gymnotiform mode, and inhabits the floodplains of the Amazon River which are commonly dominated by macrophyte stems and heavy vegetation (Mitch and Gosselink, 1993; Crampton, 1996; Albert and Crampton, 2005). It

8 has been suggested that the inundated vegetation of the floodplains provides a structurally and hydrodynamically complex habitat which has potentially driven the ecomorphological traits of most South American fishes (Prado et al., 2016). While gymnotiform swimming is recognized for being efficient at low speeds and a mode that enhances maneuverability, it is less understood how fishes that swim using the gymnotiform mode perform turning maneuvers given the presence of an atypical control surface (Blake, 1983; Youngerman et al., 2014).

This study aimed to investigate how Apteronotus albifrons, a fish with an atypical control surface, performs turning maneuvers. The specific aims of this study are as follows: Aim (1) assess the contributions of the body, pectoral fins, and ribbon fin during steady swimming and turning. It is expected that steady swimming depends primarily on the ribbon fin and less on the pectoral fins and the body. We predict that the pectoral fins contribute primarily to small turns, and that large turns are dominated by all three control surfaces. Aim (2) characterize the fluid dynamics of the ribbon fin during steady swimming and turning. We predict that vortex circulation and size increases as turning amplitude increases.

Methods

Animal care

Six juvenile Black ghost knifefish (Apteronotus albifrons; Linneaus, 1766; 10.2 ± 0.86 cm; Fig. 2) were obtained from a local supplier in Kennesaw, Georgia. Individuals were housed separately in 151 L tanks filled with dechlorinated freshwater. Tanks were maintained at an average temperature of 25.7 ± 1°C, a pH of 7-8, and under a 12 h: 12 h light: dark photoperiod.

All tanks included enrichment (i.e., plants, PVC pipe). The individuals received bloodworms ad libitum. Prior to experimentation, individuals were trained to approach and follow an oscillating

9 feeder. Acclimation to the flow tank occurred for 30 minutes prior to experimentation. All animal care and experimental procedures adhered to Kennesaw State University’s IACUC protocol #20-008.

Experimental design

Experiments took place in a Brett-type 90L recirculating flow tank (Loligo Systems,

Swim-90, Tjele, Denmark) with an average water temperature of 25.7 ± 1°C (Fig. 3). To ensure laminar flow, a flow rectifier was placed upstream of the working section (66 x 20 x 20 cm).

This experiment used a single flow speed, 1.8 BL s-1. This speed is comparable to cruising speeds of A. albifrons and was necessary to inhibit the fish from excessive rolling behaviors when feeding (Ortega-Jimenez and Sanford, 2021). Treatments were differentiated using an oscillating feeder. The oscillating feeder was secured to a custom platform and centered in the working section and consisted of a feeding tube attached to the control arm of a waterproof 20 kg digital servo motor which was programmed by an Arduino Uno R3 microcontroller (ARDUINO,

Italy) (Fig. 3B). The feeding tube was a small plastic cylinder with a 1 mm diameter hole in the center to hold bloodworms as described in Ortega-Jimenez and Sanford, 2021.

The three treatments included in this study were steady forward swimming, small maneuvers, and large maneuvers. Removing power from the Arduino allowed the feeder to stay motionless in order to permit the fish to swim straight behind the feeder. This treatment served as the control for this experiment. The two additional maneuvers were programmed so that the feeder would oscillate at identical frequencies (0.75 Hz) but different amplitudes. The small and large amplitudes were 30° and 45° respectively. Sequences in which a full turn was completed without significant rolling or interruptions to the ribbon fin waves were selected for analysis.

Turns made to the left and to the right were found to not significantly differ from one another in most kinematic measurements and were therefore not separated for further statistical analysis.

Maneuvers were recorded in high-speed using two Hi-Spec4 cameras filming at 250 fps-1

(1696 x 1710 pixels; Fastec Imaging, San Diego, CA). Cameras were placed orthogonal and ventral to the working section (Fig. 3). The cameras were calibrated using a 24-point calibration cube and direct linear transformation software (DLT, version 7.1) for Matlab (Hedrick, 2008;

Matlab 2020b, Mathworks, Natick, MA, USA). DLT software was also used to track the movement of the body, pectoral fins, and ribbon fin during maneuvers. On the body, digitization landmarks were placed at the tip the of the snout, in between the pectoral fins, behind the pectoral fins, in the middle of the body at two locations, at the end of the ribbon fin attachment, and the caudal fin. Landmarks used to digitize the pectoral fins were placed on the tip of the most distal fin ray and at the base of the pectoral fins. Ribbon fin landmarks were placed on the base of a single fin ray towards the center of the ribbon fin, on the distal end of the same fin ray, and on the tip of a distal fin ray located on a contiguous crest. See Figure 4 for detailed information on landmark placement.

Kinematic measurements

A custom Matlab script was used to calculate all kinematic measurements. Example measurements using digitized landmarks can be found in Figure 4. Pitch angle (°) and the body bending coefficient were calculated using the 7 body landmarks. Pitch angle referred to the vertical change in body orientation in the y plane. The body bending coefficient (ßb), as described by Azizi and Landberg 2002, serves as a dimensionless metric that is used to assess whole-body curvature in fishes. The coefficient is calculated as follows:

퐿푐 훽푏 = 1 − 퐿푏 in which the distance between the tip of the snout and the end of the caudal fin (Lc) is divided by the total body length (Lb) and subtracted from 1. Values near 1 indicate little to no body bending while values over 1 suggest body curvature.

Pectoral fin landmarks were used to calculate pectoral fin flapping frequency (Hz), the dorso-ventral pectoral abduction angle (°), right and left pectoral cranio-dorsal abduction angles

(°), and the Asynchronous Index (AI). All pectoral fin variables except for the right and left pectoral abduction angles and AI used the left pectoral fin only as it was visible in both the ventral and lateral views. The remaining variables were calculated using only ventral sequences.

The following equation for the Asynchronous Index (AI) used in this study was adapted and modified from Gerry 2008:

∑ |퐷𝑖푓 − 퐷𝑖푓 | 퐴푠푦푛푐ℎ푟표푛표푢푠 𝑖푛푑푒푥 (퐴퐼) = [ 푙푒푓푡 푟𝑖푔ℎ푡 ] 2(푓푟푎푚푒푠 − 1) in which AI is equal to the sum of the absolute value of the difference in contiguous x positions of the left and right pectoral fins over time divided by two multiplied by the number of frames in the sequence minus one. If the x positions of the left and right pectoral fins are dissimilar over time, the index will fall closer to 1, suggesting fin asynchrony. If x positions are similar, the index will be closer to 0, suggesting fin synchrony. The cutoff used to differentiate asynchrony from synchrony is 0.5 (Gerry, 2008).

Landmarks on the ribbon fin were used to calculate ribbon fin amplitude (°), frequency

(Hz), wavelength (cm), and wave speed (cm/s). Ribbon fin amplitude was defined as the angle formed between the base and distal tip of a centrally located fin ray, while frequency was calculated as the inverse period of the wave determined by the same two landmarks. Wavelength

12 was quantified using the distance between the tips of two contiguous crests. Wave speed was calculated using the first derivative of the MSE-quintic spline function (Walker, 1998; Ortega-

Jimenez and Sanford, 2021).

Particle image velocimetry and analysis

Digital particle image velocimetry (DPIV) was used to characterize the fluid dynamics of the ribbon fin during all three maneuvers. Sequences were filmed from the ventral view at 500 fps-1 using a HiSpec4 camera. A 532 nm 5-watt class-4 laser (Opto Engine LLC, Midvale, UT,

USA) illuminated plastic particles (50 µm) to form a horizontal laser sheet. Two individuals were filmed performing each maneuver and sequences were kept where the ribbon fin intersected the horizontal laser sheet. After background subtraction of bulk flow, time resolved paired images were analyzed using PIVlab in Matlab (Thielicke and Stamhuis, 2014). Interrogation windows of 64 pixels2 to 32 pixels2 (50% step) were applied to all sequences. Vectors greater than five standard deviations from the average flow patterns were removed. After confirming visible vortex structures using velocity profiles, vorticity (s-1) fields were extracted and used to extract circulation values (m2s-1). Circulation refers to the vorticity of an area within a closed loop (Tytell, 2011). Circulation for clockwise and counterclockwise rotating paired vortices was extracted from processed vorticity fields using the tangential velocity draw tool in PIVlab.

Statistical analysis

A Repeated Measures ANOVA was used to determine the effect of treatment on the means of each of the kinematic variables quantified. The Bonferroni pairwise comparison test

13 served as post hoc analysis when needed to assess significant differences between mean values of the kinematic variables for steady swimming, small turns, and large turns. For both the

ANOVA and the post hoc tests, the alpha value was 0.05. Normality assumptions were confirmed using a QQ plot. Most outliers present in the data were not removed as they were not classified as extreme. All data are presented as mean ± s.e. (standard error).

To understand how the kinematic variables from the body, pectoral fins, and ribbon fin contribute to each of the maneuvers investigated using multivariate analysis, a canonical discriminant analysis (CDA) similar to Youngerman et al. 2014 was performed. The dorso- ventral pectoral abduction angle, and right and left cranio-caudal pectoral angles were excluded from analysis due to their inability to meet the homogeneity of covariance assumption of

MANOVA. All other variables were included in the model. The multivariate normality assumption was visually confirmed through the use of a QQ plot. Wilk’s lambda was used to determine the discriminant axes that significantly contributed to the maximum separation of the treatments (α = 0.05). A Two-Way Mixed Model ANOVA was used to test the significant effects of treatment and individuals on each of the variables used in the model (α = 0.05).

Comparisons among clockwise and counterclockwise rotating vortices were made visually and statistically. For statistical comparison of vortices, student’s t-tests were used to assess significant differences in circulation (m2s-1) between counter rotating vortices within each maneuver (α = 0.05). Comparisons across maneuvers were made using a Repeated Measures

ANOVA and Bonferonni pairwise comparisons were used when necessary (α = 0.05). R version

4.1.1 was used for all statistical analyses (R Core Team, 2019).

Results

Body kinematics

Average pitch angle decreased significantly as the maneuvers changed from steady swimming to large turns (F2,10 =6.45, p = 0.02; Table 1, Fig. 5A). The average pitch during steady swimming was 6.16 ± 2.00 (°), nearly doubling the average pitch during large turns (-6.45

± 1.71 (°); Table 2). There was a significant difference in pitch between steady swimming and large turn treatments (Bonferroni; t(5) = 3.78, p = 0.04; Table 2). No significant differences were found between steady swimming and small turns or small turns and large turns (Bonferroni; t(5)

= 1.64, p = 0.49 and t(5) = 1.92, p = 0.34 respectively; Table 2).

Treatment significantly influenced body bending coefficient values and these values increased from steady swimming to large turns (F2,10 = 43.22, p < 0.0001; Table 1, Fig. 5B). A highly significant difference in the average body bending coefficients occurred between steady swimming and large turns as well as between small and large turns (Bonferroni; t(5) = -7.91, p <

0.01 and t(5) = -5.93, p < 0.01 respectively; Table 2). The average body bending coefficient for steady swimming was significantly lower than the average for small turns (Bonferroni; t(5) = -

4.43, p = 0.02; Table 2).

Pectoral fin kinematics

The average pectoral flapping frequency and average dorso-ventral pectoral abduction angle were not found to be significantly impacted by treatment and therefore the means across treatments did not differ significantly (F2,10 = 0.36, p = 0.71 and F2,10 = 0.64, p = 0.55 respectively; Table 1, 2, Fig. 6). Right and left cranio-caudal pectoral fin angle did not change significantly with treatment (F2,10 = 0.24, p = 0.79 and F2,10 = 1.81, p = 0.21 respectively, Table

1, Fig. 7).

The average Asynchronous Index (AI) was found to be significantly influenced by treatment with the AI values decreasing from steady swimming to the large turn treatment (F2,10

=7.87, p < 0.01; Table 2, Fig. 8A). The average AI for steady swimming was 0.48 ± 0.02 and was closest to the index cutoff of 0.5 to differentiate between fin asynchrony and fin synchrony

(Table 2). Average AI for steady swimming was significantly different from the average AI of the large turn treatment (Bonferroni; t(5) = 4.69, p = 0.02; Table 2). No significant differences were observed in average AI values of the steady swimming and small turns as well as between the small and large turn treatments (Bonferroni; t(5) = 1.86, p = 0.37 and t(5) = 1.88, p = 0.36 respectively; Table 2).

Ribbon fin kinematics

Average ribbon fin frequency increased from steady swimming to large turns and differences observed were significantly affected by treatment (F2,10 = 5.35, p = 0.03; Table 1, Fig.

9A). The average ribbon fin frequency for large turns was significantly higher than the averages for small turns but not steady swimming (Bonferroni; t(5) = -3.89, p = 0.03 and t(5) = -2.57, p =

0.15 respectively; Table 2).

Similar to ribbon fin frequency, average wavelength increased from steady swimming to large turns (Fig. 9B). Differences among the averages were significantly influenced by treatment

(F2,10 = 7.84, p = 0.009; Table 1). The average wavelength for the small turn treatment was 0.86

± 0.15 cm which was almost two times the average wavelength of the steady swimming treatment (Table 2). Wavelength for the large turns was significantly higher than that of steady swimming (Bonferroni; t(5) = -3.76, p = 0.04; Table 2).

From steady swimming to large turns, average ribbon fin amplitude decreased, although treatment did not appear to have a significant effect (F2,10 = 2.44, p = 0.14; Table 1, Fig. 9C).

Similar to average ribbon fin frequency and average wavelength, average ribbon fin wave speed increased with from steady swimming to large turns (Fig. 9D). Differences in wave speed were attributed to treatment (F2,10 = 12.41, p < 0.01; Table 1). Average ribbon fin wave speed for the small turns was found to be significantly higher than steady swimming wave speed but not significantly lower than the average wave speed during large turns (Bonferroni; t(5) = -3.98, p =

0.03 and t(5) = -1.85, p = 0.37 respectively; Table 2). The average wave speed for large turns was 8.14 ± 0.62 cm/s and nearly tripled the average wave speed for steady swimming- therefore the means differed significantly (Bonferroni; t(5) = -4.96, p = 0.01; Table 2).

Canonical discriminant analysis

Out of the two discriminant axes, the first axis had discriminating power of 98.3% and significantly contributed to the maximum separation of the maneuvers (p < 0.05; Table 3, Fig.

10). Ribbon fin wavelength, wave speed, ribbon fin frequency, pectoral fin flapping frequency, and the body bending coefficient were all positively correlated with the first discriminant axis while the Asynchrony Index, ribbon fin amplitude, and pitch angle were negatively correlated

(Fig. 10). Ribbon fin wavelength, wave speed, and the Asynchrony Index correlated positively with the second axis while ribbon fin amplitude, pitch angle, pectoral fin frequency, and the body bending coefficient correlated negatively (Fig. 10).

Particle image velocimetry

During steady swimming, pairs of small counter rotating vortices were observed (Fig.

11A). Circulation for clockwise rotating vortices was significantly higher than circulation of counterclockwise rotating vortices (Student’s t-test; t(10.90) = 2.88, p = 0.02; Table 5). During small turns, paired counter rotating vortices were still present, but appeared larger towards the center of the ribbon fin as the individual initiated the maneuver (Fig. 9B). Circulation for the vortices was not significantly different (Student’s t-test; t(17.92) = 0.42, p = 0.68, Table 5). The largest paired vortices were observed during large turns (Fig. 9C). Similar to the small turn treatment, no significant differences were observed in circulation values for the paired vortices

(Student’s t-test; t(7.58) = -0.44, p = 0.67; Table 5). While differences in vortex size and intensity among the treatments appeared visually distinct, circulation for both clockwise and counterclockwise rotating vortices were not found to be significantly different (F3,1 = 1.37, p =

0.54 and F3,1 = 3.56, p = 0.37 respectively; Table 5).

Discussion

Turning is a maneuver that is crucial to fish survival. Most of what is known about turning in fishes has focused on fishes with typical control surfaces, while the mechanism of turning in fishes with atypical control surfaces is remains largely unexplored. To address this, we investigated how a gymnotiform swimmer A. albifrons performs turning maneuvers using a combination of 3D kinematics and analysis of fluid flows. In A. albifrons it was expected that of the three major control surfaces (body, pectoral fins and ribbon fin) the ribbon fin would be the main contributor to steady swimming, pectoral fins would dominate small turns, and large turns would employ all three control surfaces. During steady swimming and large turns, A. albifrons

18 uses all three control surfaces although the ribbon fin’s role in turning appears to play a more dominant role than other control surfaces. Small turns were dominated by the pectoral fins and ribbon fin. The second aim of this study was to evaluate the fluid dynamics associated with the ribbon fin during steady swimming and turning maneuvers. We predicted that vortex size and intensity would increase during large turns and indeed the results support this. This study demonstrates the importance of the ribbon fin to turning maneuvers of the gymnotiform swimmer, A. albifrons, through both kinematic and hydrodynamic analysis thus suggesting its role in turning maneuvers has previously been underestimated.

During steady swimming, all three control surfaces were used. The body variable closely associated with turning was pitch angle (Fig. 5A, Fig. 10). During steady swimming, individuals held their body in a slight head-up orientation which has been documented in other studies of forward swimming in A. albifrons (Ruiz-Torres et al., 2013; Youngerman et al., 2014; Ortega-

Jimenez and Sanford, 2021). It has been suggested that an increase in pitch angle (nose down) during steady swimming will counterbalance torque forces that occur from upward thrust generated by ribbon fin undulations (Ruiz-Torres, 2013). This upward thrust can also be mitigated using the pectoral fins. During steady swimming, the Asynchronous Index (AI) of the pectoral fins was significantly higher when compared to large maneuvers, but below the asynchronous cutoff (Table 2, Fig. 8). Asynchronous movements of the pectoral fins may be an additional means for stability in addition to changing pitch angle during steady swimming (Ruiz-

Torres et al., 2013). In a study on forward swimming in Amia calva that also has a ribbon fin, pectoral fin movements were synchronous but were not found to impact swimming speed

(Jagnandan and Sanford, 2013). This supports the idea that the pectoral fins in A. albifrons may be used more for stabilization rather than thrust generation during steady forward swimming.

Ribbon fin amplitude was highest in the steady swimming while ribbon fin frequency, wavelength, and wave speed were low when compared to turning maneuvers (Table 2, Fig. 9).

Visualizations of paired counter rotating vortex pairs also appeared smaller during steady swimming when compared to turning maneuvers, but match the observations of forward swimming from previous work (Shirgaonkar et al., 2008; Ortega-Jimenez and Sanford, 2021;

Fig. 11). Overall, pitch angle, AI, and ribbon fin amplitude contributed to the separation of steady swimming from the two turning maneuvers thus suggesting all three control surfaces are used during forward swimming (Fig. 10).

During small and large turns, the body exhibited significantly more body bending than observed during steady swimming (Table 2, Fig. 5B). Early studies of forward swimming in A. albifrons suggest that turning maneuvers in this species are rare and body bending is not common (Blake, 1983; MacIver et al., 2001; MacIver et al., 2010). However, in this study A. albifrons bend their bodies to follow the oscillating feeder. This follows observations of Ortega-

Jimenez and Sanford 2021 in which increased body bending in A. albifrons occurred in response to swimming downstream of an oscillating cylinder. In the current study, body bending in this species is common in spite of any potential constraints on the electro-sensory system. Kasapi et al. 1993, also found that body bending was largely responsible for escape maneuvers in the

African knifefish (Xenomystus nigri), another weakly electric fish with a ribbon fin. In addition to the body, the pectoral fins and ribbon fin were also integral to escape maneuvers (Kasapi et al., 1993). In pectoral fins, AI is lower (more synchronous) in small and large turns compared to steady swimming (Table 2, Fig. 8). The prediction that asynchronous fin movements should be more common during turning maneuvers (Drucker and Lauder, 2002a; Drucker and Lauder,

2004) was not supported in this study. Though the AI for turning maneuvers was low, it does not

20 imply that asynchronous movements did not occur. For small and large turns, pectoral fin asynchrony was observed at the beginning of the turn, but eventually returned to synchronous movements when completing the turn. In A. albifrons more pectoral fin synchrony was observed during large turns similar to the pectoral fin movements of X. nigri during escape maneuvers

(Kasapi et al., 1993). Most of the thrust used to power turning appears to come from the ribbon fin. Ribbon fin wavelength was similar and contributed significantly to turning (Table 2, 5; Fig.

9B, 10). Given that A. albifrons may have active control over fin ray curvature, larger wavelengths could be used to increase fluid loading (Youngerman et al., 2014). Wave speed of the ribbon fin can also contribute to fluid loading, which was supported by the observation that wave speed increased significantly during large turns (Table 1, 5; Fig. 9D, 10). It is possible that increased wave speed provides instantaneous thrust and contributes to turning. The ribbon fin has been shown to generate heave forces (upwards force) as a result of paired streamwise vortex rings (Shirgaonkar et al., 2008). If the fish increases wave speed to complete large turns, it is expected that the fish would experience upwards force and large vortices. The decrease in the pitch angle during large turns in which the body is tilted in a head down orientation (Fig. 5A) could counter heave forces resulting from increased wave speed. Additionally, vortex size increased during turns when compared to steady swimming (Fig. 11). It is unclear if instantaneous increases in wave speed during turning in A. albifrons result in higher energetic costs. It is also notable that the ribbon fin allows this fish to move in almost any direction at high speeds and the fin has high hydrodynamic efficiency which may act to reduce energetic costs during unsteady swimming maneuvers such as turning (Blake, 1983).

This study highlights the importance of investigating how atypical control surfaces are used in the context of turning and remains largely unexplored. In the case of A. albifrons,

21 understanding how this fish may be navigating the complex environments of the Amazon is insightful to ecologists and conservation management. In the broader context of the evolution of ribbon finned fishes, this study demonstrates that the use of alternate control surfaces are important in turning. This study demonstrates the importance of expanding our knowledge of alternate control surfaces that can contribute to turning. In the case of A. albifrons the ribbon fin is particularly important for large turns, while small turns were dominated by movements of the pectoral fins and the ribbon fin. Future studies should investigate turning in other ribbon fin swimmers with different anatomical positions of the ribbon fin to better understand the ecomorphology of these species and the evolutionary drivers behind ribbon fin swimming.

References

Albert, J.S. (2001). Species diversity and phylogenetic systematics of American knifefishes (Gymnotiformes, Teleostei). Misc. Publ. Mus. Zool. Univ. Michigan 190, 1–127.

Albert, J.S., Crampton, W.G.R. (2005). Diversity and phylogeny of Neotropical electric fishes (Gymnotiformes). In Electroreception (ed. R.R. Fay, A.N. Popper, T.H. Bullock, C.D. Hopkins), pp.360-409. Springer Handbook of Auditory Research, vol. 21. New York: Springer Publishing.

Aziz, E. and Landberg, T. (2002). Effects of metamorphosis on the aquatic escape response of the two-lined salamander (Eurycea bislineata). J. Exp. Biol. 205: 841–849.

Blake, R. W. (1976). On seahorse locomotion. J. Mar. Biol. Assoc. UK. 56, 939–949.

Blake, R. W. (1977). On ostraciiform locomotion. J. Mar. Biol. Assoc. UK. 57, 1047–1055.

Blake, R.W. (1978) On balistiform locomotion. J. Mar. Biol. Assoc. UK. 58, 73-80.

Blake, R.W. (1980). Undulatory median fin propulsion of two teleosts with different modes of life. Can. J. Zool. 58, 2116–2119.

Blake, R.W. (1983) Swimming in the electric eels and knifefishes. Can. J. Zool. 61, 1432– 1441.

Blake, R.W. (2004). Fish functional design and swimming performance. J. Fish. Biol. 65, 1193- 1222.

Breder, C. M. (1926). The locomotion of fishes. Zool. 4, 159–297

Crampton, W.G.R. (1996). Gymnotiform fish: an important component of Amazonian floodplain fish communities. J. Fish. Biol. 48, 298-301.

Curet, O.M., Patankar, N.A., Lauder, G.V., MacIver, M.A. (2011a) Aquatic maneuvering with counter-propagating waves: a novel locomotive strategy. J. R. Soc. Interface. 8, 1041– 1050.

Drucker, E.G., and Lauder, G.V. (2001). Wake dynamics and fluid forces of turning maneuvers in sunfish. J. Exp. Biol. 204, 431-442.

Drucker, E.G. and Lauder, G.V. (2002a) Wake Dynamics and Locomotor Function in Fishes: Interpreting Evolutionary Patterns in Pectoral Fin Design. Intgr. Comp. Biol. 42, 997–1008.

English, E., Liu, H., and Curet, O.M. (2019) Robotic device shows lack of momentum enhancement for gymnotiform swimmers. Bioinsp. Biomim. 14(2).

Epps, B.P., and Techet, A.H. (2007). Impulse generated during unsteady maneuvering of swimming fish. Exp. Fluids. 43, 691-700.

Gerry, S. P. (2008). Feeding mechanics of a trophic generalist and a specialist shark species: A comparison of diet, behavior and function. PhD thesis, University of Rhode Island, South Kingstown, Rhode Island.

Gerstner, C. L. (1999). Maneuverability of four species of coral-reef fish that differ in body and pectoral-fin morphology. Can. J. Zool. 77, 1102–1110.

Hedrick, T.L. (2008). Software techniques for two- and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinsp. Biomim. 3, 034001.

Hurley, I.A., Mueller, R.L., Dunn, K.A., Schmidt, E.J., Freidman, M., Ho, R.K., Prince, V.E., Yang, Z., Thomas, M.G., Coates, M.I. (2007). A new time-scale for ray-finned fish evolution. Proc. Biol. Sci. 274, 489‐498.

Jagnandan K., and Sanford, C.P. (2013). Kinematics of ribbon-fin locomotion in the bowfin, Amia calva. J. Exp. Zool. A. 319, 569–83.

Kasapi, M. A., Domenici, P. D., Blake, R. W., Harper, D. G. (1993). The kinematics and performance of escape responses of the knifefish Xenomystus nigri. Can. J. Zool. 71, 189–195.

Korsmeyer, K. E., Steffensen, J. F. & Herskin, K. (2002). Energetics of median and paired fin swimming, body and caudal fin swimming, and gait transition in parrot fish (Scarus schlegeli) and triggerfish (Rhinecanthus aculeatus). J. Exp. Biol. 205, 1253–1263.

Lannoo, M.J., and Lannoo, S.J. (1993). Why do electric fishes swim backwards? An hypothesis based on gymnotiform foraging behavior interpreted through sensory constraints. Environ. Biol. Fishes. 36, 157-165.

Lauder, G.V., and Drucker, E.G. (2003). Morphology and experimental hydrodynamics of piscine control surfaces. In “Biology inspired Maneuvering Hydrodynamics for AUV Application” (Fish, F.E., Ed.). pp.C1-C26. Proceedings of the 13th International Symposium on Unmanned Untethered Submersible Technology. Autonomous Undersea Systems Institute, Durham, NH.

Lauder, G.V., and Drucker, E.G. (2004). Morphology and experimental hydrodynamics of fish fin control surfaces. IEEE J. Ocean. Eng. 29, 556–571.

Lauder, G.V., Madden, P.G.A., Mittal, R., Dong, H., Bozkurttas, M. (2006). Locomotion with flexible propulsors. I. Experimental analysis of pectoral fin swimming in sunfish. Bioinsp. Biomim. 1, S25–S34.

Lighthill, J., and Blake, R. W. (1990). Biofluiddynamics of balistiform and gymnotiform locomotion. Part 1. Biological background, and analysis by elongated-body theory. J. Fluid Mech. 212, 183–207.

Lindsey, C. C. (1978). Form, function and locomotory habits in fish. In Fish Physiology, Vol. 7 (ed. W.S. Hoar, and J.D. Randall), pp. 1–100. London: Academic Press.

Lissman, H.W. (1958). On the function of electric organs in fish. J. Exp. Bio. 35, 156-191.

Lissman, H.W. (1962). Zoology, locomotory adaptations and the problem of electric fish. In Cell and organism. (ed. J. A. Ramsey and V. B. Wigglesworth), pp. 301-307. Cambridge: Cambridge University Press.

Liu, H. and Curet, O.M. (2018). Swimming performance of a bio-inspired robotic vessel with undulating fin propulsion. Bioinsp. Biomim. 13, 056006.

MacIver, M.A., Sharabash, N.M., Nelson, M.E. (2001) Prey-capture behavior in gymnotid electric fish: Motion analysis and effects of water conductivity. J. Exp. Biol. 204, 543–557.

MacIver, M.A., Fontaine, E., Burdick, J.W. (2004). Designing Future Underwater Vehicles: Principles and Mechanisms of the Weakly Electric Fish. IEEE J. Ocean. Eng. 29, 651-659.

MacIver, M.A., Patankar, N.A., Shirgaonkar, A.A. (2010) Energy-Information Trade-Offs between Movement and Sensing. PLoS Comput Biol 6(5), e1000769.

Mitsch, W. and Gosselink, J. (1993). Wetlands. New York: Van Nostrand Reinhold.

Near, T.J., Eytan, R.I., Dornburg, A., Kuhn, K.L., Moore, J.A., Davis, M.P., Wainwright, P.C., Friedman, M., Smith, W.L. (2012). Resolution of rayfinned fish phylogeny and timing of diversification. Proc Natl Acad Sci USA 109:13698–13703

Neveln, I.D., Bai, Y., Snyder, J.B., Solberg, J.R., Curet, O.M., Lynch, K.M., MacIver, M.A. (2013). Biomimetic and bio-inspired robotics in electric fish research. J. Exp. Biol. 216, 2501– 2514.

Ortega-Jimenez, V.M., and Sanford, C.P. (2021). Beyond the Kármán Gait: Knifefish swimming in periodic and irregular vortex streets. J. Exp. Bio. doi: 10.5061/dryad.sqv9s4n37.

Prado, A.V.R., Goulart, E., Pagotto, J.P.A. (2016). Ecomorphology and use of food resources: inter- and intraspecific relationships of fish fauna associated with macrophyte stands. Neotrop. Ichthyol. 14, e150140.

R Core Team. (2014). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org/.

Ruiz-Torres, R., Curet, O.M., Lauder, G.V., MacIver, M.A. (2013). Kinematics of the ribbon fin in hovering and swimming of the electric ghost knifefish. J. Exp. Biol. 216, 823–834.

Sefati, S., Neveln, I.D., Roth, E., Mitchell, T.R.T., Snyder, J.B., MacIver, M.A., Fortune, E.S., Cowan, N.J. (2013). Mutually opposing forces during locomotion can eliminate the tradeoff between maneuverability and stability. Proc. Natl. Acad. Sci. USA. 110, 18798–18803.

Shirgaonkar, A.A., Curet, O.M., Patankar, N.A., MacIver, M.A. (2008). The hydrodynamics of ribbon-fin propulsion during impulsive motion. J. Exp. Biol. 211, 3490–3503.

Sprinkle, B., Bale, R., Bhalla, A.P.S., MacIver, M.A., Patankar, N.A. (2017). Hydrodynamic optimality of balistiform and gymnotiform locomotion. Eur. J. Comp. Mech. 26, 31-43.

Sterba, G. (1962). Freshwater fishes of the world. Vista, London.

Thielicke, W., Stamhuis, E.J. (2014). PIVlab – Towards User-friendly, Affordable and Accurate Digital Particle Image Velocimetry in MATLAB. Journal of Open Research Software 2(1): e30. doi: 10.5334/jors.bl

Tytell, E.D. (2011). Experimental Hydrodynamics. In: Farrell A.P., (ed.), Encyclopedia of Fish Physiology: From Genome to Environment, volume 1, pp. 535–546. San Diego: Academic Press.

Walker, J.A. (2000) Does a rigid body limit maneuverability? J. Exp. Biol. 203, 3391-3396.

Walker, J.A. (1998). Estimating velocities and accelerations of animal locomotion: a simulation experiment comparing numerical differentiation algorithms. J. Exp. Biol. 201, 981 -995.

Webb, P. W. (1984a). Body form, locomotion and foraging in aquatic vertebrates. Amer. Zool. 24, 107–120.

Webb, P.W. (1981). Composition and mechanics of routine swimming of rainbow trout, Oncorhynchus mykiss. Can. J. Fish. Aquat. Sci. 48, 583-590.

Webb, P.W. (2000). Maneuverability versus stability? Do fish perform well in both? Proceedings of the 1st International Symposium on Aqua Bio-Mechanisms/International Seminar on Aqua Bio-Mechanisms (ISABMEC 2000), August, Tokai University Pacific Center, Honolulu, HI.

Webb, P. W. and Blake, R. W. (1985). Swimming. In Functional Vertebrate Morphology (ed. M. Hildebrand, D.M. Bramble, K.F. Liem, and D.B. Wake), pp. 111–128. Harvard: Belknap Press.

Webb, P. W. and Gerster, C. L. (2000). Swimming behaviour: predictions from hydromechanical principles. In Biomechanics in Animal Behaviour (ed. P.D. Domenici, and R.W. Blake), pp. 59–77. Oxford: Bios Scientific Publishers Ltd.

Youngerman, E. D., Flammang, B.E., Lauder, G.V. (2014). Locomotion of free-swimming ghost knifefish: anal fin kinematics during four behaviors. Zool. 117, 337-348.

Tables

Table 1. Repeated Measures ANOVA results investigating the effect of treatment on each kinematic variable of interest across the three maneuvers performed by Apteronotus albifrons (n=6). Data used for this analysis consists of the averages for each variable per individual (n=6 per treatment). Differences among maneuvers are considered significant when p < 0.05). Kinematic variable F statistic p value Pitch angle (°) 6.45 0.02 Body bending coefficient 43.22 < 0.0001 Pectoral fin flapping frequency (Hz) 0.36 0.71 Dorso-ventral pectoral fin angle (°) 0.64 0.55 Cranio-caudal left pectoral angle (°) 1.81 0.21 Cranio-caudal right pectoral angle (°) 0.24 0.79 Asynchronous Index 7.87 < 0.01 Ribbon fin frequency (Hz) 5.35 0.03 Ribbon fin amplitude (°) 2.44 0.14 Ribbon fin wavelength (cm) 7.84 < 0.01 Ribbon fin wave speed (cm/s) 12.41 <0.01

Table 2. Kinematic variable results by maneuver for Apteronotus albifrons (n=6) with post-hoc statistical analysis. Results are reported as mean ± s.e. (standard error) calculated using the means of all individuals during steady swimming (n=35), small maneuvers (n=47), and large maneuvers (n=48). Letters indicate statistical significance using Bonferroni pairwise comparison tests (p < 0.05). Steady Small Large Kinematic variable Swimming maneuver maneuver Pitch angle (°) 6.16 ± 2.00a -0.38 ± 2.87a,b -6.45 ± 1.71b Body bending coefficient 1.04 ± 0.01a 1.10 ± 0.02b 1.17 ± 0.02b,c Pectoral fin flapping frequency (Hz) 6.34 ± 0.17a 6.38 ± 0.15a 6.57 ± 0.23a Dorso-ventral pectoral angle (°) 43.95 ± 2.15a 39.35 ± 3.30a 42.37 ± 1.89a Cranio-caudal left pectoral angle (°) 33.55 ± 1.52a 29.70 ± 1.53a 30.90 ± 0.92a Cranio-caudal right pectoral angle (°) 29.91 ± 1.36a 28.45 ± 2.35a 30.19 ± 1.42a Asynchronous Index 0.48 ± 0.02a 0.38 ± 0.04a,b 0.31 ± 0.04b Ribbon fin frequency (Hz) 6.62 ± 0.14a,b 6.64 ± 0.25a 7.56 ± 0.26b Ribbon fin amplitude (°) 78.52 ± 6.34a 68.85 ± 3.08a 64.98 ± 6.55a Ribbon fin wavelength (cm) 0.43 ± 0.11a 0.86 ± 0.15a,b 1.11 ± 0.10b,c Ribbon fin wave speed (cm/s) 2.76 ± 0.73a 5.66 ± 0.96b 8.14 ± 0.62b,c

Table 3. Canonical discriminant analysis output from two discriminant axes. Results represent all observations from six individuals for steady swimming (n=35), small maneuvers (n=47), and large maneuvers (n=48). A canonical axis is considered to significantly contribute to maximum separation of the treatments when p < 0.05.

Discriminant axis Eigenvalue Percent Correlation Wilk's Lambda Probability 1 3.19 98.26 0.76 0.23 < 0.0001 2 0.06 100 0.05 0.95 0.45

Table 4. Results of Two-way Mixed Model ANOVA assessing differences in variables associated with treatment type and differences attributed to individuals (N=6, α = 0.05). Results are based off variables included in the MANOVA (Wilks; F16,234 = 16.26, p < 0.001).

Kinematic variable F statistictreatment Ptreatment F statisticindividual Pindividual Pitch angle (°) 42.04 < 0.001 1.06 0.30 Body bending coefficient 122.83 < 0.001 2.34 0.13 Pectoral fin flapping frequency (Hz) 1.14 0.32 1.77 0.18 Asynchronous Index 29.10 < 0.001 0.13 0.72 Ribbon fin frequency (Hz) 3.63 0.03 0.05 0.82 Ribbon fin amplitude (°) 4.97 < 0.001 2.25 0.14 Ribbon fin wavelength (cm) 28.60 < 0.001 0.26 0.61 Ribbon fin waves peed (cm/s) 28.73 < 0.001 0.05 0.26

Table 5. Average circulation (m2s-1) for clockwise and counterclockwise circulating vortices by treatment (N=2). Values are reported as means ± s.e. (standard error). Letters indicate significance from student’s t-tests within each treatment (α = 0.05). Repeated measures ANOVA results suggest no significant difference in circulation for clockwise circulating vortices or counter clockwise circulating vortices among maneuvers (F3,1 = 1.37, p = 0.54 and F3,1 = 3.56, p = 0.37 respectively, α = 0.05).

Clockwise circulation Counter clockwise circulation Maneuver (m2s-1) (m2s-1) n Steady swimming 1.03 x 10-5 ± 7.23 x 10-7 a 7.96 x 10-6 ± 3.99 x 10-7 b 8 Small turn 1.15 x 10-5 ± 9.45 x 10-7 a 1.08 x 10-5 ± 1.35 x 10-6 a 11 Large turn 1.48 x 10-5 ± 1.29 x 10-6 a 1.60 x 10-5 ± 1.29 x 10-6 a 6

Figures

Amiiform

Gymnotiform

Balistiform

Figure 1. Actinopterygiian phylogeny with emphasis on the convergent evolution of ribbon fin swimming. Representatives from several orders in which ribbon fin swimming has evolved are illustrated, but do not represent all ribbon fin swimmers. Red text indicates the descriptive mode of locomotion within ribbon fin swimming. Reproduced and modified from Jagnandan and Sanford, 2013 and Near et al., 2012)

A Body

Ribbon fin

Pectoral fins

Figure 2. Lateral (A) and ventral (B) views of the Black ghost knifefish, Apteronotus albifrons. All three control surfaces of interest are identified. Photo provided by Victor Ortega-Jimenez.

3 5 4

A 1

5 7

4 3

2 B

Figure 3. Schematic of the aerial view (A) and magnified lateral view (B) of the experimental set-up. Two Hi-Spec4 high speed cameras were positioned laterally (1) and ventrally (2) towards the center of the working section of the flow tank. A honeycomb (3) was placed upstream of the working section and a mesh (4) was placed downstream. A digital programmable servo motor (5) connected to an Arduino Uno R3 microcontroller (6) was used to control the oscillating feeder (7). Direction of flow (1.8 BL s-1) is indicated by an arrow. A green dotted line indicates the laser sheet used for digital particle image velocimetry (DPIV). Schematic not drawn to scale.

horizontal line DVA

pitch

∆푟푥푦푧 푉 = 푅푓 ∆푡

Lb Lc

CCA left

퐿푐 훽푏 = 1 − right 퐿푏

∑ |퐷𝑖푓푙푒푓푡 − 퐷𝑖푓푟𝑖푔ℎ푡| 퐴푠푦푛푐ℎ푟표푛표푢푠 𝑖푛푑푒푥 (퐴퐼) = [ ] 2(푓푟푎푚푒푠 − 1)

Figure 4. Schematic of digitized landmarks used in the calculation of pitch, dorso-ventral pectoral fin abduction angle (DVA), wave speed (VRf), body bending coefficient (ßb), cranio-caudal pectoral abduction angle (CCA), ribbon fin amplitude, ribbon fin wavelength, ribbon fin frequency, and the Asynchronous Index (AI). See methods for detailed information on each variable. Figure reproduced and modified from Ortega-Jimenez and Sanford 2021.

Figure 5. Averages for pitch angle (A) and the body bending coefficient (B) by treatment (n=6). Outliers are removed for graphical representation. Descriptive and test statistics are provided in Table 2. Letters indicate results of Bonferroni pairwise comparisons following a One-Way Repeated Measures ANOVA (α = 0.05).

Figure 6. Averages for pectoral fin flapping frequency (A) and the dorso-ventral pectoral abduction angle (B) by treatment (n=6). Outliers are removed for graphical representation. Descriptive and test statistics are provided in Table 2. Letters indicate results of Bonferroni pairwise comparisons following a One-Way Repeated Measures ANOVA (α = 0.05).

Figure 7. Averages for right (A) and left (B) cranio-caudal pectoral fin abduction angle by treatment (n=6). Outliers are removed for graphical representation. Silhouettes indicate the abducted fin and the angle of interest from the ventral perspective. Descriptive and test statistics are provided in Table 2. Letters indicate results of Bonferroni pairwise comparisons following a One-Way Repeated Measures ANOVA (α = 0.05).

Figure 8. Averages for the Asynchronous Index by treatment (n=6). Outliers are removed for graphical representation. For the AI, values that are 0-0.5 suggest synchronous use of the fins while values above 0.5 to 1 suggest asynchronous use of the fins. Descriptive and test statistics are provided in Table 2. Letters indicate results of Bonferroni pairwise comparisons following a One-Way Repeated Measures ANOVA (α = 0.05).

Figure 9. Averages for ribbon fin frequency (A), wavelength (B), ribbon fin amplitude (C), and wave speed (D) by treatment (n=6). Outliers are removed for graphical representation. Descriptive and test statistics are provided in Table 2. Letters indicate results of Bonferroni pairwise comparisons following a One-Way Repeated Measures ANOVA (α = 0.05).

RFwlength

2 )

% Wspeed

7 .

1 Small

(

2 AI

n +

0 a

C + Steady La+rge ampRF Freq_pec FreqRF

2 bbcoef - Pitch

-6 -4 -2 0 2 4 6 8

Can1 (98.3%)

Figure 10. Canonical discriminant analysis (CDA) using observations from six individuals to separate steady swimming (n=35), small turns (n=47), and large turns (n=48) by kinematic variables representing each control surface. Canonical scores for each group are represented in light blue circles for steady swimming, dark blue circles for small turns, and green circles for large turns. Ellipses indicate 68% probability of scores falling near the mean (represented by a cross). All kinematic variables of interest are included except the three measurements of pectoral abduction angle. The first canonical axis significantly contributes to the maximum separation of treatments (p < 0.05).

Figure 11. Vorticity fields representing the steady swimming (A), small turns (B), and large turns (C) treatments. Black masks in the fields represent the approximate position of the ribbon fin as it intersects the horizontal laser sheet. Red vortices indicate clockwise rotation while blue vortices indicate counter clockwise rotation. Scale bar represents 1 cm.