FISH FINS AND FAST-STARTS: MULTI-LEVEL ANALYSES REVEAL

FUNCTIONAL VARIATION WITHIN MEDIAN FINS OF BLUEGILL SUNFISH

BY

BRAD A. CHADWELL

A Dissertation Submitted to the Graduate Faculty of

WAKE FOREST UNIVERSITY

GRADUATE SCHOOL OF ARTS AND SCIENCE

in Partial Fulfillment of the Requirements

for the Degree of

DOCTOR OF PHILOSOPHY

in the Department of Biology

May 2010

Winston-Salem, North Carolina

Approved By:

Miriam A. Ashley-Ross, Ph.D., Advisor

Examining Committee:

Susan E. Peters, Ph.D., Chair

Robert A. Browne, Ph.D.

William E. Conner, Ph.D.

Wayne L. Silver, Ph.D.

ii

DEDICATION

To Rhonda, the other half of my smile.

Thank you for your love, support and unwavering belief in me! iii

ACKNOWLEDGEMENTS

I offer my sincere gratitude to my advisor, Dr. Miriam Ashley-Ross, for the instruction, guidance and support she offered through the years. She has provided much appreciated encouragement and advocacy, as well as academic counsel. I thank my committee members, Dr. Sue Peters, for a solid foundation; Dr. Bill Conner, for direction and clarification in writing; Dr. Bob Browne for assistance in statistical analyses; and Dr. Wayne Silver for instruction in neuroscience. I also thank my colleagues Dr. Jesse Barber and Mr. Jake Saunders for the many scientific discussions that contributed to my overall knowledge of biology as well as my specific project, and Mr. Jeff Muday for his expert assistance in computer science. Financial support for travel to international conferences so that I could present my research to the scientific community was provided by the Biology Department Cocke Travel Fund and the Graduate School Alumni Travel.

Chapter-Specific Acknowledgements

Chapter 1: I thank Mr. Ben Hunter, an outstanding undergraduate student, for his assistance in the preparation and measurements of all the individual fin-rays and muscle masses. To Dr. Anita McCauley, I offer my gratitude for her expert assistance and instruction in microscopy, which was vital in capturing the images of the fins used for measurements.

Chapters 2 and 3: I thank Dr. George V. Lauder at Harvard University for allowing me the use of his lab and cameras to record of the escape responses of the bluegill sunfish. I also thank the members of his lab for their contributions. In particular, Dr. Em Standen for assistance with the setup and recording of the sequences, and Dr. Peter Madden for providing his custom digitizing program, Digimat, used to obtain the 3-D data needed for such an intensive analysis. This trip was funded by the Biology Department Vecellio Fund. iv

TABLE OF CONTENTS

Page

LIST OF TABLES ...... vi

LIST OF FIGURES ...... vii

SYMBOLS AND ABBREVIATIONS ...... x

ABSTRACT ...... xii

INTRODUCTION TO THE DISSERTATION ...... 1

CHAPTER 1 ...... 8 Musculoskeletal morphology and regionalization within the dorsal and anal fins of bluegill sunfish (Lepomis macrochirus)

Abstract ...... 9

Introduction ...... 10

Methods and Materials ...... 15

Results ...... 22

Discussion ...... 31

Literature Cited ...... 43

CHAPTER 2 ...... 101 3-D kinematic analysis of the dorsal and anal fins during the fast-start of the bluegill sunfish (Lepomis macrochirus) I: Fin-ray orientation and movement

Abstract ...... 102

Introduction ...... 103

Methods and Materials ...... 107

Results ...... 121

Discussion ...... 127

Literature Cited ...... 138

v

CHAPTER 3 ...... 181 3-D kinematic analysis of the dorsal and anal fins during the fast-start of the bluegill sunfish (Lepomis macrochirus) II: Fin-ray curvature

Abstract ...... 182

Introduction ...... 183

Methods and Materials ...... 186

Results ...... 193

Discussion ...... 196

Literature Cited ...... 201

APPENDIX: Matlab codes for kinematic analysis and visualization ...... 223

Introduction ...... 224

Appendix A: Axial Codes ...... 227

Appendix B: Fin Codes ...... 234

Appendix C: Data Visualization ...... 240

SCHOLASTIC VITA ...... 246

vi

LIST OF TABLES

Page

Table 2.1 Escape Response Kinematic Parameters by Fish ...... 141

Table 2.2 Spiny Dorsal Fin-Ray Kinematic Parameters by Fish ...... 142

Table 2.3 Kendall’s W and Friedman’s χ2 for Spiny Dorsal Fin-Ray Kinematic Parameters ...... 143

Table 2.4 Soft Dorsal Fin-Ray Kinematic Parameters by Fish ...... 144

Table 2.5 Anal Fin-Ray Kinematic Parameters by Fish ...... 145

Table 2.6 Kendall’s W and Friedman’s χ2 for Soft Dorsal Fin-Ray Kinematic Parameters ...... 146

Table 2.7 Kendall’s W and Friedman’s χ2 for Anal Fin-Ray Kinematic Parameters ...... 147

Table 2.8 Multigroup W for Soft Dorsal vs. Anal Fin-Ray Kinematic Parameters ...... 148

Table 3.1 Soft Dorsal Fin-Ray Curvature Parameters by Fish ...... 203

Table 3.2 Anal Fin-Ray Curvature Parameters by Fish ...... 204

Table 3.3 Kendall’s W and Friedman’s χ2 for Soft Dorsal Fin-Ray Curvature Parameters ...... 205

Table 3.4 Kendall’s W and Friedman’s χ2 for Anal Fin-Ray Curvature Parameters ...... 206

vii

LIST OF FIGURES

Page

Figure 1.1 Skeletal supports of the anal fin ...... 45

Figure 1.2 Schematic of fin-ray joints and muscles ...... 47

Figure 1.3 Illustration of bluegill sunfish and its fins ...... 49

Figure 1.4 Length vs. spine position ...... 51

Figure 1.5 Regional contributions to ray length vs. position ...... 53

Figure 1.6 Regional lengths vs. ray position ...... 55

Figure 1.7 Relative regional lengths vs. ray position ...... 57

Figure 1.8 Rank order of regional lengths vs. ray position ...... 59

Figure 1.9 Rank order of relative lengths vs. ray position ...... 61

Figure 1.10 Difference in regional lengths vs. position between dorsal and anal rays ...... 63

Figure 1.11 Difference in relative regional lengths vs. ray position ...... 65

Figure 1.12 Rank order of regional differences vs. ray position ...... 67

Figure 1.13 Rank order of relative regional differences vs. ray position ...... 69

Figure 1.14 Contributions to fin-ray muscle mass vs. spine position ...... 71

Figure 1.15 Fin-ray muscle mass vs. spine position ...... 73

Figure 1.16 Relative fin-ray muscle mass vs. spine position ...... 75

Figure 1.17 Rank order of fin-ray muscle mass vs. spine position ...... 77

Figure 1.18 Rank order of relative fin-ray muscle mass vs. spine position ...... 79

Figure 1.19 Contributions to fin-ray muscle mass vs. ray position ...... 81

Figure 1.20 Fin-ray muscle mass vs. ray position ...... 83

viii

Figure 1.21 Relative fin-ray muscle mass vs. ray position ...... 85

Figure 1.22 Rank order of fin-ray muscle mass vs. ray position ...... 87

Figure 1.23 Rank order of relative fin-ray muscle mass vs. ray position ...... 89

Figure 1.24 Difference in fin-ray muscle mass vs. position between dorsal and anal rays ...... 91

Figure 1.25 Difference in relative fin-ray muscle mass vs. ray position ...... 93

Figure 1.26 Rank order of muscle mass differences vs. ray position ...... 95

Figure 1.27 Rank order of relative muscle mass differences vs. ray position . . . . 97

Figure 1.28 Muscle mass vs. fin-ray length ...... 99

Figure 2.1 Stages of a C-start ...... 149

Figure 2.2 The bluegill sunfish ...... 151

Figure 2.3 Schematic of the flow tank set-up for video capture ...... 153

Figure 2.4 The reconstructed dorsal fin surface and ray angles ...... 155

Figure 2.5 Center of mass kinematics throughout a C-start ...... 157

Figure 2.6 Axial turning rate throughout a C-start ...... 159

Figure 2.7 Sweep angles of the spiny dorsal fin-rays ...... 161

Figure 2.8 Sweep parameters of the spiny dorsal fin-rays ...... 163

Figure 2.9 Span axis angles of the spiny dorsal fin-rays ...... 165

Figure 2.10 Span axis parameters of the spiny dorsal fin-rays ...... 167

Figure 2.11 Elevation and fin area parameters of the spiny dorsal fin-rays . . . . 169

Figure 2.12 Sweep angles of the soft dorsal and anal fin-rays ...... 171

Figure 2.13 Sweep parameters of the soft dorsal and anal fin-rays ...... 173

Figure 2.14 Span axis angles of the soft dorsal and anal fin-rays ...... 175

ix

Figure 2.15 Span axis parameters of the soft dorsal and anal fin-rays ...... 177

Figure 2.16 Elevation and fin area parameters of the soft dorsal and anal fin-rays . 179

Figure 3.1 Curvature in the dorsal fin ...... 207

Figure 3.2 Spanwise curvature of the soft dorsal fin-rays over time ...... 209

Figure 3.3 Spanwise curvature of the anal fin-rays over time ...... 211

Figure 3.4 Spanwise curvature parameters of the fin-rays ...... 213

Figure 3.5 Chordwise curvature of the soft dorsal fin-rays over time ...... 215

Figure 3.6 Chordwise curvature of the anal fin-rays over time ...... 217

Figure 3.7 Chordwise curvature parameters of the fin-rays ...... 219

Figure 3.8 Reconstructed bluegill and median fins ...... 221

x

SYMBOLS AND ABBREVIATIONS

Chapter 1 AF Anal fin. ARy Rays of the anal fin. ASp Spines of the anal fin. Br Length of the branched portion of a ray, measured in mm. DF Dorsal fin, the spiny and soft dorsal fins collectively. DRy Rays of the dorsal fin. DSp Spines of the dorsal fin. mDepr Mass of the depressor muscle, measured in mg. mErec Mass of the erector muscle, measured in mg. mInc Mass of the inclinator muscle, measured in mg. mTM Total mass of the inclinator, erector and depressor muscles, measured in mg. RL Total length of a ray, measured in mm. rBr Relative length of the branched portion of a ray, as a percent of total length. rDepr Relative mass of the depressor muscle, as a percent of total muscle mass. rErec Relative mass of the erector muscle, as a percent of total muscle mass. rInc Relative mass of the inclinator muscle, as a percent of total muscle mass. rSg Relative length of the segmented portion of a ray, as a percent of total length. Sg Length of the segmented portion of a ray, measured in mm. SpL Total length of a spine, measured in mm sfD Soft dorsal fin. spD Spiny dorsal fin. UBr Length of the unbranched portion of a ray, measured in mm. USg Length of the unsegmented portion of a ray, measured in mm. ΔX Difference between anal and dorsal fin-rays, where X represents any length or mass parameter (absolute or relative) . Chapters 2 and 3 Abbreviations COM Center of mass. sfA Soft region of the anal fin sfD Soft dorsal fin. spD Spiny dorsal fin. Rs Rostrum. Op Operculum. Ant Anterior trunk. Mid Middle trunk. Post Posterior trunk. DRy# Dorsal rays, where # indicates its numbered position within the fin. DSp# Dorsal spines, where # indicates its numbered position within the fin. ARy# Anal rays, where # indicates its numbered position within the fin. ASp# Anal spines, where # indicates its numbered position within the fin. xi

Subscripts Seg Body segment identifier. (t) Parameter values over the entire C-start sequence max1 First maximum peak event of a parameter. max2 Second maximum peak event of a parameter. tr Directional transition event, i.e., change in direction of rotation or orientation. r Fin-ray identifier Symbols A〈r〉 Area between fin-rays. a Acceleration of the COM parallel to the fish trajectory. C Chord axis of the fin surface. cT Tangent to the chordwise curve. D Displacement of the center of mass. Fr Frontal axis, a.k.a., normal to the frontal plane. L Lateral axis, a.k.a. normal to the fin surface. S1 Stage 1 of the C-start. S2 Stage 2 of the C-start. S Span axis of the fin surface. Sg Sagittal axis, a.k.a., normal to the sagittal plane. sT Tangent to the spanwise curve. T0 Time zero. Tr Transverse axis, a.k.a., normal to the transverse plane. tX Time of a given parameter, where X is the event of a given parameter. v Velocity of the COM parallel to the fish trajectory. α¯ Average span axis angle of a fin-ray. ΔtX Time difference between a given fin-ray parameter and its corresponding axial event, where X is the event of a given parameter. φ¯ Average elevation of a fin-ray. κspan0 Spanwise curvature, perpendicular to the fin surface. κchord Chordwise curvature, perpendicular to the fin surface and span axis. θ′ Turning rate, i.e., the first time derivative of yaw. ω¯ Average sweep angle of a fin-ray. xii

ABSTRACT

Brad A. Chadwell

FISH FINS AND FAST STARTS: MULTI-LEVEL ANALYSES REVEAL FUNCTIONAL VARIATION WITHIN MEDIAN FINS OF BLUEGILL SUNFISH

Dissertation under the direction of Miriam A. Ashley-Ross, Ph.D., Associate Professor of Biology

Fins act as control surfaces by which fish can generate and react to hydrodynamic forces during a variety of locomotor behaviors. Within the ray-finned fish, the unique segmented, bilaminar design of their fin rays, for which they are named, provide the fish with the ability to independently control the degree of stiffness and curvature of each ray, enabling them to modulate the fin surface and the resultant hydrodynamic forces. While fin morphology and kinematic properties have been studied extensively, previous researchers have looked at the fins as a whole, overlooking variation between rays within the same fin. This work focused on describing the morphological and kinematic variation among fin-rays within the dorsal and anal fins of the bluegill sunfish, Lepomis macrochirus.

Examining several musculoskeletal features of individual fin-rays within the dorsal and anal fins of bluegill, variation in (1) spine and ray lengths, (2) the proportion of the rays that were segmented or branched and (3) masses of the muscle slips that actuate the fin-rays were found; differences were correlated to longitudinal position within the fin. The quantitative results matched with a qualitative assessment of positional variations in fin-ray flexibility and joint mobility. Based on variation in morphological and biomechanical properties, regional differences in fin-ray kinematics xiii during locomotion, allowing discrete regions of the fins to perform distinct functional roles, were proposed.

Three-dimensional kinematics of selected individual fin-rays were quantified during the escape response of bluegill sunfish, a stereotypical behavior in which the fish undergoes a rapid acceleration and displacement to avoid predation. During this behavior, timing and magnitude of angular displacement and curvatures among fin-rays also differed predictably with longitudinal position.

Most interestingly, a chordwise cupping of all three fins during Stage 1 of the fast-start was consistent with recent findings that median fins contribute to thrust forces generated by the body. Furthermore, a traveling wave along the lengths of the posterior rays of the soft dorsal and anal fins may be integral in determining the final direction of water jet to optimize the fin’s thrust component, rather than generating only lateral, stabilizing forces.

1

INTRODUCTION TO THE DISSERTATION

2

‘There is war between the larger and the lesser fishes: for the big fishes prey

on the little ones.’ – Aristotle, The History of Animals, 350 BCE

And the war continues to this day; though the little fishes are not without their defenses. Perhaps the most ubiquitous defense against predation among fish is the escape response, found in a wide range of fish phylogenies, including lamprey (Currie and

Carlsen, 1987), sharks (Domenici et al., 2004), and within all branches of the

Actinopterygii (Domenici and Blake, 1997; Eaton et al., 1977; Hale et al., 2002;

Westneat et al., 1998). Similar escape responses have been described in amphibians as well (Azizi and Landberg, 2002; Hews and Blaustein, 1985). In most species studied, the

Mauthner cell, a giant neuron, plays a primary role in the neural control of the escape response (reviewed by Eaton et al., 1977; Nissanov et al., 1990). The escape response is a stereotyped fast-start behavior, lasting < 1 s, in which the fish undergoes a burst of acceleration to distance itself from the threat. While there are variations in the form of the escape response, the C-start is the most common and has been studied extensively in a variety of teleost species (reviewed by Domenici and Blake, 1997). In the first mathematical model of the C-start, Weihs (1973) described three kinematic events: the preparatory stage (Stage 1), in which the body bends to one side, forming the aptly named ‘C-shape’; the propulsive stroke (Stage 2), during which the fish accelerates away from the threat; and the variable stage (Stage 3), in which the fish either continues to swim away, glides to a stop or performs a braking maneuver.

As a determining factor for avoiding predation, fish with greater escape response performances have a selective advantage (Ghalambor et al., 2003; Walker et al., 2005). It has been hypothesized that fish with enlarged dorsal and anal fins positioned close to the 3 caudal fin could act as an accessory tail to increase acceleration and thrust forces (Weihs,

1973), though it has been shown that this is not the only way to maximize performance as fish with different body forms achieve similar maximum accelerations (Webb, 1976).

Despite the recognition that large median fins play an integral role in the performance of the escape response for fish that possess them, previous studies have paid little attention to the actual movement of the median fins. At most, it has been reported that the splaying of the fins (either some or all) occurs simultaneously with the onset of

Stage 1 (Eaton et al., 1977) and/or that the fins are fully erected prior to, or soon after, the acceleration of Stage 2 (Webb, 1977; 1978). This alone provides no information as to what the fin is doing and how it might be contributing to the performance of the escape response.

The large dorsal and anal fins of the bluegill sunfish (Lepomis macrochirus) have been shown to contribute to the thrust forces during steady swimming (Drucker and

Lauder, 2001; Tytell, 2006) and most recently, the C-start (Tytell and Lauder, 2008).

While hydrodynamic analyses are vital in demonstrating the contribution of the fins, they do not provide the details necessary to explain how the fins are interacting with the flow to generate and orient the flow of water. In order to provide further insight into the role of the median fins during the escape response, I carried out a multilevel analysis of the morphology and three-dimensional kinematics of individual fin-rays within the dorsal and anal fins of the bluegill sunfish.

In Chapter 1, I show that the morphology of the dorsal and anal fins of bluegill sunfish are not uniform, but instead individual fin-rays vary in their musculoskeletal design and biomechanical properties based on their position within the fins. I measured 4 the mass of the muscle slips for each fin-ray, and lengths of the individual spines and rays of the dorsal and anal fin, as well as the portion of each ray that was segmented vs. unsegmented and branched vs. unbranched. The pattern of variation in the musculoskeletal parameters among the fin-rays matched with the variation in the degree of flexibility and joint mobility observed, with the anterior supports of the fin being less flexible with a more restricted range of mobility than the posterior fin-rays. From the morphological regionalization of the fins, I propose distinct functional roles during locomotion, in which the stiffer anterior regions of the fins resist lateral forces and act to stabilize the fish, while the flexible posterior regions are used to direct the orientation of the flow to optimize the thrust component of the wake forces generated during locomotion.

In Chapters 2 and 3, I present detailed kinematic analyses of individual spines and rays of the dorsal and anal fins during the C-start escape response of the bluegill sunfish.

True three-dimensional coordinates of the body and fin-rays were digitized from video sequences captured by three synchronized high-speed cameras. In Chapter 2, I quantify movement and orientation of the fin-rays, relative to the body axis. As predicted from the morphological results, maximum angular displacement was greatest among the more flexible and mobile posterior rays of the fin. Second, the timing of angular displacement supported the hypothesis that the fins are actively resisting hydrodynamic forces that would tend to oppose the movement of the fins.

In Chapter 3, I extend the kinematic analysis of the soft dorsal and anal fins by examining the spanwise and chordwise curvature of the fin surface throughout the C-start sequence. Unlike the maximum angular displacements, maximum curvature among the 5 fin-rays did not vary consistently with position, though the spanwise curvature of the posterior fin-rays tended to be greater than the anterior fin-rays. Timing of maximum curvature was either uniform among the fin-rays or showed no consistent pattern with fin-ray position. However, the fin surface underwent a stereotypical postero-distal undulation. Among the anterior fin-rays, a wave of chordwise curvature in the fin surface traveled posteriorly along the chord length of the fin over time. Within the posterior region of the fin, a wave of spanwise curvature traveled distally along the lengths of the fin-rays, increasing in magnitude. Initiation of the surface undulation started midway though Stage 1 of the C-start, reaching the trailing edge of the fins soon after the start of

Stage 2.

Supporting the previous electromyographic (EMG) studies of the inclinator muscles of the dorsal fin (Jayne et al., 1996) and hydrodynamic (Tytell and Lauder,

2008) studies of the median fins during the C-start of the bluegill sunfish, I have shown that the kinematic patterns of the individual fin-rays within the median fins vary to produce a complex, yet stereotyped undulation of the fin surface. From the regional variations observed, I suggest functionally distinct roles within the fins. Specifically, the elevation and cupping of the anterior spiny dorsal fin increases the lateral depth of the body, thereby increasing the volume of water upon which the fish can exert force to generate acceleration. Second, a chordwise undulation within the anterior region of the soft dorsal and anal fins moves the water posteriorly along the fin, helping to overcome the inertia of the water. Third, a spanwise undulation of the posterior fin region accelerates the flow of the water caudally to optimize the thrust component of the hydrodynamic forces generated by the fin. The simple outward appearance of the median 6 fins belies the complexity of their design and function. To truly understand the intricacy of the fins as control surface requires the integration of detailed analysis at all levels of study: morphology, biomechanical properties, EMG, kinematics and hydrodynamics.

All three chapters are in preparation to be submitted for publication. Chapter 1 will be submitted to the Journal of Morphology with Ben Hunter and Miriam A. Ashley-

Ross as co-authors. Chapters 2 and 3 will be submitted to the Journal of Experimental

Biology, with Emily M. Standen, George V. Lauder and Miriam A. Ashley-Ross as co- authors.

LITERATURE CITED

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

Currie SN, Carlsen RC. 1987. Functional significance and neural basis of larval lamprey startle behaviour. J Exp Biol 133:121-135.

Domenici P, Blake RW. 1997. The kinematics and performance of fish fast-start swimming. J Exp Biol 200:1165-1178.

Domenici P, Standen EM, Levine RP. 2004. Escape manoeuvres in the spiny dogfish (Squalus acanthias). J Exp Biol 207:2339-2349.

Drucker EG, Lauder GV. 2001. Locomotor function of the dorsal fin in teleost fishes: Experimental analysis of wake forces in sunfish. J Exp Biol 204:2943-2958.

Eaton RC, Bombardieri RA, Meyer DL. 1977. The Mauthner-initiated startle response in teleost fish. J Exp Biol 66:65-81.

Ghalambor CK, Walker JA, Reznick DN. 2003. Multi-trait selection, adaptation, and constraints on the evolution of burst swimming performance. Integr Comp Biol 43:431-438.

Hale ME, Long JH, Jr., McHenry MJ, Westneat MW. 2002. Evolution of behavior and neural control of the fast-start escape response. Evolution 56:993-1007.

Hews DK, Blaustein AR. 1985. An investigation of the alarm response in Bufo boreas and Rana cascadae tadpoles. Behavioral and Neural Biology 43:47-57. 7

Jayne BC, Lozada GF, Lauder GV. 1996. Function of the dorsal fin in bluegill sunfish: Motor patterns during four distinct locomotor behaviors. J Morphol 228:307-326.

Nissanov J, Eaton RC, DiDomenico R. 1990. The motor output of the Mauthner cell, a reticulospinal command neuron. Brain Res 517:88-98.

Tytell ED. 2006. Median fin function in bluegill sunfish Lepomis macrochirus: Streamwise vortex structure during steady swimming. J Exp Biol 209:1516-1534.

Tytell ED, Lauder GV. 2008. Hydrodynamics of the escape response in bluegill sunfish, Lepomis macrochirus. J Exp Biol 211:3359-3369.

Walker JA, Ghalambor CK, Griset OL, McKenney D, Reznick DN. 2005. Do faster starts increase the probability of evading predators? Funct Ecol 19:808-815.

Webb PW. 1976. The effect of size on the fast-start performance of rainbow trout Salmo gairdneri, and a consideration of piscivorous predator-prey interactions. J Exp Biol 65:157-177.

Webb PW. 1977. Effects of median-fin amputation on fast-start performance of rainbow trout (Salmo gairdneri). J Exp Biol 68:123-135.

Webb PW. 1978. Fast-start performance and body form in seven species of teleost fish. J Exp Biol 74:211-226.

Weihs D. 1973. The mechanism of rapid starting of slender fish. Biorheology 10:343- 350.

Westneat MW, Hale ME, McHenry MJ, Long JH. 1998. Mechanics of the fast-start: Muscle function and the role of intramuscular pressure in the escape behavior of Amia calva and Polypterus palmas. J Exp Biol 201 (Pt 22):3041-3055.

8

CHAPTER 1

MUSCULOSKELETAL MORPHOLOGY AND REGIONALIZATION WITHIN THE

DORSAL AND ANAL FINS OF BLUEGILL SUNFISH (LEPOMIS MACROCHIRUS)

9

ABSTRACT

Ray-finned fishes actively control the shape and orientation of their fins to either generate or resist hydrodynamic forces. Due to the emergent mechanical properties of their segmented, bilaminar fin rays, lepidotrichia, and actuation by multiple muscles, fish can control the rigidity and curvature of individual rays independently, thereby varying the resultant forces across the fin surfaces. Expecting that differences in fin-ray morphology should reflect variation in their mechanical properties, we measured several musculoskeletal features of individual spines and rays of the dorsal and anal fins of bluegill sunfish, Lepomis macrochirus, and assessed their mobility and flexibility. We separated the fin-rays into four groups based on the fin (dorsal or anal) or fin-ray type

(spine or ray) and measured the length of the spines/rays and the mass of the three median fin-ray muscles: the inclinators, erectors and depressors. Within the two ray groups, we measured the portion of the rays that were segmented vs. unsegmented and branched vs. unbranched. For the majority of variables tested, we found that variations between fin-rays within each group were significantly related to position within the fin and these patterns were conserved between the dorsal and anal rays. Based on positional variations in fin-ray and muscle parameters, we suggest that each fin can be divided into anterior and posterior regions that perform different functions when interacting with the surrounding fluid. Specifically, we suggest that the stiffer anterior rays of the soft dorsal and anal fins maintain stability and keep the flow across the fins steady. The posterior rays, which are more flexible with a greater range of motion, fine-tune their stiffness and orientation, directing the resultant flow in a direction to generate lateral and thrust forces, thus acting as accessory caudal fins. 10

INTRODUCTION

Actinopterygian fishes can actively control the shape and curvature of their fins due to the unique design feature of the supporting bony fin-rays (Fig. 1.1). Named for this defining characteristic, ray-finned fishes are able to adjust the stiffness and curvature of individual fin-rays, known as lepidotrichia, allowing for fine-tuned manipulation of the fin surface and resulting fin conformation (Alben et al., 2007; 1971; Lauder, 2006;

McCutchen, 1970; Videler, 1977).

Although detailed structural descriptions of lepidotrichia and their mechanical properties are available from only a few teleost species: gourami and goldfish (Haas,

1962); trout (McCutchen, 1970); tilapia (Geerlink and Videler, 1987; Videler, 1977) and bluegill sunfish (Alben et al., 2007), the general structure of lepidotrichia has been found to be consistent across all ray-finned fishes examined (Arita, 1971; Eaton, 1945;

Goodrich, 1904). Each lepidotrich is composed of two halves, or hemitrichia (Fig. 1.1C), located opposite each other on each side of the fin bound together by flexible collagen fibers (Haas, 1962; Videler, 1977). The proximal third of each hemitrich is a single piece of unsegmented bone, while the remaining portion, which is often branched, consists of several bony segments (Fig. 1.1). The proximal end of each unsegmented bone expands to form the head, which articulates with the underlying endoskeletal fin supports and serves as the attachment sites for the muscles of the fin-ray (Figs. 1.1 and 1.2). The most distal segments are bound by an unmineralized, extracellular matrix of collagenous fibrils, known as actinotrichia (Haas, 1962; Videler, 1977), which prevent the distal segments from being able to move relative to one another. 11

In the dorsal and anal fins, three muscles attach to the heads of both hemitrichia: the inclinator, erector and depressor muscles (Winterbottom, 1974). Originating from the fascia between the skin and axial musculature, the inclinator inserts laterally onto the head and is responsible for lateral movement of the fin-ray (Fig. 1.2B). The erector and depressor muscles originate from the lateral surfaces of the rays’ endoskeletal support

(the pterygiophores) and insert onto anterolateral and posterolateral processes of the head

(erector and depressor, respectively) and serve to erect or depress the fin-ray (Fig. 1.2B).

The complex arrangement described above, coupled with the mechanical properties of the composite materials comprising the structure, allows the fish to control the bending and stiffness of individual lepidotrichia. A force parallel to the long axis of the lepidotrich applied to one side displaces the two hemitrichia relative to one another, causing the ray to curve to one side and stiffen. Previously thought to be a passive reaction to hydrodynamic loading during swimming to prevent over bending and to maximize propulsive thrust generated by the fins (McCutchen, 1970), later studies demonstrated that fish have a more active role in controlling the ray curvature and stiffness (Alben et al., 2007; Arita, 1971; Geerlink and Videler, 1987; Videler, 1977).

Fish can activate fin muscles of the rays to not only reduce or prevent fin bending but to potentially modulate the hydrodynamic forces generated by actively controlling the shape and rigidity of the entire fin surface (Alben et al., 2007).

In derived teleost fishes, primarily within Acanthopterygii, specialized lepidotrichia composed of a single unbranched bony element, known as spines, support the anterior regions of the dorsal and anal fins (Fig. 1.1A and 1.3). Spines typically have the same complement of muscles attaching to them as lepidotrichia (Fig. 1.2D); however, 12 spine movement is restricted primarily to elevation/depression, with little to no lateral deflection (Eaton, 1945; Geerlink and Videler, 1973). Widely accepted as an anti- predator device (Hoogland et al., 1956), the suggested role of the spines during locomotion is to act as a keel or cutwater (Eaton, 1945). However, to our knowledge, no study has investigated what hydrodynamic role, if any, spiny regions of the median fins play during swimming behaviors, with the exception of the observation that the orientation and velocity of flow at the region of the spiny dorsal fin does not change during slow swimming speeds (Drucker and Lauder, 2001a).

Within the literature, the wide range of locomotor behaviors observed among ray- finned fishes has long been attributed to the variability in the anatomy and mechanics of the fins used for a particular swimming mode, e.g. undulation of the body and caudal fin vs. movement of the pectoral fins (see Blake, 2004; Lauder, 2006; Walker, 2004 for recent reviews). Despite the observation that fish are capable of controlling fin conformation depending on the swimming behavior employed, few studies have examined whether variations in fin-ray morphology within the fins exist and what effect they may have on their mechanical properties and/or kinematic parameters during locomotion (Arita, 1971; Lauder and Madden, 2007; Standen and Lauder, 2005; Taft et al., 2008).

The focus of studies for more than a decade, the bluegill sunfish, Lepomis macrochirus (Perciformes), displays a repertoire of different locomotor behaviors. The combination of fins used and their kinematic patterns are equally varied, based on the swimming mode employed (Drucker and Lauder, 2000; 2001a; b; Jayne et al., 1996;

Lauder and Drucker, 2004; Lauder and Madden, 2007; Standen and Lauder, 2005). For 13 example, during steady swimming at low speeds (< 1 body length per sec), the paired pectoral fins are used exclusively; however, as swimming speed increases, axial undulations concurrent with the oscillation of the dorsal and anal fins contribute to the propulsive forces (Drucker and Lauder, 2000; 2001a; Standen and Lauder, 2005).

Despite the extensive studies of the kinematics and wake forces generated by the various fins of the bluegill during different modes of swimming behaviors, and the few studies that have attempted to evaluate kinematic variations within a fin (Jayne et al., 1996;

Standen and Lauder, 2005), differences in the musculoskeletal morphology of individual fin-rays and their effect on fin kinematics have not been investigated.

Upon examination, it becomes evident that variations in the lengths of fin-rays based on their position within the fin plays a clear role in fin-shape (Figs. 1.1A and 1.3) and it is the consistency in this pattern among conspecifics that establishes the characteristic fin-shape for a species. Building upon this observation, if the lengths of fin-rays demonstrate a predictable pattern of variation, do other morphological characteristics of fin-rays also demonstrate patterns of variation based on their position within the fin? While changes in hydrodynamic forces applied to the fin surface contribute to the final fin shape, it is the morphology and mechanical properties of the fin-rays and their muscle slips that establishes the range of possible shapes and orientations.

As the dorsal and anal fins act as control surfaces and the mechanism by which forces are transmitted between the trunk and water, fin-rays and their muscles provide the only means by which fish can independently control the rigidity and orientation of the fin surface to either resist or generate hydrodynamic forces. While it has been accepted that 14 subtleties among the position and movement of individual fin-rays can influence fin shape and hydrodynamics, only a few studies have looked at individual fin-ray movement during locomotion and even fewer have compared differences in fin-ray morphology to their kinematic properties (Standen and Lauder, 2005; Taft et al., 2008).

In this study, we assess musculoskeletal traits of individual fin-rays of the dorsal and anal fins of L. macrochirus, quantifying patterns of morphological variation between fin-rays, based on their position within the fins (location along the long axis of the body) and fin type (dorsal vs. anal fin). From cleared and stained specimens, we measured the total spine or ray length, and the portion of each ray that was either unsegmented or segmented, and branched or unbranched. From preserved specimens, we measured the mass of the three individual muscle slips of each spine and ray: the inclinators, erectors and depressors (Winterbottom, 1974), comparing both the individual masses of the three muscles among the fin-rays as well as the total mass of the three muscles.

From the morphological variation found between rays, we suggest there exists variations in their mechanical properties, altering the kinematic and hydrodynamic properties over the fin surface, resulting in functional regionalization with the dorsal and anal fins. 15

MATERIALS AND METHODS

Animals

Lepomis macrochirus (Rafinesque, 1819) were acquired from a local fish hatchery (Foster Lake & Pond Management, Inc, Garner, NC) and maintained individually in 40 L tanks on a 12L:12D photoperiod at 23±3°C. Within 12 hours of death, specimens were fixed in 10% formalin for a minimum of 7 days. Sixteen individuals that showed no visible deformation or damage to their median fins were selected for this study, with standard length (SL, snout to caudal peduncle) ranging from

98 to 126 mm and body mass from 33.7 to 68.7 g. The dorsal fins were supported by 9-

10 spines and 13-14 lepidotrichia; anal fins were composed of 3 spines and 12-13 lepidotrichia.

Terminology

We follow the terminology established by Eaton (1945) when discussing the skeletal supports of the median fins. The term ‘rays’ indicates lepidotrichia that remain segmented and capable of bending versus the modified lepidotrichia that have fused into spines (Fig. 1.1). The term ‘fin-rays’ is used when referring to the external fin supports collectively and the distinction between rays and spines is ignored.

The pterygiophores provide the internal support of the dorsal and anal fins, their distal ends articulating with the head of the fin-rays. Each pterygiophore originates as a series of three cartilaginous radials, which may or may not fuse during ossification.

When the radials remain separate, they are called the proximal, middle and distal radials

(or proximal and distal if only two persist) (Figs. 1.1A and 1.2). 16

Among acanthopterygians, two distinct dorsal fins develop: an anterior fin supported by spines and a posterior fin supported by rays, called the spiny and soft dorsal fins, respectively (Mabee et al., 2002). Although the dorsal fins of L. macrochirus appear as a single continuous fin, we maintain the distinction between spiny dorsal fin and soft dorsal fin (Fig 1.3), as well as the division of the single anal fin into spines and rays.

Fin Skeleton

Seven fixed sunfish were washed with several changes of dH2O over 5 days in preparation of being cleared and stained for bone and cartilage (Song and Parenti, 1995).

Specimens were stained for cartilage with Alcian blue in an acidic ethanol solution over a

3 day period. Muscle and connective tissues were cleared over a 10 day period with trypsin in an aqueous sodium borate solution. Finally, specimens were stained for bone with Alizarin red S in a 0.5% potassium hydroxide solution for 24 hours. Specimens were transferred through a series of 30%, 70% and 100% glycerol changes for long-term storage.

Digital images of the whole fish were taken (DiMage S404 digital camera;

Minolta, Osaka, Japan). The dorsal and anal fins, including their ptyergiophores, were removed and examined under a stereomicroscope (Leica MZ16FA; Leica Microsystems,

Inc, Heerbrugg, Switzerland) coupled with a digital camera (Retiga 4000R; Q-Imaging,

Surrey, BC, Canada) and acquisition software (Image-Pro Plus v6.2; Media Cybernetics,

Inc, Bethesda, MD). Digital images of the dorsal and anal fins were captured with the rays and spines splayed and secured so that individual rays did not overlap. Illuminating the fins from underneath, the segmentation and branching patterns of the rays were easily distinguishable. 17

Digital images were imported into ImageJ (Rasband, 2008) for all measurements, with an object of known length in frame for scale. From images of the whole fish, SL was measured to take into account the shrinkage that occurs during the clearing and staining process (Mabee et al., 1998). From the close-up images of the fins, the lengths of three distinguishable regions of each lepidotrich were measured to the nearest 0.1 mm: the proximal, unsegmented region; the middle, segmented but unbranched region and the distal, segmented and branched region (Fig. 1.1C). As a single, unbranched bone, only the total lengths of the spines were measured.

From these regions, five skeletal variables were established for each ray: the total ray length (RL; sum of all three regions), unsegmented (USg) vs. segmented length (Sg; middle + distal) and unbranched (UBr; proximal + middle) vs. branched length (Br) (Fig

1.1D). In addition to their absolute lengths, the relative segmented (rSg) and branched

(rBr) lengths of each ray were calculated as percent of ray length, allowing comparison among the rays independent of length. Finally, to evaluate the symmetry between the rays of the dorsal and anal fins, dorsal ray values were subtracted from the corresponding anal ray values at the same ranked position to calculate ΔX (where X represents any variable, absolute or relative). For spines, total length (SpL) was the only variable measured and analyzed; due to the disparity in the number of spines and their longitudinal position (Fig. 1.3), differences in spine lengths between the dorsal and anal fins were not calculated.

Manipulations of the intact fins were performed by hand to assess the mobility of the spines and rays at their joints. Individual rays were then removed and manipulated to evaluate the flexibility and connection between hemitrichia. 18

Fin Muscles

From the remaining nine preserved fish, the muscle slips that actuate the fin-rays of the dorsal and anal fins were examined (Eaton, 1945; Winterbottom, 1974). With the exception of the last two rays of the sfD and AF (described below in Results), each fin- ray was actuated by three pairs of muscle slips (Fig. 1.2B,D). Removing the skin surrounding the base of each fin exposed the inclinator muscle slips (mInc). Because mInc attaches to the underlying fascia of the skin, special care was required to prevent the accidental loss of these muscle slips during skinning. Erector and depressor muscle slips

(mErec and mDepr, respectively) are located deep to mInc and the surrounding axial musculature, enclosed in a connective tissue sheath. Throughout the dissection,

Weigert’s solution was periodically applied to stain the myofibers, making it easier to distinguish between muscle and connective tissues.

From fish in which all muscle slips were still intact throughout the dissection, the mass of each individual muscle slip (left side only) was recorded to the nearest 0.1 mg with an electronic microgram scale. For each fin-ray, the masses of its three muscle slips were summed to get the total muscle mass (mTM). Similar to the skeletal variables, the relative mass of each muscle slip (rInc, rErec and rDepr) was calculated as a percent of mTM and the difference between the paired dorsal and anal ray muscle masses were calculated (ΔX).

Statistical Analysis

To avoid complications resulting from empty cells, specimens that had only 9 dorsal spines or 12 anal rays were excluded; in the few cases of individuals that had 14 dorsal rays, the first anterior ray was removed from the analysis. Six cleared and stained 19 specimens met this condition and were included for analysis of the skeletal variables. For the muscular analysis, five preserved specimens were included.

Fin-rays were assigned to one of four groups based on its fin-ray type (spine or ray) and fin (dorsal or anal): Dorsal Spine (DSp), Dorsal Ray (DRy), Anal Spine (ASp) and Anal Ray (ARy). Within each group, fin-rays of each individual were numbered according to its ranked longitudinal position within the fin, starting with the anterior most fin-ray. Due to a significant degree of heteroscedasticity within several variables, which was not eliminated even after a logarithmic or square root transformation, ANOVAs were deemed inappropriate for this analysis and a series of nonparametric tests were employed to examine the musculoskeletal variation within the four groups.

For the absolute and relative variables, position effects within each fin-ray group was tested using Freidman’s method for randomized blocks (χ2), with each specimen as a block and its fin-rays as the treatment levels (Sokal and Rohlf, 1981; Zar, 1984). In addition, Kendall’s coefficient of concordance (W) was calculated to estimate the degree of agreement in the rank order among fin-rays, providing a means to easily compare the consistency among fish. Ranging from 0 to 1, higher W scores signify an increasing degree of concordance, with perfect consistency in rank order among all fish resulting in

W = 1. Spearman’s rank correlation (rs) was calculated to assess the direction (positive or negative) and magnitude of the rank correlation between the positions of the fin-rays and their morphological features.

The other question we addressed was to determine what, if any, differences among the morphological variants existed between DRy and ARy. For variables with significant position effects (χ2) within both ray groups, multigroup coefficients of 20 concordance (W) were computed to test whether the observed position effect within the two fin groups were the same (Zar, 1984). Similar to W, increasing levels of agreement in rank order both within and between groups results in a W coefficient that approaches

1; significant concordance between variables of the two fins was determined by

comparing its Z-score (normal deviate) against the critical value (Zα) of the normal curve.

To evaluate the symmetry between DRy and ARy, fin effects were tested by performing a two-tailed, sign test on ΔX (both absolute and relative values) to establish whether the morphological traits of the rays of one fin were consistently larger than the other (Sokal and Rohlf, 1981; Zar, 1984). Positionfin interactions were examined by performing Friedman’s method (χ2) on ΔX of all variables to look for variation in symmetry between the paired rays of DRy and ARy. The coefficient of concordance (W) and Spearman’s rank correlation (rs) was also calculated to facilitate the description of the interactions.

Using the average fin-ray lengths from the six cleared and stained specimens and the average mass of each muscle slip from the five preserved fish, we calculated

Pearson’s product-moment correlation coefficients (r) between the spine/ray lengths

(dorsal and anal) and mass of their three muscles. Although not a statistically valid comparison, as the fin-ray lengths and muscle masses were not measured from the same individuals, it still provides an estimate to the relationship between fin-ray length and muscle mass.

Custom written programs, based on the equations of Zar (1984), were developed in MatLab v7.6 (Natick, MA) to perform the sign test and the concordance between groups (W and Z). All other statistical calculations were performed in SPSS v15.0 21

(Chicago, IL). It should be noted that because W was calculated from the χ2 obtained from Freidman’s method and shares the same P-value, the statistical interpretation for a trait’s concordance and its position effect (or interaction) are equivalent. To control for

Type I errors resulting from multiple comparisons of the skeletal (37) and muscular (49) characteristics, P-values were compared to corrected α-levels using the sequential

Bonferroni adjustment (Rice, 1989). As the majority of P-values were much less than the minimum adjusted α-level for both sets of characteristics (ca. 0.001), this correction affected only a few of the tests. 22

RESULTS

Fin Skeleton

Spines

Spine length varied significantly with longitudinal position within DSp (χ2 = 42.1; df = 5, 9; P < 0.001) and ASp (χ2 = 12.0: df = 5, 2; P < 0.001). Among the three spines of the anal fin, average spine length (SpL) consistently increased posteriorly for all individuals, from ca. 15 to 25 mm, revealing complete concordance (W = 1) in the rank order of SpL among the fish and a perfect positive rank correlation (rs = 1) between length and position (Fig. 1.4). Within DSp, SpL also increased with spine position; however, a consistent increase in spine length occurred only among the anterior four spines, from ca. 7 to 19 mm. Among the posterior 7 spines, average SpL remained similar, ca. 20 ± 1.5 mm (mean ± 1 s.d.), with no clear agreement in their rank order between individuals, resulting in a moderate degree of concordance (W = 0.78) and rank correlation (rs = 0.73), compared to that seen in ASp (Fig. 1.4).

Rays

Located opposite each other at approximately the same longitudinal position along the body (Fig. 1.2), rays of the soft dorsal and anal fins demonstrated similar patterns of changes in ray lengths (Figs. 1.5). For each of the seven skeletal variables studied, dorsal and anal rays at the same position within the fins show very little difference in their average lengths and had the same overall pattern in length changes with ray position (Figs. 1.6 and 1.7). Ray position had a significant effect on all seven variables within both DRy and ARy (χ2 > 35; df = 5, 12; P < 0.001) and between the two ray groups (Z > 10; P < 0.001). 23

When ranked by absolute length, all five skeletal variables (RL, USg, Sg, UBr and Br) showed a high degree of concordance among individuals within DRy and ARy

(W > 0.80) with the relationship between ray position and length falling into one of two generalized patterns (Fig. 1.8). Rank order of RL, USg and UBr lengths were highly correlated with position (rs ca. -0.90), with average lengths decreasing steadily with position within DRy and ARy (Figs. 1.6A,B,D and 1.8A,B,D). However, unlike the nearly uniform decrease in length across all ray positions observed in USg and UBr, average RL initially increased slightly among the anterior two or three rays (Fig. 1.6A).

Within DRy, the decrease in RL among the middle rays was small, but progressed rapidly among the posterior rays (Fig. 1.6A). In addition to strong position effects observed within DRy and ARy, all three variables also displayed high degrees of concordance between the two groups (W ≥ 0.95; Fig. 1.8).

The pattern of initial increase in ray length is attributable to Sg and Br, which increased initially, reaching maximum length at the 4th to 7th ray. Posterior to that range, average lengths decreased, producing rank orders that more closely resembled 2nd order polynomial curves than linear correlations (Figs. 1.6C, E and 1.8C, E). Within ARy, Sg and Br lengths were still moderately correlated with position (rs ca. -0.80); however, within DRy, the rank correlation within Sg and Br was much lower (rs = -0.60 and -0.29, respectively). For the position effects detected within DRy and ARy, the degree of concordance between ray groups was high for Sg (W = 0.88) but only moderately concordant for Br (W = 0.50) (Fig. 1.8C, E).

Within DRy and ARy, rSg increased with position from ca. 50 to 75% among the first eight rays after which rSg gradually decreased back to ca. 60% (Fig. 1.7A). This 24 curvilinear position effect was supported by strong degrees of concordance both within

DRy and ARy (W > 0.8) and between ray groups (W = 0.77; Fig. 1.9A). In contrast, rBr generally increased with ray position from ca. 30 to 55%, dropping slightly over the last two rays; however, increases in rBr from one ray to the next were inconsistent, particularly within ARy (Fig. 1.7B). Despite the variation in the rank order among individuals, rBr displayed strong to moderate levels of concordance within DRy and ARy

(W = 0.81 and 0.49, respectively) and between ray groups (W = 0.59), with moderately positive correlations between rBr and ray position (rs = 0.71 and 0.59, respectively; Fig.

1.9B).

The only significant fin effects were observed in ΔUSg (ARy > DRy) and ΔrSg

(DRy > ARy) (Figs. 1.10 and 1.11). However, significant positionfin interactions were found in ΔRL, ΔUSg, ΔSg and ΔBr (χ2 > 50; df = 5, 12; P < 0.0001), with the ranked ΔX values negatively correlated with position (-0.2 > rs > -0.8) (Fig. 1.12). These interactions were discernible such that ARy > DRy among the anterior rays, while ARy ≤

DRy posteriorly (Figs. 1.6 and 1.10). No significant interactions were found for ΔUBr,

ΔrSg or ΔrBr (χ2 > 25; df = 5, 12; P > 0.05; Figs 1.12D and 1.13).

Fin-Ray Articulation and Mobility

Similar to the arrangement described in the dorsal fin of tilapia (Geerlink and

Videler, 1973), the joint of each fin-ray (with exceptions for the first spine and last two rays) is formed by the distal radial of its corresponding pterygiophore and the proximal

(or middle) radial of the subsequent pterygiophore (Fig. 1.2A,C). While the components of the joints are similar between spines and rays, the arrangement of the components differ. Movements of individual fin-rays are also influenced by neighboring fin-rays, due 25 to their connections via the fin membrane as well as a band of connective tissue between the proximal bases of adjacent fin-rays. Thus, any movement of a fin-ray, though actuated by its own musculature, can be influenced by the movement of adjacent rays.

This is most readily observed when the elevation of one fin-ray causes all the posteriorly located fin-rays to elevate as well. Lateral movement of a single fin-ray also induced lateral movement among adjacent fin-rays, though its range of influence was not as large as seen in elevation.

Spines

The pterygiophore of each spine consists of proximal and distal radials, which are so closely associated that the distinction between the two was only possible under high magnification. The head of the spine is held securely in a socket composed of its corresponding distal radial and the next proximal radial (Fig. 1.2C), forming the joint. In both fins, the first spine lacks its own corresponding pterygiophore, articulating instead on an expansion of the proximal radial corresponding with the second spine. A decrease in length and robustness of the proximal radials with spine position was the only discernable morphological difference noted.

Regardless of position, all spines could easily be elevated or depressed by manual manipulation. While lateral deflection was limited, the spines varied in the degree of lateral deflection that could be attained and the amount of applied force required to achieve deflection. The three anal spines were the most resistant to any lateral deflection and the anterior spines of spD were highly resistant. Lateral mobility among the posterior spines of spD increased slightly with position, though the degree of deflection by these spines did not approach the lateral mobility seen in the rays. 26

Rays

Unlike the spines, the number of radials that persist past ossification varied among the pterygiophores of the rays. Anteriorly, only the proximal and distal radials of rays #1-6 remained visually distinct and for the rest of the rays, all three radials

(proximal, middle & distal) persisted, though the proximal and middle radials were closely attached. Unlike the joints of the spines, the distal radial is loosely held in a socket formed by its corresponding middle (or proximal) radial and the next proximal/middle radial (Figs. 1.1A and 1.2A), which allows for the rotation of the distal radial about the long axis of the fish (i.e., lateral deflection). The two heads of the lepidotrich articulate on either side of the distal radial to complete the joint (Fig. 1.1C), which allows the ray to rotate within the median plane (i.e., elevate/depress), relative to the distal radial (Geerlink and Videler, 1973). Unlike the other rays, the last two rays (of both fins) articulate with the same distal radial and there is no ‘next’ proximal radial to form the posterior edge of the socket (Fig. 1.1A). As with the spines, a decrease in length and robustness of the radials with ray position was observed. In addition, an increase in the distance between the distal radials and their socket can be observed in the images of the cleared and stained fins (Fig. 1.1A), suggesting that degree of mobility in the joint may increase with position.

During manipulations of the intact fins and rays, all rays could be easily elevated and depressed; however, the range of motion differed with position; maximal degree of elevation decreased with axial position while maximal degree of depression increased.

Compared to the spines, lateral deflection could easily be achieved although the degree of 27 deflection increased with position while the amount of force needed to elicit the deflection decreased.

With the isolated rays (i.e., removed from the fin), bending of most rays could be achieved by pulling on the head of one hemitrich while holding the other head stationary.

For the first, second and, in some cases, third rays, bending of the ray could not be achieved by this method. During inspection of these rays, under a dissecting scope, it was noted that the proximal unsegmented regions of the two hemitrichia were fused together and could not be moved relative to each other. The degree of fusion in these rays varied between specimens. For the remaining rays, the ease with which ray bending could be elicited and the degree of curvature attained increased with position.

In comparing the rays of the dorsal and anal fins, the robustness of the pterygiophore and ray joint was greater among the anterior anal rays compared to the anterior dorsal rays. There was also a decrease in the joint mobility and ray flexibility in the anterior anal fin. No differences in the pterygiophore robustness, joint mobility or ray flexibility between the posterior dorsal and anal rays could be discerned.

Fin Muscles

All fin-rays were actuated by three pairs of distinct muscle slips: mInc, mErec and mDepr, with the exception of the last two rays of the dorsal and anal fins. In addition to sharing their articulation with the same distal radial (as described above), the last two rays shared the same fin musculature, as has been described in other species

(Winterbottom, 1974). A single tendon of mInc appears to attach laterally to the heads of both rays. In addition, the bellies of this last pair of mErec and mDepr were fused together and could not be separated, as was easily done for all other fin-rays. A broad 28 tendon from mErec/mDepr attaches to lateral processes on both heads of the rays, deep to the insertion of mInc.

Due to the peculiar muscular arrangement of this last pair of rays, the associated muscle slips were discarded from analysis, leaving 12 position levels for mTM and mInc, and 11 for mErec and mDepr (rather than the 13 levels seen in the skeletal analysis). As each spine was actuated by its own muscle slips, the number of position levels within

DSp and ASp were the same as seen in the skeletal analyses (10 and 3, respectively).

Spines

For both DSp and ASp, mErec was the largest of the three muscle slips, contributing 50 to 75% of the total mass for each spine (Figs. 1.14-1.16). Within ASp, there was a high degree of concordance (W > 0.75) in the ranking of the absolute muscle mass; however, due to the small number of position levels, the P-values obtained exceeded the adjusted α-level and the observed position effects were concluded to be nonsignificant (χ2 > 7.5; df = 4, 2; P < 0.05; Fig. 1.17). In contrast, the relative distribution of the spine musculature (rInc, rErec and rDepr) within ASp was similar among the three positions, demonstrating no position effect (χ2 ≤ 5.2; df = 4, 2, P ≥

0.075; Fig. 1.18).

Within DSp, the depressor muscles (whether expressed as absolute or relative mass) showed no significant position effect (χ2 < 25; df = 4, 9; P > adjusted α-level; Figs.

1.17D and 1.18C). In contrast, significant position effects on the mass of inclinator and erector muscles (both absolute and relative measures) were found (χ2 > 35; df = 4, 9; P <

0.001; Figs. 1.17 and 1.18). Both mInc and rInc had a strong positive rank correlation with spine position (rs = 0.96 and 0.83, respectively; Figs 1.17B and 1.18A). While rErec 29

had a strong negative rank correlation with position (rs = -0.76; Fig. 1.18B), mErec was not correlated with position (rs = -0.13); rather, its distribution would be better fit with a

3rd order polynomial curve (Fig. 1.17C). Combined, total mass of the spine musculature

(mTM) had a significant position effect (χ2 = 26.3; df = 4, 9; P = 0.0018); as seen in

rd mErec, mTM fit a 3 order polynomial curve rather than a directional rank correlation (rs

= 0.14; Fig. 1.17A).

Rays

Unlike mErec of the spines, there was not one specific ray muscle that consistently contributed the majority of total muscle mass at all ray positions for either

DRy or ARy; instead, the three muscles of each were closer in mass (Figs. 1.19-1.21).

With the exceptions of mDepr (χ2 > 23.8; df = 4, 10; P > adjusted α-level) of the DRy, ray position had a significant effect on the absolute mass of each muscle (χ2 > 30; df = 4,

11/10; P < 0.001), showing a high degree of concordance (W > 0.75) and a moderate to strong negative rank correlation with position (-0.4 > rs > -.98; Fig. 1.22). Ray position had significant effects on rErec and rDepr of both fins (χ2 > 38; df = 4, 10; P < 0.001), with rErec negatively correlated and rDepr positively correlated with position (|rs| ≥ 0.8;

Fig. 1.23). For the five parameters in which position had a significant effect on muscle mass for both fin groups (mTM, mInc, mErec, rErec and rDepr), a significant degree of concordance between DRy and ARy was also found (Z > 10, df = 4, 11/10, P < 0.001)

(Figs. 1.22 and 1.23).

Of the seven ΔX parameters, significant fin effects were found in only two:

ΔrErec (ARy > DRy) and ΔrDepr (Dy > ARy) (Figs. 1.24 and 1.25). Significant positionfin interactions were found in three: ΔmTM, ΔmInc and ΔmErec (χ2 > 30.8; df 30

= 4, 11/10; P > adjusted α-level), with each parameter negatively correlated with position

(Figs. 1.26 and 1.27). As seen in the skeletal parameters described earlier, the interactions were observed as the muscle mass of the anterior rays were larger in the anal fin, while posteriorly; the muscles masses were equal or larger in the dorsal rays (Figs

1.24A-C and 1.26A-C).

Fin-Ray Length vs. Muscle Mass

Among the spines of the dorsal and anal fins, only mInc showed a moderately positive correlation with spine length (r = 0.63; P = 0.022), while mErec and mDepr were only weakly correlated (r = 0.12 and 0.47; P = 0.7 and 0.1, respectively; Fig. 1.28A).

However, all three muscle masses were highly correlated with total lengths of the dorsal and anal rays (r > 0.8; P < 0.0001; Fig. 1.28B).

31

DISCUSSION

During any fish behavior, whether it be station holding, maneuvering or swimming, there are three potential sources of force that can act on a ray or spine: 1)

External forces; primarily the hydrodynamic forces generated from the interaction of the surrounding fluid with the fin surface. 2) Individual muscular force; i.e., forces generated by the musculature of the individual fin-ray. 3) Intra-fin forces: forces exerted on a fin- ray by the movement, or resistance, of neighboring fin-rays within a fin, transmitted by the fin webbing. The musculoskeletal design of a fin-ray determines how resistant or susceptible it is to each of these forces. Therefore, the interaction between a fin-ray’s mechanical properties and the resultant force (the summation/negation of the forces listed above) ultimately determine its orientation and shape.

From the musculoskeletal features we measured and observed, we suggest that within the soft dorsal and anal fins and the spiny dorsal fin, fin-rays differ in their resistance/susceptibility to the applied force (e.g., susceptible to bending by hydrodynamic loading but resistant to bending by muscular actuation). Moreover, from the interactions of the positional variation of several features, there is a degree of regionalization within the three fins providing different functional roles within the fins during locomotion.

Skeletal Regionalization

Spines

For all spines, mobility was restricted primarily to rotation within the sagittal plane (i.e., elevation and depression) with some degree of lateral deflection attainable when enough force was applied against the side of the spines, particularly among the 32 posterior dorsal spines. The spines were also highly resistant to bending, again with the posterior dorsal spines undergoing some bending if enough force was applied. It is not known whether the force required to achieve lateral deflection or bending would occur during normal swimming behaviors. Among spines #4-10 of DSp, spine length was uniform; the only consistent pattern in length occurred between spines 1-4 of DSp and 1-

3 of ASp (Fig. 1.4) and the change in spine length did not necessarily correlate with lateral mobility or stiffness of the spines. Instead, the difference in mobility and stiffness/flexibility may be due to the robustness of the spine and its articulation with its pterygiophores. While all spines appeared to have a tight articulation with the underlying pterygiophores (Fig 1.2C), the length and robustness of the corresponding radials, as well as the thickness of the spines, decreased with position, which we would suggest as a potential reason the posterior dorsal spines were the most susceptible to lateral deflection and bending. We suggest that the dorsal spiny fin could be divided into two functional regions: the anterior region of the fin, supported by spines 1-4, acts as the cutwater, dividing the flow of the water to either side of the fin with minimal disturbance to the direction of the flow. In contrast, the posterior region of the fin, supported by spines 4-

10, acts as a fixed keel to provide either roll and/or yaw stability to the anterior region of the trunk.

While the three anal spines are located more caudally along the longitudinal axis of the fish than the anterior four dorsal spines, preventing any statistical comparison between the two fins, the similarity in the skeletal features nonetheless suggests that the spiny region of the anal fin may also act as a cutwater, and to some extent, a fixed keel. 33

Rays

We suggest that there is an overall regionalization in the musculoskeletal features of the soft dorsal and anal fin rays. Overall, the mobility (the degree of motion at the joint) and flexibility (the compliance of the ray to bending forces) increases caudally among rays. The increased mobility of the posterior rays during manipulation at the ray- pterygiophore joint, especially notable in the degree of lateral deflection allowed, matches our observation of a loose connection between the distal radial and its socket

(Fig. 1.1A). While the attachment of the distal radial and ray permits rotation about the sagittal axis (i.e., elevation and depression), it is the connection between the distal radial and its socket that allows for the lateral rotation about the longitudinal (or transverse) axis

(Geerlink and Videler, 1973). Therefore, it is in the anterior rays, where the distal radials have a tighter attachment with their sockets, that we find a lesser degree of mobility in lateral deflection and, to some extent, their degree of elevation.

As with mobility, the anterior rays that are stiffer are more resistant to bending forces, whether applied against the fin or ray surface (simulating external hydrodynamic forces) or by pulling at the heads of the isolated ray (simulating internal muscular forces).

Furthermore, when curvature of the rays was induced, the distance between the proximal end and the point along the ray length where curvature started decreased with position, while the proportion of the ray that underwent curvature increased. As curvature occurs within the segmented region of the rays (Alben et al., 2007), differences in the length and ratio of unsegmented vs. segmented portions of rays reflected the variations observed in the isolated rays. For the unsegmented portion of the ray, absolute length decreased with position (Figs. 1.6B and 1.8B), which would account for the decreasing distance along 34 the ray length at which curvature could be elicited. While the absolute length of the segmented portion generally decreased as well, (Figs. 1.6C and 1.8C), the proportion of segmentation initially increased, especially among the first seven rays, before stabilizing or decreasing among the last six rays (Figs. 1.7A and 1.9A), again supporting the observations from our manipulations.

The length vs. ray position pattern provides an explanation for where curvature begins and the percentage of the ray that is capable of curvature when the bending force is applied either by external or internal means, but it does not explain why one ray resisted bending more than another, particularly when the one hemitrich was pulled relative to the other. The explanation for this result was found in the degree of attachment between hemitrichia, with the anterior rays having the tightest connection between hemitrichia, predominantly in the proximal unsegmented region of the ray, and in the case of the first two to three rays, these regions were fused together preventing any movement relative to each other. With the proximal segment fused or held tightly together, the capability to move the two hemitrichia relative to each other is diminished, if not impossible, thus it is unlikely that the fish can use muscular force alone to either induce ray curvature or actively resist bending forces applied externally. Instead, this may provide a degree of passive resistance to bending caused by external forces. This qualitative connection between the variation in ray stiffness and degree of curvature matches similar findings described in goldfish (Arita, 1971).

The pattern of variation in the unbranched vs. branched regions and ray position generally paralleled those seen in the unsegmented vs. segmented regions, although the branched segments had the weakest position effects observed among the skeletal features 35

(Figs. 1.8E and 1.8B). In a qualitative assessment of ray curvature, the point of maximum bending of an unloaded ray, i.e., no external forces were applied to the ray surface to resist bending induced by electrical stimulation of the ray musculature, coincided with the origin of branching (Arita, 1971). However, a recent investigation demonstrated that curvature in an unloaded ray is concentrated near the origin of segmentation but that the application of external forces cause the point of maximum curvature to move distally along the length of the ray (Alben et al., 2007).

In the pectoral fin of longhorn sculpin, maximal curvature was found to be greatest at the proximal and distal regions of the rays during station holding and steady swimming with maximum curvature varying among the rays (Taft et al., 2008; note that detailed morphology of the pectoral rays were not quantified in this study). During steady swimming and slow turning maneuvers in bluegill, variations in curvature

(measured at maximum fin excursions) along the ray lengths as well as between rays were observed; however no patterns in the position of maximum curvature were found or reported (Standen and Lauder, 2005). In our own study of ray curvature during C-starts, we found that the magnitude and position of maximum curvature along the ray length varied over time but maximum ray curvature over the entire sequence generally occurred within the distal regions of the rays (i.e., the branched and segmented regions; see

Chapter 3).

Considering the above-referenced studies together, it appears that the point of maximal bending is not relegated to a single location but rather is a function between the interactions of the intrinsic mechanical properties of the rays, the hydrodynamic loading, movement of neighboring fin-rays and muscular activity at any given point in time. 36

Therefore, how the position effects we found in segmentation and branching influences the location and degree of maximum bending under different forces is unclear. However, as ray bending should occur primarily within the segmented region (Alben et al., 2007), and both the absolute and percent length of the segmented regions increases with ray position (Fig. 1.5), we suggest that ray curvature in the proximal region of the ray (i.e., near the body) should be minimal, with the distance of the onset of curvature from the ray base decreasing among the posterior rays while the proportion of the ray capable of undergoing curvature increases.

Muscular Regionalization

Spines

The pattern in distribution of the dorsal spine muscles with position supported the anterior/posterior regionalization of the spiny dorsal fin. While the majority of muscular tissue was devoted to the erector muscles (Fig. 1.14), both in absolute and relative mass

(>50% of mTM), both values showed a significant position effect (Figs. 1.17C and

1.18B). For DSp 1-4, mErec increased with position, with average rErec of 60-75%, while mErec decreased within DSp 5-10, with average rErec of 50-60% (Fig. 1.16B). In contrast to mErec, the pattern of the inclinator muscles was reversed; both mInc and rInc increased with spine position (Figs. 1.17B and 1.18A), with rInc of DSp 1-4 averaging less than 12% and rInc of DSp 5-10 averaging 15-25% (Fig. 1.16A). Unlike the other muscles, the depressor muscle showed no significant position effect for either mInc or rInc (Figs. 1.17D and 1.18C), with both values uniformly equal among all spines (Fig.

1.14). 37

From these results, we suggest the erector muscles play a principal role to erect and maintain the elevation of the dorsal spines, with this role being more pronounced within the anterior region of the spiny dorsal fin than the posterior region. As elevation of posterior spines occurs passively when anterior spines are erected, the amount of force from the spine’s own musculature required to achieve and maintain elevation would decrease posteriorly. Depression of the spines appears to play an equal role within both regions of the spiny dorsal fin.

The role that inclinators play in resisting/initiating lateral movement of the spines is suspect due to the restricted mobility of their joint, as evidenced by the reduction or loss of the muscles among spines of several species (Winterbottom, 1974). Nonetheless, the persistence and increase in size of mInc among the posterior spines of the bluegill supports our hypothesis that the spines of this region may be more susceptible to lateral deflection and therefore greater muscle mass is required to either counteract hydrodynamic forces and/or to support the resistance of lateral deflection by the rays of the soft dorsal fin.

As with the skeletal features, the pattern of the spine musculature of ASp qualitatively matches the pattern observed among the four spines of the anterior dorsal fin, suggesting that the spiny portion of the anal fin is morphologically similar to the anterior region of the spiny dorsal fin. As the anal fin spines and their pterygiophores were larger and more robust than those of their dorsal fin counterparts, the absolute mass of their musculature was also larger, particularly mErec and mInc, suggesting a need for more muscular force to counteract the hydrodynamic loading at the anal fin. 38

Rays

Support for the regionalization of the soft portion of the dorsal and anal fins is best seen in the position effect observed in rErec and rDepr. While both muscles showed a significant position effect, they were in opposite directions (Figs. 1.19C,D 1.23B,C).

While rErec initially contributed ca. 50% of mTM to the muscles of the first ray in both fins, its fraction decreased to ca. 25%, which was mirrored by an equivalent increase in rDepr (Fig. 1.21B,C). Interestingly, when the masses of both muscles were combined, they both accounted for ca. 70% of mTM for all rays, the remaining 30% coming from rInc (Fig. 1.19C,D). This suggests that while elevation of rays is the principal role of the ray musculature within the anterior portion of the soft fins, the depression of the rays predominates within the posterior region. In the context of splaying the fin, this finding makes sense. Simply erecting all the rays together would do little to increase the surface area of the fin; however, elevating the anterior rays while concurrently depressing the posterior ones would open the fin and their opposing actions would stretch the fin causing the surface to tighten, much like collapsible hand fans.

The inclinator muscles show no position effect for rInc (Fig, 1.23A), suggesting that the role for resisting (or initiating) lateral deflection is equal between the two regions of the soft fins.

Length vs. Muscle Mass

Spines

The lack of correlation between spine length and mErec mass (Fig. 1.28) supports our suggestion that the anterior spines of the dorsal fin carry a heavier load in elevating the spiny dorsal fin. Despite being the shortest spines (Fig. 1.4A), the mass of 39 mErec for the first three spines are nearly equal to, if not larger than, those found among the longer posterior spines (Figs. 1.14A and 1.15C). Though spine length is moderately correlated with mInc, the correlation between spine position and mInc is much higher, supporting our observation that the posterior spines require more muscle mass to either resist lateral deflection and/or provide support to the anterior rays of the soft dorsal fin.

Rays

Unlike the spines, muscle mass within the soft dorsal and anal fins varies directly with ray length (Fig. 1.28), with no rays showing a disproportionate increase or decrease in their muscle complement. The high degree in correlation between ray length and mass of all three muscles closely matches the correlation between ray position and mass (Fig.

1.22). Assuming equal pressure across the fin, longer rays should be supporting a larger area of the fin surface and thus greater forces acting on them, requiring more muscle force to resist/overcome the forces (Force = Area × Pressure).

Dorsal vs. Anal Rays

For all variables tested, both skeletal and muscular, any significant position effects found in both fins were found to be equivalent between the groups. Of all the variables tested, there was only one in which a significant position effect was found in one fin, but not the other: mDepr (Fig. 1.21D). Therefore, the pattern of musculoskeletal design is highly conserved between the dorsal and anal fins. When testing for symmetry between the rays at the same rank position with the fins, significant fin effects were found in four variables: ΔUSg, ΔrSg ΔrElev and ΔrDepr (Figs. 1.10B, 1.11A and 1.25B,C, respectively). Significant finposition interactions were not found in any of the relative variables, but significant interactions were found in all but two (ΔUBr and ΔmDepr) of 40 the absolute variables tested, with the interaction pattern conserved among the tested variables. Within the anterior regions, anal rays were larger than their corresponding dorsal rays, while the posterior dorsal rays were either larger than or equal to their anal fin counterparts (Figs. 1.10,1.12, 1.24 and 1.26). We suggest that this interaction is a result of an obvious difference between the two soft fins, i.e., the large spiny dorsal fin vs. the smaller spiny region of the anal fin. For the soft dorsal fin, the 10 spines of the spiny dorsal fin can act as the cutwater and fixed keel to keep the oncoming flow steady and provide support to the rays, particularly in the anterior region. In the anal fin, only three spines are present to act as the cutwater and fixed keel; as such, the musculoskeletal features of the anterior anal rays are disproportionately large and robust in order to compensate for the reduced support of spines. This difference between anterior dorsal and anal rays is most obvious in the absolute mErec and mInc mass (Figs. 1.20B,C and

1.24B,C) as well as an increase in the robustness of the anterior pterygiophores and decrease in joint mobility in the anal fin.

Fin Regionalization and Locomotor Function

From hydrodynamic studies of steady swimming, both the soft dorsal and anal fins of the bluegill produce vortices in their wake that are oriented in such a way to produce primarily lateral forces, but also include a thrust component that accounts for up to 14% each of the total thrust generated by the fish (Drucker and Lauder, 2001a; Tytell,

2006). During steady swimming these vortices are shed by the trailing edge of the fin and have been suggested to potentially interact with the caudal fin, possibly increasing the thrust generated by the tail (Tytell, 2006). The dorsal and anal fins have also been shown to produce vortices that are integral contributors to the performance of the fast C- 41 start (Tytell and Lauder, 2008). Thus, the dorsal and anal fins of bluegill are playing multiple roles: accessory producers of thrust as well as stabilizing lateral forces. During steady swimming, the lateral forces generated by the two fins are oriented in the same direction, providing counterbalance to any roll perturbations to the body (Drucker and

Lauder, 2001a; 2005; Standen and Lauder, 2005; 2007; Tytell and Lauder, 2008). It has been suggested that the shape of the fins and their position on the body play an important role in the production and orientation of these forces, as they differ between species with different fin appearance [bluegill sunfish (Drucker and Lauder, 2001a) vs. rainbow trout

(Drucker and Lauder, 2005) vs. brook trout (Standen and Lauder, 2007)].

While whole fin measurements provide basic comprehension of how the fins interact with the surrounding fluid, understanding variation between the rays of the fin generates additional insight. The division of the dorsal and anal fins into two regions

(anterior and posterior) in a swimming fish (Fig. 1.3) is supported by an immediately obvious difference: the rays of the anterior region, particularly in the dorsal fin, are held to a higher degree of elevation with the distal edges forming the dorsal/ventral edge of the fin. The angle of elevation of the posterior region decreases to near parallel to the long axis and their distal edges form the trailing edge of the fins, i.e., the portion of the fins that shed the wake vortices resulting in the forces generated.

Thus, we suggest that these two regions may be playing functionally different roles during locomotion. Anteriorly, the less mobile and stiffer rays may be acting as an extension of the spiny fin, keeping the flow of water steady and guiding it posteriorly to the more mobile and flexible posterior region. Within the posterior fin regions, the rays are capable of fine-tuning their stiffness and orientation relative to the body in order to 42 reorient the flow in a position that will produce forces in the desired direction for the swimming behavior. As shown by Tytell (2006), the vortices generated by the two median fins not only supply thrust forces, but they are positioned in time and space to interact downstream with the caudal fin, which appears to enhance the thrust generated by the tail.

43

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Arita GS. 1971. A re-examination of the functional morphology of the soft-rays in teleosts. Copeia 1971:691-697.

Blake RW. 2004. Fish functional design and swimming performance. J Fish Biol 65:1193-1222.

Drucker EG, Lauder GV. 2000. A hydrodynamic analysis of fish swimming speed: Wake structure and locomotor force in slow and fast labriform swimmers. J Exp Biol 203:2379-2393.

Drucker EG, Lauder GV. 2001a. Locomotor function of the dorsal fin in teleost fishes: Experimental analysis of wake forces in sunfish. J Exp Biol 204:2943-2958.

Drucker EG, Lauder GV. 2001b. Wake dynamics and fluid forces of turning maneuvers in sunfish. J Exp Biol 204:431-442.

Drucker EG, Lauder GV. 2005. Locomotor function of the dorsal fin in rainbow trout: Kinematic patterns and hydrodynamic forces. J Exp Biol 208:4479-4494.

Eaton TH, Jr. 1945. Skeletal supports of the median fins of fishes. J Morphol 76:193-212.

Geerlink PJ, Videler JJ. 1973. Joints and muscles of the dorsal fin of Tilapia nilotica L. (Fam. Cichlidae). Neth J Zool 24:279-290.

Geerlink PJ, Videler JJ. 1987. The relation between structure and bending properties of teleost fin rays. Neth J Zool 37:59-80.

Goodrich ES. 1904. On the dermal fin-rays of fishes - Living and extinct. Q J Microsc Sci 47:465-522.

Haas HJ. 1962. Studies on mechanisms of joint and bone formation in the skeleton rays of fish fins. Dev Biol 5:1-34.

Hoogland R, Morris D, Tinbergen N. 1956. The spines of sticklebacks (Gasterosteus and Pygosteus) as means of defence against predators (Perca and Esox). Behaviour 10:205-236.

Jayne BC, Lozada GF, Lauder GV. 1996. Function of the dorsal fin in bluegill sunfish: Motor patterns during four distinct locomotor behaviors. J Morphol 228:307-326.

Lauder GV. 2006. Locomotion. In: Evans DH, Claiborne JB, editors. The Physiology of Fishes. 3rd ed. Boca Raton: CRC Press. p 3-46.

Lauder GV, Drucker EG. 2004. Morphology and experimental hydrodynamics of fish fin control surfaces. IEEE J Oceanic Eng 29:556-571. 44

Lauder GV, Madden PGA. 2007. Fish locomotion: Kinematics and hydrodynamics of flexible foil-like fins. Exp Fluids 43:641-653.

Mabee PM, Aldridge E, Warren E, Helenurm K. 1998. Effect of clearing and staining on fish length. Copeia 1998:346-353.

Mabee PM, Crotwell PL, Bird NC, Burke AC. 2002. Evolution of median fin modules in the axial skeleton of fishes. J Exp Zool 294:77-90.

McCutchen CW. 1970. The trout tail fin: A self-cambering hydrofoil. J Biomech 3:271- 272.

Rasband WS. 2008. ImageJ. Version 1.41g. Bethesda, MD: U.S. National Institutes of Health. http://rsb.info.nih.gov/ij/

Rice WR. 1989. Analyzing tables of statistical tests. Evolution 43:223-225.

Sokal RR, Rohlf FJ. 1981. Biometry. New York: WH Freeman. 805 p.

Song JK, Parenti LR. 1995. Clearing and staining whole fish specimens for simultaneous demonstration of bone, cartilage, and nerves. Copeia 1995:114-118.

Standen EM, Lauder GV. 2005. Dorsal and anal fin function in bluegill sunfish Lepomis macrochirus: Three-dimensional kinematics during propulsion and maneuvering. J Exp Biol 208:2753-2763.

Standen EM, Lauder GV. 2007. Hydrodynamic function of dorsal and anal fins in brook trout (Salvelinus fontinalis). J Exp Biol 210:325-339.

Taft NK, Lauder GV, Madden PGA. 2008. Functional regionalization of the pectoral fin of the benthic longhorn sculpin during station holding and swimming. J Zool 276:159-167.

Tytell ED. 2006. Median fin function in bluegill sunfish Lepomis macrochirus: Streamwise vortex structure during steady swimming. J Exp Biol 209:1516-1534.

Tytell ED, Lauder GV. 2008. Hydrodynamics of the escape response in bluegill sunfish, Lepomis macrochirus. J Exp Biol 211:3359-3369.

Videler JJ. 1977. Mechanical properties of fish tail joints. Fortsch Zool 24:183-194.

Walker JA. 2004. Kinematics and performance of maneuvering control surfaces in teleost fishes. IEEE J Oceanic Eng 29:572-584.

Winterbottom R. 1974. A descriptive synonymy of the striated muscles of the Teleostei. Proc Acad Nat Sci Phila 125:225-317.

Zar JH. 1984. Biostatistical Analysis. Englewood Cliffs: Prentice-Hall. 469 p.

45

Figure 1.1. Skeletal supports of the anal fin.

A: Photograph of a cleared and stained anal fin of L. macrochirus, viewed laterally, showing the external fin-ray supports [spines (Sp) and rays (Ry)] and endoskeletal supports [proximal (p), middle (m) and distal (d) radials]. The generalized design of lepidotrichia found in ray-finned fishes comprises three distinct regions: an unsegmented base (usg), a series of short segments (sg) and the distal branched (br) segments. B:

Close-up of several rays and their three regions. C: Viewed caudally, the two hemitrichia

(h) of a lepidotrich can be seen. The associated distal radial is positioned between the heads of the two unsegmented bases. D: Schematic of a lepidotrich, viewed laterally, and its three regions color-coded: unsegmented base (blue without striations), unbranched segments (yellow with striations) and branched segments (red with striations). For comparative analyses, the three regions were combined into one of five variables: total ray length (all three regions), unsegmented (USg) vs. segmented (Sg) or unbranched (UBr) vs. branched (Br).

46

Figure 1.1

47

Figure 1.2. Schematic of fin-ray joints and muscles.

A: Ray-pterygiophore articulation. B: Muscles of the ray. C: Spine-pterygiophore articulation. D: Muscles of the spine. Symbols: p (proximal radial); lr (lateral ridge); m

(middle radial); d (distal radial); mInc (inclinator muscle, shown transected and reflected), mErec (erector muscle) and mDepr (depressor muscle).

48

Figure 1.2

A Ry B mInc

mErec d m lr p

mDepr

C Sp D mInc

d mErec

lr p

mDepr 49

Figure 1.3. Illustration of bluegill sunfish and its fins.

The anterior spiny dorsal fin (spD; shaded region) is supported by 10 spines (thick, solid lines) with the most anterior spine positioned just above the center of mass (COM) and the soft dorsal fin (sfD) is supported by 13 rays (thin, broken lines). Although spD and sfD are developmentally independent, they appear as a single, continuous dorsal fin (DF) in bluegill. The single anal fin (AF), positioned just behind the vent (v), is support by 3 spines and 13 rays. Fin-ray supports of the caudal fin (Cd) and the paired pectoral (Pc) and pelvic (Pv) fins are not shown.

50

Figure 1.3 A

COM Cd Pc

v Pv 51

Figure 1.4. Length vs. spine position.

A: Length (in mm) of dorsal spines (DSp; blue squares) and anal spines (ASp; red circles). B: Rank order of DSp and ASp lengths. Numerical values provided are

Kendall’s coefficient of concordance (W; df = 5, 9 and 5, 2 for DSp and ASp, respectively) and Spearman’s rank correlation (rs) for DSp (blue text) or ASp (red text).

Statistically significant W and rs are indicated by an asterisk (*). The dashed lines represent the best-fit line (linear) between the ranked lengths and position of DSp and

ASp. The best-fit line for ASp is hidden by its connecting lines due to the complete concordance among all specimen and perfect rank correlation between their lengths and positions. Symbols are mean ± 1 s.d.; some error bars are concealed by their respective symbol (n = 6 fish).

52

Figure 1.4

30 A DSp 25 ASp

20

10

15

5

0 1 2 3 4 5 6 7 8 9 10

12 B

10

8

6

4

2 W =0.78*; rs = 0.73* W =1*; rs = 1* 0 1 2 3 4 5 6 7 8 9 10 Spine Position 53

Figure 1.5. Regional contributions to ray length vs. position.

A-B: Mean contribution to ray length (in mm) of the unsegmented base (unstriated, blue bars), unbranched segments (striated, yellow bars) and branched segments (striated, red bars) for DRy and ARy, respectively. C-D: Mean relative contribution to ray length (as a percent of total ray length; % RL) of the three regions of DRy and ARy, respectively.

The relationship between the lengths and longitudinal position of the rays can be compared, including the five tested variables: total ray length (all three regions),

Unsegmented (USg; blue bars) vs. Segmented (Sg; yellow + red bars) and Unbranched

(UBr; blue + yellow bars) vs. Branched (Br; red bars). Error bars not shown to improve clarity.

54

Figure 1.5

35 35 Br A B Sg 30 30 UBr USg 25 25

20 20

15 15

10 10

5 5

0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 3 4 5 6 7 8 9 10 11 12 13 100 100

67 67

33 33

0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 3 4 5 6 7 8 9 10 11 12 13 Ray Position (DRy) Ray Position (ARy) 55

Figure 1.6. Regional lengths vs. ray position.

A: Total ray length (RL). B: Unsegmented length (USg). C: Segmented length (Sg).

D: Unbranched length (UBr). E: Branched length (Br). (n = 6 fish). Symbols as in

Figure 1.4.

56

Figure 1.6

35 DRy 30 ARy 25

20

15

10 5 A 0 1 2 3 4 5 6 7 8 9 10 11 12 13 25

20

15

10

5 B 0 1 2 3 4 5 6 7 8 9 10 11 12 13 25

20

15

10

5 C 0 1 2 3 4 5 6 7 8 9 10 11 12 13 25

20

15

10

5 D 0 1 2 3 4 5 6 7 8 9 10 11 12 13 25

20

15

10

5 E 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Ray Position 57

Figure 1.7. Relative regional lengths vs. ray position.

A: Relative segmented length (rSg). B: Relative branched length (rBr). (n = 6 fish).

Symbols as in Figure 1.4.

58

Figure 1.7

100 A DRy ARy

75

50

25

0 1 2 3 4 5 6 7 8 9 10 11 12 13 100 B

75

50

25

0 1 2 3 4 5 6 7 8 9 10 11 12 13 Ray Position 59

Figure 1.8. Rank order of regional lengths vs. ray position.

A: Total ray length (RL). B: Unsegmented length (USg). C: Segmented length (Sg).

D: Unbranched length (UBr). E: Branched length (Br). Numerical values provided are

Kendall’s coefficient of concordance (W; df = 5, 12 for both fins) and Spearman’s rank correlation (rs) for DRy and ARy and the multigroup coefficient of concordance (W).

Statistically significant W, rs and W are indicated by an asterisk (*). Dashed lines represent the best-fit line (linear) between rank order and position. In panels A, B and D, one or both best-fit lines are completely, or partially, hidden by connecting lines due to a high degree of concordance and rank correlation between the regional length and position of the rays. Some error bars are concealed by their respective symbol (n = 6 fish).

Symbols as in Figure 1.4.

60

Figure 1.8

14 DRy 12 ARy

10

8

6 W =0.97*; rs = –0.94* 4 W =1.00*; rs = –0.99* W = 0.95* 2 A 0 1 2 3 4 5 6 7 8 9 10 11 12 13

14

12

10

8

6 W =0.99*; rs = –0.99* 4 W =1.00*; rs = –0.99* 2 B W = 0.99* 0 1 2 3 4 5 6 7 8 9 10 11 12 13

14

12

10

8

6 W= 0.95*; rs = –0.60* 4 W= 0.98*; rs = –0.80* 2 C W = 0.88* 0 1 2 3 4 5 6 7 8 9 10 11 12 13

14

12

10

8

6 W= 0.98*; r = –0.99* 4 s W= 0.98*; rs = –0.99* 2 D W = 0.98* 0 1 2 3 4 5 6 7 8 9 10 11 12 13

14

12

10

8

6

4 W =0.81*; rs = –0.29* 2 W =0.88*; rs = –0.82* E W = 0.50* 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Ray Position 61

Figure 1.9. Rank order of relative lengths vs. ray position.

A: Relative segmented length (rSg). B: Relative branched length (rBr). Numerical values provided are Kendall’s coefficient of concordance (W; df = 5, 12 for both fins) and

Spearman’s rank correlation (rs) for DRy and ARy and the multigroup coefficient of concordance (W). Statistically significant W, rs and W are indicated by an asterisk (*).

Dashed lines represent the best-fit line (linear) between the ranked length and position of the rays. Some error bars are concealed by their respective symbol (n = 6 fish). Symbols as in Figure 1.4.

62

Figure 1.9

14 A DRy ARy 12

10

8

6

4 W=0.87*; rs = 0.26* 2 W=0.81*; rs = 0.44* W = 0.77* 0 1 2 3 4 5 6 7 8 9 10 11 12 13

14 B W =0.81*; rs = 0.71* W =0.49*; rs = 0.59* 12 W = 0.59*

10

8

6

4

2

0 1 2 3 4 5 6 7 8 9 10 11 12 13 Ray Position 63

Figure 1.10. Difference in regional lengths vs. position between dorsal and anal rays.

A: Difference in total ray length (∆RL). B: Difference in unsegmented length (∆USg).

C: Difference in segmented length (∆Sg). D: Difference in unbranched length (∆UBr).

E: Difference in branched length (∆Br). The values in the upper right corner of each panel specify the number of rays for each fin that were larger than the rays at the same longitudinal position from the other fin. Using the sign test, statistically significant fin effects are indicated by an asterisk (*). Symbols are mean ± 1 s.d. of ARy – DRy at similar longitudinal positions (n = 6 fish).

64

Figure 1.10

5 ARy DRy 4 39 37 3 2 1 0 -1 -2 -3 A -4 1 2 3 4 5 6 7 8 9 10 11 12 13 5 *ARy DRy 4 60 16 3 2 1 0 -1 -2 -3 B -4 1 2 3 4 5 6 7 8 9 10 11 12 13 5 DRy ARy 4 47 28 3 2 1 0 -1 -2 -3 C -4 1 2 3 4 5 6 7 8 9 10 11 12 13 5 DRy ARy 4 41 34 3 2 1 0 -1 -2 -3 D -4 1 2 3 4 5 6 7 8 9 10 11 12 13 5 ARy DRy 4 39 37 3 2 1 0 -1 -2 -3 E -4 1 2 3 4 5 6 7 8 9 10 11 12 13 Ray Position 65

Figure 1.11. Difference in relative regional lengths vs. ray position.

A: Difference in relative segmented length (∆rSg). B: Difference in relative branched length (∆rBr). The values in the upper right corner of each panel specify the number of rays for each fin that were larger than the rays at the same longitudinal position from the other fin. Using the sign test, statistically significant fin effects are indicated by an asterisk (*). (n = 6 fish). Symbols as in Figure 1.10.

66

Figure 1.11

15 *DRy ARy A 72 6 12

9

6

3

0

-3

-6

-9 1 2 3 4 5 6 7 8 9 10 11 12 13

15 ARy DRy B 42 35 12

9

6

3

0

-3

-6

-9 1 2 3 4 5 6 7 8 9 10 11 12 13 Ray Position 67

Figure 1.12. Rank order of regional differences vs. ray position.

A: Difference in total ray length (∆RL). B: Difference in unsegmented length (∆USg).

C: Difference in segmented length (∆Sg). D: Difference in unbranched length (∆UBr).

E: Difference in branched length (∆Br). Numerical values provided are Kendall’s coefficient of concordance (W; df = 5, 12) and Spearman’s rank correlation (rs).

Statistically significant W and rs are indicated by an asterisk (*). The dashed lines represent the best-fit line (linear) between the ranked differences and position. Some error bars are concealed by their respective symbol (n = 6 fish). Symbols as in Figure

1.10.

68

Figure 1.12

14 W =0.95*; rs = –0.73*

12

10

8

6

4 2 A 0 1 2 3 4 5 6 7 8 9 10 11 12 13

14 W =0.87*; rs = –0.87*

12

10

8

6

4 2 B 0 1 2 3 4 5 6 7 8 9 10 11 12 13

14 W =0.79*; rs = –0.49*

12

10

8

6

4 2 C 0 1 2 3 4 5 6 7 8 9 10 11 12 13

14 W= 0.22; rs = –0.24

12

10

8

6

4 2 D 0 1 2 3 4 5 6 7 8 9 10 11 12 13

14 W =0.73*; rs = –0.61*

12

10

8

6

4 2 E 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Ray Position 69

Figure 1.13. Rank order of relative regional differences vs. ray position.

A: Difference in relative segmented length (∆rSg). B: Difference in relative branched length (∆rBr). Numerical values provided are Kendall’s coefficient of concordance (W; df

= 5, 12) and Spearman’s rank correlation (rs). Statistically significant W and rs are indicated by an asterisk (*). Dashed lines represent the best-fit line (linear) between the ranked differences and position. (n = 6 fish). Symbols as in Figure 1.10.

70

Figure 1.13

14 A W=0.29; rs = 0.30

12

10

8

6

4

2

0 1 2 3 4 5 6 7 8 9 10 11 12 13

14 B W =0.31; rs = –0.36

12

10

8

6

4

2

0 1 2 3 4 5 6 7 8 9 10 11 12 13 Ray Position 71

Figure 1.14. Contributions to fin-ray muscle mass vs. spine position.

A-B: Mean contribution to fin-ray muscle mass (in mg) from the three muscle slips of

DSp and ASp, respectively: inclinator (mInc; blue bars), erector (mErec; yellow bars) and depressor (mDepr; red bars). C-D: Mean relative contribution to fin-ray muscle mass (as a percent of total fin-ray muscle mass; % mTM) from mInc, mErec and mDepr of DSp and ASp, respectively. Error bars not shown to improve clarity.

72

Figure 1.14

25 25 A mInc B 20 mErec 20 mDepr

15 15

10 10

5 5

0 0 1 2 3 4 5 6 7 8 9 10 1 2 3 100 100

67 67

33 33

0 0 1 2 3 4 5 6 7 8 9 10 1 2 3 Spine Position (DSp) (ASp) 73

Figure 1.15. Fin-ray muscle mass vs. spine position.

A: Total fin-ray muscle mass (mTM). B: Inclinator muscle mass (mInc). C: Erector muscle mass (mErec). D: Depressor muscle mass (mDepr). (n = 5 fish). Symbols as in

Figure 1.4.

74

Figure 1.15 32 A Dorsal 28 Anal

24

20

16

12

8

4

0 1 2 3 4 5 6 7 8 9 10 24 B 20

16

12

8

4

0 1 2 3 4 5 6 7 8 9 10 24 C 20

16

12

8

4

0 1 2 3 4 5 6 7 8 9 10 24 D 20

16

12

8

4

0 1 2 3 4 5 6 7 8 9 10 Spine Position 75

Figure 1.16. Relative fin-ray muscle mass vs. spine position.

A: Relative inclinator muscle mass (rInc). B: Relative erector muscle mass (rErec). C:

Relative depressor muscle mass (rDepr). (n = 5 fish). Symbols as in Figure 1.4.

76

Figure 1.16

100 A Dorsal Anal

75

50

25

0 1 2 3 4 5 6 7 8 9 10 100 B

75

50

25

0 1 2 3 4 5 6 7 8 9 10 100 C

75

50

25

0 1 2 3 4 5 6 7 8 9 10 Spine Position 77

Figure 1.17. Rank order of fin-ray muscle mass vs. spine position.

A: Total fin-ray muscle mass (mTM). B: Inclinator muscle mass (mInc). C: Erector muscle mass (mErec). D: Depressor muscle mass (mDepr). Numerical values provided are Kendall’s coefficient of concordance (W; df = 4, 9 and 4, 2 for DSp and ASp, respectively) and Spearman’s rank correlation (rs). Statistically significant W and rs are indicated by an asterisk (*). The dashed lines represent the best-fit line (linear) between the ranked lengths and position of DSp and ASp. Some error bars are concealed by their respective symbol (n = 5 fish). Symbols as in Figure 1.4.

78

Figure 1.17

A Dorsal 10 Anal

8

6

4

2 W= 0.58*; rs = 0.14 W = 0.76; rs = 0.80 0 1 2 3 4 5 6 7 8 9 10 B 10

8

6

4

2 W =0.93*; rs = 0.96 W = 0.84; rs = 0.90 0 1 2 3 4 5 6 7 8 9 10

C W= 0.78*; rs = – 0.13 W = 0.84; r = 0.30 10 s

8

6

4

2

0 1 2 3 4 5 6 7 8 9 10

D W = 0.40; rs = 0.26 W = 0.76; r = 0.80 10 s

8

6

4

2

0 1 2 3 4 5 6 7 8 9 10 Spine Position 79

Figure 1.18. Rank order of relative fin-ray muscle mass vs. spine position.

A: Relative inclinator muscle mass (rInc). B: Relative erector muscle mass (rErec). C:

Relative depressor muscle mass (rDepr). Numerical values provided are Kendall’s coefficient of concordance (W; df = 4, 9 and 4, 2 for DSp and ASp, respectively) and

Spearman’s rank correlation (rs). Statistically significant W and rs are indicated by an asterisk (*). The dashed lines represent the best-fit line (linear) between the ranked lengths and position of DSp and ASp. Some error bars are concealed by their respective symbol (n = 5 fish). Symbols as in Figure 1.4.

80

Figure 1.18

A DSp ASp 10

8

6

4

2 W= 0.83*; rs = 0.80* W =0.52; rs = 0.50 0 1 2 3 4 5 6 7 8 9 10

B W =0.82*; rs = – 0.76 10 W =0.52; rs = – 0.20

8

6

4

2

0 1 2 3 4 5 6 7 8 9 10 C 10

8

6

4

2 W= 0.49; rs = 0.02 W =0.04; rs = – 0.10 0 1 2 3 4 5 6 7 8 9 10 Spine Position 81

Figure 1.19. Contributions to fin-ray muscle mass vs. ray position.

A-B: Mean contribution to fin-ray muscle mass (in mg) from the three muscle slips of

DRy and ARy, respectively: inclinator (mInc; blue bars), erector (mErec; yellow bars) and depressor (mDepr; red bars). For the two most posterior fin rays, mErec and mDepr are fused as a single muscle slip and their combined mass is provided (hatched, orange bars); see text for details. C-D: Mean relative contribution to fin-ray muscle mass (as a percent of total fin-ray muscle mass; % mTM) from mInc, mErec and mDepr of DRy and

ARy, respectively. Error bars not shown for clarity.

82

Figure 1.19

20 20 A mInc B mErec 16 16 mDepr

12 12

8 8

4 4

0 0 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 100 100

67 67

33 33

0 0 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 Ray Position (DRy) Ray Position (ARy) 83

Figure 1.20. Fin-ray muscle mass vs. ray position.

A: Total fin-ray muscle mass (mTM). B: Inclinator muscle mass (mInc). C: Erector muscle mass (mErec). D: Depressor muscle mass (mDepr). (n = 5 fish). Symbols as in

Figure 1.4.

84

Figure 1.20

25 A Dorsal Anal 20

15

10

5

0 1 2 3 4 5 6 7 8 9 10 11 12 10 B 8

6

4

2

0 1 2 3 4 5 6 7 8 9 10 11 12 10 C

8

6

4

2

0 1 2 3 4 5 6 7 8 9 10 11 12 10 D

8

6

4

2

0 1 2 3 4 5 6 7 8 9 10 11 12 Ray Position 85

Figure 1.21. Relative fin-ray muscle mass vs. ray position.

A: Relative inclinator muscle mass (rInc). B: Relative erector muscle mass (rErec). C:

Relative depressor muscle mass (rDepr). Some error bars are concealed by their respective symbol (n = 5 fish). Symbols as in Figure 1.4.

86

Figure 1.21

100 A Dorsal Anal

75

50

25

0 1 2 3 4 5 6 7 8 9 10 11 12 100 B

75

50

25

0 1 2 3 4 5 6 7 8 9 10 11 12 100 C

75

50

25

0 1 2 3 4 5 6 7 8 9 10 11 12 Ray Position 87

Figure 1.22. Rank order of fin-ray muscle mass vs. ray position.

A: Total fin-ray muscle mass (mTM). B: Inclinator muscle mass (mInc). C: Erector muscle mass (mErec). D: Depressor muscle mass (mDepr). Numerical values provided are Kendall’s coefficient of concordance (W; df = 4, 11 for mTMa and mInc, df = 4, 10 for mErec and mDepr) and Spearman’s rank correlation (rs) for DRy and ARy and the multigroup coefficient of concordance (W). Statistically significant W, rs and W are indicated by an asterisk (*). Dashed lines represent the best-fit line (linear) between rank order and position. In panels A and C, one or both best-fit lines are partially hidden by connecting lines due to a high degree of concordance and rank correlation between the regional length and position of the rays. Some error bars are concealed by their respective symbol (n = 5 fish). Symbols as in Figure 1.4.

88

Figure 1.22

A Dorsal 12 Anal

10

8

6

4 W =0.84*; rs = –0.88 2 W =0.97*; rs = –0.98 W = 0.88* 0 1 2 3 4 5 6 7 8 9 10 11 12 B 12

10

8

6

4 W =0.76*; rs = –0.64 2 W =0.95*; rs = –0.97 W = 0.65* 0 1 2 3 4 5 6 7 8 9 10 11 12 C 12

10

8

6

4 W =0.91*; rs = –0.95 2 W =0.97*; rs = –0.98 W = 0.92* 0 1 2 3 4 5 6 7 8 9 10 11 12

D W =0.48; rs = –0.45 12 W= 0.80*; rs = –0.63 W = NA 10

8

6

4

2

0 1 2 3 4 5 6 7 8 9 10 11 12 Ray Position 89

Figure 1.23. Rank order of relative fin-ray muscle mass vs. ray position.

A: Relative inclinator muscle mass (rInc). B: Relative erector muscle mass (rErec). C:

Relative depressor muscle mass (rDepr). Numerical values provided are Kendall’s coefficient of concordance (W; df = 4, 11 for rInc, df = 4, 10 for rErec and rDepr) and

Spearman’s rank correlation (rs) for DRy and ARy and the multigroup coefficient of concordance (W). Statistically significant W, rs and W are indicated by an asterisk (*).

Dashed lines represent the best-fit line (linear) between rank order and position. Some error bars are concealed by their respective symbol (n = 5 fish). Symbols as in Figure

1.4.

90

Figure 1.23

A Dorsal 12 Anal

10

8

6

4 W = 0.48; rs = –0.17 2 W = 0.36; rs = –0.17 W = NA 0 1 2 3 4 5 6 7 8 9 10 11 12

B W =0.77*; rs = –0.84 12 W =0.82*; rs = –0.87 W = 0.78* 10

8

6

4

2

0 1 2 3 4 5 6 7 8 9 10 11 12 C 12

10

8

6

4 W= 0.74*; rs = 0.80 2 W= 0.87*; rs = 0.91 W = 0.76* 0 1 2 3 4 5 6 7 8 9 10 11 12 Ray Position 91

Figure 1.24. Difference in fin-ray muscle mass vs. position between dorsal and anal rays.

A: Difference in total fin-ray muscle mass (∆mTM). B: Difference in inclinator muscle mass (∆mInc). C: Difference in erector muscle mass (∆mErec). D: Difference in depressor muscle mass (∆mDepr). Positive values indicate ray positions where the muscle mass of ARy was greater than DRy. The values in the upper right corner of each panel specify the number of ray muscle slips of each fin that were larger than the muscle slip of the rays at the same longitudinal position from the other fin. Using the sign test, statistically significant fin effects are indicated by an asterisk (*). (n = 5 fish). Symbols as in Figure 1.10.

92

Figure 1.24

8 A ARy DRy 34 25 6

4

2

0

-2

-4 1 2 3 4 5 6 7 8 9 10 11 12 5 B ARy DRy 35 22 4

3

2

1

0

-1

-2 1 2 3 4 5 6 7 8 9 10 11 12 5 *ARy DRy C 38 16 4

3

2

1

0

-1

-2 1 2 3 4 5 6 7 8 9 10 11 12 5 D ARy DRy 21 33 4

3

2

1

0

-1

-2 1 2 3 4 5 6 7 8 9 10 11 12 Ray Position 93

Figure 1.25. Difference in relative fin-ray muscle mass vs. ray position.

A: Difference in relative inclinator muscle mass (∆rInc). B: Difference in relative erector muscle mass (∆rErec). C: Difference in relative depressor muscle mass

(∆rDepr). Positive values indicate ray positions where the muscle mass of ARy was greater than DRy. The values in the upper right corner of each panel specify the number of ray muscle slips of each fin that were larger than the muscle slip of the rays at the same longitudinal position from the other fin. Using the sign test, statistically significant fin effects are indicated by an asterisk (*). (n = 5 fish). Symbols as in Figure 1.10.

94

Figure 1.25

20 A ARy DRy 16 35 25 12

8

4

0

-4

-8

-12

-16 1 2 3 4 5 6 7 8 9 10 11 12 20 B *ARy DRy 16 40 15 12

8

4

0

-4

-8

-12

-16 1 2 3 4 5 6 7 8 9 10 11 12 20 C *DRy ARy 16 42 13 12

8

4

0

-4

-8

-12

-16 1 2 3 4 5 6 7 8 9 10 11 12 Ray Position 95

Figure 1.26. Rank order of muscle mass differences vs. ray position.

A: Difference in total fin-ray muscle mass (∆mTM). B: Difference in inclinator muscle mass (∆mInc). C: Difference in erector muscle mass (∆mErec). D: Difference in depressor muscle mass (∆mDepr). Numerical values provided are Kendall’s coefficient of concordance (W; df = 4, 11 for mTMa and mInc, df = 4, 10 for ΔmErec and ΔmDepr) and Spearman’s rank correlation (rs). Statistically significant W and rs are indicated by an asterisk (*). The dashed lines represent the best-fit line (linear) between the ranked differences and position (n = 5 fish). Symbols as in Figure 1.10.

96

Figure 1.26

A W= 0.78*; rs = –0.77 12

10

8

6

4

2

0 1 2 3 4 5 6 7 8 9 10 11 12

B W= 0.59*; rs = –0.55 12

10

8

6

4

2

0 1 2 3 4 5 6 7 8 9 10 11 12

C W= 0.78*; rs = –0.81 12

10

8

6

4

2

0 1 2 3 4 5 6 7 8 9 10 11 12

D W= 0.41; rs = –0.19 12

10

8

6

4

2

0 1 2 3 4 5 6 7 8 9 10 11 12 Ray Position 97

Figure 1.27. Rank order of relative muscle mass differences vs. ray position.

A: Difference in inclinator relative muscle mass (∆rInc). B: Difference in relative erector muscle mass (∆rErec). C: Difference in relative depressor muscle mass

(∆rDepr). Numerical values provided are Kendall’s coefficient of concordance (W; df = 4,

11 for ΔrInc, df = 4, 10 for ΔrErec and ΔrDepr) and Spearman’s rank correlation (rs).

Statistically significant W and rs are indicated by an asterisk (*). Dashed lines represent the best-fit line (linear) between the ranked differences and position (n = 5 fish).

Symbols as in Figure 1.10.

98

Figure 1.27

A W = 0.27; rs = 0.13 12

10

8

6

4

2

0 1 2 3 4 5 6 7 8 9 10 11 12

B W = 0.22; rs = –0.28 12

10

8

6

4

2

0 1 2 3 4 5 6 7 8 9 10 11 12

C W = 0.47; rs = 0.37 12

10

8

6

4

2

0 1 2 3 4 5 6 7 8 9 10 11 12 Ray Position 99

Figure 1.28. Muscle mass vs. fin-ray length.

A: Muscle mass vs. spine length. B: Muscle mass vs. ray length. Lines represent the best-fit line (linear), with the coefficients of determination (r2) between the average fin- ray lengths (n = 6 fish) and the average muscle masses (n = 5 fish) provided.

100

Figure 1.28

A 16

12

8 r2= 0.01 mInc 4 mErec r2= 0.22 mDepr r2= 0.39 0 0 5 10 15 20 25 Spine Length (mm)

8 B

6 r2= 0.84

4 r2= 0.66

2 r2= 0.94

0 0 5 10 15 20 25 30 35 Ray Length (mm) 101

CHAPTER 2

3-D KINEMATIC ANALYSIS OF THE DORSAL AND ANAL FINS DURING THE

FAST-START OF THE BLUEGILL SUNFISH (LEPOMIS MACROCHIRUS) I:

FIN-RAY ORIENTATION AND MOVEMENT

102

ABSTRACT

The escape response of fish is a determining factor in avoiding predation and greater performance is of selective advantage. Large median dorsal and anal fins located near the tail have been hypothesized to increase acceleration away from the threat. To investigate the role of median fins, C-start escape responses of bluegill sunfish (Lepomis macrochirus) were recorded by three high-speed, high resolution cameras at 500 fps and the 3-D kinematics of individual dorsal and anal fin-rays were analyzed. Movement and orientation of the fin-rays relative to the body axis were calculated throughout the duration of the C-start. We found that (1) timing and magnitude of angular displacement varied among fin-rays based on position within the fin and (2) kinematic patterns support the prediction that fin-rays are actively resisting hydrodynamic forces and transmitting momentum into the water. Furthermore, we suggest that regions within the fins have different roles. First, the anterior region of the fin, in particular the spiny dorsal fin, is rapidly elevated to increase the volume of water that the fish may interact with and transmit force into, thus generating greater total momentum. Second, the movement pattern of the fin-rays creates traveling waves that move posteriorly along the length of the fin, moving water as they do so. The flexible posterior fin regions ultimately act to accelerate this water toward the tail and thereby increase thrust forces of the escape response. Despite their simple appearance, median fins are highly complex and versatile control surfaces that modulate locomotor performance. 103

INTRODUCTION

Among aquatic predator-prey interactions, the fast-start can determine who eats and who is eaten. Fast-starts are swimming maneuvers associated with production of high acceleration over a brief period of activity. Most commonly, fast-starts are used to evade predators (Eaton et al., 1977; Webb, 1976; 1978; Weihs, 1973) and capture prey

(Hoogland et al., 1956; Rand and Lauder, 1981; Webb and Skadsen, 1980). However, fast-starts have also been observed in behaviors such as post-feeding turns (Canfield and

Rose, 1993) and social interactions (Fernald, 1975).

Within the kinematic literature, fast-starts of fish have been classified as either a

C-start or S-start, based on the shape the body forms at the end of the initial phase of the behavior (reviewed by Domenici and Blake, 1997; Wakeling, 2001). While S-starts are used by some fish species during escape responses, (Harper and Blake, 1990; Schriefer and Hale, 2004; Spierts and Leeuwen, 1999; Webb, 1976), the majority of fish species studied to date have been described as performing the C-start escape response (Domenici and Blake, 1991; Eaton et al., 1977; Webb, 1978). Regardless of the type, fast-starts have been divided into three kinematic stages: a preparatory stroke (Stage 1) in which the long axis of the body bends into the characteristic ‘C’ or ‘S’ shape; a propulsive stroke

(Stage 2) that accelerates the fish; and a variable stage (Stage 3) that can include continued swimming strokes, braking maneuvers, or simply gliding to a stop (Domenici and Blake, 1997; Weihs, 1973; Fig. 2.1).

The majority of kinematic papers describe the stereotypic maneuver of the axial body and tail, paying particular attention to the timing and magnitude of the turning rate of the head, and the overall performance of the center of mass (i.e., displacement, 104 maximum velocity and acceleration). Only a few papers make mention of fin movements, with most simply referring to a qualitative observation that the median fins are splayed (elevated) during the behavior (Eaton et al., 1977; Webb, 1977; 1978). In part, the paucity of fin kinematics is a result of observational set-up, wherein a single camera is positioned either above or below the observation tank with a lighted background, creating a silhouette of the fish body. Under these conditions, the only time a fin could be distinguished was when it was displaced to one side of the body.

The lack of data quantifying fin kinematics and the role they play during fast- starts is puzzling considering that, in his seminal description, Weihs (1973) suggested that enlarged dorsal and anal fins close to the caudal fin could potentially act as a second tail to enhance the performance of fast-starts. In the ecological literature, there is evidence that predator avoidance plays a key role in the evolution of fish morphology and escape performance (Bergstrom, 2002; Ghalambor et al., 2003; Langerhans et al., 2004).

Several papers have noted the correlation between body form (to which the median fins contribute) and performance (Harper and Blake, 1990; Law and Blake, 1996; Webb,

1978) and even studied the effect of fin amputation on performance (Webb, 1977). A recent study using particle image velocimetry (PIV) demonstrated for the first time that the dorsal and anal fins do in fact contribute a thrust component to the acceleration of the fish (Tytell and Lauder, 2008). However, no studies have addressed the movement of fins and how they may be generating this force.

We examined two aspects of individual fin-ray kinematics during the performance of a fast C-start of the bluegill sunfish, Lepomis macrochirus. First, does the timing and magnitude of individual fin-ray kinematics differ within the fins, as predicted based on 105 the variability observed in the musculoskeletal design? As described in Chapter 1, fin- rays of the dorsal and anal fins differ in several musculoskeletal features according to their position within the fins. The primary finding from that study revealed that the anterior spines and rays of the dorsal and anal fins were more rigid and restricted in their mobility than the posterior fin-rays. We predict that these morphological differences should translate to variations in individual kinematic performances during locomotion; specifically, that the timing and magnitudes of fin-ray displacement should be related to fin-ray position, i.e., the more flexible and mobile posterior fin-rays should have a greater degree of deflection which occurs sooner than the more rigid anterior fin-rays.

Second, we will investigate the prediction that the fin-rays are actively resisting the lateral hydrodynamic forces that deflect the fin-rays (Jayne et al., 1996; Standen and

Lauder, 2007) and that the ability to resist these forces will vary among fin-rays. During the C-start, the axial body rotates to one side, changes direction and then rotates in the opposite direction. During the two rotational phases, as the angular velocity of the body increases, hydrodynamic forces also increase which would oppose fin movement, causing them to be deflected in the opposite direction of axial rotation. During the change in direction, angular velocity of axial rotation decreases until it reaches zero and reverses direction. In response, the opposing forces should also decrease and change directions, causing an eventual change in the orientation of the fin relative to the body.

If the fin-rays are actively resisting lateral deflection and resistance decreases with fin-ray position, as we predict, we would expect that the posterior fin-rays will (1) have increased angular displacement, (2) reach maximum deflection sooner than the anterior fin-rays, and (3) undergo a directional transition later than the anterior rays. 106

We show that, as predicted, fin-ray kinematics varied with position and supported the prediction that they are resisting lateral deflection, with the spines and anterior rays demonstrating a greatest ability. Additionally, the soft dorsal and anal fin demonstrates a traveling wave in angular displacement, moving posteriorly along the longitudinal length of the fin as it increases in amplitude. We suggests that this wave accelerates the water to increase the thrust component shown to be generated by the fins during an escape response (Tytell and Lauder, 2008). Furthermore, the spiny dorsal fin plays an integral role in the formation of this thrust component and is not merely a defense mechanism.

From this detailed kinematic analysis, we show that the fin surface of the dorsal and anal fin does not act as a uniform structure. Rather, it is highly deformable and complex with regional functional roles. To understand the role of the fins during locomotion, detailed kinematic analyses of the fins are required in conjunction with other analyses. 107

MATERIALS AND METHODS

ANIMALS

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 L:D photoperiod at a mean water temperature of 20ºC (± 1ºC). Detailed kinematics were quantified from three individuals of similar size, total length (TL) of

17.1 ± 1.7 cm (mean ± s.d.; range 16-19 cm).

In the specimens used for kinematic analysis, the dorsal fins (DF) were comprised of 10 anterior, rigid spines and 12 posterior, flexible rays. Though morphologically continuous, the dorsal fin is composed of two developmentally distinct fins (Mabee et al.,

2002), the anterior spiny dorsal fin (spD), supported by the 10 spines and the soft dorsal fin (sfD), supported by the last dorsal spine and the 12 rays. The anal fin (AF) is supported by 3 anterior spines and 12 posterior rays (Fig. 2.2). Throughout the paper, the term ‘fin-ray’ is used to refer to all external skeletal fin supports when the distinction between spines and rays is disregarded (see Chapter 1 for details).

RECORDING THE C-START

All video recordings were performed in the laboratory of Dr. George Lauder at

Harvard University. To reduce wall effects, it was important that the fish was at least 6 cm from any wall of the tank throughout Stages 1 and 2 of the fast-start. Additionally, to produce consistent and comparable escape responses, it was important that the startle stimulus always occurred from a similar direction. Both of these conditions were met when the fish swam at a steady speed, approximately 0.75 TL s-1, in the center of the working volume of a variable speed flow tank (28 cm wide, 28 cm deep and 80 cm long). 108

At swimming speeds below 1 TL s-1, bluegills use only their pectoral fins for propulsion and the body, median and caudal and fins exhibit minimal movements (Standen and

Lauder, 2005). Furthermore, most kinematic and EMG variables did not vary significantly between fast-starts evoked while at a standstill versus when swimming at steady speeds up to 1.6 TL s-1 (Jayne and Lauder, 1993).

As the fish held a centered position in the tank, we elicited a fast-start by dropping a battery (size “C”) into the tank behind and to the left of the fish (Fig. 2.3). C-starts were recorded with three synchronized high-speed video cameras (two Photron Fastcam

1280x1024 pixels and a Photron APX system 1024x1024 pixels) at 500 frames s-1

(1/2000 s shutter speed). The cameras were positioned to provide us with clear ventral, dorsal and lateral views of the entire fish throughout the duration of the C-start (Fig. 2.3), enabling us to record the simultaneous movements of the anal and dorsal fins. To avoid distortion in the dorsal image caused by surface waves, a Plexiglas ‘boat’ was partially immersed at the surface below the dorsal camera, effectively negating any distortion; the ventral view was filmed by using a mirror mounted below the tank (Fig. 2.3). Fish were allowed to rest a minimum of 30 minutes between trials, during which time the circulation of the flow tank was shut off.

IMAGE CALIBRATION

Video sequences were analyzed using DigiMat (Madden, 2004), a custom digitizing program written for Matlab (version 7.6.0.324 (R2008a), Mathworks, Natick,

MA, USA). The three camera images were calibrated to the shared three-dimensional volume in a three-step procedure described in Standen & Lauder (2005) with some modifications, due to a larger volume shared by the three cameras. A larger calibration 109 cube was needed to fill the entire field of view for each camera pair and had no less than

95 known points visible to both the lateral and dorsal cameras (or the lateral and ventral camera). A direct linear transformation (DLT) algorithm was used to calculate the 11 camera coefficients that determined the positions of the cameras relative to our calibration cube (Reinschmidt and van den Bogert, 1997). To align the dorsal-lateral and ventral-lateral volumes to the same coordinate system (i.e., the same origin and

X,Y,Z-axes), images captured from the three cameras that simultaneously shared, at minimum, eight identifiable points from a second calibration object were digitized for each camera pair. Using these two sets of 3-D points, a companion code to Digimat generated a transformation matrix, which was applied to the 3-D coordinates from the dorsolateral view to rotate and transform the points to the same volume, origin and orientation as the ventrolateral 3-D space. The final volume was oriented to the flow tank, with the X-axis parallel to water flow, the Y-axis parallel to the width of the flow tank and the Z-axis parallel to the vertical height of the water column (Fig 2.3). As water circulated through the flow tank, fish swam against the current with its body parallel to the direction of flow. Within this 3-D coordinate system, a downstream displacement represents a positive change in the x-coordinate. A positive change in the y-coordinate indicates movement toward the right and a positive change in the z-coordinate represents an increase in the vertical height (Fig. 2.3).

KINEMATIC ANALYSIS

A total of 46 escape responses from eight fish were captured and the general pattern of axial and fin movements during each C-start was reviewed. To reduce the variability in fin kinematics due to variations in the performance of the escape response, a 110 satisfactory C-start required: 1) The fish held a relatively constant position in the center of the flow tank’s working area prior to the presentation of the startle stimulus so that any wall effects were negligible. 2) Stage 2 was completed no later than 60 msec after onset of the response. 3) The entire body was still in view 70 msec after onset. Of the eight fish, three individuals had at least three satisfactory C-start recordings (N = 3 sequences per fish). While the fish performed a right-handed C-start the majority of the time (i.e., the initial lateral movement of the head was to the right), a few C-starts were left-handed.

To simplify the analysis and discussion of the movements, independent of the handedness of the escape response, all left-handed C-starts were converted into right-handed C-starts by reversing the sign of all lateral components (y-coordinate) of the sequence.

For each sequence, the first frame to show a clear, lateral displacement of the head was noted and the frame prior to this event was designated frame zero (F0) and time zero (T0). Pre-startle posture was established by digitizing F0 and the preceding nine frames (F-9 – F-1). The succeeding 35 frames (F1 – F35) were digitized to provide a kinematic description throughout the entire duration of Stages 1 and 2 into Stage 3. For each sequence, a total duration of 82 msec was analyzed (12 msec prior to T0 and 70 msec post-T0). All calculations performed on the 3-D coordinates obtained from Digimat

(Madden, 2004), were performed within Matlab, using custom programs written by BAC.

For details regarding the reconstruction of the axial body and calculations of the following axial parameters, see Appendix A.

Axial Kinematics

To track axial movements throughout the C-start, 15 points were digitized along the dorsal and ventral midlines, from the tip of the snout to a position above (or below) 111 the caudal peduncle (Fig. 2.2B). The 15 points were fit to a cubic smoothing spline function to generate the smoothest interpolant to the points with a mean squared error

(MSE) of ca. 0.1 mm3 (Walker, 1998), from which 21 evenly spaced points were interpolated. Using these midlines, the body was divided into 5 segments, each accounting for 20% of the standard length (SL, distance from snout to caudal peduncle;

Fig. 2.2A). The anterior two segments, the rostrum (Rs) and the operculum (Op), make up the head and the remaining three segments make up the trunk of the fish: the anterior

(Ant), middle (Mid) and posterior (Post) segments. This was done in order to compare the orientation and movement of the fins relative to the body segment to which they are attached, e.g., the spiny dorsal fin is primarily attached to Ant and the soft dorsal and anal fins are connected to Mid (Fig. 2.2B).

For each time point of the sequence, t, the three orthogonal planes and their corresponding axes (or normals) were defined for each body segment: transverse

(TrSeg(t)), sagittal (SgSeg(t)) and frontal (FrSeg(t)), where Seg represent the body segment of interest (Fig. 2.2A). Relative to the X,Y,Z-coordinate system of the tank, the yaw

(rotation about the FrSeg(t)-axis), pitch (rotation about the SgSeg(t)-axis) and roll (rotation about the TrSeg(t)-axis) angles could be defined and tracked over time for each body segment.

Axial Rotation

Fitting the angle of yaw, θ(t), from each time point to a quintic smoothing spline function (MSE=2.5°), the first time derivative of yaw, θ′(t), over the duration of the sequence, provided the turning rate (angular velocity, dθ/dt). A positive turning rate (θ′(t)

> 0) indicates a counterclockwise lateral rotation of the body about FrSeg(t), with a 112

clockwise rotation resulting in a negative turning rate (θ′(t) < 0). A counterclockwise rotation of the head, Rs and Op, are to the left side, but because the axis of rotation of the body lies near the center of mass, a counterclockwise rotation of the trunk segments, Ant,

Mid and Post, are to the fish’s right side. Thus, when the head and trunk both rotate to the same side of the fish, the sign of θ′(t) for the head and trunk segments are reversed. A change in the sign of θ′(t) indicates a rotational transition of the body segment, i.e., a change in direction.

Turning rate of the rostrum, θ′(t), was used to determine the stages of the escape response, according to standard definitions (Domenici and Blake, 1997). Stage 1 (S1) is defined as the period from the time point just prior to the first visible detection of lateral movement by the rostrum (T0) until the time of the first rotational transition, tθ′tr1, i.e.,

θ′(t) changes sign, or goes to zero. Stage 2 (S2) is defined as the period from tθ′tr1 until the time of the second rotational transition, tθ′tr2. As the rotational transitions of the rostrum define the C-start, tθ′tr1 and tθ′tr2, will often be referenced within the text as the

S1/S2 and S2/S3 transitions, respectively. To confirm that C-start performances by the fish were similar, the duration of Stage 2, ΔS2 (=tθ′tr2- tθ′tr1), and maximum turning rates of the rostrum during Stages 1 and 2, θ′max1 and θ′max2 respectively, were also recorded.

In order to compare the rotation/movement of the fins and their fin-rays to the movement of their respective trunk segments, five kinematic variables from θ′(t) for Ant and Mid segments were measured: tθ′max1 and θ′max1, the time and magnitude of the maximum turning rate during the initial rotation of the body segments; tθ′tr, the time of rotational transition; and tθ′max2 and θ′max2, the time and magnitude of the maximum turning rate during the second rotation of the body segments. 113

Center of Mass

Using several preserved specimens, the location of the center of mass was determined by capturing images of the fish suspended by a string, once at a point just anterior to the first dorsal spine and a second time at a point just posterior to the soft dorsal fin. Superimposing one image over the other so one fish image exactly overlaid the other, the intersection of the two string trajectories represents the stretched-straight center of mass (COM). Located within Op, just behind and above the ‘ear’ of the operculum (Figs. 2.1A and 2.2), COM was at a longitudinal position ca. 35% of SL and at a lateral depth ca. 33% of the body at that position.

For each digitized frame, the position relative to the two midlines that matched the corresponding percent values was used as the 3-D coordinates for the estimated COM of the experimental fish. The COM coordinates from each time point were fit to a quintic smoothing spline function (MSE=0.125 mm3), allowing for the calculation of displacement, velocity and acceleration of COM over the duration of the C-start.

Displacement, D(t), is the distance of the COM’s position, at time t, from its initial position at T0. Velocity and acceleration are the first and second time derivatives, respectively, calculated from the spline function fit to COM’s trajectory. At each time point, the velocity and acceleration of COM was divided into the components parallel and perpendicular to the trajectory of the head at that moment, i.e., TrRs(t). The components of velocity and acceleration of COM parallel with the heading of the fish are represented by v(t) and a(t), respectively. From these values, DS1 and DS2, the displacement of COM at the ends of Stages 1 and 2; vmax, the maximum velocity achieved during the C-start; and amax1 and amax2, the two peak accelerations, were determined. 114

Fin Kinematics

To track the kinematics of the fins, four spines (numbers DSp1, DSp4, DSp7 and

DSp10) and four rays (numbers DRy2, DRy5, DRy8 and DRy12) from the dorsal fins and two spines (numbers ASp1 and ASp3) and four rays (numbers ARy2, ARy5, ARy8 and ARy12) from the anal fin were selected for digitizing. Six points along the length of the selected spines and rays were digitized, with the exception of DSp1 (only four points were used due to its short length; Fig. 2.2B). The 1st point was at the base of the fin-ray before it disappeared into the skin and musculature; points 2-6 followed the posterior edge of the fin-ray, with the 6th point always at the distal tip. For each fin-ray, the six (or four) points were fit to a cubic smoothing spline function (MSE=0.1 mm3) and 21 equally spaced points along the length of the fin-ray curve were interpolated. Thus, point numbers represent the same relative position along the length of each fin-ray, e.g., point 1 of all fin-rays represents the 0% position, with each successive point moving distally at

5% intervals along the length of the fin-ray curve. For details regarding the reconstruction of the fin surface and calculations of the following fin-ray parameters, see

Appendix B.

Fin Surface

From the coordinates of the 21 interpolated points of every digitized fin-ray (both spines and rays), the surface of the entire dorsal and anal fins were reconstructed for each frame (Fig. 2.4A) and evaluated, by fitting all the points to a bivariate tensor function

(Kreyszig, 1991):

f (r, p),

where f is a cubic spline function based on r, the fin-rays, and p, the interpolated points

! 115 of each fin-ray. For any fin-ray, all the points along its length describe the spanwise curve of the fin surface and the chordwise curve of the fin surface is described by the same point number of all the fin-rays (Fig. 2.4A). Note that the subscript (t) will not be included to reduce the number of subscripts; instead, it is implied that each parameter describing the fin surface is calculated for each time point.

With a tensor function, descriptions of the fin surface at any given point can be computed by taking the two partial derivatives of the function, i.e., by holding one variable constant, f can be differentiated with respect to the other variable:

"f "f fr = and f p = , "r "p where fr equals the partial derivative of f with respect to r as p is held constant, and fp equals the partial derivative! of f with respect to p as r is held constant. From these two partial derivatives, the following vectors for any point on the fin, P(a,b), where the subscript a represents the fin-ray number and the subscript b represents the interpolated point number:

sT = f and cT = f , (a,b) p(a,b) (a,b) r(a,b) where sT(a,b) and cT(a,b) are the tangents parallel to the spanwise and chordwise curves, respectively, and! define the fin surface at P(a,b) (Fig. 2.4B). Using these two tangents, the three orthogonal axes of the fin surface at P(a,b) were calculated:

cT(a,b) " sT(a,b) L(a,b) = , cT(a,b) " sT(a,b)

sT(a,b) S(a,b) = , sT(a,b)

L(a,b) " S(a,b) C(a,b) = , L " S (a,b) (a,b)

! 116

where straight brackets indicate the magnitude of the enclosed variable and  indicates the cross product of the vectors. L(a,b), the lateral axis and the normal to the fin surface at

P(a,b), is perpendicular to sT(a,b) and cT(a,b) and directed to the left of the fin surface. S(a,b), the span axis, is parallel to both the fin surface and sT(a,b) and directed toward the distal end of the fin-ray. C(a,b), the chord axis, is parallel to the fin surface and perpendicular to sT(a,b), but not necessarily parallel to cT(a,b) and directed toward the anterior edge of the fin-ray. (Fig. 2.4B,C).

With the L,S,C (a,b)-axes, the orientation of the fin surface relative to any reference system could then be calculated; for our investigation, the relevant reference system was the planes of the body segment to which the fins were attached; in particular,

SgAnt(t) for the spiny dorsal fin, and SgMid(t) for the soft dorsal and anal fins. For each point of the fins, three angles of the fin surface, relative to its reference planes, were calculated: span axis rotation, sweep, and elevation (Fig. 2.4C). Span axis rotation,α(a,b), is the angle of the fin-ray about the S(a,b)-axis, relative to the SgSeg(t) plane; sweep, ω(a,b), is the angle of S(a,b) from the sagittal plane; and elevation, φ(a,b), is the angle of S(a,b) to

-TrSeg(t), the reversed transverse axis directed caudad (rather than rostral), within the

SgSeg(t) plane. The details for these calculations can be found in Appendix B.

For each fin-ray, the average span axis, sweep, and elevation angles were calculated from the values of the 21 points along the length of each fin-ray to get α¯r(t), ω¯ r(t), and φ¯r(t). Due to the location of the dorsal and anal fins on opposite midlines, the signs of the angles were adjusted to reflect the direction of fin-ray orientation relative to the fish’s body. A positive α¯r(t) indicates a rotation of the fin-ray such that the anterior edge (i.e., the C-axis) is directed to the left of SgSeg(t). A positive ω¯r(t), indicates that the 117

fin-ray (i.e., the S-axis) is directed to the right of SgSeg(t). A positive φ¯r(t) represents abduction of the fin-ray away from -TrSeg(t) (Fig. 2.4C).

Fin Surface Area

The fin area between adjacent fin-rays was calculated by fitting a triangular mesh to the 21 points of the two fin-rays and summing the area of each triangle, A〈r〉(t), where

〈r〉 represents the region between fin-ray r and the next posterior fin-ray, e.g., A〈DRy5〉(t) indicates the fin area between DRy5 and DRy8 (Fig. 2.2B). The sum of A〈r〉(t) that compose each fin gives the total fin areas, A〈Fin〉(t), where Fin represents the specific fin: spD, sfD or AF. Reported areas are true 3-D areas of the fins, not 2-D projected planar values.

Fin-Ray Kinematics

For α¯r(t) and ω¯r(t), five kinematic variables for each sequence was determined: t¯x max1 and ¯xmax1, time and magnitude of maximum α¯r(t) or ω¯r(t) during the initial rotation of the body segment to which the fin-ray is connected; t¯xtr, the time of directional transition, i.e., when α¯r(t) or ω¯r(t) changes signs or goes to zero; and t¯xmax2 and ¯xmax2, time and magnitude of maximum α¯r(t) or ω¯r(t) during the second rotation of the body segment.

From φ¯r(t), tφ¯max and φ¯max, the timing and magnitude of the maximum elevation achieved during the C-start was recorded. From A〈r〉(t) and A〈Fin〉(t), only tA〈r〉max and tA〈Fin〉max were reported, the time of maximum area achieved during the C-start.

Based on our null hypothesis, if the fin-rays are merely being dragged behind the portion of the trunk to which they are attached, then the timing of their kinematic events should be linked to the timing of the kinematic events of that axial segment, i.e., tθ′max1, tθ′tr, and tθ′max2. As the turning rate of the trunk increases, the hydrodynamic forces 118 acting against the fin surface should also increase, causing the sweep and span axis rotation of the fin-rays to be deflected in the opposite direction of trunk rotation, with t¯x max1/2 occurring before tθ′max1/2, and t¯xtr occurring after tθ′tr. Therefore, the timing of the span axis and sweep events were adjusted to the timing of the corresponding axial turning rates:

"tx max1 = tx max1 # t% max1$ , "tx tr = tx ttr # t% tr$ " tx max2 = tx max2 # t% max2$ .

As there was only a single timing event for fin-ray elevation and fin areas, which did not appear to be associated! with maximum turning rate of the body, their timings were adjusted to determine whether the time of maximum elevation and area occurred before or after the change in rotational direction of the body segment:

"t# max = t# max $ t& tr% ,

"tA r max = tA r max $ t& tr% ,

"tA Fin max = tA Fin max $ t& tr% .

STATISTICAL ANALYSIS

To test for !systematic differences in the C-start performances of the three fish, a one-way multivariate analysis of covariance, MANCOVA, was performed on the 19 axial and COM kinematic variables, using total duration of Stages 1 and 2 (tθ′tr2) as the covariate.

Excluding ASp1, each digitized fin-ray was assigned to one of three groups based on the fin it supported (Fig. 2.2): DSp1, DSp4, DSp7 and DSp10 were grouped together in spD; DSp10, DRy2, DRy5, DRy8 and DRy12 were grouped together as sfD; and

ASp3, ARy2, ARy5, ARy8 and ARy12 together formed the sfA group. Because the two 119 dorsal fins are continuous, DSp10 provides both the posterior-most support of spD and the anterior-most support of sfD and it spans the point of division between the Ant and

Mid body segments. Therefore, it was included in both the spD and sfD groups, with its angles and timing calculated according to the axial segment associated with its respective fin group.

Although each fin-ray is actuated by individual musculature and capable of independent movement, it is most likely that its orientation and movement is influenced by neighboring fin-rays due to their connection via the fin membrane (see Chapter 1).

Therefore, ANOVAs were deemed inappropriate to test for difference in kinematics between fin-rays within the fins. Instead, the position effect within each fin group was tested using Freidman’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).

To avoid any pseudo-replication from using multiple sequences from each fish, the average value of each kinematic variable was calculated and ranked between fin-rays within each group. The ranked average values from each of the three fish were then tested for a position effect in the average timing and magnitude of the fin-ray kinematics.

It is commonly considered that a fast-start escape response requires maximum performance by the fish and because the absolute values for fin kinematics determine the interaction with the surrounding water, we deemed it important to measure the maximal performance by a fish for each fin-ray parameter. Therefore, from the maximum fin-ray magnitudes from each sequence of a fish, the maximal angular deflection achieved was 120 determined and the position effect was tested for the ranked maximal values of the three fish.

As a means to easily assess the degree of agreement between the three fish for each variable, Kendall’s coefficient of concordance (W) was also calculated (Sokal and

Rohlf, 1981; Zar, 1984). To determine whether any significant position effects observed within both sfD and sfA were conserved between the two groups, multigroup coefficients of concordance (W) were computed (Zar, 1984).

Wilk’s λ, Friedman’s χ2, and Kendall’s W and their associated P-values were calculated using SPSS v16.0 (Chicago, IL); a custom program, based on the equations of

Zar (1984), was written in Matlab to calculate W and its Z-score. See Chapter 1 for details regarding the interpretation of χ2,W and W. To control for Type I errors resulting from multiple comparisons of the 18 variables of each fin group, P-values were compared to corrected α-levels using a sequential Bonferroni adjustment (Rice, 1989).

121

RESULTS

C-Start Performance

For the nine C-starts analyzed, kinematic differences among the three fish were consistent and were not statistically significant (Wilk’s λ = 6.80; df= 10, 2; P = 0.135).

Mean values for the 20 C-start parameters for each of the three fish and the grand means for all sequences are provided in Table 2.1.

At the end of S1, displacement of COM was minimal, ca. 3 mm, and its velocity was typically only a third of the maximum velocity achieved by the end of S2 (Fig. 2.5,

Table 2.1). Over the duration of the C-start, two acceleration peaks were consistently observed, the first peak occurring near tθ′tr1, i.e., the S1/S2 transition, and a second, smaller peak occurring during the latter part of S2 (Fig. 2.5C).

During Stage 1, both the rostrum and mid-trunk rotate to the right side of the fish

(though their directions of rotation are opposite, clockwise vs. counterclockwise) with the rotational transition of Mid to the left occurring a millisecond or two prior to the end of

S1 (Fig. 2.6, Table 2.1). In the sequence shown, a second rotational transition of Mid back to the right occurs several milliseconds prior to the end of S2 (Fig. 2.6C); however, this was not observed among all sequences (data not shown). The timing of the maximum turning rates for Mid, tθ′max1 and tθ′max2, always occurred during S1 and S2, respectively. While the timing of the rostrum and mid-trunk were closely coordinated, rotation of the anterior trunk was delayed, with no considerable rotation occurring until midway through S1, at which point it rotated clockwise to the fish’s left with tθ′tr occurring midway through S2 (Fig. 2.6B). Timing of maximum turning rates of Ant, 122

tθ′max1 and tθ′max2, was nearly concurrent with tθ′tr1 and tθ′tr2, i.e., S1/S2 and S2/S3 transitions (Fig. 2.6B, Table 2.1).

FIN-RAY KINEMATICS

Spiny Dorsal Fin

The mean kinematic performances of the four spines of the spD group by fish can be found in Table 2.2.

Sweep

Figure 2.7 shows the typical sweep pattern of the dorsal spines during a C-start from a single fish. During the initial rotation of Ant-trunk to the left, all spines underwent a sweep to the right with maximum sweep angles occurring 3-15 msec prior to the first maximum turning rate, tθ′max1 (Figs. 2.7 and 2.8A, Table 2.2). The transition of the spines from the right to the left also preceded the rotational transition of Ant to the right, tθ′tr (Fig 2.8C). With the exception of DSp10, maximum sweep to the left by the anterior three spines always preceded tθ′max2 by several msec (Fig 2.8D). While ω¯max1 and ω¯max2 of the anterior three spines was minimal (<10°), maximum sweep angles of

DSp10 were typically 2-3× greater (Fig. 2.8B,E). Despite the high degree of concordance among the fish, particularly for the initial sweep parameters (W>0.90), and the trend of increasing Δtω¯max1 and ω¯max1 with spine position, no significant position effects were found among the five sweep parameters (Table 2.3).

Span Axis

Figure 2.9 shows the typical span axis pattern of the dorsal spines during a C-start from a single fish. Unlike the timing of sweep angles, average timing of all three span axis events occurred concurrently with the turning rate events of Ant, within ca. ± 5 msec 123

(Fig. 2.10A,C,D, Table 2.2)., with neither a significant position effect (Table 2.3) nor a clear pattern among the spine position. However, a significant position effect was found for α¯max1 and α¯max2, for both the mean and maximal fish values (Table 2.3). During initial rotation of Ant to the left, the anterior two spines underwent a negative span axis rotation, i.e., the anterior edges were directed to the right of the fish, while the posterior two spines were directed to the left, with the signed magnitudes increasing with position

(Figs. 2.9 and 2.10B). This pattern indicates a chordwise cupping of the spiny dorsal fin surface, with its concavity directed toward the right when viewed dorsally (Fig. 2.1C).

During the second rotation of Ant to the right, the direction and increase in the angles of the span axis angles were reversed with position (Fig. 2.10E), with the fin’s concavity directed to the left.

Elevation and Area

Soon after the onset of a C-start, spine elevation and fin area increased, with Δtφ¯ max, ΔtA〈r〉max and ΔtA〈spD〉max of the spines preceding tθ′tr with such little difference between spines that they occurred almost simultaneously (Fig. 2.11A,C, Table 2.2), showing no position effect among the spines (Table 2.3). Among spines, φ¯max was significantly related to position, with mean and maximal φ¯max decreasing with spine position (Fig. 2.11B, Tables 2.2 and 2.3). Change in spine elevation and fin area after the initial increase varied among the sequences, with three generalized patterns emerging: maintenance of maximum elevation/fin area; decrease in the elevation/fin area that persisted throughout the rest of the C-start; or a transient depression/decrease followed by an increase in elevation/fin area (data not shown). 124

Soft Dorsal and Anal Fins

The last spine of the dorsal and anal fins (DSp10 and ASp3, respectively) provides the anterior-most support of the soft region of the fins and both are included in the analyses of sfD and sfA. When referring to the fin-rays of the sfD and sfA groups collectively, the two spines will be referred to as Sp0, due to the discrepancy in their number, and the rays, which are numbered the same, will be referred to as Ry2, Ry5, Ry8 and Ry12. The mean kinematic performances of the five fin-rays by fish for each fin group can be found in Table 2.4 (sfD) and Table 2.5 (sfA).

Sweep

During the initial rotation of the Mid-trunk to the right, all fin-rays underwent a sweep to the left followed by a sweep to the right during the succeeding rotation of Mid to the left; for Sp0, this initial sweep was quite small, ca. 2-3° (Fig. 2.12). For both fin groups, the time difference between each sweep event (max1, tr, and max2) and their corresponding Mid-trunk tθ′ events increased with fin-ray position (Figs. 2.12 and

2.13A,C,D, Tables 2.4 and 2.5). All three time parameters showed a significant position effect within sfD (Table 2.6); within sfA, a significant position effect was found in Δtω¯ max1 and Δtω¯tr, but not Δtω¯max2 (Table 2.7).

Both ω¯max1 and ω¯max2 increased with position within sfD and sfA (Fig. 2.13B,E), with significant position effects for all both the mean and maximal values (Tables 2.6 and

2.7). For all sweep parameters in which significant position effects were found in both the sfD and AF fin groups, a significant degree of concordance between groups was also found (Table 2.8). 125

Span Axis

Soon after the onset of the C-start, the four anterior fin-rays undergo a span axis rotation to the right while Ry12 rotates to the left (Fig. 2.14). Each fin-ray undergoes a second span axis rotation in the opposite direction. As described in the spiny dorsal fin, opposite directions in span axis rotation between fin-rays indicates a chordwise cupping of the fin surface. In both sfD and afA, the initial concavity of the fin cupping is directed first toward the right and then, later in the C-start, to the left.

Among the first four fin-rays, Δtα¯max1, Δtα¯tr and Δtα¯max2 increased with position, while the timing of Ry12 usually occurred at the same time as Sp0 or Ry2 (Fig. 2.15,

Tables 2.4 and 2.5). Significant position effects were found for Δtα¯max1, and Δtα¯tr, but not Δtα¯max2 for both sfD (Table 2.6) and sfA (Table 2.7).

During the initial span axis rotation, α¯max1 to the right increased with fin-ray position among Sp0, Ry2 & Ry5, at Ry8, α¯max1to the right decreased and by Ry12, α¯max1 was directed to the left. A similar pattern in the reverse direction was observed for α¯max2

Fig. 2.15B,E). For both sfD and sfA, mean α¯max1, but not maximal, was significantly related to position (Tables 2.6 and 2.7). In sfD, but not sfA , significant position effects were found for both mean and maximal α¯max2. For all span axis parameters in which significant position effects were found in both the sfD and sfA fin groups, a significant degree of concordance between sfD and sfA was also found (Table 2.8).

Elevation and Area

Elevation and fin area of sfD and sfA fin-rays increased after the onset of the C- start, with Δtφ¯max, ΔtA〈r〉 max, and ΔtA〈Fin〉 max typically occurring after tθ′tr of the Mid- trunk (Fig. 2.16A,C, Tables 2.4 and 2.5). However, Δtφ¯max and ΔtA〈r〉 max where highly 126 variable between fin-rays and no significant position effects in the timing of maximum elevation and fin areas were found for either group (Tables 2.6 and 2.7). For both groups,

φ¯max decreased with fin-ray position (Fig. 2.16B, Tables 2.4 and 2.5) and significant position effects for both mean and maximal φ¯max were found in both sfD (Table 2.6) and sfA (Table 2.7). A significant degree of concordance between sfD and sfA was also found for both φ¯max measurements (Table 2.8). 127

DISCUSSION

Each fin-ray is capable of rotation about all three of its axes: lateral, span and chord axes, though the morphology and emergent biomechanical properties of a fin-ray and its joint limit the range of motion and flexibility. During locomotion, fin-ray kinematics are the result of the interaction between the fin-ray’s inherent structural properties and its resistance/susceptibility to the combination of forces acting on it: external hydrodynamic forces, activity of its intrinsic muscles, and intra-fin forces transmitted via the fin webbing by the movement of adjacent fin-rays.

Over the course of a fast-start, the fin-rays of the dorsal and anal fins demonstrated variations in their timing and magnitude for several kinematic parameters, based on position within the fin. Furthermore, these variations were generally in agreement with our expectations from previously discussed differences in musculoskeletal and biomechanical properties, supporting our hypothesis that there is functional regionalization within the dorsal and anal fins of the bluegill sunfish (see

Chapter 1). While the data supported our hypothesis that fin-rays are capable of resisting deflecting forces, the pattern in timing of the maximum sweep angles did not always match our original predictions about fin-ray resistance to lateral deflection relative to the axial body. This suggests that that our original assumptions about either the forces acting on the fin-rays and/or the kinematic performance of the fin-rays due to their resistance/susceptibility to lateral deflection are more complex than the simple model we had proposed. 128

Spiny Dorsal Fin Kinematics

At the onset of the C-start, the spines of the dorsal fin underwent a lateral sweep to the right of the fish (Fig. 2.7) and a rapid increase in elevation and fin surface area, usually preceding any appreciable rotation by the anterior trunk. As Stage 1 proceeded, a chordwise cupping of the spiny dorsal fin occurred synchronous with a lateral bending of the anterior trunk as the anterior and posterior regions of the fin underwent span axis rotations in opposite direction, with concavity for both the fin and body directed to the right (Figs. 2.1C and 2.8).

By the end of S1 most spines had undergone a directional sweep transition and were now at a sweep angle oriented toward the left of the fish, although the anterior trunk was still undergoing its initial rotation to the left, with the sweep angle to the left persisting throughout the majority of S2 (Fig. 2.7). Midway through S2, span axis rotation underwent a direction transition followed by a second chordwise cupping of the fin, matching the lateral bend of the anterior trunk, directed toward the left (Figs. 2.1E and Fig. 2.9). Elevation and fin area during S2 was highly variable between sequences, either maintaining the same degree of elevation/fin area or depressing the spines/decreasing fin area, which may or may not be followed by a second elevation and increase of fin area..

Spine Sweep

As expected, the spines generally resisted lateral deflection; however, the sweep parameters within spD were neither closely linked with the turning rate of Ant nor significantly correlated with spine position (Figs. 2.8, Table 2.3). With the exception of

DSp10, timing and magnitude of the sweep parameters were moderately uniform among 129 the anterior three spines, with all time variables preceding the corresponding turning rate parameters of Ant, in many cases by more than 15 msec (Fig. 2.8). In fact, the directional transition of the anterior three spines even preceded the initial maximum turning rate of

Ant (as indicated by Δtθ′max1 in Fig. 2.8C). Though the low degrees of freedom (df=2, 3) and the conservative nature of the α-adjustment precluded any significant conclusions, the trend for the first maximum sweep to increase with spine position matched the increased joint mobility observed in the manipulation of preserved specimens (see

Chapter 1). However, the timing of maximum sweep angle of the anterior three spines relative to maximum turning rate of Ant did not conform to our initial expectations.

Rather than the sweep angles of the spines increasing with Ant turning rate, as we had predicted, maximum sweep angle to the right often occurred before any appreciable rotation of the anterior trunk had begun.

Two potential explanations for this pattern are: (1) Due to the restrictive nature of the spine joint, maximum lateral deflection of the spines, as measured by the sweep parameter, is limited and quickly met, with no further increase in deflection despite any increase in angular velocity and the resulting opposing forces exerted on the spines. By retaining their inclinator muscles (Chapter 1), spines may be capable of initiating lateral deflection independent of axial rotation and may be able to overcome opposing hydrodynamic forces or transmit forces into the flow. (2) Our initial hypothesis on the opposing hydrodynamic forces generated during the escape response was incorrect.

During S1, rotation of the anterior trunk is delayed ca. 10 msec; however, this does not mean that there was no movement. From analyzing videos of the sequence, as the head and posterior trunk segments rotate to the right, the anterior trunk undergoes lateral 130 translation to the left, i.e. a linear displacement rather than angular. Under this circumstance, opposing hydrodynamic force would direct spine deflection to the right, as was observed (Fig. 2.7).

Spine Span Axis

Timing of span axis rotation in spD was coupled with the timing of axial rotation of Ant, with no significant position effect or discernable pattern in the timing between spines (Fig. 2.10A,C,D). While maximum span axis rotation was correlated with position

(Fig. 2.10B,E, and Table 2.3), note that the restrictive joints of the spines do not permit the actual rotation of the spines about their span axis (Chapter 1); instead, the observed change in span axis orientation is a result of lateral bending of the anterior trunk. Thus, the chordwise cupping of spD during the two phases of axial rotation, as indicated by the opposite directions between the anterior and posterior spines, mirrors the lateral bend in the trunk (Fig. 2.1C,D).

Spine Elevation

Elevation of the spines and increase in fin area always occurred within 1 or 2 frames after the onset of a C-start, reaching both maximum elevation and fin area well before the rotational transition of the anterior trunk (Fig. 2.11). The near synchronous elevation of the spines is in agreement with the observation that manual elevation of a single spine in preserved specimens caused a corresponding elevation in succeeding posterior spines, due to the connection of the spines via the connective tissues of the fin membrane (see Chapter 1). Timing of maximal elevation does not appear to be determined by rotation of the anterior trunk, rather, erection of the spines is most likely 131 tied to the onset of the C-start, with maximum elevation and area typically reached within

10-15 msec from T0 (data not shown).

Soft Dorsal and Anal Fin Kinematics

Kinematic patterns between the soft dorsal and anal fins were generally the same.

As with the spines, the fin-rays were erected and fin area increased soon after the onset of the C-start, usually reaching maximum values by the end of S1. As the middle trunk rotated toward the right, the fins underwent a sweep to the left, with the time and magnitude of maximum sweep increasing posteriorly along the longitudinal length of the fin, similar to a traveling wave (Fig. 2.12). Likewise, a wave in clockwise span axis rotation occurred along the longitudinal length of the fins (Fig, 2.14), ultimately resulting in the right side of the fin surface to be directed caudad. During the initiation of this wave of span axis rotation within the anterior fin region, a brief counterclockwise span axis rotation of the posterior edge of the fin occurred, which resulted in a transient chordwise cupping of the posterior fin, directed to the right.

At the end of S1, Mid had undergone its transition and rotation was now directed to the left. The fins underwent a rapid sweep transition, with its sweep orientation now directed to the right. As with S1, the time and magnitude of maximum sweep increased with position, though they occurred at a much faster rate (Fig. 2.12). The span axis rotation of the fin also changed direction, with the right side of the fin facing rostrally, and a slight cupping of the posterior fin surface to the left, due to an oppositely directed span axis rotation of the posterior edge of the fin (Fig. 2.14). As with spD, fin-ray elevation and fin area during S2 varied among sequences. 132

Fin-Ray Sweep

As predicted, all maximum sweep angles were significantly correlated with fin- ray position, with the posterior rays showing the greatest degree of deflection (Fig.

2.13B,E, Tables 2.6 and 2.7). Timing of the sweep parameters was coupled with axial rotation, with significant position effects for all parameters except the second maximum sweep of sfA (Fig. 2.13, Tables 2.6 and 2.7). As predicted, the timing of the directional transition of the posterior rays occurred soon after, and even shortly before, the rotational transition of Mid, while the transition of Sp0 and Ry2 occurred ca. 5 msec prior, often before Mid reached its maximum turning rate of (as indicated by Δtθ′max1 in Fig. 2.13C).

This supports the hypothesis that the fin-rays are actively resisting lateral deflection and in the case of the anterior fin-rays that they are overcoming the opposing forces and are able to ‘lean into’ the direction of movement.

However, the timing of maximum sweep angle relative to maximum turning rate of Mid did not agree with our expectations. As in spD, the anterior supports of the fins,

Sp0 and Ry2, reached their maximum small degree of sweep, as well as directional transition, in advance of maximum turning rate by Mid (Figs. 2.12B and 2.13). As such, the same explanations provided for the spines of the dorsal fin may also apply to the spine and anterior rays of sfD and sfA, which were found to have joints that are more restrictive than posterior rays (Chapter1). What was more perplexing, however, was the consistency in which Δtω¯max1 of Ry5 and Ry8 occurred after tθ’max1, ca. 5 msec (Figs.

2.12D,E and 2.13A), demonstrating that sweep angle among these rays increased, even while axial turning rate was decreasing, suggesting that an opposing force, not related to the rate of axial rotation, was acting on the fin-ray. 133

A previous study found that muscle activity in the left dorsal inclinator muscles of bluegill sunfish, during right-handed C-starts, began prior to the end of axial rotation of the trunk, while muscle activity of the right inclinators had ceased (Jayne et al., 1996).

Among the rays tested, time of activation and duration of activity in the left inclinators were correlated with position, occurring sooner and lasting longer among the posterior rays tested. This matches with our results, suggesting that as axial rotation to the right is slowing down, muscle activity of the left fin-ray musculature is causing the fin-rays to increase their sweep angle to the left, possibly to stiffen them in preparation for the subsequent rotation to the left and opposing hydrodynamic forces. However, other external or intra-fin forces may also contribute to this phenomenon.

Fin-Ray Span Axis

The timing of span axis rotation in sfD and sfA was coupled with axial rotation with significant position effects for the timing of the first maximum, but not the second, span axis rotation and transition (Fig. 2.15A,C,D). Both the first and second maximum span axis rotations of sfD were significantly correlated with position (with the exception of the first maximal values, which was precluded by the α-adjustment). However, within sfA, only the mean value of first maximum span axis was significantly correlated with position (as in sfD, the maximal value was precluded by the α-adjustment; Fig. 2.15B,D,

Tables 2.6 and 2.7). Nonetheless, the reversal in direction of span axis direction of the final ray (Ry12), like spD, indicates a cupping of the chordwise surface of the fin. Unlike the spines, the less restrictive joint of the fin-rays appears to allow some degree of span axis rotation at the joint. The lack of a significant position effect in the maximal values 134

of α¯max1 for both sfD and sfA suggests that all the rays are capable of rotating about their span axis to the same degree.

Fin-Ray Elevation

As seen in the spiny dorsal fin, maximum elevation within sfD and sfA was significantly correlated with position (Tables 2.4 and 2.5), with maximum elevation decreasing posteriorly (Fig. 2.16B). Timing of maximum elevation and fin areas typically occurred after the rotational transition of the middle trunk; however, the timing was variable both within the fins as well as between fish, showing no position effect in either fin. As with the spines, the connective tissues of the fin membrane keeps the timing of maximum elevation and fin area closely uniform; however, the variability observed may indicate more independent control of elevation among the more flexible rays than seen in the spines. Although the timing appears associated with the rotational transition of Mid, synchronicity with the turning rate of the rostrum, i.e., the end of Stage

1, confounds any interpretation of whether or not fin-ray elevation and fin area are linked to axial rotation or the onset of the C-start.

For the sweep and span axis, parameters associated with the S2 period of the C- start, typically showed the lowest degree of concordance between fish, particularly for the timing values. This is expected, as the later stage of escape responses show the most variability with in the performance parameters tested (Domenici and Blake, 1997; Law and Blake, 1996; Webb, 1978). Multigroup comparisons of significant parameters showed that, as predicted, the kinematic performances were conserved between the soft dorsal and anal fins, showing significant degrees of concordance between the two groups for all position effects found (Table 2.8). 135

Hydrodynamic Role of the Fins

The traditional interpretation of the role of the dorsal and anal spines was as a defense mechanism, preventing capture by gape-limited predators and/or to inflict damage to predators that strike at that region (Hoogland et al., 1956). From our kinematic analysis, the immediate erection of the spines soon after the onset of an escape response supports that role. However, our kinematic analysis in the context of the study by Tytell and Lauder (2008) on the hydrodynamics of the escape response in bluegill, support a role in the performance of the C-start by all three fins. In their study, three distinct jets of fluid, representing the momentum added to the water by the fish’s movements, were produced by the body and tail: one at the trailing edge of the caudal fin, a second at the body in the location of the initial C-bend and a third at the mid-trunk, opposite from the second jet. From their analysis, the second jet provided the primary source of thrust for accelerating the fish in the direction of its escape trajectory.

Additionally, they found that a jet of fluid was produced by both the dorsal and anal fins that also contributed to the momentum of the second jet, (ca. 37% of total momentum, combined) in addition to a lateral component of momentum that is likely for stability as previously suggested (Jayne et al., 1996)

Though the movement of the fins were not distinguished (Tytell and Lauder,

2008), we suggest that the role of the spiny dorsal fin differs from the soft dorsal in the production of the fluid jet. As Tytell and Lauder (2008) showed, lateral bending of the body during S1 forms a suction force that draws the fluid into the bend. The initial formation of the jet occurs in the area of the anterior trunk and the spiny dorsal fin. It is likely then that the increase in lateral depth and synchronous chordwise bending of the 136 erected spD adds to the volume of water entrained in the suction and raises the total momentum transmitted into the water. While sfD and sfA may also contribute to the volume of water and the resulting momentum, we suggest that the traveling wave directed posteriorly in the sweep and span axis angles functions to accelerate the fluid during the end of Stage 1, when peak acceleration often occurs.

Interestingly, Tytell and Lauder (2008) did not report any contribution by the fins to the third fluid jet formed during S2, which they suggested may provide a steering component to the escape response due to its orientation. Based on our kinematic data, we would expect some contribution by the dorsal and anal fins to the momentum of the fluid.

This may be due to differences in C-start performances between the two studies. As with our study, they controlled the variability among sequences by presenting the startle stimulus in the same location as the fish maintained a position in the center of the experimental tank, resulting in C start performances with low variability. While the total duration of the C-start was nearly equal for both studies, S1 was longer and S2 shorter (34 and 18 msec, respectively) compared to our results (22 and 29 msec, respectively).

Additionally, we observed two peaks in acceleration of COM, one at the end of S1 and another late in S2 (Fig. 2.5C) while they only observed a single acceleration peak that occurred prior to the end of S1 (Tytell and Lauder, 2008). Therefore, the formation and orientation of jet 3 may show a higher degree of variability among C-starts with different performances.

As shown by multiple studies, the dorsal and anal fins of bluegill sunfish are under active muscular control (Jayne et al., 1996) and capable of producing both lateral and thrust forces during steady swimming (Drucker and Lauder, 2001a; Tytell, 2006), 137 maneuvering (Drucker and Lauder, 2001b) and fast-starts (Tytell and Lauder, 2008).

However, combining these studies with detailed 3-D analysis of fin-ray kinematics that treat the fins as functionally regionalized structures will increase our understanding of how the fins are able to modify and generate the flow of water as they perform their role as control surfaces. 138

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141

Table 2.1

Escape Response Kinematic Parameters by Fish

Parameter Axial Region (units) Fish A Fish B Fish C All Fish

DS1 (mm) 3.1 + 1.30 2.7 + 1.08 2.1 + 1.11 2.6 + 1.09

DS2 (mm) 35.7 + 7.20 29.4 + 4.03 33.1 + 3.66 32.7 + 5.30 -1 COM vmax (m s ) 1.1 + 0.18 1.5 + 0.18 1.5 + 0.11 1.4 + 0.24 -2 amax1 (m s ) 66.9 + 11.7 55.6 + 4.53 58.4 + 2.23 60.3 + 8.15 -2 amax2 (m s ) 37.3 + 17.1 47.3 + 6.87 45.1 + 10.5 43.2 + 11.6

tθ tr1 (msec) 23.3 + 1.15 21.0 + 3.61 20.7 + 1.53 21.7 + 2.40 ΔS2 (msec) 32.0 + 4.00 24.7 + 4.04 29.7 + 2.31 28.8 + 4.47

Rostrum tθ tr2 (msec) 55.3 + 4.16 45.7 + 0.58 50.3 + 2.52 50.4 + 4.85 -1 θ max1 (° msec ) -3.3 + 0.17 -4.0 + 0.08 -3.5 + 0.19 -3.6 + 0.35 -1 θ max2 (° msec ) 1.4 + 0.59 3.1 + 0.18 3.0 + 0.39 2.5 + 0.88

tθ max1 (msec) 23.7 + 1.53 21.7 + 3.21 21.7 + 1.53 22.3 + 2.18 -1 θ max1 (° msec ) -2.4 + 0.16 -2.7 + 0.19 -2.5 + 0.36 -2.5 + 0.26

Ant-Trunk tθ tr (msec) 40.7 + 3.51 35.3 + 4.62 36.3 + 0.58 37.4 + 3.81

tθ max2 (msec) 56.3 + 7.09 45.0 + 4.36 49.0 + 1.73 50.1 + 6.55

-1 θ max2 (° msec ) 1.1 + 0.48 2.3 + 0.15 2.6 + 0.42 2.0 + 0.77

tθ max1 (msec) 12.3 + 1.15 11.3 + 1.15 11.0 + 1.00 11.6 + 1.13 -1 θ max1 (° msec ) 1.5 + 0.03 1.5 + 0.07 1.4 + 0.12 1.5 + 0.08

Mid-Trunk tθ tr (msec) 19.7 + 0.58 17.7 + 2.52 18.0 + 1.00 18.4 + 1.67

tθ max2 (msec) 33.0 + 1.00 29.7 + 3.51 29.0 + 1.00 30.6 + 2.65

-1 θ max2 (° msec ) -3.1 + 0.23 -3.6 + 0.32 -3.2 + 0.45 -3.3 + 0.36 Axial Region indicates the region from which the C-start parameters were calculated. See text for a description of the parameters. Values are mean±1 s.d., n=3 sequences for each fish.

142

Table 2.2

Spiny Dorsal Fin-Ray Kinematic Parameters by Fish

ΔTime (msec from tθ event) Mean Angle (deg) Max Angle (deg) Parameter Spine Fish A Fish B Fish C Fish A Fish B Fish C A B C SP1 -12.9 + 8.3 -9.6 + 4.8 -4.5 + 4.3 3.3 + 2.2 3.2 + 1.7 8.7 + 1.8 5.6 4.2 10.8 SP4 -18.4 + 0.4 -14.9 + 2.4 -13.4 + 2.9 1.0 + 0.5 1.7 + 0.2 2.2 + 1.0 1.6 2.0 2.9 max1 SP7 -10.8 + 0.3 -9.2 + 4.5 -9.7 + 0.9 5.8 + 0.7 4.4 + 1.1 8.0 + 1.1 6.6 5.6 9.1 SP10 -1.6 + 3.2 -1.7 + 1.6 -4.1 + 1.4 18.9 + 1.3 20.0 + 3.0 22.1 + 4.7 19.9 22.9 27.6 SP1 -27.7 + 7.6 -17.1 + 1.2 -8.0 + 7.5 ------SP4 -30.3 + 1.9 -24.0 + 4.8 -23.2 + 1.7 ------tr SP7 -17.9 + 1.5 -15.0 + 3.1 -16.1 + 2.1 ------SP10 -3.5 + 0.7 -0.5 + 2.5 -3.6 + 7.4 ------Sweep Events SP1 -33.1 + 7.4 -20.0 + 6.0 -14.2 + 11.4 -6.1 + 1.2 -2.8 + 2.8 -7.0 + 3.5 -7.5 -6.0 -11.0 SP4 -29.2 + 4.9 -18.6 + 0.7 -22.3 + 2.3 -7.9 + 1.5 -7.2 + 3.2 -6.0 + 1.8 -9.5 -10.7 -7.6 max2 SP7 -11.7 + 8.6 -11.0 + 14.1 -20.1 + 11.3 -10.1 + 0.6 -6.0 + 3.6 -6.2 + 2.5 -10.8 -10.0 -8.7 SP10 -1.6 + 7.9 0.6 + 1.2 0.0 + 0.4 -16.2 + 4.2 -17.0 + 1.2 -25.1 + 10.3 -19.2 -17.8 -33.4 SP1 -4.2 + 2.2 -4.0 + 0.5 -2.5 + 0.4 -16.5 + 2.9 -18.1 + 9.2 -20.6 + 5.8 -19.5 -23.4 -26.0 SP4 10.9 + 4.6 0.0 + 2.5 2.0 + 2.6 -3.2 + 1.2 -3.8 + 1.1 -8.8 + 3.1 -4.0 -5.0 -12.2 max1 SP7 1.4 + 3.8 -2.1 + 4.9 2.7 + 2.5 15.9 + 2.4 13.8 + 0.2 13.5 + 0.6 18.3 14.0 14.1 SP10 0.5 + 1.6 -1.3 + 1.3 -2.2 + 2.0 39.7 + 1.1 36.2 + 3.3 35.6 + 1.2 40.5 38.3 36.7 SP1 -3.3 + 1.3 3.7 + 9.3 -0.5 + 1.7 ------SP4 13.0 + 8.2 -6.8 + 2.9 6.9 + 3.7 ------tr SP7 -0.6 + 1.5 2.2 + 0.7 -2.3 + 1.8 ------SP10 5.2 + 1.6 2.9 + 1.2 4.8 + 2.5 ------

Span Axis Events SP1 -6.3 + 5.5 3.1 + 5.1 -1.9 + 2.5 12.8 + 3.0 10.1 + 10.9 15.2 + 2.6 15.4 22.5 18.2 SP4 2.7 + 5.7 -6.2 + 9.0 0.5 + 8.7 1.8 + 0.6 3.7 + 0.9 8.6 + 5.5 2.5 4.3 14.0 max2 SP7 -5.7 + 9.1 -0.3 + 1.5 -3.0 + 1.3 -8.1 + 0.4 -8.3 + 1.2 -13.6 + 3.3 -8.6 -9.1 -17.1 SP10 -4.3 + 1.7 2.2 + 0.3 2.5 + 2.3 -14.0 + 4.5 -21.8 + 4.5 -23.8 + 4.9 -19.2 -24.6 -28.7 SP1 -26.0 + 2.6 -23.3 + 1.2 -24.3 + 1.5 96.1 + 1.0 99.7 + 0.9 108.5 + 2.4 97.0 100.6 110.8 Max SP4 -24.0 + 2.6 -18.0 + 4.0 -24.3 + 0.6 75.9 + 0.7 81.6 + 1.7 84.0 + 1.7 76.6 83.3 85.3 Elevation SP7 -24.7 + 1.5 -22.0 + 3.5 -20.3 + 0.6 59.1 + 1.2 61.9 + 1.6 64.5 + 1.6 60.4 63.5 65.9 SP10 -18.0 + 4.6 -15.3 + 1.2 -23.7 + 10.0 55.4 + 1.2 54.1 + 1.3 57.1 + 2.1 56.8 55.3 58.9 DSp1 4.7 + 10.7 -27.3 + 4.6 -17.0 + 13.9 ------Max DSp4 -24.0 + 4.4 -17.3 + 4.6 -24.3 + 0.6 ------Areas DSp7 -25.3 + 2.1 -10.0 + 15.9 -23.0 + 1.7 ------spD -25.3 + 2.1 -20.7 + 1.2 -23.0 + 1.7 ------ΔTime is the difference in time of a given parameter (individual rows) from the corresponding kinematic event of the Ant-trunk (tθ′event). Mean Angle is the average for all sequences for each fish. Max Angle is the maximal angle of the parameter that was achieved by the fish, observed in any sequence. For ΔTime and Mean Angle, values are mean ± 1 s.d.. See text for details. n=3 sequences for each fish.

143

Table 2.3

Kendall’s W and Friedman’s χ2 for Spiny Dorsal Fin-Ray Kinematic Parameters

ΔTime Mean Angle Max Angle Parameters W χ2 P-value W χ2 P-value W χ2 P-value max1 0.91 8.20 0.017 0.91 8.20 0.017 0.91 8.20 0.017 Sweep tr 0.91 8.20 0.017 ------Events max2 0.73 6.60 0.075 0.64 5.80 0.148 0.64 5.80 0.148 max1 0.78 7.00 0.054 1.00 9.00 0.002 1.00 9.00 0.002 Span Axis tr 0.24 0.53 0.608 ------Events max2 0.29 2.60 0.524 1.00 9.00 0.002 1.00 9.00 0.002 Max Elevation 0.66 5.90 0.115 1.00 9.00 0.002 1.00 9.00 0.002 Max Area r 0.11 0.67 0.944 ------See Table 2.2 for the description of ΔTime, Mean Angle and Max Angle. See text for a description of the parameters. Significant analyses with P-values less than their adjusted α-levels are indicated in bold. For Sweep, Span Axis and Elevation, df=2, 3; for Area, df=2, 2.

144

Table 2.4

Soft Dorsal Fin-Ray Kinematic Parameters by Fish

ΔTime (msec from tθ event) Mean Angle (deg) Max Angle (deg) Parameter Fin-Ray Fish A Fish B Fish C Fish A Fish B Fish C A B C DSp10 -9.5 +0.4 -5.9 +0.6 -7.3 +1.9 -0.6 +0.3 -1.5 + 0.5 -0.9 +0.2 -1.0 -2.1 -1.2 DRy2 -0.8 +1.3 -0.8 +1.8 -2.8 +1.9 -4.4 +1.0 -5.1 + 2.0 -1.4 +1.0 -5.5 -7.0 -2.0 max1 DRy5 4.4 +1.3 2.4 +2.8 3.6 +0.9 -13.4 +2.2 -12.7 + 3.7 -7.1 +1.0 -15.9 -16.9 -7.8 DRy8 4.4 +1.3 4.1 +1.1 4.6 +0.2 -27.2 +3.6 -24.4 + 4.3 -16.4 +0.8 -31.1 -29.0 -17.3 DRy12 -0.5 +0.9 0.8 +1.4 0.9 +0.7 -25.7 +3.2 -28.2 + 3.7 -30.6 +1.1 -29.0 -30.5 -31.4 DSp10 -14.1 +0.8 -9.5 +2.1 -12.1 +0.4 ------DRy2 -3.9 +1.7 -3.4 +0.7 -7.1 +3.3 ------tr DRy5 1.6 +0.7 1.1 +0.7 0.2 +1.0 ------DRy8 2.8 +0.6 2.7 +1.1 1.9 +0.6 ------

Sweep Events DRy12 0.4 +0.6 0.1 +1.4 -0.1 +0.9 ------DSp10 -18.7 +0.2 -14.8 +2.0 -15.3 +1.9 6.4 +1.8 7.8 + 0.7 12.1 +2.3 7.5 8.6 14.8 DRy2 -8.2 +1.3 -7.8 +0.6 -7.4 +3.1 16.5 +1.6 18.1 + 2.5 21.2 +3.2 17.4 20.7 24.9 max2 DRy5 -4.4 +1.0 -4.5 +0.6 -4.0 +2.8 36.0 +4.8 37.9 + 4.1 40.7 +4.2 39.2 42.6 45.2 DRy8 -2.2 +1.2 -2.8 +0.4 -1.0 +2.8 51.3 +5.0 50.4 + 6.5 52.2 +2.5 54.6 57.6 54.9 DRy12 -3.1 +1.6 -2.9 +3.2 0.7 +1.0 44.4 +2.6 48.0 + 14.0 40.6 +1.1 47.3 62.5 41.9 DSp10 -1.8 +1.1 0.0 +2.2 -0.6 +1.2 -10.0 +0.7 -6.8 + 5.4 -11.9 +4.0 -10.7 -12.4 -16.5 DRy2 1.8 +0.1 0.4 +0.9 0.1 +1.5 -10.6 +0.5 -9.8 + 3.8 -12.4 +1.9 -10.9 -12.7 -14.5 max1 DRy5 2.2 +0.4 4.7 +1.9 5.8 +1.1 -11.0 +0.2 -12.3 + 2.2 -18.3 +2.6 -11.1 -14.8 -20.0 DRy8 9.4 +1.6 7.0 +3.6 9.7 +0.7 -8.4 +1.1 -12.1 + 8.3 -14.0 +4.5 -9.4 -21.6 -17.0 DRy12 2.4 +1.3 3.9 +1.5 1.9 +4.9 16.5 +3.7 14.6 + 3.7 6.3 +2.5 20.8 18.8 9.2 DSp10 -3.0 +0.8 -2.8 +0.6 -3.3 +0.2 ------DRy2 0.9 +0.4 -1.1 +0.5 -1.5 +0.2 ------tr DRy5 2.5 +1.3 3.8 +0.8 4.9 +0.6 ------DRy8 6.8 +2.2 6.0 +0.3 8.5 +2.9 ------DRy12 1.7 +0.6 1.9 +0.5 1.1 +1.5 ------Span Axis Events DSp10 -7.0 +7.1 -6.7 +7.0 -0.4 +9.1 11.9 +3.7 14.7 + 1.7 15.7 +1.0 15.7 16.7 16.5 DRy2 2.7 +6.5 -4.0 +5.5 0.0 +8.1 17.8 +2.2 20.1 + 0.7 15.3 +6.0 20.3 20.7 21.0 max2 DRy5 3.2 +4.1 -2.0 +2.3 1.2 +3.5 24.0 +2.5 18.0 + 3.2 17.2 +0.7 26.8 20.9 18.0 DRy8 1.0 +0.3 0.7 +0.8 2.9 +3.8 24.7 +4.5 23.4 + 3.1 23.9 +6.6 28.1 26.9 27.8 DRy12 -2.6 +3.2 -4.1 +0.5 -3.2 +3.6 -28.9 +4.8 -24.0 + 2.8 -25.0 +4.9 -32.7 -27.2 -29.6 DSp10 3.0 +8.9 4.3 +13.1 -6.0 +7.0 51.6 +1.1 53.2 + 0.9 52.1 +1.5 52.9 54.1 53.8 DRy2 -0.3 +12.6 3.7 +10.8 0.0 +8.7 42.7 +3.1 48.8 + 0.4 45.6 +2.1 46.3 49.2 48.0 Max DRy5 5.0 +14.7 11.0 +1.7 2.7 +8.1 37.6 +3.0 41.9 + 2.1 37.4 +1.4 39.7 44.3 39.0 Elevation DRy8 13.7 +0.6 11.7 +0.6 8.0 +9.8 33.2 +3.7 36.8 + 2.4 32.4 +3.4 35.6 38.7 34.6 DRy12 11.7 +23.0 -6.3 +5.5 -8.0 +2.6 -13.0 +1.9 -5.5 + 1.0 -9.4 +1.7 -11.7 -4.4 -8.0 DSp10 17.0 +5.2 10.3 +14.4 6.0 +7.9 ------DRy2 7.0 +1.0 6.3 +0.6 6.7 +2.5 ------Max DRy5 6.3 +7.4 7.0 +4.6 8.0 +4.6 ------Areas DRy8 11.7 +24.7 17.7 +7.8 -6.7 +9.1 ------sfD 7.7 +6.7 3.0 +5.6 8.7 +5.9 ------See Table 2.2 for the description of ΔTime, Mean Angle and Max Angle. See text for the description of the parameters. n = 3 sequences per fish. 145

Table 2.5

Anal Fin-Ray Kinematic Parameters by Fish

ΔTime (msec from tθ event) Mean Angle (deg) Max Angle (deg) Parameter Fin-Ray Fish A Fish B Fish C Fish A Fish B Fish C A B C ASp3 -10.2 +1.7 -9.2 +0.3 -8.5 +0.7 -1.0 +0.3 -1.3 + 0.3 -0.8 +0.3 -1.2 -1.4 -1.0 ARy2 -0.3 +0.8 -1.3 +0.9 0.0 +0.8 -5.3 +1.2 -3.0 + 0.3 -4.0 +1.7 -6.7 -3.2 -5.9 max1 ARy5 2.9 +0.3 1.7 +0.2 2.9 +0.7 -12.3 +0.7 -7.0 + 1.3 -10.0 +0.9 -13.1 -8.5 -10.8 ARy8 2.6 +0.5 2.3 +0.1 3.4 +0.9 -24.9 +1.6 -16.0 + 5.5 -21.7 +2.1 -26.7 -19.7 -23.1 ARy12 -1.3 +1.1 1.0 +0.8 0.7 +1.1 -17.5 +5.4 -20.1 + 4.2 -22.0 +9.9 -23.3 -24.5 -33.3 ASp3 -14.5 +0.7 -13.0 +1.7 -15.2 +1.7 ------ARy2 -3.8 +0.8 -4.9 +1.6 -4.0 +0.2 ------tr ARy5 0.4 +0.5 -1.4 +1.1 -0.1 +1.0 ------ARy8 0.9 +0.6 0.4 +1.3 1.1 +1.2 ------

Sweep Events ARy12 -2.0 +1.1 -1.0 +1.9 -0.4 +1.4 ------ASp3 -16.0 +1.2 -15.3 +2.5 -15.5 +1.8 8.2 +0.8 6.4 + 1.2 5.3 +1.7 8.7 7.1 6.9 ARy2 -1.6 +2.7 -4.6 +3.6 -4.6 +4.4 24.7 +7.0 25.9 + 2.9 23.2 +1.0 29.1 28.4 24.0 max2 ARy5 -3.5 +0.7 -3.5 +1.8 -3.7 +3.5 45.5 +9.7 40.9 + 7.1 34.6 +4.0 52.1 45.2 38.5 ARy8 -2.2 +0.9 -1.9 +1.3 -2.6 +2.9 60.0 +6.6 50.1 + 5.0 45.9 +6.0 65.4 55.6 52.9 ARy12 -3.0 +2.3 -2.1 +1.7 -5.0 +2.4 52.2 +5.3 45.6 + 6.4 42.4 +2.7 57.0 51.9 45.4 ASp3 -2.0 +1.4 -2.5 +1.7 -2.5 +0.8 -10.2 +1.6 -3.3 + 3.2 -6.2 +1.5 -12.0 -6.9 -7.2 ARy2 -0.8 +1.4 -1.7 +1.2 -2.0 +0.3 -14.6 +1.7 -7.5 + 2.0 -8.3 +2.2 -16.6 -9.2 -10.1 max1 ARy5 6.3 +0.8 5.0 +1.2 4.1 +0.4 -14.8 +0.9 -18.4 + 2.6 -17.3 +0.8 -15.8 -20.7 -18.0 ARy8 11.9 +2.1 7.2 +2.0 6.6 +0.3 -5.5 +1.3 -16.4 + 3.4 -12.9 +4.3 -6.4 -19.6 -16.6 ARy12 -0.4 +0.8 -0.6 +1.9 1.6 +0.9 22.8 +4.8 8.4 + 11.3 11.7 +5.1 28.3 21.5 17.5 ASp3 -4.3 +1.2 -6.4 +2.6 -5.0 +0.4 ------ARy2 -1.1 +0.5 -4.4 +1.1 -4.1 +1.3 ------tr ARy5 4.3 +1.5 3.7 +0.4 2.7 +0.9 ------ARy8 7.6 +2.4 7.1 +1.9 4.0 +0.6 ------ARy12 0.4 +1.0 -4.8 +1.7 -1.1 +1.2 ------Span Axis Events ASp3 -3.7 +7.4 -3.1 +2.4 -6.3 +5.2 20.8 +10.6 21.9 + 1.1 13.6 +4.8 28.6 22.7 18.8 ARy2 -4.7 +3.5 -5.9 +3.5 -4.8 +6.0 17.1 +6.7 26.7 + 1.5 14.2 +5.5 23.4 28.3 19.2 max2 ARy5 -2.2 +1.0 -1.1 +1.2 -1.3 +2.9 19.4 +2.7 16.4 + 4.1 19.2 +3.0 22.4 21.0 22.6 ARy8 0.2 +1.6 -0.2 +1.3 1.0 +2.6 11.4 +4.8 12.4 + 3.2 18.4 +3.9 16.9 14.7 22.7 ARy12 -4.8 +1.6 -4.7 +0.7 -3.1 +4.3 -30.9 +3.5 -34.1 + 10.1 -22.9 +10.4 -33.7 -45.6 -34.9 ASp3 -4.3 +11.6 -9.7 +2.5 2.0 +11.4 57.9 +6.8 57.6 + 4.1 65.7 +2.5 65.4 60.5 67.7 ARy2 12.3 +3.5 7.0 +10.4 3.3 +11.0 48.4 +4.0 52.5 + 3.5 53.3 +3.1 52.8 54.7 55.5 Max ARy5 11.7 +2.5 6.3 +8.1 4.0 +7.9 45.1 +5.1 48.0 + 5.6 48.2 +4.2 50.6 53.3 51.0 Elevation ARy8 12.3 +1.5 8.3 +8.1 6.0 +7.9 29.8 +5.9 35.5 + 2.2 39.4 +4.3 36.1 36.8 42.3 ARy12 7.7 +17.9 8.3 +20.8 -2.0 +6.1 -10.2 +2.6 9.0 + 14.3 0.7 +4.0 -7.9 24.9 3.3 ASp1 -5.0 +10.4 -7.0 +6.1 8.7 +16.6 ------ARy2 12.3 +3.5 10.3 +6.7 -2.7 +7.2 ------Max ARy5 1.7 +13.9 -0.3 +7.6 1.3 +5.5 ------Areas ARy8 -2.3 +2.5 -3.0 +1.7 -1.3 +1.5 ------sfA -2.3 +11.6 -9.7 +8.0 -1.3 +3.2 ------See Table 2.2 for the description of ΔTime, Mean Angle and Max Angle. See text for the description of the parameters. n = 3 sequences per fish. 146

Table 2.6

Kendall’s W and Friedman’s χ2 for Soft Dorsal Fin-Ray Kinematic Parameters

ΔTime Mean Angle Max Angle Parameters W χ2 P-value W χ2 P-value W χ2 P-value max1 0.96 11.47 0.001 0.96 11.47 0.001 0.96 11.47 0.001 Sweep tr 1.00 12.00 <0.001 ------Events max2 0.96 11.47 0.001 0.96 11.47 0.001 0.89 10.67 0.004 max1 0.96 11.47 0.001 0.87 10.40 0.001 0.73 8.80 0.038 Span Axis tr 1.00 12.00 <0.001 ------Events max2 0.82 9.87 0.015 0.89 10.67 0.004 0.96 11.47 0.001 Max Elevation 0.69 8.27 0.056 1.00 12.00 <0.001 1.00 12.00 <0.001 Max Area r 0.15 1.35 0.781 ------See Table 2.2 for the description of ΔTime, Mean Angle and Max Angle. See text for a description of the parameters. Significant analyses with P-values less than their adjust α-levels are indicated in bold. For Sweep, Span Axis and Elevation, df=2, 4; for Area, df=2, 3.

147

Table 2.7

Kendall’s W and Friedman’s χ2 for Anal Fin-Ray Kinematic Parameters

ΔTime Mean Angle Max Angle Parameters W χ2 P-value W χ2 P-value W χ2 P-value max1 0.95 11.44 0.001 0.97 11.59 <0.001 0.97 11.59 <0.001 Sweep tr 0.95 11.44 0.001 ------Events max2 0.69 8.27 0.056 1.00 12.00 <0.001 1.00 12.00 <0.001 max1 1.00 12.00 <0.001 0.87 10.40 0.005 0.78 9.33 0.026 Span Axis tr 0.96 11.47 0.001 ------Events max2 0.82 9.87 0.015 0.60 7.20 0.117 0.56 6.67 0.163 Max Elevation 0.63 7.52 0.083 1.00 12.00 <0.001 1.00 12.00 <0.001 Max Area r 0.20 1.80 0.727 ------See Table 2.2 for the description of ΔTime, Mean Angle and Max Angle. See text for a description of the parameters. Significant analyses with P-values less than their adjust α-levels are indicated in bold. For Sweep, Span Axis and Elevation, df=2, 4; for Area, df=2, 3.

148

Table 2.8

Multigroup W for Soft Dorsal vs. Anal Fin-Ray Kinematic Parameters

ΔTime Mean Angle Max Angle Parameters W Ζ P-value W Ζ P-value W Ζ P-value max1 0.93 5.57 <0.001 0.96 5.73 <0.001 0.96 5.73 <0.001 Sweep tr 0.97 5.80 <0.001 ------Events max2 N/A N/A N/A 0.97 5.80 <0.001 0.93 5.60 <0.001 max1 0.97 5.80 <0.001 0.87 5.20 0.000 N/A N/A N/A Span Axis tr 0.97 5.80 <0.001 ------Events max2 N/A N/A N/A N/A N/A N/A N/A N/A N/A Max Elevation N/A N/A N/A 1.00 6.00 <0.001 1.00 6.00 <0.001 Max Area r N/A N/A N/A ------See Table 2.2 for the description of ΔTime, Mean Angle and Max Angle. See text for a description of the parameters. Between group analyses were not performed for parameters in which one or both fin groups did not have a significant position effect, indicated by N/A. Significant analyses with P-values less than their adjust α-levels are indicated in bold.

149

Figure 2.1. Stages of a C-start.

Still images from the dorsal view of the C-start of a bluegill sunfish at: A. The frame prior to lateral rotation of the head (t = 0). B. Midway through Stage 1 (t = 10). C. The end of Stage 1 (t =18). D. Midway through Stage 2 (t = 30). E. The end of Stage 2

(t = 50). Vertical bar represents the initial position of the center of mass.

150

Figure 2.1

151

Figure 2.2. The bluegill sunfish.

A. Illustration of the bluegill. The unpaired median fins: dorsal fins (DF), composed of two developmentally separate fins, the spiny dorsal (spD) and soft dorsal (sfD) fins; anal fin (AF); and caudal fin (Cd). Paired fins: pectoral (Pc) and pelvic (Pv). Fin supports of

DF and AF are shown: spines (thick, solid lines) and rays (thin, dashed lines). The body was divided into five equal segments [20% of the body length from the tip of the snout

(s) to the caudal peduncle (pd)]: rostrum (Rs) and Operculum (Op), which comprise the head, and the anterior (Ant), middle (Mid) and posterior (Post) segments of the trunk.

Orthogonal axes and planes of the body, shown only for the Mid segment: transverse

(TrMid; grey plane), sagittal (SgMid; orange plane) and frontal (FrMid; plane not shown).

Other symbols: position of the center of mass (COM) indicated by the corresponding symbol, ‘ear’ of the operculum and vent (v). B. Still image of the bluegill sunfish.

Yellow dots represent the approximate location of the 15 points used to define the dorsal and ventral midlines. Orange lines indicate the digitized fin-rays and the approximate location of the 4-6 points (white dots) used to define each fin-ray. The associated text identifies each fin-ray based on its location, dorsal (D) vs. anal (A), fin-ray type, spine

(Sp) vs. ray (Ry), and numbered position within their respective fin. A〈DRy5〉 represents the fin area between rays DRy5 and DRy8.

152

Figure 2.2

153

Figure 2.3. Schematic of the flow tank set-up for video capture.

A. Dorsal view and B. Lateral view, showing the orientation of the X,Y,Z-axes relative to the flow tank and positions of the three cameras. The mirror was positioned to facilitate the view for the ventral camera. The Plexiglas ‘boat’ was used to negate distortion caused by surface waves for the dorsal camera. Drop Zone is the approximate location in which the startle stimulus (size “C” battery) was presented.

154

Figure 2.3

A. Dorsal View

Y

Drop Zone

X

Lateral Camera

Dorsal Camera

B. Lateral View Plexiglas ‘boat’ Drop Zone

Z

X

Ventral Camera 155

Figure 2.4. The reconstructed dorsal fin surface and ray angles.

A. The entire reconstructed dorsal fin. Black lines represent the 8 digitized fin-rays (i.e., the spanwise curves) of the fin. Blue lines represent the chordwise curve of the fin. The intersections of the black and blue lines indicate the 21 interpolated points of each fin- ray, from which all measurements were calculated. B. Close-up of the dorsal fin surface and the vectors calculated at the given point, P(a,b). The spanwise (sT) and chordwise (cT) tangents, parallel to their respective curve, and the orthogonal lateral (L), span (S) and chord (C) axes that define the 3-D orientation of the fin surface at P(a,b). C. Orientation of a dorsal ray relative to the axes of the Mid-trunk segment: span axis rotation (α¯), sweep (ω¯), and elevation (φ¯). See Figure 2.2 for a definition of the body segment axes.

156

Figure 2.4

A

B S = sT

C cT

P(a,b) L

Fr C Mid

S C α L ω

φ

SgMid -TrMid 157

Figure 2.5. Center of mass kinematics throughout a C-start.

A. Displacement; DS1 and DS2, COM displacement at the end of Stages 1 and 2, respectively. B. Velocity; vmax, maximum COM velocity achieved during the two stages.

C. Acceleration.; amax1 and amax2, the two peak COM accelerations during the two stages. In all panels, the light gray region indicates the period of Stage 1 (S1), starting from T0 (onset of C-start), and the darker grey region indicated the period of Stage 2 (S2).

All time sequences shown are from the same fish.

158

Figure 2.5 60 A S2 40 S1

D(S2) 20

T D(S1) 0 0

1.5 B

vmax 1.0

0.5

0

a 60 max1 a C max2 40 20 0 -20 -10 0 10 20 30 40 50 60 Time (msec) 159

Figure 2.6. Axial turning rate throughout a C-start.

A. Turning rate of the rostrum with the two rotational transitions, tθ′tr1 and tθ′tr2, indicated (white dots). Stage 1 (S1), time period between T0 (time zero) and tθ′tr1; Stage

2 (S2), time period between tθ′tr1 and tθ′tr2. B. Turning rate of the anterior trunk and the time of the two maximal rotations and rotational transitions, tθ′max1, tθ′max2 and tθ′tr, indicated. C. Turning rate of the middle trunk and its three kinematic events, tθ′max1, tθ′tr and tθ′max2 , indicated. Shaded regions as in Figure 2.5.

160

Figure 2.6

4 A. Rs 2 S1 0 tθ`tr1 t `tr2 T0 θ -2 S2 -4

4 B. Ant tθ`max2 2 0 tθ`tr -2 tθ`max1 -4

4 C. Mid 2 tθ`max1 0 tθ`tr -2

-4 tθ`max2 -10 0 10 20 30 40 50 60 Time (msec) 161

Figure 2.7. Sweep angles of the spiny dorsal fin-rays.

A. Turning rate of Ant; shown to provide reference for the movements of the associated fin-rays. B-E. Sweep angles of individual spines. The time of the two maximum sweep angles and directional transition, tω¯max1, tω¯max2, and tω¯max2, indicated for one spine

(DSp10). Shaded regions as in Figure 2.5.

162

Figure 2.7

4 A Ant-Trunk T tθ`max2 0 0 tθ`tr -4 tθ`max1

20 B DSp1 0

-20

20 C DSp4 0

-20

20 D DSp7 0

-20

20 E DSp10 tωmax1 0 tωtr -20 tωmax2

-10 0 10 20 30 40 50 60 Time (msec) 163

Figure 2.8. Sweep parameters of the spiny dorsal fin-rays.

A. Average timing of the first maximum sweep angle. B. Average of the first maximum sweep angle. C. Average timing of the directional sweep transition. D. Average timing of the second maximum sweep angle. E. Average of the second maximum sweep angle.

All timing parameters are in relations to the corresponding time event of the Ant-trunk turning rate, tθ′event. The dashed line in panel C represents the average time difference between the first maximum turning rate and the rotational transition of the anterior trunk,

Δtθ′max1=tθ′max1−tθ′tr. For each parameter, Kendall’s coefficent of concordance, W, is provided, significant position effects are indicated in bold with an asterisk. Bars are means ± 1 SEM, n=9 sequences from 3 fish.

164

Figure 2.8

DSp1

DSp4

DSp7 W=0.91 W=0.91

A DSp10 B -20 -15 -10 -5 0 0 5 10 15 20 25

ΔtSweepmax1 (msec from tθ`max1) Sweepmax1 (°)

DSp1

Δtθ`max1 DSp4

DSp7 W=0.91 C DSp10 -30 -20 -10 0

ΔtSweeptr (msec from tθ`tr)

DSp1

DSp4

DSp7 W=0.64 W=0.73 D DSp10 E -30 -20 -10 0 0 -5 -10 -15 -20 -25

ΔtSweepmax2 (msec from tθ`max2) Sweepmax2 (°) 165

Figure 2.9. Span axis angles of the spiny dorsal fin-rays.

A. Turning rate of Ant; shown to provide reference for the movements of the associated fin-rays. B-E. Span axis angles of individual spines. The time of the two maximum sweep angles and directional transition, tα¯max1, tα¯max2, and tα¯max2, indicated for one spine

(DSp10). Shaded regions as in Figure 2.5.

166

Figure 2.9

4 A Ant-Trunk T tθ`max2 0 0 tθ`tr -4 tθ`max1

DSp1 20 B 0 -20

DSp4 20 C 0 -20

DSp7 20 D 0 -20

50 E DSp10 tαmax1 t 0 αtr

tαmax2 -50 -10 0 10 20 30 40 50 60 Time (msec) 167

Figure 2.10. Span axis parameters of the spiny dorsal fin-rays.

A. Average timing of the first maximum span axis angle. B. Average of the first maximum span axis angle. C. Average timing of the directional span axis transition. D.

Average timing of the second maximum span axis angle. E. Average of the second maximum span axis angle. Symbols as in Figure 2.8.

168

Figure 2.10

DSp1

DSp4

DSp7 W=0.78 W=1* A DSp10 B -10 -5 0 5 10 -40 -20 0 20 40 60

ΔtSpanmax1 (msec from tθ`max1) Span Axismax1 (°)

DSp1

DSp4

DSp7 W=0.24 C DSp10 -10 -5 0 5 10

ΔtSpantr (msec from tθ`tr)

DSp1

DSp4

DSp7 W=0.29 W=1* D DSp10 E -10 -5 0 5 10 -30 -20 -10 0 10 20

ΔtSpanmax2 (msec from tθ`max2) Span Axismax2 (°) 169

Figure 2.11. Elevation and fin area parameters of the spiny dorsal fin-rays.

A. Average timing of maximum elevation. B. Average of maximum elevation. C.

Average timing of maximum fin areas. D. Average timing of the second maximum span axis angle. E. Average of the second maximum span axis angle. Symbols as in Figure

2.8.

170

Figure 2.11

DSp1

DSp4

DSp7

W=0.66 W=1* A DSp10 B -30 -20 -10 0 0 25 50 75 100 125

ΔtElevmax (msec from tθ`tr) Elevationmax (°)

W=0.11 C -30 -20 -10 0

ΔtAreamax (msec from tθ`tr) 171

Figure 2.12. Sweep angles of the soft dorsal and anal fin-rays.

A. Turning rate of Mid; shown to provide reference for the movements of the associated fin-rays. B-E. Sweep angles of individual fin-rays. The time of the two maximum sweep angles and directional transition, tω¯max1, tω¯max2, and tω¯max2, indicated for one ray

(ARy2). Blue traces represent the dorsal fin-rays, red traces for the anal fin-rays. Shaded regions as in Figure 2.5.

172

Figure 2.12

4 A Mid-Trunk tθ`max1 T tθ`tr 0 0

-4 tθ`max2

B Sp0 Dorsal 20 Anal 0 -20

tωmax2 20 C Ry2 0 tωmax1 tωtr -20

50 D Ry5 0 -50

50 E Ry8 0 -50

50 F Ry12 0 -50 -10 0 10 20 30 40 50 60 Time (msec) 173

Figure 2.13. Sweep parameters of the soft dorsal and anal fin-rays.

A. Average timing of the first maximum sweep angle. B. Average of the first maximum sweep angle. C. Average timing of the directional sweep transition. D. Average timing of the second maximum sweep angle. E. Average of the second maximum sweep angle.

Dorsal fin-rays in blue, anal fin-rays in red. All timing parameters are in relations to the corresponding time event of the Mid-trunk turning rate, tθ′event. The dashed line in panel

C represents the average time difference between the first maximum turning rate the rotational transition of the middle trunk, Δtθ′max1=tθ′max1−tθ′tr. For each parameter,

Kendall’s coefficent of concordance, W, and, if applicable, the multigroup coeffiecient of concordance, W, are provided. Significant position effects are indicated in bold with an asterisk. Bars are means ± 1 SEM, n=9 sequences from 3 fish.

174

Figure 2.13

Dorsal Sp0 Anal

Ry2

Ry5 W=0.96* W=0.96* W=0.95* Ry8 W=0.97* W =0.93* W =0.96* A Ry12 B -15 -10 -5 0 5 10 0 -10 -20 -30 -40

ΔtSweepmax1 (msec from tθ`max1) Sweepmax1 (°)

Sp0

Ry2

Ry5 W=1.0* W=0.95* Δtθ`max1 Ry8 W =0.97* C Ry12 -20 -15 -10 -5 0 5

ΔtSweeptr (msec from tθ`tr)

Sp0 W=0.96* W=1.0* Ry2 W =0.97*

Ry5 W=0.96* W=0.69 Ry8 W =N/A D Ry12 E -20 -15 -10 -5 0 0 15 30 45 60

ΔtSweepmax2 (msec from tθ`max2) Sweepmax2 (°) 175

Figure 2.14. Span axis angles of the soft dorsal and anal fin-rays.

A. Turning rate of Mid; shown to provide reference for the movements of the associated fin-rays. B-E. Span axis angles of individual fin-rays. The time of the two maximum sweep angles and directional transition, tα¯max1, tα¯max2, and tα¯max2, indicated for one ray

(ARy10). Blue traces represent the dorsal fin-rays, red traces for the anal fin-rays.

Shaded regions as in Figure 2.5.

176

Figure 2.14

4 A Mid-Trunk tθ`max1 T tθ`tr 0 0

-4 tθ`max2

B Sp0 Dorsal 20 Anal 0 -20

Ry2 20 C tαmax2 tαtr 0 tαmax1 -20

20 D Ry5 0 -20

20 E Ry8 0 -20

20 F Ry12 0 -20

-10 0 10 20 30 40 50 60 Time (msec) 177

Figure 2.15. Span axis parameters of the soft dorsal and anal fin-rays.

A. Average timing of the first maximum span axis angle. B. Average of the first maximum span axis angle. C. Average timing of the directional span axis transition. D.

Average timing of the second maximum span axis angle. E. Average of the second maximum span axis angle. Symbols as in Figure 2.13.

178

Figure 2.15

Dorsal Sp0 Anal

Ry2

Ry5 W=0.96* W=0.87* W=1.0* Ry8 W=0.87* W =0.97* W =0.87* A Ry12 B -5 0 5 10 15 -20 -10 0 10 20 tSpan (msec from t ` Δ max1 θ max1) Span Axismax1 (°)

Sp0

Ry2

Ry5 W=1.0* W=0.96* Ry8 W =0.97* C Ry12 -10 -5 0 5 10

ΔtSpantr (msec from tθ`tr)

Sp0

Ry2

Ry5 W=0.89* W=0.82 W=0.60 W=0.82 Ry8 W =N/A W =N/A D Ry12 E -8 -6 -4 -2 0 2 4 -40 -20 0 20 40

ΔtSpanmax2 (msec from tθ`max2) Span Axismax2 (°) 179

Figure 2.16. Elevation and fin area parameters of the soft dorsal and anal fin-rays.

A. Average timing of maximum elevation. B. Average of maximum elevation. C.

Average timing of maximum fin areas. D. Average timing of the second maximum span axis angle. E. Average of the second maximum span axis angle. Symbols as in Figure

2.13.

180

Figure 2.16

Dorsal Anal Sp0

Ry2

Ry5 W=0.69 W=1.0* W=0.63 Ry8 W=1.0* W =N/A W =1.0* A Ry12 B -10 -5 0 5 10 15 -20 0 20 40 60 80

ΔtElevmax (msec from tθ`tr) Elevationmax (°)

W=0.15 W=0.20 Ry8 W =N/A < > C -10 -5 0 5 10 15 20

ΔtAreamax (msec from tθ`tr) 181

CHAPTER 3

3-D KINEMATIC ANALYSIS OF THE DORSAL AND ANAL FINS DURING THE

FAST-START OF THE BLUEGILL SUNFISH (LEPOMIS MACROCHIRUS) II:

FIN-RAY CURVATURE

182

ABSTRACT

While the movement and orientation of individual fin-rays provides valuable insight into the contribution of median fins in the performance of a C-start, it paints an incomplete picture of the complex interaction of the flexible fin surface and surrounding fluid. To expand our kinematic analysis of the median fins during the C-start escape responses of bluegill sunfish (Lepomis macrochirus), the pattern of spanwise and chordwise curvature of the soft dorsal and anal fin surface was examined from the same video sequences used in our analysis of the fin-ray movement and orientation. We found that the fin surface undergoes a stereotypical pattern of deformation in which both the span and chord undergo an undulation of curvature, starting in the anterior region of either fin. Initiated early in Stage 1 of the C-start, the undulation travels in a postero- distal direction, reaching the trailing edge of the fins during the early period of Stage 2.

Although maximum spanwise curvature typically occurred among the more flexible posterior fin-rays, a consistent correlation between maximum curvature and fin-ray position was not found. Nonetheless, we suggest different roles for the fin regions. First, undulation of the anterior fin region is directed primarily chordwise, initiating a transfer of momentum into the water to overcome the inertia of the flow, and direct the water posteriorly. Within the posterior region, undulation is predominantly directed spanwise, and, as the flexible posterior fin-rays are directed caudad, the posterior fin region acts to ultimately accelerate this water toward the tail and thereby increase thrust forces of the escape response. The treatment of the median fins as a uniform structure does not do justice to their complexity and effectiveness as a control surface. 183

INTRODUCTION

Three-dimensional 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; these results suggested that different regions of the fins were playing distinct roles during the C-start escape response of the bluegill sunfish (Chapter 2). While that study provided insight for understanding the role of the median fins, it provides an incomplete picture of the median fin function. Visual analysis of videos shows that fin surface shape is influenced by the curvature within the fin-rays (Fig. 3.1). Actinopterygian fins are flexible structures that interact with the surrounding flow as curved surfaces (Lauder et al., 2006; Walker, 2004; Walker and Westneat, 2002). Therefore, it is essential to quantify fin curvature as well as the motions of individual fin-rays to understand how fins may function.

Although the flexibility of the fins have 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. 184

As it is the shape of the fin, as well as its movement, that ultimately defines the resultant forces generated by the interaction of the fins and the water, understanding how the fin shape is modified during locomotion will provide insight into the hydrodynamic roles of the fins as control surfaces (Lauder and Drucker, 2004). Therefore, we expanded our kinematic analysis of the dorsal and anal fins to examine the spanwise and chordwise curvature of the median fin surface during the performance of the C-start escape response of bluegill sunfish (Lepomis macrochirus). In addition to describing the pattern of the surface curvatures of the fin, we addressed two specific questions. First, does fin-ray curvature vary based on position within the fin as predicted by the morphological variations reported in Chapter 1? From that study, 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 our hypothesis that the fins are actively resisting opposing hydrodynamic forces during the C-start and contributing to the thrust forces generated by the fish?

We found that, as predicted, the anterior rays underwent less spanwise curvature than the posterior rays, although the difference was less notable during Stage 2 of the C- start, providing further evidence that the musculoskeletal variations we have reported contribute to the kinematic variability of fin-rays during locomotion. Furthermore, we found that while the fin-rays were unable to completely resist bending during the fast- start, the observation of an initial curvature of the fin-rays at the onset of the C-start directed into the opposing hydrodynamic forces support the hypothesis that they are actively resisting bending, matching the findings from a previous EMG study (Jayne et al., 1996). Additionally, a traveling wave was observed in both the spanwise and 185 chordwise curvature of the fins. The spanwise curvature moved along the length of the fin-rays, increasing in magnitude distally. The chordwise curvature traveled along the chord length, but did not change in magnitude. These patterns mirrored the kinematic patterns of the sweep and span axis rotation described in Chapter 2. Combining these observations, we report that during the C-start, the fin surface undergoes a stereotypical movement in which the deflection of the fin surface increases over time in a postero- distal direction, starting in the anterior region of the soft dorsal and anal fins. As the fin- rays of the posterior regions are directed caudad, we suggest that the two waves

(spanwise and chordwise) are interacting, thereby accelerating the water to increase the thrust forces generated by the fins. 186

MATERIALS AND METHODS

ANIMALS

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 L:D photoperiod at a mean water temperature of 20ºC (± 1ºC). As in previous chapters, the term ‘fin-ray’ is used to refer to all external skeletal fin supports when the distinction between spines and rays is disregarded (see Chapter 1 for details).

VIDEO CAPTURE AND CALIBRATION

Analysis of fin-ray curvatures was performed on the same sequences of the three individuals used for kinematic analyses, recorded at Harvard University in the Lauder

Laboratory. Three synchronized high-speed, high-resolution cameras at 500 fps 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 (see Fig. 2.3). Video images were calibrated for 3-D digitization using a direct linear transformation algorithm

(Reinschmidt and van den Bogert, 1997) incorporated into the custom digitizing program

Digimat (Madden, 2004). See Chapter 2 for details of the calibration and digitization of the video sequences.

KINEMATIC ANALYSIS

The same axial kinematics quantified in Chapter 2 were used in determining the kinematic performances of the C-starts, e.g., onset of the C-start, timing of Stage 1 (S1) and Stage 2 (S2), turning rates of the body segments (see Fig. 2.2) and the center of mass

(COM) movement throughout the duration of the digitized sequences (see Appendix A).

In two of the nine sequences, the initial C-bend was to the left. To simplify the 187 comparison between the sequences, these sequences were converted to right-handed C- starts by reversing the sign of the y-coordinates (see Chapter 2).

Fin Reconstruction

To calculate the curvature of the fin-rays relative to the fin surface, the entire fin surfaces were reconstructed as described in Chapter 2. The 4-6 points digitized from the selected fin-rays (see Fig. 2.2B) were fit to a cubic smoothing spline with a mean square error (MSE) of ca. 0.1 mm3 (Walker, 1998) and 21 equally spaced points along the fin- ray were interpolated. The 21 interpolated points from all fin-rays of a fin were fit to a bivariate tensor function (Kreyszig, 1991):

f (r, p), where f is a cubic spline function based on r, the fin-rays, and p, the interpolated points of each fin-ray. See Appendix B for! details.

Fin-Ray Curvature

At any point on the surface, two curvature values could be determined: spanwise and chordwise. For our analysis, spanwise curvature is a measure of surface curvature along the length of the fin-ray, i.e. the span of the fin, and is synonymous with fin-ray curvature, as reported in other studies of fin curvatures (Standen and Lauder, 2005; Taft et al., 2008). Chordwise curvature is a measure of surface curvature perpendicular to the fin-rays, i.e. the chord of the fin. In both studies, chordwise curvature was never measured, at most it was an observational assessment (Standen and Lauder, 2005) and

3-D fin-ray curvature, κ, was calculated as:

dT " = , ds

! 188 where κ is the change in the tangent (T) to the curve over the arc length (s). While this provides an adequate measure of curvature of the fin-ray in 3-D space, it fails to provide vital information about the direction of the curvature relative to the fin surface. For example, is the fin-ray curving to the left or to the right of the fin- surface? Does the direction of curvature change along the length of the fin-ray or over time? Second, this measure invariably includes curvature of the fin-ray parallel to the fin surface, which would introduce confounding results. For example, if the fin were to lie completely flat so that the entire surface were confined to a single plane, curvature within the fin-ray could still be measured by either a natural bend within the fin or introduced by digitizing errors. In either scenario, the measured curvature is an artifact rather than a meaningful measure of the fin-rays’ deformation.

To address these issues in our analysis, the spanwise and chordwise curvatures for each point of the fin-ray were decomposed into components that were parallel and perpendicular to the fin surface, analogous to decomposing 3-D velocity into its horizontal and vertical components. The advantage of this technique is three-fold: (1) only the relevant curvature of the fin-ray perpendicular, i.e. lateral, to the fin is considered; (2) any curvature introduced by digitizing error is potentially reduced, and

(3) direction of the curvature can easily be evaluated as being to the left or right of the fin surface. This allowed us to make meaningful comparisons of curvature along the length of a single fin-ray, between fin-rays, and over time.

The curvatures of the fin surface at each point of the fin-rays were calculated using the partial derivatives of f(r,p): 189

"f "2 f fr = and frr = , "r "r2

"f "2 f f p = and f pp = , "p "p2 where fr and frr represent the first and second order partial derivatives with respect to r as p is held constant, and !fp and fpp represent the first and second order partial derivatives with respect to p as r is held constant.

Calculation of the spanwise curvature at any point, P(a,b), where the subscript a represents the fin-ray number and the subscript b represents the interpolated point number, was performed as follows:

sT(a,b) = fr(a,b), sB(a,b) = fr(a,b) " frr(a,b),

sB(a,b) # = , span(a,b) 3 sT(a,b) where sT and sB are the tangent and binormal of the spanwise curve at P(a,b), straight brackets indicate the magnitude! of the enclosed vector and  indicates the cross product of the vectors. Chordwise curvature at P(a,b) was calculated as:

cT(a,b) = fr(a,b), cB(a,b) = fr(a,b) " frr(a,b),

cB(a,b) , #chord(a,b) = 3 cT(a,b) where cT and cB are the tangent and binormal of the chordwise curve at P(a,b).

Spanwise curvature! was divided into components that were parallel and perpendicular to the fin surface at P(a,b), defined by its unit normal, a.k.a. the lateral axis,

L(a,b): 190

cT(a,b) " sT(a,b) L(a,b) = . cT " sT (a,b) (a,b)

Chordwise curvature was divided into its components parallel and perpendicular to both the fin surface, L(a,b), and! sT(a,b). The sign of curvature denotes the direction, relative to the fin surface, with a positive value indicating the concavity faces toward the right of the fin (and the fish) and a left-facing concavity represented by a negative value. Details of these calculations can be found in Appendix B. For the remainder of this paper, the perpendicular curvatures will simply be referred to as either spanwise or chordwise curvature and the perpendicular components of the spanwise and chordwise curvatures at

P(a,b) are represented by κspan(a,b) and κchord(a,b), respectively, for any given time point.

Maximum Fin-Ray Curvatures

For each time point, t, of each fin-ray, the maximum positive and negative spanwise and chordwise curvatures were recorded to represent the maximum degree of fin-ray curvature to either side of the fin surface. Throughout Stages 1 and 2 of the C- start, the time and magnitude of three spanwise curvature events were recorded: the maximum curvature to the right, tκspan0 and κspan0, during S1; the maximum curvature to the left, tκspan1 and κspan1; and the maximum curvature to the right during S2, tκspan2 and

κspan2. As the maximum spanwise curvature was predicted to be coupled to the turning rate of the mid-trunk, tκspan0 and tκspan1 were adjusted to the time of maximum turning rate of the mid-trunk to the right during S1 (tθ′max1), and tκspan2 was adjusted to the time of maximum turning rate of the mid-trunk to the left during S2 (tθ′max2):

"t#span0 = t#span0 $ t& max1% ,

"t#span1 = t#span1 $ t& max1% ,

"t#span2 = t#span2 $ t& max2% .

! 191

The time and magnitude of two chordwise curvature events were recorded: the maximum curvature to the left, tκchord1 and κchord1 and the maximum curvature to the right, tκchord2 and κchord2. As neither event appeared to be closely associated with maximum turning rate of the body, their timings were adjusted to determine whether the time of maximum curvatures occurred before or after the change in rotational direction of the body segment (tθ′tr):

"t# = t# $ t& % , chord1 chord1 tr "t#chord2 = t#chord2 $ t& tr% .

STATISTICAL ANALYSIS

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: DSp10, DRy2, DRy5, DRy8 and DRy12 were included in the sfD group and ASp3, ARy2, ARy5, ARy8 and ARy12 made up the sfA group (Fig. 2.2B). When using a cubic spline, the curvature returned for the ends 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.

As discussed in Chapter 2, 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 Freidman’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 fins-rays for each group. 192

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 (see Chapter 2). 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 (W) 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 (Chicago, IL). A custom program, based on the equations of Zar (1984), was written in Matlab to calculate W and its Z-score. See Chapter 1 for details regarding the interpretation of χ2, W and W. To control for Type I errors resulting from multiple comparisons of the 15 variables of each fin group, P-values were compared to corrected

α-levels using a sequential Bonferroni adjustment (Rice, 1989) 193

RESULTS

The anterior-most support of the soft regions of the dorsal and anal fins are the last spines of the fins, DSp10 (which also provides the posterior-most support of the contiguous spiny dorsal fin) and ASp3 respectively (see Fig. 2.2) were included in the analyses of sfD and sfA. 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. The curvature parameters of the five fin-rays by fish for each fin group can be found in Table

3.1 (sfD) and Table 3.2 (sfA).

Spanwise Curvature

Within 8-10 msec from the onset of the C-start (T0) and rotation toward the right by the mid-trunk, a curvature toward the right 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. 3.2 and 3.3). At 12-14 msec from T0, the proximal regions of the rays began to bend to the left; the curvature also increased in magnitude as it moved distally along the ray over time. For both sfD and sfA, κspan0 and κspan1 increased among the posterior fin-rays; however, a significant position effect was found for mean and maximal κspan0 but not for κspan1 (Fig. 3.4, Tables 3.3 and 3.4). Δtκspan0 was nearly synchronous with the time of maximum turning rate of the mid-trunk, with Δtκspan1 occurring shortly afterward

(Fig. 3.4A,C). Position effects were not found in either time parameter (Tables 3.3 and

3.4).

During the rotation of Mid to the left, i.e., during the 18-50 msec time period of the sequences, curvature toward the right developed in the proximal region of the fin-rays 194 and traveled distally along the ray-lengths, but an increase in curvature was not always observed; rather, the curvature was distributed along the fin-ray lengths (Figs. 3.2 and

3.3). In both fins, curvature was greatest among the posterior fin-rays with a high degree of concordance among the fish (Fig. 3.4F), but a significant position effect was only found in mean κspan2 for sfA (Tables 3.3 and 3.4). Δtκspan2 occurred shortly before Mid reached its maximum turning rate to the left (Fig. 3.4E), with no position effect found for either fin (Tables 3.3 and 3.4).

Over the course of the C-start, the greatest fin-ray curvatures, in either direction, typically occurred during the 14-26 msec period of the sequence, during the rotational transition of the mid-trunk, as the turning rate to the right decreased and changed direction to the left (Figs. 3.2 and 3.4). It is also during this time that many of the rays develop an S-curve as the proximal and distal regions are curving in opposite directions

(Figs. 3.1A, 3.2 and 3.3).

Chordwise Curvature

Compared to spanwise curvature, chordwise curvature was typically uniform along the length of the fin-rays with alternating chordwise direction occurring between neighboring fin-rays, creating an S-curve in the chord length of the fins (Figs. 3.5 and

3.6). During rotation of the mid-trunk to the right (the 2-20 msec time period of the sequence) time of maximum chordwise curvature toward the left was nearly synchronous with the rotational transition of the mid-trunk, tθ′tr, with the greatest curvature occurring at Ry2 (Fig. 3.7A,B). A significant position effect found only for maximal κchord1 of sfA

(Tables 3.3 and 3.4). 195

Maximum chordwise curvature to the right occurred after tθ′tr, as the mid-trunk began its rotation to the left, with κchord2 more uniform among the fin-rays (Fig. 3.7C,D).

No significant position effects were found for either sfD or sfA (Tables 3.3 and 3.4).

Dorsal vs. Anal Fins

Of the 15 curvature parameters, significant position effects in both fin groups were found only for mean and maximal κspan0 (Tables 3.3 and 3.4), both of which showed a significant degree of concordance between sfD and sfA (W ≥ 0.8; Z ≥ 4.8; P<0.0001). 196

DISCUSSION

The soft region of the dorsal and anal fins is highly deformable, due not only to the variation in movement and orientation of individual fin-rays (see Chapter 2) but also due to variation in curvature in both the spanwise and chordwise directions of the fin

(Figs. 3.2, 3.3, 3.5, 3.6 and 3.8). In contrast, the curvature of the spiny regions of the fins is restricted in the spanwise direction of the fin (data not shown) because of its fused, non-segmented design and restrictive joint (see Chapter 1).

Throughout the C-start, curvature of the soft dorsal and anal fins followed a stereotypical pattern in both the spanwise and chordwise directions. Within 10-12 msec after the onset of the C-start, the fin began to curve toward the right, into the flow (Figs

3.8B,C). This curvature would not be expected if the fin-rays were passive structures; instead, this supports the hypothesis that the fins are actively resisting opposing forces.

However, this curve to the right was quickly replaced by a subsequent curvature of the fin to the left as the axial turning rate increased (Fig. 3.8C,D,E). A second curvature of the fin to the right quickly developed after the rotational transition of the mid-trunk (Fig.

3.8G). For all three spanwise curvatures, the location and magnitude of the curvature increased distally over time; however, the greatest amount of spanwise curvature occurred during the period of rotational transition of the mid-trunk, κspan0 and κspan1 (Figs.

3.2, 3.3, 3.8E,F)

Midway through Stage 1, a chordwise undulation was also observed in which the anterior region of the fin surface was initially cupped to the left, which propagated posteriorly along the chord of the fin surface (i.e., among the individual fin rays) over time (Figs. 3.5 and 3.6; note progression of blue curvature from panel B to C to D). A 197 chordwise cupping of the anterior fin region to the right was initiated soon after the rotational transition of the mid-trunk, though the propagation along the fin chord was weaker than the first chordwise curvature (Figs. 3.5 and 3.6; compare progression of orange curvature in panels B-D).

Spanwise Curvature

During Stage 1 (S1), fin-rays initially underwent a spanwise curvature to the right, in the direction of the oncoming flow of the water, followed closely by curvature to the left (Figs. 3.2 and 3.3). The initial spanwise curvature toward the right supports the hypothesis that the fin-rays are actively resisting the forces as this curvature into the flow would not be expected if the fin-rays were reacting passively to the opposing hydrodynamic forces generated by axial rotation. Curvature into the flow has also been observed in the pectoral fin of the bluegill during turning maneuvers (Drucker and

Lauder, 2001).

However, the curving of the fin into the flow of water is short lived as the fin-rays undergo curvature to the left as the mid-trunk rotation to the right slows downs and changes direction at the end of S1. During this transitional period, a transient S-curve is formed along the length of several of rays, with ray curvature in the proximal region directed to the left at the same time as the distal region of the ray curves to the right (Figs.

3.2 and 3.3). This S-curve is observable in the video sequence (Fig. 3.1A) and the digital reconstruction of the fins (Fig. 3.8C,D).

A third spanwise curvature of the fin-rays, directed to the right, occurs as the turning rate of the mid-trunk to the left increases during Stage 2 (S2). During S2, the degree of curvature and variation between fin-rays and along the ray lengths is much less 198 than what was observed during S1 and the S1/S2 transition (Figs. 3.2, 3.3, and 3.4B,D,F).

Although the maximum spanwise curvatures were greatest among the posterior rays, the correlation between fin-ray position and κspan1 and κspan2 was inconsistent (Tables 3.3 and

3.4), suggesting that, unlike κspan0, the fin-rays were able to equally resist spanwise curvature.

These observations match the electromyography (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, 1987). 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 the axial musculature. The initial curvature of the fin rays to the right coincides with this activity.

Onset of EMG activity among the contralateral dorsal inclinators occurred prior to the end of trunk rotation to the right, lasting throughout most of S2 (Jayne et al., 1996). This muscular activity coincides with the second curvature of the fin-ray to the left, which also begins prior to rotational transition of the mid-trunk. During rotation of the mid-trunk to the left during S2, muscular activity is actively resisting the opposing hydrodynamic forces, but does not appear to be able to completely prevent fin-ray bending.

With most fin-rays reaching maximum curvature within a few msec of each other, timing of maximum curvatures was not significantly related to position. However, within each ray, spanwise curvature was initiated within the proximal region of a ray and over time, curvature moved distally along the ray and increased in magnitude over time. This pattern of curvature indicates a traveling wave of spanwise curvature that moves distally along the ray lengths. 199

Chordwise Curvature

Unlike spanwise curvature, chordwise curvatures along the length of the fin-rays were generally uniform, with only an occasional change in direction (Figs. 3.5 and 3.6).

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 undulation in the fin surface, which can be seen in the video sequence (Fig. 3.1B).

Toward the end of S1, chordwise curvature of the anterior fin surface was directed toward the left, with the greatest degree of curvature within Ry2 (Fig. 3.7A,B). As the mid-trunk rotated to the left during S2, the chord surface was curved to the right (Fig.

3.7C,D). The chordwise curvature observed most likely is the result of the variation in the span axis rotation described in Chapter 2. With the exception of the maximal κchord1 parameter of sfA, there was no significant correlation between the tested chordwise parameters and fin-ray position (Tables 3.3 and 3.4), suggesting that on average, maximum chordwise curvature across the fin surface is uniform.

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 fin curvature.

Hydrodynamic Implications

The results of both the spanwise and chordwise curvature demonstrate an undulation of the fin surface that is initiated within the proximal and anterior region of the soft dorsal or anal fin and spreads across the surface in a postero-distal direction.

Along the distal direction, the magnitude of the curvature tends to increase. This 200 movement is most likely analogous to the traveling waves in the sweep and span axis rotation of the fin-rays reported in Chapter 2. As discussed in Chapter 2, the movement of the sfD and sfA fin-rays coincides with the generation of a fluid jet that results in production of thrust forces that propel the fish away from the threat during the escape response (Tytell and Lauder, 2008).

Regional variation in curvature kinematics suggests functionally distinct roles in generating momentum. We propose that the initial chordwise undulation in the anterior region of the fins initiates the movement of fluid, overcoming the inertia of the water.

Second, the spanwise undulation along the lengths of posterior rays accelerates the fluid and as these rays are elevated in line with the long axis of the body, the momentum is directed caudad to enhance the thrust component of the fins, ca. 37% of the total moment is generated by the dorsal and anal fins, as measured by Tytell and Lauder (2008).

By extending our analysis of the fins beyond the average orientation and movement of the fin-rays to include variation both between and within the individual fin- rays, we have provided a more accurate picture of the fin kinematics throughout the performance of the C-start. Furthermore, the kinematic patterns observed provide evidence to support the hypothesis that fin-rays are resisting opposing hydrodynamic forces either by muscular activity and/or the intrinsic biomechanical properties derived from their morphology. By combining detailed kinematic analysis of the fin surface with morphological, EMG and hydrodynamics studies, we have greatly increased our understanding of how the flexible and dynamic fins contribute to the vitally important escape response of fish. 201

LITERATURE CITED

Arita GS. 1971. A re-examination of the functional morphology of the soft-rays in teleosts. Copeia 1971:691-697.

Blake RW. 1981. Influence of pectoral fin shape on thrust and drag in labriform locomotion. J Zool 194:53-66.

Breder CM. 1926. The locomotion of fishes. Zoologica 6:159-297.

Drucker EG, Lauder GV. 2001. Wake dynamics and fluid forces of turning maneuvers in sunfish. J Exp Biol 204:431-442.

Epps B, Techet A. 2007. Impulse generated during unsteady maneuvering of swimming fish. Exp Fluids 43:691-700.

Geerlink PJ, Videler JJ. 1987. The relation between structure and bending properties of teleost fin rays. Neth J Zool 37:59-80.

Jayne BC, Lozada GF, Lauder GV. 1996. Function of the dorsal fin in bluegill sunfish: Motor patterns during four distinct locomotor behaviors. J Morphol 228:307-326.

Kreyszig E. 1991. Differential Geometry. New York: Dover Publications, Inc. 352 p.

Lauder GV. 2006. Locomotion. In: Evans DH, Claiborne JB, editors. The Physiology of Fishes. 3rd ed. Boca Raton: CRC Press. p 3-46.

Lauder GV, Drucker EG. 2004. Morphology and experimental hydrodynamics of fish fin control surfaces. IEEE J Oceanic Eng 29:556-571.

Lauder GV, Madden PG, Mittal R, Dong H, Bozkurttas M. 2006. Locomotion with flexible propulsors: I. Experimental analysis of pectoral fin swimming in sunfish. Bioinspir Biomim 1:S25-34.

Madden PG. 2004. Digimat. Version 2.0. Cambridge: Organismic and Evolutionary Biology: Harvard University.

Mittal R, Dong H, Bozkurttas M, Lauder G, Madden P. 2006. Locomotion with flexible propulsors: II. Computational modeling of pectoral fin swimming in sunfish. Bioinspir Biomim 1:S35-41.

Osburn RC. 1906. The functions of the fins of fishes. Science 23:585-587.

Reinschmidt C, van den Bogert T. 1997. Kinemat: A MATLAB toolbox for three- dimensional kinematic analyses. Calgary: Human Performance Laboratory: The University of Calgary.

Rice WR. 1989. Analyzing tables of statistical tests. Evolution 43:223-225. 202

Sokal RR, Rohlf FJ. 1981. Biometry. New York: WH Freeman. 805 p.

Standen EM, Lauder GV. 2005. Dorsal and anal fin function in bluegill sunfish Lepomis macrochirus: Three-dimensional kinematics during propulsion and maneuvering. J Exp Biol 208:2753-2763.

Taft NK, Lauder GV, Madden PGA. 2008. Functional regionalization of the pectoral fin of the benthic longhorn sculpin during station holding and swimming. J Zool 276:159-167.

Tytell ED, Lauder GV. 2008. Hydrodynamics of the escape response in bluegill sunfish, Lepomis macrochirus. J Exp Biol 211:3359-3369.

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

Walker JA. 2004. Kinematics and performance of maneuvering control surfaces in teleost fishes. IEEE J Oceanic Eng 29:572-584.

Walker JA, Westneat MW. 2002. Performance limits of labriform propulsion and correlates with fin shape and motion. J Exp Biol 205:177-187.

Zar JH. 1984. Biostatistical Analysis. Englewood Cliffs: Prentice-Hall. 469 p.

203

Table 3.1

Soft Dorsal Fin-Ray Curvature Parameters by Fish

"Time (msec from t# event) Mean ! (mm-1) Max ! (mm-1) Parameter Fin-Ray Fish A Fish B Fish C Fish A Fish B Fish C A B C DSp10 -1.5 + 8.4 0.5 + 2.8 -1.1 + 4.5 0.04 + 0.03 0.03 + 0.01 0.06 + 0.02 0.07 0.04 0.07

DRy2 -0.7 + 6.8 -3.1 + 1.0 -3.8 + 1.1 0.08 + 0.02 0.06 + 0.07 0.04 + 0.02 0.10 0.14 0.06 max0 DRy5 0.9 + 1.4 0.8 + 0.8 -0.9 + 1.1 0.11 + 0.03 0.12 + 0.02 0.11 + 0.02 0.14 0.14 0.12 DRy8 1.2 + 1.1 0.9 + 1.1 0.9 + 0.5 0.35 + 0.13 0.31 + 0.05 0.14 + 0.04 0.49 0.37 0.18

DRy12 -4.9 + 0.8 2.3 + 3.8 -2.1 + 0.9 0.17 + 0.07 0.17 + 0.13 0.25 + 0.15 0.24 0.32 0.39

DSp10 -1.5 + 8.5 1.8 + 4.9 7.1 + 10.0 -0.03 + 0.02 -0.04 + 0.02 -0.04 + 0.03 -0.05 -0.05 -0.06 DRy2 4.3 + 1.4 3.9 + 3.4 5.1 + 0.3 -0.08 + 0.04 -0.22 + 0.05 -0.15 + 0.03 -0.12 -0.28 -0.18 max1 DRy5 9.9 + 1.1 9.7 + 0.2 9.9 + 0.7 -0.28 + 0.16 -0.26 + 0.05 -0.26 + 0.05 -0.46 -0.31 -0.32 DRy8 10.5 + 1.0 10.1 + 1.3 10.0 + 1.4 -0.23 + 0.11 -0.37 + 0.23 -0.22 + 0.05 -0.35 -0.59 -0.27 DRy12 1.8 + 0.5 4.1 + 5.3 4.0 + 4.9 -0.23 + 0.03 -0.36 + 0.15 -0.27 + 0.07 -0.27 -0.53 -0.32 Spanwise Curvature DSp10 -8.0 + 2.6 -6.4 + 2.7 0.9 + 12.4 0.03 + 0.01 0.07 + 0.03 0.04 + 0.02 0.04 0.09 0.07 DRy2 -6.5 + 1.8 -3.8 + 1.8 6.8 + 0.2 0.06 + 0.02 0.13 + 0.04 0.14 + 0.01 0.07 0.16 0.15 max2 DRy5 -4.8 + 0.6 -2.6 + 2.9 -1.7 + 3.7 0.08 + 0.03 0.13 + 0.04 0.15 + 0.02 0.11 0.18 0.17 DRy8 -5.9 + 1.0 -1.2 + 2.5 -1.4 + 4.2 0.09 + 0.03 0.14 + 0.02 0.20 + 0.06 0.12 0.16 0.26 DRy12 -4.6 + 0.9 3.0 + 1.2 3.2 + 4.9 0.12 + 0.03 0.16 + 0.07 0.15 + 0.02 0.14 0.24 0.17 DSp10 1.0 + 11.2 -4.5 + 1.3 -5.7 + 0.5 -0.05 + 0.00 -0.09 + 0.02 -0.08 + 0.01 -0.05 -0.10 -0.09 DRy2 0.1 + 0.7 0.2 + 0.7 -0.5 + 0.5 -0.07 + 0.01 -0.16 + 0.03 -0.13 + 0.01 -0.08 -0.20 -0.15 max1 DRy5 4.5 + 2.5 4.6 + 0.5 3.5 + 2.0 -0.04 + 0.01 -0.11 + 0.03 -0.11 + 0.02 -0.06 -0.14 -0.13 DRy8 1.0 + 2.7 2.7 + 3.1 1.9 + 1.9 -0.05 + 0.00 -0.08 + 0.06 -0.06 + 0.01 -0.05 -0.14 -0.08 DSp10 16.3 + 5.7 10.5 + 3.9 10.6 + 8.6 0.05 + 0.01 0.11 + 0.02 0.08 + 0.02 0.07 0.13 0.10 DRy2 12.8 + 6.9 2.9 + 10.3 6.4 + 1.8 0.08 + 0.02 0.09 + 0.03 0.07 + 0.02 0.09 0.13 0.09 max2

Chordwise Curvature DRy5 14.7 + 4.0 13.6 + 5.0 5.6 + 9.3 0.03 + 0.01 0.04 + 0.01 0.05 + 0.01 0.04 0.06 0.06 DRy8 -6.3 + 0.8 6.1 + 12.3 2.2 + 1.0 0.07 + 0.00 0.10 + 0.01 0.12 + 0.02 0.07 0.10 0.13 ΔTime is the difference in time of a given parameter (individual rows) from the corresponding kinematic event of the Mid-trunk (tθ′event). Mean κ is the average curvature for all sequences for each fish. Max κ is the maximal curvature that was achieved by the fish, observed in any sequence. For ΔTime and Mean κ, values are mean ± 1 s.d.. See text for details. n=3 sequences for each fish. 204

Table 3.2

Anal Fin-Ray Curvature Parameters by Fish

"Time (msec from t# event) Mean ! (mm-1) Max ! (mm-1) Parameter Fin-Ray Fish A Fish B Fish C Fish A Fish B Fish C A B C ASp3 -7.0 + 1.6 2.2 + 9.7 -2.2 + 3.9 0.01 + 0.01 0.02 + 0.00 0.01 + 0.01 0.02 0.02 0.02

ARy2 -4.2 + 1.1 -2.7 + 2.5 -1.3 + 1.3 0.05 + 0.03 0.06 + 0.03 0.05 + 0.02 0.08 0.08 0.07 max0 ARy5 0.1 + 1.0 -0.1 + 1.3 0.7 + 0.6 0.09 + 0.04 0.15 + 0.07 0.13 + 0.05 0.12 0.22 0.18 ARy8 -0.6 + 0.6 0.7 + 1.1 0.9 + 0.8 0.29 + 0.13 0.37 + 0.19 0.17 + 0.10 0.43 0.58 0.26

ARy12 -3.5 + 3.9 -2.1 + 1.9 -2.7 + 1.6 0.09 + 0.03 0.09 + 0.03 0.10 + 0.06 0.12 0.11 0.14

ASp3 -5.1 + 4.8 8.4 + 7.2 5.9 + 5.7 -0.01 + 0.00 -0.03 + 0.00 -0.02 + 0.01 -0.01 -0.03 -0.02 ARy2 5.7 + 2.3 3.6 + 1.8 4.1 + 1.1 -0.08 + 0.02 -0.10 + 0.02 -0.08 + 0.01 -0.10 -0.12 -0.08 max1 ARy5 11.0 + 1.3 8.1 + 1.7 7.8 + 0.4 -0.14 + 0.01 -0.21 + 0.07 -0.21 + 0.10 -0.15 -0.29 -0.27 ARy8 12.3 + 1.2 7.9 + 0.6 10.2 + 1.1 -0.20 + 0.10 -0.22 + 0.03 -0.20 + 0.05 -0.27 -0.23 -0.24 ARy12 7.4 + 4.4 6.4 + 1.6 2.3 + 2.7 -0.23 + 0.08 -0.37 + 0.08 -0.16 + 0.03 -0.32 -0.46 -0.18 Spanwise Curvature ASp3 -9.0 + 3.2 1.8 + 7.5 -0.1 + 6.5 0.03 + 0.02 0.02 + 0.01 0.03 + 0.00 0.04 0.03 0.03 ARy2 -0.1 + 1.3 2.4 + 5.4 -5.1 + 6.9 0.05 + 0.01 0.10 + 0.04 0.09 + 0.02 0.06 0.15 0.12 max2 ARy5 -3.2 + 3.4 -6.2 + 1.4 -5.2 + 2.9 0.07 + 0.01 0.08 + 0.02 0.09 + 0.03 0.08 0.10 0.12 ARy8 -2.8 + 1.2 -2.4 + 4.3 -3.4 + 2.8 0.08 + 0.01 0.10 + 0.04 0.15 + 0.04 0.09 0.14 0.18 ARy12 -6.5 + 1.4 -4.6 + 1.3 -2.3 + 2.8 0.10 + 0.04 0.14 + 0.09 0.16 + 0.01 0.14 0.24 0.17 ASp3 -7.3 + 1.1 -8.1 + 2.9 3.3 + 18.5 -0.02 + 0.00 -0.04 + 0.01 -0.03 + 0.01 -0.03 -0.05 -0.04 ARy2 -0.3 + 1.2 -1.4 + 0.5 -0.9 + 0.5 -0.15 + 0.03 -0.38 + 0.29 -0.09 + 0.01 -0.18 -0.72 -0.10 max1 ARy5 -3.8 + 5.9 4.0 + 0.8 -3.6 + 4.6 -0.04 + 0.01 -0.05 + 0.00 -0.05 + 0.02 -0.05 -0.05 -0.06 ARy8 8.6 + 5.3 -0.6 + 4.5 1.7 + 1.3 -0.05 + 0.01 -0.06 + 0.02 -0.05 + 0.01 -0.05 -0.07 -0.06 ASp3 14.5 + 0.8 10.3 + 5.6 13.8 + 6.8 0.10 + 0.04 0.08 + 0.03 0.06 + 0.02 0.15 0.11 0.08 ARy2 3.1 + 19.1 -7.3 + 1.8 17.1 + 11.4 0.04 + 0.01 0.09 + 0.02 0.04 + 0.01 0.06 0.11 0.05 max2

Chordwise Curvature ARy5 1.4 + 1.7 5.9 + 5.8 4.8 + 13.5 0.06 + 0.01 0.06 + 0.01 0.06 + 0.01 0.07 0.06 0.07 ARy8 -7.7 + 0.9 -5.4 + 2.2 -1.9 + 6.8 0.06 + 0.00 0.06 + 0.01 0.08 + 0.02 0.07 0.07 0.09 See Table 3.1 for the description of ΔTime, Mean κ and Max κ. See text for the description of the parameters. n = 3 sequences per fish. 205

Table 3.3

Kendall’s W and Friedman’s χ2 for Soft Dorsal Fin-Ray Curvature Parameters

#Time Mean Curvature Max Curvature Parameters W !2 P-value W !2 P-value W !2 P-value max0 0.56 6.67 0.163 0.91 10.93 0.003 0.91 10.93 0.003 "span max1 0.82 9.87 0.015 0.80 9.60 0.017 0.82 9.87 0.015 Events max2 0.47 5.60 0.253 0.87 10.40 0.005 0.75 9.02 0.029 "chord max1 0.84 7.55 0.028 0.70 6.31 0.108 0.87 7.82 0.0208 Events max2 0.64 5.80 0.148 0.64 5.80 0.148 0.54 4.86 0.208 See Table 3.1 for the description of ΔTime, Mean κ and Max κ. See text for a description of the parameters. Significant analyses with P-values less than their adjusted α-levels are indicated in bold. For κspan, df=2, 4; for κchord, df=2, 3. 206

Table 3.4

Kendall’s W and Friedman’s χ2 for Anal Fin-Ray Curvature Parameters

#Time Mean Curvature Max Curvature Parameters W !2 P-value W !2 P-value W !2 P-value max0 0.49 5.87 0.236 0.96 11.47 0.001 1.00 12.00 0.000 "span max1 0.56 6.67 0.163 0.82 9.87 0.015 0.82 9.87 0.015 Events max2 0.31 3.73 0.493 0.89 10.67 0.004 0.82 9.87 0.015 "chord max1 0.20 1.80 0.727 0.47 4.20 0.300 0.98 8.79 0.004 Events max2 0.56 5.00 0.207 0.29 2.59 0.545 0.31 2.79 0.500 See Table 3.1 for the description of ΔTime, Mean κ and Max κ. See text for a description of the parameters. Significant analyses with P-values less than their adjusted α-levels are indicated in bold. For κspan, df=2, 4; for κchord, df=2, 3. 207

Figure 3.1. Curvature in the dorsal fin.

Still images from the dorsal view of the C-start of a bluegill sunfish: A. 12 msec and B.

20 msec after the onset of the escape response. Both the soft dorsal (sfD) and anal fin can be seen (AF). White arrow in Panel A indicates the formation of an S-curve in the span direction of the fin. The two white arrows in Panel B indicate the chordwise undulation in the fin.

208

Figure 3.1

A t = 12 msec

sfD

AF

B t = 20 msec 209

Figure 3.2. Spanwise curvature of the soft dorsal fin-rays over time.

A. Turning rate of Mid and its three kinematic events, maximum Stage 1 turning rate

(tθ′max1), rotational transition (tθ′tr) and maximum Stage 2 turning rate (tθ′max2), indicated by the white dots; shown to provide reference for the curvature of the associated fin-rays.

B-F. Spanwise curvature along the percent length of each fin-ray within the soft dorsal fin group (sfD) for each time point of a single C-start sequence. In Panel A, the light gray region indicates the period of Stage 1, starting from T0 (onset of C-start), and the darker grey region indicates the period of Stage 2. Color bar represents the intensity and direction of the spanwise curvature, with positive values (orange-red-dark red) indicating spanwise curvature to the right and negative values (purple-blue-dark blue) indicating spanwise curvature to the left. All time sequences shown are from the same fish.

210

Figure 3.2

211

Figure 3.3. Spanwise curvature of the anal fin-rays over time.

A. Turning rate of Mid and its three kinematic events; shown to provide reference for the curvature of the associated fin-rays. B-F. Spanwise curvature along the percent length of each fin-ray within the anal fin group (sfA) for each time point of a single C-start sequence. Symbols, shading and color bar as in Figure 3.2.

212

Figure 3.3

213

Figure 3.4. Spanwise curvature parameters of the fin-rays.

A. Average timing of the initial maximum spanwise curvature to the right. B. Average of the initial maximum spanwise curvature to the right. C. Average timing of the following maximum spanwise curvature to the left. D. Average of the following maximum spanwise curvature to the left. E. Average timing of the second maximum spanwise curvature to the right. F. Average of the second maximum spanwise curvature to the right. Dorsal fin-rays in blue, anal fin-rays in red. All timing parameters are in relation to the corresponding time event of the Mid-trunk turning rate, tθ′event. For each parameter, Kendall’s coefficient of concordance, W, and, if applicable, the multigroup coefficient of concordance, W, are provided. Significant position effects are indicated in bold with an asterisk. Bars are means ± 1 SEM, n=9 sequences from 3 fish.

214

Figure 3.4

Dorsal Sp0 Anal

Ry2 W=0.91* W=0.96* Ry5 W =0.82* W=0.56 W=0.49 Ry8 W =N/A A Ry12 B -5 0 5 10 15 0 0.10 0.20 0.30 0.40 -1 Δtκspan0 (msec from tθ`max1) κspan0 (mm )

W=0.82 Sp0 W=0.80 W=0.56 W=0.82 =N/A W =N/A W Ry2

Ry5

Ry8

C Ry12 D -5 0 5 10 15 0 -0.10 -0.20 -0.30 -0.40 -1 Δtκspan1 (msec from tθ`max1) κspan1 (mm )

W=0.87 W=0.47 Sp0 W=0.31 W=0.89* W =N/A W =N/A Ry2

Ry5

Ry8

E Ry12 F -9 -6 -3 0 3 6 0 0.05 0.10 0.15 0.20 -1 Δtκspan2 (msec from tθ`max2) κspan2 (mm ) 215

Figure 3.5. Chordwise curvature of the soft dorsal fin-rays over time.

A. Turning rate of Mid and its three kinematic events; shown to provide reference for the curvature of the associated fin-rays. B-E. Chordwise curvature along the percent length of each fin-ray within the soft dorsal fin group (sfD) for each time point of a single C- start sequence. Color bar represents the intensity and direction of chordwise curvature, with positive values (orange-red-dark red) indicating chordwise curvature to the right and negative values (purple-blue-dark blue) indicating chordwise curvature to the left.

Symbols and shading as in Figure 3.2.

216

Figure 3.5

217

Figure 3.6. Chordwise curvature of the anal fin-rays over time.

A. Turning rate of Mid and its three kinematic events; shown to provide reference for the curvature of the associated fin-rays. B-E. Chordwise curvature along the percent length of each fin-ray within the anal fin group (sfA) for each time point of a single C-start sequence. Symbols and shading as in Figure 3.2. Color bar as in Figure 3.5.

218

Figure 3.6

219

Figure 3.7. Chordwise curvature parameters of the fin-rays.

A. Average timing of the maximum chordwise curvature to the left. B. Average of the maximum chordwise curvature to the left. C. Average timing of the maximum chordwise curvature to the right. D. Average of the maximum chordwise curvature to the right. Symbols as in Figure 3.4. 220

Figure 3.7

Dorsal Sp0 Anal

Ry2

W=0.70 W=0.84 Ry5 W=0.20 W=0.47 W =N/A W =N/A A Ry8 B -10 -5 0 5 10 15 20 0 -0.10 -0.20 -0.30 -1 Δtκchord1 (msec from tθ`tr) κchord1 (mm )

W=0.64 W=0.47 W=0.56 Sp0 W=0.29 W =N/A W =N/A Ry2

Ry5

C Ry8 D -10 -5 0 5 10 15 20 0 0.05 0.10 0.15 -1 Δtκchord2 (msec from tθ`tr) κchord2 (mm ) 221

Figure 3.8. Reconstructed bluegill and median fins.

The digitally reconstructed bluegill displaying the spanwise curvature across the median fins at different time points over the C-start. A. Representation of the fish axis, estimated center of mass (COM) and median fins prior to the onset of the C-start (t = 0 msec). B-G. Close up images of the soft dorsal fin at consecutive time points. Color bar as in Figure 3.2.

222

Figure 3.8

223

APPENDIX

MATLAB CODES FOR KINEMATIC ANALYSIS AND VISUALIZATION 224

INTRODUCTION

For the complex kinematic analyses to be performed, there were no commercially available computer programs that I could use to calculate the movement, orientation and curvature of the body and fin-rays using the 3-D coordinates obtained from digitizing the videos of the axial body and fins. Therefore, it was necessary to write a series of computer programs, within MatLab, to perform the necessary calculations to obtain, organize and visualize the kinematic variables I needed. Within this appendix are the primary codes I wrote, using functions either native to MatLab or written by myself.

Axial Codes

The script file, ‘axialKinematics.m’ (App. A.1), was developed to calculate, organize and save the kinematic parameters of the axial body for all the digitized frames of a C-start sequence. For each frame, the 15 points of the dorsal and ventral midlines were passed to the ‘findAxial.m’ function (App. A.2), which fit the midlines to a cubic smoothing spline, using MatLab’s ‘spaps.m’ function, from which 21 evenly spaced points along the midlines were interpolated. Using the interpolated points, ‘findAxial.m’ defined the five body segments and their orthogonal axes (frontal, transverse, and sagittal) and estimated the 3-D coordinates for the center of mass (COM). The orthogonal axes were then passed to ‘fishRotation.m’ (App. A.3), which calculated the orientation (yaw, pitch, and roll) of each body segment, relative to the X,Y,Z-coordinate system of the flow tank. After the yaw of each body segment and the COM coordinates had been calculated for all time points of a sequence, the turning rate for each body segment and the displacement, velocity and acceleration of the COM was calculated.

Within ‘axialKinematics.m’, a series of plots were generated for each body segment that 225 allowed me to select the time points for the maximum turning rates and transition point.

Displacement of COM from its position at the onset of the C-start was calculated for each time point. COM coordinates were passed to ‘motionFUN.m’ (App. A.4), which returned the magnitude and vectors for velocity and acceleration. Within

‘axialKinematics.m’, velocity and acceleration were decomposed into components perpendicular and parallel to the fish’s trajectory, i.e. the transverse axis of the rostrum.

The final displacement, velocity and acceleration parameters were then determined for the sequence. Once all the axial parameters had been collected and organized, they were saved and exported to files that could be opened within MS Excel for analysis.

Fin Codes

The script file, ‘finSurface.m’ (App. B.1), was developed to calculate, organize and save the kinematic parameters of the fin-rays for all the digitized frames of a C-start sequence. For each frame, the corresponding body axes (frontal, sagittal and transverse) calculated from ‘axialKinematics.m’ (App. A.1) were imported. Using the native

MatLab code, ‘spaps.m’, the digitized points for each fin-ray were fit to a cubic smoothing cubic spline and 21 evenly spaced points along the curve were interpolated.

The 3-D coordinates from each of the 21 points for all digitized fin-rays of a given fin (8 fin-rays for Dorsal; 6 fin-rays for Anal) were fit to a cubic tensor spline (also using

‘spaps.m’). From the tensor spline for each fin, ‘surfCurvature.m’ (App. B.2) used the partial derivatives of the tensor spline to generate the axes of the fin surface at each point

(lateral, span, and chord) as well as the spanwise and chordwise curvature parallel and perpendicular to the fin surface. The fin axes were then passed to ‘surfRotation.m’ (App.

B.3), to calculate the orientation of the fin-ray and its surface at each point (sweep, span 226 axis and elevation angles). Using the 21 interpolated points of each fin-ray, ‘finArea.m’

(Appx B.3) calculated the area between adjacent digitized fin-rays for the entire fin. A series of time plots were generated from which I could select the time points of the fin- ray kinematics events. The collected data was organized, saved and exported to files that could be analyzed in MS Excel.

Data Visualization

The final code, ‘FishPlot2.m’ (App. C.1) was developed within MatLab to generate a graphical user interface (GUI). From the main figure of the GUI, the paired data files generated by ‘axialKinematics.m’ (App. A.1) and ‘finSurface.m’ (App. B.1) for a single C-start sequence could be selected and loaded into the program. Once loaded, two additional figures were generated showing the turning rate of the axial body, sweep and elevation angles of each fin-ray and the selected fin-ray parameter for each point of the selected dorsal and anal fin-ray over time, similar to Figure 3.2. Within the main figure, a 3-D reconstruction of the fish body and median fins were displayed at a given time of the C-start sequence. The fin surface is color coded to show the magnitude and direction (right or left) of the selected parameter over the entire fin surface. A scrollbar allows the user to advance back and forth through the sequence, to view how the orientation of the fish, its fins and the fin-ray parameters change from one frame to the next. Buttons on the main figure allow the user to select which fin-ray parameter is to be displayed and which fin-ray to plot in the two accessory figures. This GUI was helpful in viewing the movement of the fish, its fins and to see how the fin-ray parameters varied across the fin surface and over time all at once. Figures 3.2, 3.3, 3.5, 3.6, and 3.8 were generated using modified versions of the functions within this code. 227

APPENDIX A

AXIAL CODES

Appendix A.1: axialKinematics.m

%% 1) Select the Rotated & Combined points files from rotateFrames MT='Select The Combined Points Files'; fn=uigetfile('*.mat',MT,'multiselect','on'); if isequal(fn,0), return, else N=length(fn); end load(fn{1}, 'FileData') Bend=FileData.C_Bend;

%% 2) Estimate the body segments, their orthonormal axes and % orientation for each frame of the sequence.

Frames=nan(N,3); AXL=cell(N,1); PltAxl=cell(N,1); XYZ=nan(N,3,5); TMF=nan(N,3,3,5); YPR=nan(N,3,5); for f=1:N load(fn{f},'Time','DPts','VPts'); Frames(f,1:2)=Time; [lmk AXL{f} PltAxl{f}]=findAxial(DPts,VPts); XYZ(f,:,:)=permute(lmk(:,:,1),[3,2,1]); TMF(f,:,:,:)=permute(lmk(:,:,2:4),[4,2,3,1]); ypr=fishRotation(lmk(:,:,2),lmk(:,:,3),'deg'); YPR(f,:,:)=permute(ypr,[3,2,1]); end T=Frames(:,2);

%% 3) Evaluate the Yaw parameters of the Body Segments. T1=T*1000; ypr=permute(YPR,[1,3,2]); yaw=ypr(:,:,1)-repmat(ypr(1,:,1),N,1); sYaw=nan(5,N); YSpl=cell(5,1); Seg={'Rostrum','COM','Ant','Mid','Post'}; dYaw=nan(N,5); ZR=nan(7,3,5); f1=figure('visible','off'); for y=1:5 sp0=spaps(T1,yaw(:,y),0); mx=roundn(max(abs(fnval(fnder(sp0),(T1(1):2:T1(end))))),-1); if mx<2, mx=2; end

tol=2*mx; w=ones(N,1); [spl sYaw(y,:)]=spaps(T1,yaw(:,y),tol,w,3); YSpl{y}=spl; dYaw(:,y)=fnval(fnder(spl),T1);

z1=mean(fnzeros(fnder(spl),[2 T1(end)]));

228

if numel(z1)>=3 zr=z1(1:3); elseif numel(z1)==2 z2=mean(fnzeros(fnder(spl,2),[ceil(z1(2)) T1(end)])); if isempty(z2) z3=mean(fnzeros(fnder(spl,3),[ceil(z1(2)) T1(end)])); elseif ceil(z2(1))>=T1(end) z3=nan; else z3=mean(fnzeros(fnder(spl,3),[ceil(z2(1)) T1(end)])); end zz=[z2 z3]; set(f1,'name',['Turning Rate of 'Seg{y}],'numbertitle','off',... 'position',[500 258 760 420],'visible','on'); subplot(2,1,1) plot([-20;200],[0;0],'-k'), hold on fnplt(spl,'k',1) plot(z1,fnval(spl,z1),'ko') plot(z2,fnval(spl,z2),'r.') plot(z3,fnval(spl,z3),'bo') text(z2,fnval(spl,z2),num2str((1:length(z2))'),... 'verticalalignment','bottom') text(z3,fnval(spl,z3),num2str((1:length(z3))'+length(z2)),... 'verticalalignment','top'),hold off xlim([T1(1) T1(end)])

subplot(2,1,2) plot([-20;200],[0;0],'-k'), hold on fnplt(fnder(spl),'k',1) plot(z1,fnval(fnder(spl),z1),'ko') plot(z2,fnval(fnder(spl),z2),'r.') plot(z3,fnval(fnder(spl),z3),'bo') text(z2,fnval(fnder(spl),z2),num2str((1:length(z2))'),... 'verticalalignment','bottom') text(z3,fnval(fnder(spl),z3),num2str((1:length(z3))'+length(z2)),... 'verticalalignment','top'),hold off xlim([T1(1) T1(end)])

option.WindowStyle='normal'; pk=inputdlg('Select the 3rd Time Point',Seg{y},1,{''},option); pk=str2double(pk); if ~isnan(pk), zr=[z1(1:2) zz(pk)]; else zr=[z1(1:2) nan]; end elseif numel(z1)==1 z2=mean(fnzeros(fnder(spl,2),[ceil(z1) T1(end)])); if isempty(z2) z3=mean(fnzeros(fnder(spl,3),[ceil(z1) T1(end)])); elseif ceil(z2(1))>=T1(end) z3=nan; else z3=mean(fnzeros(fnder(spl,3),[ceil(z2(1)) T1(end)])); end zz=[z2 z3]; set(f1,'name',['Turning Rate of 'Seg{y}],'numbertitle','off',... 'position',[500 258 760 420],'visible','on'); subplot(2,1,1) plot([-20;200],[0;0],'-k'), hold on 229

fnplt(spl,'k',1) plot(z1,fnval(spl,z1),'ko') plot(z2,fnval(spl,z2),'r.') plot(z3,fnval(spl,z3),'bo') text(z2,fnval(spl,z2),num2str((1:length(z2))'),... 'verticalalignment','bottom') text(z3,fnval(spl,z3),num2str((1:length(z3))'+length(z2)),... 'verticalalignment','top'),hold off xlim([T1(1) T1(end)])

subplot(2,1,2) plot([-20;200],[0;0],'-k'), hold on fnplt(fnder(spl),'k',1) plot(z1,fnval(fnder(spl),z1),'ko') plot(z2,fnval(fnder(spl),z2),'r.') plot(z3,fnval(fnder(spl),z3),'bo') text(z2,fnval(fnder(spl),z2),num2str((1:length(z2))'),... 'verticalalignment','bottom') text(z3,fnval(fnder(spl),z3),num2str((1:length(z3))'+length(z2)),... 'verticalalignment','top'),hold off xlim([T1(1) T1(end)])

option.WindowStyle='normal'; pk=inputdlg('Select the 2nd Time Point?',Seg{y},1,{''},option); pk=str2double(pk); if ~isnan(pk), zr=[z1(1) zz(pk) nan]; else zr=[z1(1) nan(1,2)]; end end

ZR(1,:,y)=round(zr); ZR(2,:,y)=round(zr)./ZR(1); ZR(3,:,y)=fnval(spl,zr); ZR(4,:,y)=fnval(fnder(spl),zr);

s1=fnval(fnder(spl),(1:1:zr(1))'); [mx1 I1]=max(abs(s1));

if isnan(zr(2)) zr(2)=T1(end); end s2=fnval(fnder(spl),(floor(zr(1)):1:zr(2))'); [mx2 I2]=max(abs(s2));

ZR(5,1:2,y)=[I1, I2+floor(zr(1))-1]; ZR(6,1:2,y)=[I1, I2+floor(zr(1))-1]./ZR(1); ZR(7,1:2,y)=[s1(I1), s2(I2)];

if ~isnan(zr(3)) s3=fnval(fnder(spl),(floor(zr(2)):1:zr(3))'); [mx3 I3]=max(abs(s3)); ZR(5,3,y)=I3+floor(zr(2))-1; ZR(6,3,y)=(I3+floor(zr(2))-1)/ZR(1); ZR(7,3,y)=s3(I3); end end close(f1) C_Stages=ZR(1:2,1:2,1); 230

Yaw.Raw=yaw; Yaw.Smooth=sYaw'; Yaw.Rate=dYaw; Yaw.Time=roundn(ZR,-2); Yaw.Spline=YSpl; Frames(:,3)=T1./C_Stages(1); %% 4) Calculate the displacement, velocity and acceleration parameters % of the COM. mXYZ=XYZ(:,:,2)*.001; spl=spaps(T,mXYZ',0,3); spd=motionFUN(spl,T); mxS=max(spd); if mxS<1, mxS=1; end tol=mxS*2e-3; w=ones(N,1)*1000; w(1:4)=[10 10 100 100]; [spl spXYZ]=spaps(T,mXYZ',tol,w,3); spXYZ=spXYZ'; COM.Spline=spl;

ST=[0;C_Stages(1,:)']*.001; i0=find(T==0); i1=find(T<=ST(2),1,'last'); i2=find(T<=ST(3),1,'last');

SP=fnval(spl,ST)'; DP=vectornorms(SP);

D=(vectornorms(spXYZ)-DP(1))*1000; % Distance (in mm) from position at T0 SD=(DP(2:3)-DP(1))'*1000;

COM.Time=[C_Stages(1,:);SD];

[spd acc curv COM.TNB]=motionFUN(spl,T); nT=TMF(:,:,1,2); nM=TMF(:,:,2,2); nF=TMF(:,:,3,2);

V=COM.TNB(:,:,1).*repmat(spd,1,3); vT=vectordecomp(V,nT); sT=vectornorms(vT).*sign(dot(vT,nT,2)); vM=vectordecomp(V,nM); sM=vectornorms(vM).*sign(dot(vM,nM,2)); vF=vectordecomp(V,nF); sF=vectornorms(vF).*sign(dot(vF,nF,2)); COM.Vel=[D spd sT sM sF];

[mxV1 V1]=max(sT(i0:i1)); [mxV2 V2]=max(sT(i1+2:i2+2)); COM.Time(3:4,:)=[T1(V1+i0-1) T1(V2+i1+1); mxV1 mxV2];

Acc=COM.TNB(:,:,4).*repmat(acc(:,1),1,3); AT=vectordecomp(Acc,nT); aT=vectornorms(AT).*sign(dot(AT,nT,2)); AM=vectordecomp(Acc,nM); aM=vectornorms(AM).*sign(dot(AM,nM,2)); AF=vectordecomp(Acc,nF); aF=vectornorms(AF).*sign(dot(AF,nF,2)); COM.Accel=[acc aT aM aF];

[mxA1 A1]=max(aT(i0:i1)); [mxA2 A2]=max(aT(i1+2:i2+2)); COM.Time(5:6,:)=[T1(A1+i0-1) T1(A2+i1+1); mxA1 mxA2];

%% 5) Save the data sfn=[fn{1}(1:13) 'AXcomp.mat']; save(sfn,'Bend','Frames','AXL','PltAxl','XYZ','TMF','YPR','C_Stages', 231

'Yaw','COM');

Appendix A.2: findAxial.m function [AxLM AXL PltAx]=findAxial(DPts,VPts) %% FINDAXIAL estimates the positions & axes of the axial body. n=size(DPts,1); dXYZ=DPts(1:15,:); vXYZ=VPts(1:15,:);

[dvD fr1]=vectornorms(dXYZ-vXYZ); r=roundn(dvD/2,-2); cpt=(dXYZ+vXYZ)/2; [cXYZ AXL.cSp AXL.cCrv]=smintCurv(cpt,21,0); fr2=vectornorms(dXYZ-cXYZ,'unit'); frt=vectornorms(fr1+fr1+fr2,'unit');

AXL.Pnts(:,:,1)=dXYZ; AXL.Pnts(:,:,2)=vXYZ; AXL.Pnts(:,:,3)=cXYZ;

% Rostrum=pt4, COM=pt8, Ant=pt11; Mid=pt15; Post=pt19; Frt=zeros(21,3); s=[4,8,11,15,19]; for a=1:21 if a<=3; Frt(a,:)=vectornorms(frt(2,:)+3*frt(3,:)+frt(4,:),'unit'); elseif a>=20 Frt(a,:)=vectornorms(frt(19,:)+3*frt(20,:)+frt(21,:),'unit'); else Frt(a,:)=vectornorms(frt(a-1,:)+3*frt(a,:)+frt(a+1,:),'unit'); end end vect=[cXYZ(1,:)-cXYZ(2,:); cXYZ(1:20,:)-cXYZ(2:21,:)]; [w1 trv]=vectordecomp(vect,Frt); Trv=vectornorms(trv,'unit'); Msg=vectornorms(cross(Frt,Trv),'unit');

AXL.TMF(:,:,1)=Trv; AXL.TMF(:,:,2)=Msg; AXL.TMF(:,:,3)=Frt; dc=.35*r(8); COM=cXYZ(8,:)+dc*Frt(8,:);

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Appendix A.3: fishRotation.m function [varargout]=fishRotation(tr,ms,unit) %% FISHROTATION calculates yaw, pitch and roll of the body segments.

if nargin<3, unit='deg'; end m=size(tr,1); i=size(ms,1); if m~=i, error('fishrotation: Normals have unequal lengths'), end

[yaw pitch]=angles2D(tr,[-1 0 0],unit); ry=zeros(i,3); for a=1:i ry(a,:)=rotatePts([0 -1 0],[yaw(a) -pitch(a) 0],unit); end s=vectorcomp(cross(ry,ms,2),tr,-13); s(s==0)=1; roll=angles(ms,ry,unit).*s; if nargout==1 varargout{1}=[yaw -pitch roll]; elseif nargout==3 varargout{1}=yaw; varargout{2}=-pitch; varargout{3}=roll; varargout{4}=dYaw; end

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Appendix A.4: motionFUN.m function [Speed Accel Curvs TNB Jerk]=motionFUN(fun,T,varargin) % MOTIONFUN uses the supplied function to generate the time derivatives passed onto motion3D. d=[]; sgn=[]; if ~isempty(varargin) for v=1:length(varargin) if ischar(varargin{v}), d=lower(varargin{v}); else sgn=varargin{v}; end end end

[r c]=size(T); if r==1 && c>1, T=T'; elseif r>1 && c>1, error('Time Matrix Has Too Many Input Vecotrs') end s=length(fun); switch s case 1 der1=fnval(fnder(fun,1),T); der1=der1'; der2=fnval(fnder(fun,2),T); der2=der2'; der3=fnval(fnder(fun,3),T); der3=der3';

case 3 if iscell(fun), Xfun=fun{1}; Yfun=fun{2}; Zfun=fun{3}; elseif isstruct(fun), Xfun=fun(1); Yfun=fun(2); Zfun=fun(3); end

dx1=fnval(fnder(Xfun,1),T); dx2=fnval(fnder(Xfun,2),T); dx3=fnval(fnder(Xfun,3),T); dy1=fnval(fnder(Yfun,1),T); dy2=fnval(fnder(Yfun,2),T); dy3=fnval(fnder(Yfun,3),T); dz1=fnval(fnder(Zfun,1),T); dz2=fnval(fnder(Zfun,2),T); dz3=fnval(fnder(Zfun,3),T);

der1=[dx1 dy1 dz1]; der2=[dx2 dy2 dz2]; der3=[dx3 dy3 dz3];

otherwise error('motionFUN: Number of Input Function can only be 1 or 3') end

[Speed Accel Curvs TNB Jerk]=motion3D(der1,der2,der3,d,sgn);

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APPENDIX B

FIN CODES

Appendix B.1: finSurface.m

%% 1) Load the TMF normals of the axial file from axialKinematics. MT1='Select The Axial Kinematics Files'; fn=uigetfile('*.mat',MT1,'multiselect','off'); if isequal(fn,0), return, end ax=load(fn,'Bend','Frames','C_Stages','TMF');

Frames=ax.Frames; Bend=ax.Bend;

P=size(Frames,1); %Stg=ax.C_Stages(1,:); aTMF=ax.TMF(:,:,:,3); mTMF=ax.TMF(:,:,:,4);

%% 2) Select the Rotated & Combined points files from rotateFrames. MT='Select The Combined Points Files'; fn=uigetfile('*.mat',MT,'multiselect','on'); if isequal(fn,0), return, else N=length(fn); end if N~=P, error('The number of time points do not match.'), end msg='Loading Files'; wb=waitbar(0,msg);

% preparatory matrices and constants np=21; tol=.01; m=2; dRy=[1,4,7,10,12,15,18,21]; aRy=[1,3,5,8,11,14];

PltFin=cell(N,1); area=nan(N,4); dsrf=nan(np,N,6,9); dMN=nan(N,9,6,2); dMx=nan(N,9,3,2); dMn=nan(N,9,3,2); asrf=nan(np,N,6,6); aMN=nan(N,6,6,2); aMx=nan(N,6,3,2); aMn=nan(N,6,3,2); for f=1:N if ~ishandle(wb), return, end load(fn{f},'DPts','VPts')

F=Frames(f,1); 235

waitbar((f-1)/N,wb,sprintf('Processing Frame #%.0f (%.0f of %.0f)',[F,f,N]))

% Evaluate the Dorsal Fin-Rays DPts(1:16,:)=[]; dpt=nan(np,3,8);

s=-1:7:size(DPts,1); a=abs(s); b=s+5; for r=1:8 pts=DPts(a(r):b(r),:); w=ones(size(pts(:,1))); dpt(:,:,r)=smintCurv(pts,np,tol,w,m); end area(f,1)=finArea(dpt(:,:,1:4)); area(f,2)=finArea(dpt(:,:,4:8));

dXYZ=permute(dpt,[3,1,2]);

dKs=nan(np,9,3); dSES=nan(np,9,3); dCLS=nan(np,3,3,8); tspd=spaps({dRy,1:np,1:3},dXYZ,{0,0,0},{m,m,m}); for i=1:8 [ks kc1 kc2dCLS(:,:,:,i)]=surfCurvature(tspd,dRy(i),1:np,'DF'); if i<=4 dKs(:,i,1)=ks(:,2); dKs(:,i,2)=kc1(:,2); dKs(:,i,3)=kc2(:,2); [dSES(:,i,1) dSES(:,i,2) dSES(:,i,3)]= surfRotation(dCLS,aTMF(f,:,:),'DF','deg'); end if i>=4 dKs(:,i+1,1)=ks(:,2); dKs(:,i+1,2)=kc1(:,2); dKs(:,i+1,3)=kc2(:,2); [dSES(:,i+1,1) dSES(:,i+1,2) dSES(:,i+1,3)]= surfRotation(dCLS,mTMF(f,:,:),'DF','deg'); end end dMN(f,:,1:3,1)=mean(dKs(2:20,:,:)); dMN(f,:,1:3,2)=std(dKs(2:20,:,:)); [dMx(f,:,:,1) Ix]=max(dKs(2:20,:,:)); dMx(f,:,:,2)=Ix.*.05; [dMn(f,:,:,1) In]=min(dKs(2:20,:,:)); dMn(f,:,:,2)=In.*.05; dMN(f,:,4:6,1)=mean(dSES(2:20,:,:)); dMN(f,:,4:6,2)=std(dSES(2:20,:,:)); dsrf(:,f,1:3,:)=permute(dKs,[1,4,3,2]); dsrf(:,f,4:6,:)=permute(dSES,[1,4,3,2]);

PltFin{f}.DtSpl=tspd; PltFin{f}.DFin=permute(dpt,[1,3,2]); PltFin{f}.DCurv=dKs; PltFin{f}.DAngs=dSES; PltFin{f}.DCLS=dCLS;

% Evaluate the Anal Fin-Rays VPts(1:16,:)=[]; apt=nan(np,3,6);

a=1:7:size(VPts,1); b=a+5; 236

for r=1:6 pts=VPts(a(r):b(r),:); w=ones(size(pts(:,1))); apt(:,:,r)=smintCurv(pts,np,tol,w,m); end area(f,3)=finArea(apt(:,:,1:2)); area(f,4)=finArea(apt(:,:,2:6));

aXYZ=permute(apt,[3,1,2]);

aKs=nan(np,6,3); aSES=nan(np,6,3); aCLS=nan(np,3,3,8); tspa=spaps({aRy,1:np,1:3},aXYZ,{0,0,0},{m,m,m}); for i=1:6 [ks kc1 kc2 aCLS(:,:,:,i)]=surfCurvature(tspa,aRy(i),1:np,'AF'); aKs(:,i,1)=ks(:,2); aKs(:,i,2)=kc1(:,2); aKs(:,i,3)=kc2(:,2); [aSES(:,i,1) aSES(:,i,2) aSES(:,i,3)]= surfRotation(aCLS,mTMF(f,:,:),'AF','deg'); end aMN(f,:,1:3,1)=mean(aKs(2:20,:,:)); aMN(f,:,1:3,2)=std(aKs(2:20,:,:)); [aMx(f,:,:,1) Ix]=max(aKs(2:20,:,:)); aMx(f,:,:,2)=Ix.*.05; [aMn(f,:,:,1) In]=min(aKs(2:20,:,:)); aMn(f,:,:,2)=In.*.05; aMN(f,:,4:6,1)=mean(aSES(2:20,:,:)); aMN(f,:,4:6,2)=std(aSES(2:20,:,:)); asrf(:,f,1:3,:)=permute(aKs,[1,4,3,2]); asrf(:,f,4:6,:)=permute(aSES,[1,4,3,2]);

PltFin{f}.AtSpl=tspa; PltFin{f}.AFin=permute(apt,[1,3,2]); PltFin{f}.ACurv=aKs; PltFin{f}.AAngs=aSES; PltFin{f}.ACLS=aCLS; end Area.Raw=area; Area.Smooth=smooth4diff(area);

Surf.DSurf=dsrf; Surf.DMean=dMN; Surf.DMax=dMx; Surf.DMin=dMn;

Surf.ASurf=asrf; Surf.AMean=aMN; Surf.AMax=aMx; Surf.AMin=aMn;

%% waitbar(N/N,wb,'All Frames Processed. Saving Data to File.'), pause(1) sfn=[fn{1}(1:13),'FScomp.mat']; save(sfn,'Frames','Bend','PltFin','Surf','Area'); close(wb)

237

Appendix B.2: surfCurvature.m function [Kspan Kchord1 Kchord2 CLS]=surfCurvature(tSpl,row,column,fin) if nargin<4, fin='DF'; end if strcmpi(fin,'AF'), sa=-1; else sa=1; end

% Calculate 1st & 2nd partial derivatives with respect to Spanwise (tdS) and Chordwise (tdC) variables. tdS=cell(2,1); tdC=cell(2,1); for j=1:2 tdS{j}=fnder(tSpl,[0 j 0]); tdC{j}=fnder(tSpl,[j 0 0]); end dim=1:3; sd1(:,:,1)=squeeze(fnval(tdS{1},{row, column, dim})); sd2(:,:,1)=squeeze(fnval(tdS{2},{row, column, dim})); cd1(:,:,1)=squeeze(fnval(tdC{1},{row, column, dim})); cd2(:,:,1)=squeeze(fnval(tdC{2},{row, column, dim}));

[sds sT]=vectornorms(sd1(:,:,1)); sden=sds.^3; [snum sB]=vectornorms(cross(sd1(:,:,1),sd2(:,:,1),2)); sk=snum./sden;

[cds cT]=vectornorms(cd1(:,:,1)); cden=cds.^3; [cnum cB]=vectornorms(cross(cd1(:,:,1),cd2(:,:,1),2)); ck=cnum./cden;

L=vectornorms(cross(cT,sT,2),'unit'); % L=Lateral Axis C=vectornorms(cross(L,sT,2),'unit'); % C=Chord Axis (C~=cT) V=vectornorms(cross(L,cT,2),'unit'); % V=Vertical Axis to (cTxL)

% span curvature: parallel (1) & perpendicular (2) to L. [sB1 sB2]=vectordecomp(sB,L); sk1=vectornorms(sB1).*sk.*sign(dot(sB1,L,2)); sk2=vectornorms(sB2).*sk.*sign(dot(sB2,C,2));

% chord curvature: parallel (1) & perpendicular (2) to L % as well as parallel (3) & perpendicular (4) to C (ie, LxS). [cB1 cB2]=vectordecomp(cB,L); [cB3 cB4]=vectordecomp(cB2,C); ck1=vectornorms(cB1).*ck.*sign(dot(cB1,L,2)); ck2=vectornorms(cB2).*ck.*sign(dot(cB2,V,2)); ck3=vectornorms(cB3).*ck.*sign(dot(cB3,C,2)); ck4=vectornorms(cB4).*ck.*sign(dot(cB4,V,2));

238

Appendix B.3: surfRotation.m function varargout=surfRotation(CLS,TMF,fin,unit,tol) if nargin<5 || isempty(tol), tol=eps; end if nargin<4 || isempty(unit), unit='deg'; end if nargin<3 || isempty(fin), fin='DF'; end if nargin<2 || isempty(TMF), TMF=[1 0 0;0 1 0;0 0 1]; end n=size(CLS,1);

C=CLS(:,:,1); L=CLS(:,:,2); S=CLS(:,:,3);

[a b c]=size(TMF); if a==1 && c==3 TMF=squeeze(TMF)'; end if strcmpi(fin,'AF'), f=-1; else f=1; end

T=repmat(TMF(1,:),n,1); M=repmat(TMF(2,:),n,1); F=repmat(TMF(3,:),n,1);

[m1 I1]=vectornorms(cross(M*f,S,2)); [w1 I1(m1<=tol,:)]=vectordecomp(C(m1<=tol,:),M(m1<=tol,:)); s1=diag(sign(dot(I1,C,2))); I1=s1*I1;

I2=cross(I1,M*f,2); s2=diag(sign(dot(I2,repmat(S(1,:),n,1),2))); I2=s2*I2; sw=angles3D(S,I2,(s2*C)*f,unit); el=angles3D(I2,-T,M*f,unit); sp=angles3D(C,I1,(s2*S)*f,unit); if nargout==1 varargout{1}=[sw el sp]; else varargout{1}=sw; varargout{2}=el; varargout{3}=sp; end

239

Appendex B.4: finArea.m function area=finArea(Pts,out) if nargin<2, out='total'; end [n c r]=size(Pts);

AS=nan(n-1,r-1);

for s=1:r-1 tL=nan(n-1,6); tU=nan(n-1,6); for i=1:n-1 tL(i,:)=[Pts(i,:,s+1)-Pts(i,:,s), Pts(i+1,:,s+1)-Pts(i,:,s)]; tU(i,:)=[Pts(i+1,:,s)-Pts(i,:,s), Pts(i+1,:,s+1)-Pts(i,:,s)]; end LA=areaTri2Vect(tL); UA=areaTri2Vect(tU); AS(:,s)=LA+UA; end switch lower(out) case 'total' area=sum(sum(AS)); case 'between' area=sum(AS); case 'both' area=[sum(AS) sum(sum(AS))]; end

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APPENDIX C

DATA VISUALIZATION

Appendix C.1: FishPlot2.m function varargout = FishPlot2(varargin) % FISHPLOT2 M-file for FishPlot2.fig

% Begin initialization code - DO NOT EDIT gui_Singleton = 1; gui_State = struct('gui_Name', mfilename, ... 'gui_Singleton', gui_Singleton, ... 'gui_OpeningFcn', @FishPlot2_OpeningFcn, ... 'gui_OutputFcn', @FishPlot2_OutputFcn, ... 'gui_LayoutFcn', [] , ... 'gui_Callback', []); if nargin && ischar(varargin{1}) gui_State.gui_Callback = str2func(varargin{1}); end if nargout [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:}); else gui_mainfcn(gui_State, varargin{:}); end % End initialization code - DO NOT EDIT

% --- Executes just before FishPlot2 is made visible. function FishPlot2_OpeningFcn(hObject, eventdata, handles, varargin) cameratoolbar('Show'); set(handles.axes3D,'xtick', [],'ytick',[],'ztick',[],... 'nextplot','replacechildren') camzoom(handles.axes3D,2) handles.new=0; handles.fig1=figure('name','Fin-Ray Angles','numbertitle','off','nextplot','add','visible','off'); handles.fig3=figure('name','Fin-Ray Surface','numbertitle','off',... 'nextplot','add','visible','off'); handles.output = hObject; guidata(hObject, handles);

% --- Outputs from this function are returned to the command line. function varargout = FishPlot2_OutputFcn(hObject, eventdata, handles) uicontrol(handles.loadbutton) varargout{1} = handles.output;

% --- Executes on button press in loadbutton. function loadbutton_Callback(hObject, eventdata, handles) fn=uigetfile('.mat','Choose The AX- & RY-comp Files.','MultiSelect','on'); 241 if length(fn)~=2 return end load(fn{1},'PltAxl','Yaw','Frames'); load(fn{2},'PltFin','Surf'); fseq=fn{1}(1:12);

T=Frames(:,2)*1000; N=length(T); TP=sprintf('Time: %4.0f msec',T(1)); T1=Yaw.Time(1,1,1); T2=Yaw.Time(1,2,1); T3=Yaw.Time(1,1,4); T4=Yaw.Time(1,2,4); S1=sprintf('R1: %4.0f ms',T3); S2=sprintf('R2: %4.0f ms',T4); set(gcf,'Name',fseq); set(handles.raymenu,'Enable','on','Value',1); set(handles.parammenu,'Enable','on','Value',1); set(handles.slider1,'Enable','on','Max',N,'Min',1,'Value',1,... 'sliderstep',[1/(N-1) 1/(N-1)]); set(handles.tptext,'visible','on','String',TP); set(handles.S2text,'visible','on','String',S1); set(handles.S3text,'visible','on','String',S2); dry=permute(PltFin{1}.DFin(:,4,:),[1,3,2]); ary=permute(PltFin{1}.AFin(:,2,:),[1,3,2]); axes(handles.axes3D) if handles.new==1, cla, end handles.fish=drawFish(PltAxl{1}); axis equal handles.fins=drawFinSurf(PltFin{1},1); handles.rys=plot3(dry(:,1),dry(:,2),dry(:,3),'-c',... ary(:,1),ary(:,2),ary(:,3),'-m','linewidth',2); xlim([-1000 1000]), ylim([-1000 1000]), zlim([-1000 1000]) grid off, if handles.new==0, camzoom(5); end

% get yaw rate of rostrum, ant- & mid-trunk dYaw=Yaw.Rate(:,[1,3,4]); DAng=Surf.DMean(:,5:9,4:5,1); idS=repmat(mean(DAng(1:6,:,1)),N,1); idE=repmat(mean(DAng(1:6,:,2)),N,1); AAng=Surf.AMean(:,2:6,4:5,1); iaS=repmat(mean(AAng(1:6,:,1)),N,1); iaE=repmat(mean(AAng(1:6,:,2)),N,1);

% Create the Sweep/Elevation figure figure(handles.fig1) if handles.new~=0 cla else set(gcf,'visible','on') end handles.Kin=nan(2,2); subplot(3,1,1) if handles.new~=0, cla, end 242 set(gca,'xtick',-16:4:80,'ytick',-6:2:6,'yminortick','on',... 'nextplot','add') plot([-20;80],[0;0],'-k',[0;0;nan;T1;T1;nan;T2;T2],[-10;10;nan;- 10;10;nan;-10;10],':k',... [T3;T3;nan;T4;T4],[-10;10;nan;-10;10],'--k') plot(T,dYaw(:,1),'-k',T,dYaw(:,2),'--k',T,dYaw(:,3),'-g') xlim([T(1) T(end)]), ylim([-5 5]) subplot(3,1,2) if handles.new~=0 cla end set(gca,'xtick',-16:4:80,'ytick',- 90:30:90,'yminortick','on','nextplot','add') plot([-20;80],[0;0],'-k',[0;0;nan;T1;T1;nan;T2;T2],... [-100;100;nan;-100;100;nan;-100;100],':k',... [T3;T3;nan;T4;T4],[-100;100;nan;-100;100],'--k') plot(T,DAng(:,:,1)-idS,'-.','color',[.75 .75 1]) plot(T,AAng(:,:,1)-iaS,'-.','color',[1 .75 .75]) handles.Kin(:,1)=plot(T,DAng(:,1,1)-idS(:,1),'-b',T,AAng(:,1,1)- iaS(:,1),'-r','linewidth',1); xlim([T(1) T(end)]), ylim([-65 65]) subplot(3,1,3) if handles.new~=0 cla end set(gca,'xtick',-16:4:80,'ytick',- 30:10:30,'yminortick','on','nextplot','add') plot([-20;80],[0;0],'-k',[0;0;nan;T1;T1;nan;T2;T2],... [-100;100;nan;-100;100;nan;-100;100],':k',... [T3;T3;nan;T4;T4],[-100;100;nan;-100;100],'--k') plot(T,DAng(:,:,2)-idE,'-.','color',[.75 .75 1]) plot(T,AAng(:,:,2)-iaE,'-.','color',[1 .75 .75]) handles.Kin(:,2)=plot(T,DAng(:,1,2)-idE(:,1),'-b',... T,AAng(:,1,2)-iaE(:,1),'-r','linewidth',1); xlim([T(1) T(end)]), ylim([-30 30])

% Create the Curvature figure figure(handles.fig3) if handles.new==0 set(gcf,'visible','on') end handles.crv=nan(N,2); handles.sub=nan(2,1); subplot(3,1,1) if handles.new~=0 cla end set(gca,'xtick',-16:4:80,'ytick',- 6:2:6,'yminortick','on','nextplot','add') plot([-20;80],[0;0],'-k',[0;0;nan;T1;T1;nan;T2;T2] ,... [-10;10;nan;-10;10;nan;-10;10],':k',... [T3;T3;nan;T4;T4],[-10;10;nan;-10;10],'--k') plot(T,dYaw(:,1),'-k',T,dYaw(:,2),'--k',T,dYaw(:,3),'-g') xlim([T(1)-2 T(end)+2]), ylim([-5 5]) a=colorbar; set(a,'visible','off'), box on

243 handles.sub(1)=subplot(3,1,2); if handles.new~=0, cla, end set(gca,'xtick',-16:4:80,'ytick',0:.2:1,'nextplot','add') handles.crv(:,1)=graphSurf(T,Surf.DSurf(:,:,:,5),1,gca); xlim([T(1)-2 T(end)+2]), ylim([0 1]), box on handles.sub(2)=subplot(3,1,3); if handles.new~=0 cla end set(gca,'xtick',-16:4:80,'ytick',0:.2:1,'nextplot','add') handles.crv(:,2)=graphSurf(T,Surf.ASurf(:,:,:,2),1,gca); xlim([T(1)-2 T(end)+2]), ylim([0 1]), box on handles.new=1; handles.Time=T; handles.AX=PltAxl; handles.Fin=PltFin; handles.dCrv=Surf.DSurf(:,:,:,5:9); handles.aCrv=Surf.ASurf(:,:,:,2:6); handles.dAngs=DAng; handles.aAngs=AAng; figure(handles.menu) guidata(hObject,handles);

% --- Executes on selection change in raymenu. function raymenu_Callback(hObject, eventdata, handles)

T=handles.Time; N=length(T); f=round(get(handles.slider1,'Value')); ry=get(handles.raymenu,'Value'); pr=get(handles.parammenu,'Value'); if pr>=3, pr=pr+1; end dry=permute(handles.Fin{f}.DFin(:,ry+3,:),[1,3,2]); ary=permute(handles.Fin{f}.AFin(:,ry+1,:),[1,3,2]); axes(handles.axes3D) delete(handles.rys) handles.rys=plot3(dry(:,1),dry(:,2),dry(:,3),'- c',ary(:,1),ary(:,2),ary(:,3),'-m','linewidth',2);

DAng=handles.dAngs; idS=repmat(mean(DAng(1:6,ry,1)),N,1); idE=repmat(mean(DAng(1:6,ry,2)),N,1); AAng=handles.aAngs; iaS=repmat(mean(AAng(1:6,ry,1)),N,1); iaE=repmat(mean(AAng(1:6,ry,2)),N,1);

% Sweep figure figure(handles.fig1) delete(handles.Kin(:,:)) subplot(3,1,2) handles.Kin(:,1)=plot(T,DAng(:,ry,1)-idS,'-b',T,AAng(:,ry,1)-iaS,'- r','linewidth',1);

244 subplot(3,1,3) handles.Kin(:,2)=plot(T,DAng(:,ry,2)-idE,'-b',T,AAng(:,ry,2)-iaE,'- r','linewidth',1);

% Curvature figure figure(handles.fig3) axes(handles.sub(1)); cla handles.crv(:,1)=graphSurf(T,handles.dCrv(:,:,:,ry),pr,gca); axes(handles.sub(2)); cla handles.crv(:,2)=graphSurf(T,handles.aCrv(:,:,:,ry),pr,gca); figure(handles.menu) guidata(hObject,handles);

% --- Executes during object creation, after setting all properties. function raymenu_CreateFcn(hObject, eventdata, handles) if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end

% --- If Enable == 'on', executes on mouse press in 5 pixel border. % --- Otherwise, executes on mouse press in 5 pixel border or over raymenu. function raymenu_ButtonDownFcn(hObject, eventdata, handles)

% --- Executes on slider movement. function slider1_Callback(hObject, eventdata, handles)

T=handles.Time; f=round(get(handles.slider1,'Value')); TP=sprintf('Time: %4.0f msec',T(f)); ry=get(handles.raymenu,'Value'); pr=get(handles.parammenu,'Value'); if pr>=3, pr=pr+1; end dry=permute(handles.Fin{f}.DFin(:,ry+3,:),[1,3,2]); ary=permute(handles.Fin{f}.AFin(:,ry+1,:),[1,3,2]);

set(handles.slider1,'Value',f); set(handles.tptext,'visible','on','String',TP); axes(handles.axes3D) cla handles.fish=drawFish(handles.AX{f}); handles.fins=drawFinSurf(handles.Fin{f},pr); % select paramater handles.rys=plot3(dry(:,1),dry(:,2),dry(:,3),'-c',... ary(:,1),ary(:,2),ary(:,3),'-m','linewidth',2); figure(handles.fig1) delete(handles.TL(:,1)) subplot(3,1,1) handles.TL(1,1)=plot([T(f);T(f)],[-10;10],'-','color',[0 .7 0]); 245 subplot(3,1,2) handles.TL(2,1)=plot([T(f);T(f)],[-100;100],'-','color',[0 .7 0]); subplot(3,1,3) handles.TL(3,1)=plot([T(f);T(f)],[-10;10],'-','color',[0 .7 0]); guidata(hObject,handles);

% --- Executes during object creation, after setting all properties. function slider1_CreateFcn(hObject, eventdata, handles) if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor',[.9 .9 .9]); end

% --- Executes on button press in closebutton. function closebutton_Callback(hObject, eventdata, handles) close all hidden

% --- Executes on selection change in parammenu. function parammenu_Callback(hObject, eventdata, handles) T=handles.Time; N=length(T); f=round(get(handles.slider1,'Value')); ry=get(handles.raymenu,'Value'); pr=get(handles.parammenu,'Value'); if pr>=3, pr=pr+1; end dry=permute(handles.Fin{f}.DFin(:,ry+3,:),[1,3,2]); ary=permute(handles.Fin{f}.AFin(:,ry+1,:),[1,3,2]); axes(handles.axes3D) cla handles.fish=drawFish(handles.AX{f}); handles.fins=drawFinSurf(handles.Fin{f},pr); handles.rys=plot3(dry(:,1),dry(:,2),dry(:,3),'-c',... ary(:,1),ary(:,2),ary(:,3),'-m','linewidth',2);

% Curvature figure figure(handles.fig3) axes(handles.sub(1)); cla handles.crv(:,1)=graphSurf(T,handles.dCrv(:,:,:,ry),pr,gca); axes(handles.sub(2)); cla handles.crv(:,2)=graphSurf(T,handles.aCrv(:,:,:,ry),pr,gca); figure(handles.menu) guidata(hObject,handles); 246

SCHOLASTIC VITA

Brad Anthony Chadwell Department of Biology Wake Forest University 226 Winston Hall Winston-Salem, NC 27109 Phone: 336-758-3399; email: [email protected]

EDUCATION:

Wake Forest University, Winston-Salem, North Carolina Ph.D., Biology, 2010 Dissertation Title: Fish fins and fast-starts: Multi-level analyses reveal functional variation within median fins of bluegill sunfish. Advisor: Miriam A. Ashley-Ross

University of North Carolina at Charlotte M.S., Biology, 1999 Thesis Title: A comparison of isometric contractile properties of hindlimb muscles in two anurans. Advisor: Susan E. Peters.

Weber State University, Ogden, Utah B.S., Major: Zoology, Minor: Chemistry, Cum Laude, 1996 A.S., with High Honors, 1994

PROFESSIONAL AND TEACHING EXPERIENCE:

Wake Forest University, 2001-2009 Lab Instructor: Comparative Physiology Teaching Assistant: Comparative Anatomy, Biomechanics, Sensory Biology

Wake Forest University School of Medicine, 2000-2001 Laboratory Technician III, Dept. of Internal Medicine

University of North Carolina at Charlotte, 1998-1999 Part-time Lecturer: Principles of Biology I Part-time Lecturer and Lab Instructor: Animal Biology

University of North Carolina at Charlotte, 1996-1998 Lab Instructor: Principles of Biology II, Animal Biology Teaching Assistant: Comparative Vertebrate Anatomy

247

PUBLICATIONS:

Barber, J.R., B.A. Chadwell, N. Garrett, B. Schmidt-French and W.E. Conner. (2009) Naïve bats discriminate arctiid moth warning sounds but generalize their aposematic meaning. Journal of Experimental Biology. 212:2141-2148.

O’Flaherty, J.T., L.C. Rogers, B.A. Chadwell, J.S. Owen, A. Rao, S.D. Cramer and L.W. Daniel. (2002) 5(S)-Hydroxy-6,8,11,14-E,Z,Z,Z-eicosatetraenoate stimulates PC3 cell signaling and growth by a receptor-dependent mechanism. Cancer Research. 62: 6817-6819.

Chadwell, B.A., H.J. Hartwell and S.E. Peters. (2002) Comparison of isometric contractile properties in hindlimb extensor muscles of the frogs Rana pipiens and Bufo marinus: Functional correlations with differences in hopping performance. Journal of Morphology. 51: 309-322.

O’Flaherty, J.T., B.A. Chadwell, M.W. Kearns, S. Sergeant and L.W. Daniel. (2001) Protein kinase C translocation responses to low concentrations of arachidonic acid. Journal of Biological Chemistry. 276: 24743-24750.

PUBLISHED ABSTRACTS AND CONFERENCE PRESENTATIONS:

Chadwell, B.A., B.W. Hunter and M.A. Ashley-Ross. (2007) When designing rays, function matters. Annual Meeting of the Society for Integrative and Comparative Biology (January 2008, San Antonio). Integrative and Comparative Biology, 47: e166.

Chadwell, B.A., E.M. Standen and G.V. Lauder. (2006) Fin shape and fast starts: A 3-D kinematic analysis. Annual Meeting of the Society for Integrative and Comparative Biology (January 2007, Phoenix). Integrative and Comparative Biology, 46: e23.

Chadwell, B.A., E.M. Standen and G.V. Lauder. (2005) Dorsal and anal fin function during the C-start escape response in bluegill sunfish. Annual Meeting of the Society for Integrative and Comparative Biology (January 2006, Orlando). Integrative and Comparative Biology, 45: 975.

Chadwell, B.A., J.L. Hutcheson and M.A. Ashley-Ross. (2004) Changing the shape of things: Elevating the median fins alters the lateral profile of largemouth bass (Micropterus salmoides). Annual Meeting of the Society for Integrative and Comparative Biology (January 2005, San Diego). Integrative and Comparative Biology, 44: 682.

Chadwell, B.A., D. Vichot, C. Harris and M.A. Ashley-Ross. (2004) Deployment of dorsal fins is an integral part of the escape response in largemouth bass (Micropterus salmoides). 7th International Congress of Vertebrate Morphology (July 2004, Boca Raton). Journal of Morphology, 260: 282. 248

Chadwell, B.A., D. Vichot, C. Harris and M.A. Ashley-Ross. (2003) Dorsal fin use during the escape response in largemouth bass (Micropterus salmoides). Annual Meeting of the Society for Integrative and Comparative Biology (January 2004, New Orleans). Integrative and Comparative Biology, 43: 906.

Baker P.R.S., B. Chadwell, J.S. Owen, J.T. O'Flaherty and R.L. Wykle. (2002) 5- Oxo-6,8,11,14-eicosatetraenoic acid stimulates PAF synthesis in human eosinophils. FASEB Journal 16: A539.

Chadwell, B.A. and S.E. Peters. (1998) A comparison of hindlimb muscles of two anurans having different jumping abilities. Annual Meeting of the Society for Integrative and Comparative Biology (January 1999, Denver). Integrative and Comparative Biology, 38: 35A.

Mathias, E.R., B.A. Chadwell and R.A. Meyers. (1995) Gliding flight in gulls: The paradox of fast muscle fibers and posture. Annual Meeting of the American Society of Zoologists (December 1995, Washington D.C.). American Zoologist, 35: 119A.

RESEARCH GRANTS:

Vecellio Fund, Wake Forest University, Department of Biology, $1500, 2005.

Grant-in-aid of Research, Society of Sigma Xi, $500, 1997.

HONORS AND AWARDS:

D. Dwight Davis Award for Best Student Poster in Vertebrate Morphology, Society for Integrative and Comparative Biology, 2008.

Outstanding Senior in Zoology, Weber State University, 1996.

PROFESSIONAL SOCIETIES:

International Society of Vertebrate Morphologists, 2004-present

Society for Integrative and Comparative Biology (formerly known as the American Society of Zoologists), 1998-present