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Energetics of fast-starts in northern pike, Esox lucius Frith, Harold Russ 1990

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ENERGETICS OF FAST-STARTS IN NORTHERN PIKE, Esox lucius by HAROLD RUSS FRITH B.Sc, University of Victoria, 1979 M.Sc. University of South Carolina, U.S.A., 1985 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department of Zoology We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA December, 1990 © Harold Russ Frith, 1990 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Z o o l o g y  The University of British Columbia Vancouver, Canada Date 1 7 A P r i l ' 1 9 9 1 DE-6 (2/88) ABSTRACT Fast-starts are high powered events of short duration, used by fish for prey capture and escape from predation. Here, the energetic cost of fast-starts in escape and prey capture for a fast-start specialist, the northern pike, Esox lucius, are determined and physiological and behavioural constraints assessed. This is done by comparing costs with literature values for physiological limits set my muscle mechanics and biochemistry, and comparing costs with other components of the energy budget. The combination of high speed film analysis (200-250Hz) and hydrodynamic models are used to determine the mechanical costs, hydrodynamic efficiencies and power output of fast-starts in prey capture (S-starts) and escape behaviour (C-starts). Excess post-exercise oxygen consumption (EPOC) is used to estimate the metabolic cost of fast-starts. A comparison of model predictions with required (acceleration) force estimates shows results are within 22% and similar to previous findings at lower film speeds. The caudal region including the caudal, dorsal and anal fins contribute the most to thrust (>90%) and the dorsal and anal fins contribute 28%. Due to the necessity for deceleration of fin sections during each tail beat, kinematics are not always optimal as predicted by the Weihs model. Mechanical power output, hydrodynamic efficiency and kinematic parameters (maximum velocities and maximum angle of attack of the caudal fin) are determined for fast-starts during prey capture and escape. Hydrodynamic efficiency averages 0.37 ii (range: 0.34 to 0.39) for C-starts and 0.27 (range: 0.16 to 0.37) for S-starts. The acceleration of added mass contributes the most to power output at 39%. Power output and efficiency for S-starts are more variable than C-starts and hydromechanical efficiency increases with number of tail beats for S-starts. Maximum muscle power output and maximum muscle stress during fast-starts in comparison to literature values for muscle function shows muscle power output during fast-starts is at its physiological limit but muscle stress is not. Metabolic efficiency is higher at 0.094 for C-starts than S-starts at 0.047. However, muscle efficiency estimates are similar averaging 0.252 for both fast-start types. Mean energetic cost of fast-starts is determined to be 26.5 J/kg for C-starts and 18.6 J/kg for S-starts. Based on the observation that pike can repeatedly fast-start up to 170 times before becoming exhausted and on estimates of available energy reserves from literature values for ATP and CrP concentrations in white muscle, the duration of fast-starts is concluded to not be limited by muscle physiology. Average power output is found to be similar for C and S-starts at 406 to 412 W/kg. Only hydrolysis of ATP and CrP can supply energy at this rate. Therefore, based on fish white muscle biochemistry and mechanics, power output during fast-starts appears to be limited by muscle physiology. The cost of fast-starts represents 0.03 to 2% of maintenance costs for pike and therefore only 5 to 30 fast-starts per day would be required to increase the daily energy budget by 10%. In addition, the cost of fast-starts represents 0.52 to 27.4% of surplus energy available from assimilated prey. Therefore, the iii cost of fast-starts can be significant and reducing fast-start duration is a probable strategy for minimising activity costs and thus increasing the energy available for growth or reproduction. iv TABLE OF CONTENTS Abstract i i Table of Contents v L i s t of Tables vii L i s t of Figures v i i i Aknowledgements x Chapter 1: Introduction 1 A. Energetic Cost of Fast-Starts 4 B. Morphological and Kinematic Constraints 8 C. P h y s i o l o g i c a l Constraints 9 D. E c o l o g i c a l and Behavioural Constraints 10 E. Chapter Outline 12 Chapter 2: Mechanics of the S t a r t l e Response i n the Northern pike, Esox l u c i u s A. Introduction 14 B. Materials and Methods 16 C. Results 24 D. Discussion 52 Chapter 3: Hydromechanical E f f i c i e n c y and Mechanical Power Output During F a s t - s t a r t s by Northern pike, Esox lucius A. Introduction 58 B. Materials and Methods 59 C Results 63 D. Discussion 7 9 v Chapter 4: Metabolic Cost of F a s t - s t a r t s i n Norhtern Pike, Esox lucius A. Introduction 88 B. Materials and Methods 90 C. Results. . . . ... 93 D. Discussion 110 Chapter 5:.Mechanical Cost of F a s t - s t a r t s by Northern Pike, Esox lucius A. Introduction 118 B. Materials and Methods 120 C. Results 122 D. Discussion.... 133 Chapter 6: Summary..... 141 References 145 v i LIST OF TABLES Table 1: Kinematic c h a r a c t e r i s t i c s of three C-starts 25 Table 2: Average force contribution from i) l i f t and acce l e r a t i o n forces i i ) caudal and dorsal-anal f i n sections and i i i ) f i s h with and without median f i n s ..48 Table 3: Predicted performance parameters derived from the Weihs model and required force equation 51 Table 4: Maximum v e l o c i t i e s , angles and forces f o r the caudal f i n . 69 Table 5: Useful power estimates f o r C and S-starts 70 Table 6: Power output estimates based on p o s i t i v e power only or the absolute value of power 72 Table 7: Tot a l power and hydromechanical e f f i c i e n c y values by stage f o r C and S-starts .-. .73 Table 8: Resting metabolic rates of f i v e pike p r i o r to exercise and i n the second hour of recovery. .95 Table 9: Maximum oxygen consumption rates f o r s i x pike during 10, 20 or 30 minutes of recovery 96 Table 10: Oxygen debt f o r an i n d i v i d u a l f i s h exercised to exhaustion 109 vii LIST OF FIGURES Figure 1: A) Side-view of a Northern pike showing l o n g i t u d i n a l body section d i v i s i o n s B) Schematic showing v e l o c i t y vectors and angles used i n equation 2... 19 Figure 2: Kinematics of a C-start 27 Figure 3: Relationship between the angle of body sections and time. 29 Figure 4: Relationship between l a t e r a l v e l o c i t y of body sections and time 32 Figure 5: Relationship between perpendicular v e l o c i t y of body sections and time.... 34 Figure 6: Relationship between momentum of body sections and time 37 Figure 7: D i s t r i b u t i o n of added mass and body mass along the f i s h ' s length 39 Figure 8: V e l o c i t y and angle of attack of f i n sections 41 Figure 9: Acceleration, l i f t and t o t a l forces i n the d i r e c t i o n of motion 43 Figure 10: Force contribution from caudal f i n , dorsal-anal f i n section and a l l sections i n the d i r e c t i o n of motion 4 6 Figure 11: Kinematics of an S-start .65 Figure 12: V e l o c i t y p r o f i l e s of the f i s h ' s center of mass for three C-starts and three S-starts 67 Figure 13: Components of power loss f o r C and S-starts 75 Figure 14: Relationship between hydromechanical e f f i c i e n c y and stage number f o r C and S-starts 78 Figure 15: Relationship between hydromechanical e f f i c i e n c y and r e l a t i v e speed f o r continous, burst-and-coast and f a s t - s t a r t swimming 83 Figure 16: Histogram of oxygen consumption with time before and a f t e r exercise 98 Figure 17: Histogram of recovery times a f t e r 0 to 20 f a s t -s t a r t s 100 viii Figure 18: E f f e c t of sampling rate ( f i l m speed) on mechanical work estimates 102 Figure 19: Relationship between oxygen debt and number of f a s t - s t a r t s f o r C and S-starts 105 Figure 20: Relationship between oxygen debt and useful mechanical work f o r C and S-starts 107 Figure 21: Relationship between oxygen debt and t o t a l mechanical work f o r C and S-starts 115 Figure 22: Log-log p l o t of distance versus time f or C and S-starts 124 Figure 23: To t a l metabolic cost versus distance f o r C and S-starts. . 127 Figure 24: To t a l metabolic cost versus time f o r C and S-starts. . 129 Figure 25: Muscle power • output versus time f or C and S-starts. . 132 Figure 26: Relationship between reaction time of prey and attack distance of predator 140 i x AKNOWLEDGEMENTS I would like to thank my supervisor, Dr Robert Blake for introducing me to biomechanics and for his support and guidance throughout this project. I would also like to thank my research committee; Drs Don McPhail, Dave Randall, Dolph Schluter, Dan Ware and Roily Brett for their encouragement and advice. I am particularly indebted to fellow graduate student, Dr Dave Harper, for his assistance in the laboratory and to Dave, Paulo Domenici and other graduate students and undergraduate students in the Animal Locomotion Laboratory for many hours of valuable discussion. This thesis could not have been completed without the support of my family. I would like to thank my parents, Mr and Mrs Harold Frith for their financial and moral support throughout my graduate studies. Most of all, I would like to thank my wife, Nancy for her love, support and endurance to the very end. x CHAPTER 1 INTRODUCTION Fast-starts are rapid accelerations of fish from rest (Weihs, 1973; Webb, 1975a; Harper and Blake, 1990a,fc; Domenici and Blake, in press). This locomotor behaviour is used by most fish species for evasion from predator attack and by some specialized forms in prey capture (e.g. Webb and Skadsen, 1980; Rand and Lauder, 1981; Webb, 1984; 1986; Harper and Blake, I990a,b). Success in prey capture and escape depend, in part, on the acceleration rate and velocities achieved (Howland, 1974; Elliot et al., 1977; Vinyard, 1982; Weihs and Webb, 1984; Harper and Blake, 1988). Maximum acceleration rates ranging from 25 to 245 m/s2 and maximum velocities ranging from 0.9 to 2.7 m/s during fast-starts have been reported (see Harper and Blake, 1990a). Fast-start performance limits are assumed to depend on maximum power production by muscles and hydromechanical efficiency (Weihs, 1973). Despite the importance of fast-start performance on energy acquisition and survivorship, and its potential impact on growth and gonad production, there are few published values for power output, mechanical work done, metabolic work done, or hydromechanical efficiencies during fast-starts (Webb, 1978a; Vinyard, 1982; Puckett and Dill, 1984). It is commonly assumed that power production by muscles is maximal during fast-starts (Weihs, 1973). Though escape behaviour of carridean shrimp is reported to be constrained by muscle physiology (Daniel and Meyhofer, 1989), a similar analysis for fish fast-starts is yet to be conducted. The intensity and duration of fast-starts may also be limited 1 by biochemical energy reserves and their rate of mobilization (Hochachka and Somero, 1984). Few studies compare performance and tissue biochemistry (Bennett et al., 1984; Huey et al., 1984). Bennett et al. (1984) shows that maximum locomotory performance of lizards during escape correlates with anaerobic enzyme activity and lactate accumulation. Direct quantification . of j5 ..,.the;^  cost of locomotion and its comparison to available energy reserves is lacking and is essential for demonstrating physiological constraint of performance based on the above factors. In order for performance to be maximal during maximum power output of muscles, the efficiency of mechanical energy transfer must also be maximal (Weihs, 1973). The kinematic conditions required for maximum; hydrodynamic efficiency during a fast-start are outlined by Weihs (1973) but are rarely used to evaluate the hypothesis that efficiency is maximal. The Weihs model also predicts that the posterior placement of anal and dorsal fins in Northern pike, Esox lucius, is advantageous for fast-start performance. Whilst pike acceleration rates achieved during fast-starts are greater than trout (Harper and Blake, 1990a), the quantitative contribution of the median fins to thrust are not known. These issues are important in demonstrating that performance is constrained by morphology and kinematics in pike. In the absence of any evidence that fish perform fast-starts near their physiological maximum, observed intensity and durations may be behaviourally determined at submaximal levels. This would be advantageous if the energetic cost of fast-starts is significantly large so as to increase activity costs and reduce energy available for growth or gonad production. The significance 2 of activity costs is apparent for continous swirnming behaviour where migratory fish are observed to swim at speeds which minimize the cost of transport (Ware, 1978). Few studies have • evaluated the ecological significance of fast-start energetics (e.g. Puckett and Dill, 1984). Another common assumption for fast-starts and similar behaviours is that the duration of activity is too short for the cost of locomotion to contribute significantly to the daily energy budget or foraging costs of animals (Bennett, 1986). In the few studies on the energetics of prey capture in fish, the cost of fast-starts is reported to be small (Vinyard, 1982; Puckett and Dill, 1984). However, , in these studies prey size is small and performance of predators is sub-maximal compared to fast-start ability of fish (Harper and Blake, 1990&). Harper and Blake (1988) model the cost of activity for pursuit, attack and prey strike (i.e. fast-start) and predict that the cost of the strike is the dominant contributor to the total cost of prey capture activity. Here, the energetic cost of fast-starts during prey capture and escape behaviour in the Northern pike, Esox lucius is evaluated. The energy required for fast-starts will be compared to literature values for daily energy budget, biochemical energy reserves and rates of mobilisation, and muscle mechanics to determine whether fast-starts are ecologically or physiologically constrained. Transfer of mechanical work done by muscles into useful work for locomotion is determined and morphological constraints on performance discussed. 3 Energetic Cost of Fast-Starts: Methodology The cost of animal locomotion has been successfully determined by the combination of high speed film and biomechanical models or the direct measurement of metabolic rate (e.g. Brett, 1963; 1964; Pennycuick, 1968; Webb, 1971a,fc; Wardle and Reid, 1977; Blake, 1979; Taylor et al., 1982; Daniel, 1983; Blickhan and Full, 1987; Full, 1987; Full et al., 1990). A few studies of continous swimming in fish have combined both methods and compared the two estimates of energetic cost (Webb, \91\a,b; Webb, 1974). Using this approach, errors in assumptions of the biomechanical models are evaluated (Lighthill, 1971). However, conversion of useful mechanical work done to metabolic cost requires knowledge of propulsive and muscle efficiency which provides another potential source of error. Whilst efficiency values for continous swimming are well understood (Webb, 1975&), this is not the case for fast-starts. Sustained, aerobically fuelled activity at constant speed is studied far more frequently than unsteady, anaerobically fuelled activity (e.g. Pennycuick, 1968; Webb, \915b; Norberg, 1976; Bennett, 1986; Alexander, 1989). Because unsteady motion requires a more accurate record of kinematics than steady motion and its short duration makes anaerobic metabolism more difficult to measure directly, few studies have attempted to measure the cost of fast-starts. Recently, advances in biomechanical analysis of fast-starts and biochemistry of exercise in fish improve our ability to measure these costs accurately (Harper and Blake, 1989a,fc; Scarabello, 1989; Schulte, 1990). Harper and Blake (1989a,fr) demonstrate the importance of 4 image magnification and film speed to the magnitude of analytical error. Inaccuracies . in displacement measurements and their subsequent influence on cost estimates for unsteady motion can be minimised by maximising image magnification and choosing the optimal film speed (see equations in Harper and Blake, 1989a). The optimal speed for filming pike fast-starts was determined to be 200 to 250 Hz for a 1:1 magnification. Maximum acceleration rates are still underestimated by 30% at this speed and magnification (Harper and Blake, 1989a). The simplist model for determining the cost of fast-starts from high speed film is by measuring the displacement of the fish's center of mass and calculating work from the product of acceleration force and displacement. The acceleration force, also referred to in this study as the required force, can be written as F = (m + m) a (1) a where m is the mass of the fish, ma is the longitudinal added mass and a is the acceleration of the fish's center of mass. The added mass refers to water entrained by the fish in forward motion. Webb (1982a) experimentally determined longitudinal added mass for fast-starts by trout to be 20% of the fish's mass. This value is assumed to be the same for other species. The force required to accelerate a fish is also represented by propulsive forces generated in undulatory movements of the fish's body. Weihs (1973) modified Lighthill's large amplitude theory for application to fish fast-starts. The theory sums acceleration and lift forces over the length of the fish's body 5 and resolves the force in the direction of motion. The Weihs model is more complex than equation 1, requiring digitization of many positions along the \ fish's body which may result in the accumulation of measurement errors. In addition, large amplitude theory assumes fins act like rigid plates when they have been observed to flex (Bainbridge, 1963; McCutcheon, 1970). The comparison of required and propulsive forces provides a useful check of the propulsive model. If the only purpose was to estimate the energetic cost of fast-start activity, the simpler and less time consuming required force equation would be prefered. However, the Weihs model is required for determining total mechanical power output and hydromechanical efficiency. Weihs (1973) compares required forces with model predictions and finds a 12 to 30% discrepancy. However, film records at 64 Hz were used which is now known to be low and subject to large digitizing errors (Harper and Blake, 1989a,fc). An accuracy test of the Weihs (1973) model predictions for propulsive forces and useful work done is necessary for the higher film rates used here before power output and hydromechanical efficiency estimates can be interpreted. Hydrodynamic efficiencies for fish fast-starts have never been measured but are expected to be low. Webb (1978a) predicted that fast-start efficiency values of 0.1 to 0.2 are realistic. McCutcheon (1977) determined hydrodynamic efficiency from flow visualisation of the zebra danio wake in the push and coast mode and reported values ranging from 0.3 to 0.7. These are lower than hydrodynamic efficiency for continous swimming fish which average 0.8 to 0.9 (Webb, 1988). Muscle efficiency is approximately 20-30% for aerobic red 6 muscle in vertebrates (Goldspink, 1977; Hill, 1950). A recent study by Altringham and Johnston (1986) shows efficiency of white anaerobic muscle in fish are 50% less than red muscle. However, the muscle was stimulated to contract isometrically and whether these findings apply to isotonic contractions is as yet unknown. The direct determination of metabolic rate during fast-starts would provide a direct estimate of total cost and allow comparison of literature values for muscle efficiency with an experimentally derived value. Muscle efficiency can be expressed as a ratio of mechanical work done divided by metabolic cost. Though this ratio is affected by errors in the biomechanical model, the required force equation (equation 1) for unsteady motion does not require knowledge of drag coefficients, the major source of model error in continous swimming (Lighthill, 1971). Traditionally, estimates of metabolic cost for anaerobic activities are determined from the quantities of end product accumulated after exercise (Bennett, 1986). There are a number of problems with this method. The measurement of lactate concentrations alone are not sufficient to assess the energy state of the cell (Dobson and Hochachka, 1987). Also, handling and tissue sampling time can significantly affect tissue metabolite concentrations (Dobson and Hochachka, 1987; Schulte, 1990). This may not be so much a problem for fish exercised to exhaustion, but is more apt to influence lower levels of activity (i.e. fast-starts). Finally, the method is destructive and thus requires a large number of individuals for analysis. The alternative is to use a non-destructive method. Direct calorimetry is technically difficult whereas indirect calorimetry 7 is easily accomplished. After anaerobic exercise, animals increase oxygen consumption above resting. This excess post-exercise consumption (EPOC) was originally refered to as oxygen debt and was hypothesised to represent the energy required to metabolise lactate. More recent evidence shows a fast and a slow phase of EPOC where the fast phase is thought responsible for ATP, CrP and oxygen replenishment and the slow phase for lactate metabolism (Gaesser and Brooks, 1984). A test of the oxygen debt hypothesis in trout after exhaustive exercise clearly shows a slow and fast recovery phase (Scarabello, 1989). Given our present knowledge of the role of oxygen debt in recovery from anaerobic exercise, oxygen debt measurements are potentially a valuable, non-destructuve method for assessment of partial costs of activity. Morphological and Kinematic Constraints Maximum performance requires not only maximum power production by muscles, but maximum use of that power for the production of useful force. Weihs (1973) predicts from his model that thrust is maximized when the lateral velocities of the caudal region are high and the angle of attack; low. However, these predictions have never been experimentally . tested. Morphological characteristics of pike are considered favorable for high thrust during fast-starts due to a large surface area caudally and a high percentage of body musculature. Harper and Blake (1990a) reported the superior acceleration ability of northern pike, Esox lucius, over trout, Oncorynchus mykiss, during fast-starts. In addition, intraspecific comparisons of unsteady swimming performance for 8 coho salmon, Oncorynchus kisutch (Taylor and McPhail, 1985) and the three spined stickleback, Gasterosteus aculeatus (Taylor and McPhail, 1986), show that fish populations with greater body depth and caudal fin depth are capable of greater maximum and average velocities. Webb (1977) provides the only direct evidence that caudal surface area influences fast-start ability. Performance was reduced in trout after amputation of caudal fin lobes but not after removal of centrally placed median fins. Though the caudally placed anal and dorsal fins of pike are assumed to increase fast-start performance, the contribution of these fins td thrust has never been determined. Physiological Constraints Fast-starts are frequently assumed to be physiologically limited by their power requirements (e.g. Weihs, 1973). Maximum power output of muscles may limit acceleration rates or the duration that a particular power output can be maintained may limit average velocities. Muscle power output is limited by the rate of energy supply from ATP hydrolysis, replenishment of CrP and ATP pools by anaerobic glycolysis and the intrinsic maximum power of muscle (Bennett, 1980; Hochachka and Somero, 1984). The latter varies depending on load (Hill, 1964). Duration of a particular power output depends on the size of energy pools (Bennett, 1986). An alternative viewpoint expressed in the literature is that locomotory performance is limited by maximum stress of muscles and not maximum power output. Early studies of maximum swimming performance in fish and mammals assume performance is limited by 9 maximum muscle power (Gray, 1936). Though theory and observation did not match, differences were later resolved by using more appropriate drag coefficients and values for maximum power (Blake, 1983). Blake (1983) also shows burst swimming speeds are within limits set by maximum power of muscles. Daniel and Webb (1987) predict maximum speed should decrease with fish size assuming muscle stress is limiting. Observations do not support this prediction (Webb, 1976). Daniel and Meyhofer (1989) predict optimal size and tail morphology for escape ability in carridean shrimp based on the assumption that muscle stress is limiting. However, mechanics of isolated muscle preparations shows power and stress are interdependant where maximum power output occurs at 0.3 maximum stress (Pennycuick and Rezende, 1984). As maximum power is load dependant, both muscle power and force are required to assess performance limitations of, muscle. The rate of CrP and ATP hydrolysis is 1.5 to 6 times faster than their rate of replenishment from anaerobic glycolysis (Hochachka, 1985). The duration that maximum power can be maintained is therefore limited by CrP and ATP reserves. A lower power output can be supported for a longer time period and is limited by glycogen reserves. Alternatively, intermittent maximum power output is possible for longer periods if rest periods allow time for replenishment of CrP and ATP pools. Muscle performance will therefore be limited by CrP and ATP pool sizes if the power required for fast-starts is greater than the power supplied from anaerobic glycolysis. 10 Ecological and Behavioural Constraints Foraging models assume surplus power or net energy gain (NEG) per unit time are maximised and yet the cost of locomotion is often ignored (Ware, 1978; 1982). Movement is energetically expensive and organisms must trade-off the cost of locomotion with encounter rate of prey (Ware, 1978). The energetic cost of prey attack may also be significant. Harper and Blake (1988) predict attack by predatory fish at maximum speed is more expensive than searching or pursuit. The significance of the cost of attack is determined when expressed as a percentage of daily maintenance costs. Puckett and Dill (1984) showed that juvenile territorial salmon expend only 0.09% of daily maintenance for each prey attack. 112 attacks per day would be required to increase daily maintenance costs by 10%. However, these fish are reported to charge 192 times in 16h (Puckett, 1983) which illustrates that the cost of attack involving acceleration for short periods of time can significantly affect the daily energy budget. Given that maintenance metabolism and activity costs consume approximately 50% of assimilated energy in non-migratory fish, a 10% increase in these costs could reduce growth or reproductive output by 20 to 30% (Kitchell, 1983). More analyses of this type are clearly needed to assess the ecological costs of high powered, short term activities. Costs of prey capture can also be expressed as a percentage of the energy content of a prey. A common argument is that the energy content of prey is so much greater than the cost of capture, the latter can be ignored (Bennett, 1986). However, when the cost of capture is expressed as a percentage of the energy 11 available for growth or reproduction rather than the energy content of prey, the cost is more apt to be important. Assimilation efficiency1 for largemouth bass, a carnivorous sedentary fish, is approximately 70% and maintenance costs consume 25 to 96% of the remainder depending on ration size (Kitchell, 1983). This leaves 3 to 50% of the energy content of prey for growth, reproduction and activity. Therefore, on low rations, an activity cost of only 3% would consume all available energy for growth or reproduction. This implies that activity costs consuming a small precentage of the energy content of prey should not be ignored. The cost of an activity can constrain behaviour in other ways. Fish exercised to exhaustion require 24 to greater than 96 hours to remove lactate from white muscle and replenish glycogen reserves (Schwalme and Mackay, 1985; Dobson and Hochachka, 1987). During the recovery period, anaerobic activity is restricted, possibly increasing a fish's vulnerability to predation or ability to capture prey. This may explain the restricted use of anaerobic activity for life or death situations or for limited durations. Duration and intensity of fast-starts may be behaviourally limited to maintain maximum scope for activity. Thesis Outline . ; In chapter 2, the Weihs model is used to predict the propulsive forces generated and the mechanical work done during an escape fast-start. The predictive power of the model is tested for estimation of performance and energetic parameters by comparison of predictions with those derived from required forces. Optimal 12 morphology and kinematic predictions of the Weihs model are evaluated for pike. In chapter 3, the Weihs model is applied to fast-starts in escape and prey capture and total mechanical power and hydrodynamic efficiency determined. Power output and muscle stress are compared with literature values for isolated muscle preparations to determine whether fast-start performance is constrained by muscle physiology. Metabolic cost of fast-starts is determined in chapter 4 by comparing excess oxygen consumption after fast-start activity with mechanical cost derived from video tapes. The slope of this relationship provides an estimate of muscle efficiency. Metabolic cost estimates are compared with literature values for biochemical reserves for pike and other fish to determine if the rate of energy supply to white muscle and energy pool sizes constrain behaviour. The required force equation is applied to a larger number of replicates in chapter 5 than in previous chapters and the hydrodynamic and muscle efficiency values previously determined incorporated to estimate metabolic cost. The purpose is to see how the cost of fast-starts varies in prey capture and escape and whether any evidence for behavioural adjustment of power output or duration exists. In addition, the cost of fast-starts are compared with maintanance costs and the energy content of prey. Literature values for prey capture success, and feeding frequency are evaluated in energetic terms and the ecological significance of the cost of prey capture discussed. In chapter 6, the results and conclusions are summarised. 13 C H A P T E R 2 M E C H A N I C S OF T H E STARTLE RESPONSE IN T H E N O R T H E R N P IKE , Esox lucius INTRODUCTION Lighthill's (1971) large amplitude theory and its use by Weihs (1973) for fish fast-starts together provide a theoretical basis for determining the propulsive forces and mechanical work done during a fast-start. Before these models can be used to estimate fast-start energetics, the accuracy of model predictions for the experimental system used here must be evaluated.. In order to calculate propulsive forces, quantification of angles and velocities of all body sections is required (Weihs, 1973). In this way, the contribution of each body section to thrust can be evaluated and the contribution of median fins to thrust quantified. Though hydrodynamic theory predicts that depth of section, angle of attack and lateral velocity determine thrust, the relative contribution of each body section to thrust can only be determined by incorporation of observed kinematic parameters from high speed film records into the model. The Weihs model sums the contribution of lift and acceleration forces to thrust. High acceleration rates and a large angle of attack of propulsive sections favors large lift and acceleration forces and is optimal for maximum thrust (Weihs, 1973). However when sections decelerate or velocity is constant, acceleration forces are negative or zero and thrust is sub optimal. Similarly, 14 11 when angle of attack of propulsive sections is small, thrust is low. Due to the motion of the caudal fin during fast-start swimming, variation in velocity and angle of attack of propulsive sections is a natural consequence and optimal conditions for maximum thrust can not always be maintained. A previous description of how lift and acceleration forces interact is reported for fish turning (Weihs, 1972) but not for fast-starts. Three issues are addressed here. (1) The accuracy of the Weihs (1973) model for fastrstarts (at optimal film speeds and magnification for which analytical error is minimized, Harper and Blake, 1989a,£) in predicting eight performance parameters; total displacement, average velocity, maximum velocity, final velocity, average acceleration, maximum acceleration, maximum force and total work done. (2) The contribution of acceleration and lift forces to total thrust. (3) The relative contribution of caudal, dorsal and anal fins to total thrust. 15 MATERIALS AND METHODS Fish Thirty Northern pike, Esox lucius, (35-45 cms, 300-500g) were seined from Babtiste Lake in the Athabasca drainage system 200 km north of Edmonton, Alberta, Canada. Fish were flown to Vancouver, B.C. within 6 hours of collection and placed in 10001 holding tanks at the University of British Columbia. Tanks were supplied with dechlorinated tap water at 5 1/min and constant aeration. A one month acclimation period was allowed before experimentation began. Fish were fed every two to three days. Temperature was maintained at 10 to 14°C. Experimental Procedure •'• Fish were brought into the laboratory 24 hours before experimentation and placed in an experimental arena, a 122 x 245 x 47cm tank. A mirror angled at 45° ran the length of the tank and provided an overhead view of the entire tank for filming. A two centimeter grid was placed on the bottom of the tank for a film scale reference. The arena was provided with the same dechlorinated tap water as the holding facilities at a rate of 1-2 1/min and temperature was maintained to within 1-2°C of the holding tank (10-14°C). The experimental arena was illuminated with 2 Berkey 800 Watt beams which were switched on directly before filming. A 16mm high speed cine camera (LOCAM model 51-0002) was used with Kodak 7250 film at 250 Hz. A C-type fast-start was induced by the rapid introduction of a meter stick vertically into the water and within 16 20cm of the fish's head. The fish responded by swimming away from the stick. The camera was switched on 1-2 seconds before the fast-start was induced so that it was up to speed when the event was filmed. The camera was positioned such that the fish was approximately 1/3 to 1/2 the diagonal of the total film frame to minimize digitizing error (Harper and Blake, 198%) and include the entire fish within each frame throughout the fast-start. Fish were allowed to rest for 30 minutes to one hour after 3 to 5 successive fast-starts. The time interval between fast-starts was only 2-3 seconds but fish showed no signs of fatigue. No more than three experimental trials were conducted within a day. After 30 to 50 fast-starts were induced, the fish was anesthetized with a 5% solution of MS222, total length measured and weight taken on a beam balance to the nearest 0.1 gram. This procedure was repeated for five fish. Film Analysis Film sequences were viewed on an image analyzer (Photographic Analysis Limited Projection Analysis Unit, ZAE 76) connected directly to a computer. Three sequences from a total of 76 fast-starts showing minimal interference from tank walls and no disturbance of the water surface were chosen for further analysis. The fish image on the analyzer was divided into nine sections (Fig. la). The caudal fin, the portion of the body with the dorsal and anal fins and the head region each formed a section. Also, a section division occurred at the center of mass. Other divisions were chosen to form sections of similar length (0.11 ± 0.04L [X ± " 17 Figure 1: A) Side view of a .Northern pike, Esox lucius showing the positions of the body : sections 1-9. The star indicates the center of mass location along the length of the fish's body. B) Diagram showing the velocity vectors and angles for a propulsive section and the velocity vector, Vcm, for the for the fish's center of mass, tangent to the X-axis; V is the velocity vector for a propulsive section where w is the component perpendicular to the backbone of that section and u is the tangent component. In the magnified portion of the diagram, dl is the length of the propulsive section. The velocity vector V can also be described by vector components dy/dt and dx/dt. The iangle, 6, is that angle subtended by the vector V and u, and the angle, a, that angle subtended by the tangent to the propulsive section and the X-axis. 18 19 ls.d.]). The mid-point of' each division was digitized (i.e. x,y coordinates determined) for each frame during a fast-start until the end of the second tail flip (stage 2). C-type fast-starts involve three stages, a preparatory stage (stage 1), a propulsive stage (stage 2) and a variable third stage. Performance of fast-starts from film are commonly determined to the end of stage 2 (Weihs, 1973; Webb, 1975a; 1977; 1978ft). The coordinates were stored on computer disc for subsequent analysis. Calculations The Weihs (1973) model assumes that thrust in the direction of motion (F ) is generated by the acceleration of added mass (volume of water influenced by a propulsive section) and lift forces generated by median fins (caudal, dorsal and anal). F M = d/dt ^ row (dy/dl) dl + ^ 1/2 p S. V* CLe.e. (2) where ma is added mass, w is the velocity vector for a propulsive section perpendicular to the fish's backbone, dy/dl is the sine of the angle between the propulsive section and the fish's direction of motion (Fig. lb), dl is the length of the propulsive section and L is total fish length. In the second term on the r.h.s., p is water density (* lgm/cm3 for fresh water), S. is sectional surface area, V. is its absolute velocity, C LQ. is the rate of change of lift coefficient with angle of attack, 0., and k is the total i number of fins. 9. describes the angle between the fin section (i) 20 and its velocity vector, V. (Fig. lb). All velocities are relative to the background grid. Lighthill (1975) defines added mass as m = 1/4 S2TU p (3) where s is the depth of a propulsive section and {3 is a shape factor (* 1 for all cross-sectional shapes of pike; see Lighthill, 1970). The perpendicular velocity vector, w, was calculated by Lighthill (1971) for a continuously swimming fish in a straight line. The direction of fish's motion defines the x-axis and the water far from the fish is at rest, dy dx _ dx dy ( 4 ) dl al dl al w where dy/dt and dx/dt are velocity vectors for a propulsive section normal and tangential to the fish's direction of motion and dy/dl and dx/dl are the sine and cosine of that sections angle relative to the direction of motion (Fig. lb). The rate of change of lift coefficient relative to the angle of attack, C L Q, for steady motion is given by C - rc..AR (5) S,8 ~ 1 + 0.5 AR w (Robinson and Laurmann, 1956) where AR is the aspect ratio of a fin (AR=span2/fin area). The aspect ratios for pike median fins are 21 1.53, 1.27 and 1.83 for anal, dorsal and caudal fins respectively. The motion of fins during a fast-start is highly unsteady. The reduced frequency parameter (a = col/U where col is the angular velocity of the fin and U is the fish's velocity) provides a relative measure of the contribution of unsteady forces. An average value of 0.4 for o was calculated for pike fast-starts which indicates C L Q is 70% of the steady motion value from equation 5 (see figure lb in Daniel and Webb, 1987). C L Q for anal, dorsal and caudal fins derived from equation 5 and after correction for unsteady motion are 1.77, 1.59 and 1.95 respectively. Estimates of displacement, velocity and acceleration are calculated from the model (equation 2) and required forces (F). The latter are calculated from F • = ma , where a is the R v acceleration of the fish's center of mass and m is the virtual mass of the fish (body mass + longitudinal added mass). Estimates of acceleration, predicted from the model and required forces, are calculated as a = F/m where F = F or F . Velocities and v R M displacements are derived from acceleration estimates, where v. = v.4 + [(a. j+a.)^ ] At (6) and d. = d.mi + | [(v. +v.)/2] At (7) Model estimates are compared with those derived from required forces rather than with observed displacements or velocities to 22 ensure both estimates are subject to the same smoothing errors. The minimum smoothing necessary required a sequence of 2 point followed by 3 point averaging for each of the two differentiations involved. Smoothing results in underestimation of performance parameters for both model estimates and estimates derived from required forces. Webb (1982ft) provides the only estimate of longitudinal added mass (m^ for a fast-starting fish. Based on experiments with trout, m} = 20% of the total fish mass. Total work done (W) is calculated from required forces or model estimates of propulsive forces where n W=XF.d., n is number of frames to the end of stage 2, d is the j j j displacement of the fish's center of mass and F is the force (FR 23 RESULTS Kinematics The kinematic characteristics of the three fast-starts analyzed for a single fish (0.41m total length, 0.398 kg) are similar, and only one is described in detail (C-start #1). The bending of the fish's body follows the pattern described by Weihs (1973) for a trout C-start. Starting from a stretched straight position, the fish bends into a C-shape within 0.06s (preparatory stage, stage 1; Table 1). A change in orientation occurs during this stage. A propulsive stage (stage 2) follows, forming a C-shape in the opposite direction. The direction of motion is constant throughout the propulsive stage with little lateral movement of the head region (Fig. 2). The duration of stage 2 is the same as stage 1 for C-start #1 (0.06s, Table 1). According to Weihs (1973), large dy/dl=sin a (where a = the angle of a body section relative to the velocity vector of the fish's center of mass [CM]; Fig. lb) favors thrust efficiency (proportion of total thrust in the direction of motion of the fish's center of mass). The angle a is initially 90° (dyldl^l', Fig. 3) for all sections. This is due to the lateral displacement of the center of mass during C-formation in stage 1 (Fig. 2). By the end of stage 1/ a is again close to 90° (i.e. dy/dl = -1) for sections 1-4 (Fig. 3a,b). During stage 2, a large angle of attack is maintained (dy/dl = 0.8 to 1.0; a = 75-90°) at posterior sections (1-4). The more posterior the section position relative to the center of mass, the closer a is to 90° and the longer large angles are maintained (Fig. 3a,b). A high a directs thrust from the 24 TABLE 1: Kinematic c h a r a c t e r i s t i c s of three C-starts. C-START #1 C-START #2 C-START #3 TURNING ANGLEa degrees (radians) 29 (0.50) 65 (1.14) 115 (2.01) DURATION 0F b STAGE 1 STAGE 2 ( 0.060 0.060 0.068 0.064 0.064 0.072 aThe angle between the i n i t i a l and f i n a l o r i e n t a t i o n of the f i s h over the duration of a " f a s t - s t a r t terminating at the end of stage 2. btime zero i s the begining of the C bend from a stretched-straight p o s i t i o n . 25 Figure 2: Kinematics of Esox lucius where each line represents a tracing of the fish's backbone at 0.012s intervals. The numbers mark the head and tail of subsequent tracings. The filled circles mark the center of mass on the fish's backbone and the arrows are at the head. 26 Figure 3: The relationship between the angle of each section (dy/dl = sin(oc)) and time. The arrows indicate end of stage 1 and 2 respectively. A) Sections 1,2,3. B) Sections 4,5,6. C) Sections 7,8,9. Error bar in A) shows measurement error range. 28 — SECT 1 (0.00-0.14L) SECT 2 (0.H-0.23L) - SECT 3 (0.23-0.321) c75 — SECT 4 (0.32-0.42L) SECT 5 (0.42-0.511} - SECT 6 C0.51-0.60L; 0.5 0.0 -1.0 1 <-»'"* \ . \ y . \ ^ V • — SECT 7 (0.60 ** • • • SECT 6 (0.71 - SECT 9 (0.80 0.00 0.06 0.12 1 TIME T S1 S2 0.18 29 acceleration of added mass in the direction of motion favoring high propulsive efficiency and maximizing thrust (Weihs, 1973). Sections anterior to the center of mass (7, 8 and 9) show large angles only during C-formation in stage 1 and smaller angles in stage 2. The lateral velocities (dy/dt; Fig. 4) of the anterior sections (7-9) are maximal during bending in stage 1. The greatest lateral velocities occur in the caudal sections (1-3) during the propulsive stage (peak values of 3.0 to 4.0 m/s; Fig. 4). Sections closer to the center of mass have smaller lateral velocities and shorter durations of maximum velocities (Fig. 4). For the posterior sections (1-3) perpendicular velocities w (Fig. 5) are lower than lateral velocities dy/dt (Fig. 4), whereas for more central sections (4-6) w and dy/dt are similar (Figs. 4,5). This occurs when dxldl is close to 1 (i.e. dy/dl=0) and the body section is perpendicular to its direction of motion. Under these conditions, w has the same direction of motion as dy/dt (perpendicular to the direction of motion of the fish's center of mass) and therefore makes no contribution to thrust in the useful direction. Therefore, central sections do not have favorable angles for useful thrust despite high perpendicular velocities (w). According to Weihs (1973), dy/dt and dy/dl must both be large for thrust to be in the direction of motion (i.e. useful direction), which is the case for posterior sections (Figs. 3,4). But, perpendicular velocities (w) are low relative to lateral velocities (dy/dt) when section angles (a) are large. Even so, posterior sections (1-3) still have higher maximum perpendicular velocities than more central ones (4-6). In addition, maximum perpendicular 30 Figure 4: The change in lateral velocity, dy/dt, of each section with time. The arrows indicate the end of stage 1 and 2 respectively. A) Sections 1,2,3. B) Sections 4,5,6. C) Sections 7,8,9. Error bar in A) shows measurement error range. 31 4.0n 2.0-0.0--2.0--4.0-\ E 4.0-j m 2.0-0.0-o -2.0-§ -4.0-4.0-1 2.0-0.0--2.0--4.0-32> SECT 1 (0.00-0.14Q SECT2(0.14-0.23L) SECT 3(0^3-0.321) — SECT 4 (0.32-0.42L) • • • SECTS (0.42-0.51 L) - • SECT 6 (0.51 -0.60L) • * «s N — SECT 7 (0.60-0.71 L) • • • SECT 8 C0.71-0.80L' - SECT 8 (0.60-1.00L, 0.00 0.06 0.12 | TIME J S1 S2 0.18 32 Figure 5: The change in the velocity, w (vector perpendicular to each section) with time for sections A) 1,2 and 3 B) 4,5 and 6 and C) 7,8 and 9. Error bar in A) shows measurement error. 33 3.0J 34 velocities (w) occur during the propulsive stage for central (4-6) and posterior (1-3) sections, whereas anterior sections (7-9) show peak velocities during turning (stage 1; Fig. 5). Again, the duration of maximum velocities increases posteriorly from the center of mass. The contribution of fish body sections to the momentum of added mass (momentum=mw[dy/d/]„7>) in the opposite direction to the fish's motion is dominated by the posterior four sections during the propulsive stage (1-4; Fig. 6). The combination of large added mass (Fig. 7) and high w and a results in posterior sections contributing the most to momentum. For the caudal peduncle, w and a are high. However, ma is low and this results in a small contribution to the total momentum of this area. Sections 1 and 3 where the fins are located contribute most to the total momentum. The caudal fin has characteristics more favorable for lift than section 3 containing the dorsal and anal fins. From equation 1, lift varies directly with fin velocity and surface area. Velocity (V) and angle (0) for the caudal fin are larger and maintained longer than the dorsal and anal fins (Fig. 8). The surface area of the caudal fin (3.52 x 10"3m2) is also larger than the combined surface area of the dorsal and anal fins (2.72 x 10"3m2). ' t ] Forces Figure 9 shows two positive thrust peaks, a minor peak in stage 1 followed by a major peak ( maximum of 59.7 N) early in stage 2, and a cycle from positive to negative forces within stage 35 Figure 6: The change of momentum in the direction of motion (in Newton, seconds) with time for sections A) 1,2 and 3 B) sections 4,5 and 6 and C) 7, 8 and 9. Error bar in A) shows measurement error range. 36 -0.50J CO 0.50-1 cn 0.25 0.00 :-0.25 0.50 •» B SECT 1 (0.00-0.14L) SECT 2 (0.14—0.23L) SECT 3 (0.23-0.32L) SECT 4 (0.32-0.42L) SECT 5 (0.42-0.51 L) SECT6(0.51-0.60L) 0.50-1 C 0.25-0.00 -0.25 •0.50 0. 00 t SECT 7 (0.60-0.71 L) SECT8 (0.71-0.B0L) SECT 9 (0.60-1.00L) 0.06 0.12 TIME (s) J S1 S2 0.18 3 7 Figure 7: The distribution of added mass and body mass along length of the fish where distance is from the tail tip. 38 39 Figure 8: The change in total velocity, V, and angle of attack, 0, with time for A) caudal fin and B) dorsal-anal fin section. The solid line represents the velocity, V, and the dashed line, the angle of attack, 0. 40 A) CAUDAL FIN B) DORSAL-ANAL FINS J TIME (s) J S1 S2 4 1 Figure 9: Contribution of acceleration and lift forces to total thrust in the direction of motion. Arrows indicate beginning of stage 1 (0), end of stage 1 (I) and end of stage 2 (II). A) C-start #1 B) C-start #2 C) C-start #3. Error bar in A) shows measurement error range. 42 43 2. The result is a large positive acceleration followed by an equally large deceleration during the propulsive phase. Similar total thrust patterns are found for all three fast-starts though the major positive thrust peak is bimodal rather than unimodal in the other two fast-starts. A single stage 2 peak occurs when peak thrust from sections 1 plus 3 are in phase and two peaks result when they are out of phase; section 1 forms the second peak in stage 2 and section 3 the first peak (Fig. 10). Average acceleration forces dominate during turning in stage 1, whereas average lift forces are greater during stage 2 (Table 2). During the propulsive stage (stage 2) average acceleration forces are small relative to lift forces in all three fast-starts. However, acceleration forces cycle from positive to negative, and the contribution of acceleration forces to positive thrust in the first half of stage 2 is similar to that of lift forces (60 ± 15% for lift and 43 ± 18% for acceleration forces; Table 2). Also, maximum acceleration forces are either the same as or greater than maximum lift forces (Fig. 9). Peak lift force lags behind peak acceleration forces (Fig. 9). Positive lift forces overlap with negative acceleration forces and reduce the magnitude of negative total thrust in the second half of stage 2 (Fig. 9). Lift forces constitute 48 to 77% of total thrust i • during the positive portion of stage 2 (Table 2). The thrust-time sequence for total thrust is similar to that for section 1 and for section 1 plus 3 (Fig. 10). The average total thrust for stage 2 is generally less than that for section 1 or sections 1 plus 3 (Table 2). Section 1 contributes 81 to 93 % to 44 Figure 10: Contribution of the caudal fin (sect. 1) and the combined caudal fin and dorsal-anal fins (sect. 1 and 3) to total thrust force (all sections). Arrows indicate beginning of stage 1(0), end of stage 1 (I) and end of stage 2 (II). A) C-start #1 B) C-start #2 C) C-start #3. Error bar in A) shows measurement error range. 45 60-30< 0 - 3 0 - 6 0 J S1 1 S2 - - SECT 1 • • • SECT 1 & 3 TOTAL FORCE 0.00 0.06 0.12 TIME (s) 0.18 46 TABLE 2: Average force contributions from lift and acceleration forces, from section 1 and sections 1 plus 3 and from all body sections with (total) and without dorsal and anal fins. 47 LIFT ACCELERATION SECT 1 SECT 1&3 TOTAL-FINS3 TOTAL C-START #1 STAGE 1 STAGE 2 +STAGE 2 b -STAGE 2 b -2.14 (-54) 18.83 (160) 31.00 (77) 10.71 (-150) 6.14 ; : < 1 5 4 > -7.03 (-60) 9.32 , (23) -17.94 (248) -5.66 (-141) 11.68 (99) 29.29 (73) -4.15 (57) 1.52 (38) 14.27 (121) 43.00 (107) -6.73 (93) -1.67 (-42) 7.63 (65) 29.23 (72) -6.77 (93) 4.00 11.79 40.32 -7.22 C-START #2 STAGE 1 STAGE 2 +STAGE 2 -STAGE 2 1.49 (17) 10.69 (c) 15.12 (48) -2.42 (7) 7.41 (83) -11.05 (c) 18.47 (59) -30.70 (85) 3.28 (37) 3.79 (d) 23.88 (76) -27.76 (77) 4.29 (48) 4.68 (d) 36.86 (118) -31.67 (88) 1.78 (20) -5.38 19.15 (61) -29.75 (83) 8.90 -0.36 31.33 -35.97 C-START #3 STAGE 1 STAGE 2 +STAGE 2 -STAGE 2 -1.15 (-18) 19.66 (158) 23.69 (54) 6.52 (-21) : 7.50 (118) -7.22 (-58) 20.10 (46) -37.64 (121) -2.68 (-42) 16.03 (129) 36.46 (83) 24.37 (78) 2.10 (33) 17 .24-(139) ,46.59 (106) -28.17 (91) 2.90 (46) 10.31 (83) 36.31 (83) -30.97 (99.5) 6.35 12.44 43.79 -31.12 48 NOTE: Average force in Newtons (% of total). "Calculated using the original kinematic pattern of an intact fish but with estimates for anal and dorsal fins removed. bAverage forces for the positive (+ stage 2) and negative phases (-stage 2) of the total thrust curve in stage 2. °Total force is very small as lift and acceleration forces cancel. Percentage of total would not be very informative in this case. d Again, the total force is too small to justify expressing thrust from sections 1 and 3 as a precentage of! total thrust. The average contribution of forces from sections 1 and 3 are 3 to 4 Newtons higher than Total average forces which is similar to the other two C-starts. 49 the average thrust from sections 1 plus 3. Thrust cycles from positive to negative in stages 1 and 2. Sections 1 and 3 explain 110 % of positive total thrust and section 1 explains 77 % . During the negative total thrust, sections 1 and 3 explain 91 % of the average and section 1 explains 71 % . Therefore, during the dominant thrust phase in stage 2, the caudal fin (section 1) contributes approximately 70 % of the positive thrust contribution of the caudal fin (section 1) and the section containing the dorsal and anal fin (section 3). The anal and dorsal fins (TOTAL - [TOTAL - FINS]) contribute on average 16 and 26% to total thrust during stages 1 and 2 and 28% to positive total thrust during stage 2 (Table 2). Model estimates for performance parameters (predicted values) are compared with those derived from required forces (expected values). All parameters were determined to the end of stage 2. Six of eight performance parameters were predicted within 4 to 22% (Table 3). The two exceptions were useful work (9-31%) and final velocities (5-75%). 50 TABLE 3: Predicted performance parameters (A) derived from the model (equation 1) are compared with expected performance parameters (B) derived from required forces f o r three C-starts. C-START #1 C-START #2 C-START #3 TOTAL , % (m) A .152 (17) .142 (14) .202 (15) DISTANCE B .127 .163 .232 AVERAGE , . , (m/s) A 1.23 (17) 1.08 (15) 1.48 (15) VELOCITY B 1.02 1.24 1.70 MAXIMUM , . , (m/s) A 2.40 (5) 1.90 (75) 3.19 (47) VELOCITY B 2.51 3.32 4.68 FINAL . . , (m/s) A 1.93 (7) 1.60 (17) 3.19 (15) VELOCITY B 2.06 - • 1.32 2.71 AVERAGE , . 2 , (m/s ) A 15.63 (8) 12.09 (19) 24.65 (16) ACCELERATION B 16.83 9.81 20.80 MAXIMUM , . 2 , (m/s ) A 160.98 (19) 133.14 (4) 167 .26 (11) ACCELERATION B 129.88 138.84 185.69 MAXIMUM , , (N) A 69.7 (14) 57.6, (15) 72.4 (22) FORCE B 59.7 66.2 88.6 WORK (Joules) A 6.31 (31) 6.49 (18) 8.47 (9) DONE B 4.37 5.34 9.19 NOTE: Values i n parentheses are percent differences between predicted and expected values;; ;i 51 DISCUSSION Sources of Error ' ,  i Six of eight performance parameters predicted by the Weihs (1973) model agree with expected values to within 4 - 22%. This is the first complete test of this model for parameters dependant on instantaneous forces or average forces. Weihs (1973) compared model predictions and observed values for maximum acceleration in stage 1 (12% difference) and average acceleration in stage 2 (24% difference) for a single fast-start sequence filmed . at 64 Hz. Though we are unable to show a significant improvement of the difference between . model predictions and expected performance parameters at 250 Hz, a similar error is demonstrated for six additional performance parameters and the variability in these differences is shown for three C-starts. Expected performance parameters are also derived from film data and are subject to the same digitizing errors as model parameters. Therefore, independent of their differences, both predicted and expected maximum acceleration rates may be more accurate at 250 Hz in this study than at 64 Hz in the Weihs (1973) study. Harper and Blake (1989ft) tested the accuracy of maximum acceleration rate estimates for fish fast-starts by comparing estimates from film records with accelerometry measurements and found a 30% discrepancy at film speeds of 250 Hz. At 50 Hz, differences between film and accelerometer derived estimates were as high as 75% . Both predicted and expected parameter estimates are subject to digitizing error which typically results in under estimation of 52 true performance parameters (Harper and Blake, 1989ft). However, digitizing errors may be lower for parameters predicted from the model because lateral displacements of propulsive sections are much greater than' for the center of mass and digitizing error is inversely proportional to the observed displacement. In contrast, the integration of momentum of added mass in equation 2 involves the summation of errors for velocity and angle estimates over nine sections. The assumption that fins act like flat plates and do not flex is unlikely (Bainbridge, 1963;. McCutcheon, 1970) and this is a potential source of error for model predictions. The magnitude of this error would be difficult to assess. The longitudinal added mass used in calculating the required force is assumed to be 0.2 based on experimentally derived values for fast-starts by trout (Webb, 1982a). Given the similarity in fineness ratio and fast-start kinematics between pike and trout (Harper and Blake, 1990a), any error in this assumption is expected to be minimal. Though no other values for longitudinal added mass have been determined for a fish swimming unsteadily, added mass coefficients for fish assuming a rigid body range from 0.05 to 0.1 and suggest a 5% error in required force estimates at a maximum (see Webb, 1982a). \ , The difference between expected and predicted estimates of most performance parameters are within , 22% and none are significantly different (t-test, p<0.05). This suggests the summation of acceleration and lift forces accounts for the forces required to propel a pike during a fast-start. 53 The forces described by the model are resolved for the direction of motion of the fish's center of mass and therefore account for the linear thrust forces only. Rotation of the body and rotational motion of the center of mass during a C-start are accomplished by acceleration forces, lift forces and possibly drag, but lateral to the fish's direction of motion. Given that expected performance parameters are derived from required forces for linear displacement of the center of mass, predicted and expected forces and the performance parameters derived from them, are based on linear motion only. Contribution of Lift and Acceleration Forces The present analysis demonstrates the importance of lift during highly unsteady motion. Drag may also become important at high angles of attack, but due to the lateral direction of motion of the propulsive sections, the drag force will also act laterally and contribute little to thrust in the forward direction. For other unsteady propulsive systems, drag is commonly insignificant relative to acceleration forces (Blake, 1986; Gal and Blake, 1988; Daniel and Meyhofer, 1989). The highly unsteady motion of fast-starts implies that inertial forces should dominate, yet lift forces are the major contributor to total force averaged over the fast-start (Table 2). The large positive acceleration forces observed during the first half of the propulsive stage (stage 2) are equal in magnitude to maximum and average lift forces, but, due to the equally large negative acceleration forces in the second half of stage 2, 54 acceleration forces averaged for stage 2 are small or negative (Table 2; Fig. 9) and contribute little to average total force. In contrast, lift forces are always positive. For acceleration forces to remain positive and contribute maximally to useful thrust, propulsive elements should maintain a small angle of attack (relative to their direction of motion) during acceleration whilst maintaining values greater than or equal to 90° during deceleration (Daniel, 1984). For a fish or shrimp whose main purpose is to remove itself from the attack trajectory of an approaching predator, displacement in a short time period is more important than average velocity (Daniel and Meyhofer, 1989). Acceleration forces in this context make a significant contribution (43% of positive total forces) to the displacement of the fish during a fast-start. Accelerative forces occur sooner than lift forces and therefore result in earlier movement away from the fish's initial location and the likely path of a predator. Though negative acceleration forces cause deceleration during the latter half of the propulsive phase, the fish would have, effectively removed itself from the attack path of a predator by this time, and further displacement may not be important. The prediction from the Weihs (1973) model that for thrust to be maximal, the angle of attack of propulsive elements should be small applies to element acceleration. During decelleration, a small angle of attack results in large negative forces. However, positive lift forces counter negative acceleration forces as long as element velocities are high. Therefore, maintainance of a sharp 55 angle of attack during element decelleration benefits lift production and implies favourable and possibly optimal kinematics. Contribution of Caudal, Dorsal and Anal Fins to Total Thrust Thrust from the caudal fin and the section which contains the dorsal and anal fins account for > 88% of total thrust in the propulsive stage. The combination of higher velocities and angles (a), and larger depths in these sections all contribute to higher thrust. Of these two sections, the caudal fin contributes the most to thrust making up 81 to 93% of the total thrust and 64 to 78% of positive thrust from both sections combined. The posterior placement of dorsal and anal fins in northern pike contributes 26% of total thrust and 28% of positive thrust. The fins increase the depth of section and therefore the added mass of that section, and also generate lift forces (Weihs, 1973). Webb (1978a) found for trout that caudally placed dorsal and anal fins contribute approximately 27 % to total thrust. These results are very similar considering differences in fin shape and size. The estimates of anal and dorsal fin thrust assume these fins have the same kinematics as the fish's backbone. Though films were not sufficiently clear to record the kinematics of dorsal and anal fins, they were observed to flex resulting in greater angles relative to the the fish's direction of motion (a) than the fish's backbone. Greater a will result in lower forces produced by these fins but a greater fraction of these forces will be in the useful direction and consequently thrust force estimates of the fins based on the kinematics of the backbone are probably accurate. 56 The posterior placement of the dorsal and anal fins may serve other functions in addition to thrust enhancement. The dorsal and anal fins contribute to thrust during the propulsive stage sooner than the caudal fin and result in acceleration beginning earlier. This would benefit predator escape as well as prey capture. Dorsal and anal fins are capable of slow undulations and are important in very slow locomotion and orientation (personal observation). In addition, the posterior location of these fins may be advantageous for maneuvering towards a prey without startling it. And lastly, dorsal and anal fins may be important in balancing side forces during prey capture swhen no turn occurs in stage one and direction of motion is maintained (S-start). The placement of dorsal and anal fins only partially explains the greater accelerative performance of pike over trout. Harper and i ' " Blake (198%) show pike accelerate 100% faster than trout, and therefore have a 100% greater required force for the same body mass. Only 26 to 28% of this is explained by the contribution of dorsal and anal fins. To account for the remaining difference between pike and trout performance, hydromechanical efficiency and power output must be considered. Though other structural and physiological features of pike contribute to useful thrust, the posterior location of dorsal and anal fins in pike does enhance thrust during fast-starts. 57 CHAPTER 3 HYDROMECHANICAL EFFICIENCY AND MECHANICAL POWER OUTPUT DURING FAST-STARTS: A COMPARISON OF C AND S-STARTS INTRODUCTION The angle of turn is a major performance difference between escape (C-type) and prey attack (S-type) fast-starts in pike. C-starts involve a sharp turn whereas in S-starts directionality is maintained (Webb, 1977; Webb and Skadsen, 1980). The formation of a C shape during escape produces unbalanced side forces and results in a turn whereas the S form used in prey attack balances side forces maintaining directionality. Webb and Skadsen (1980) show differences in the distance-time relationship for S and C-starts which suggests kinematics of S and C type fast-starts influences swimming performance. A study of hydrodynamic efficiency and mechanical power production may reveal a functional basis for the observed performance difference and the assumption that fast-starts operate at a physiological maximum can be tested. The purpose here is to (1) determine and compare hydromechanical efficiencies for C and S-starts (2) determine mechanical power output for C and S-starts and compare power requirements and maximum muscle stress estimates with known limits of muscle function. 58 MATERIALS AND METHODS The collection procedure and holding facilities are described in Chapter 2. The fish used for this part of the study ranged in length from 0.396 to 0.412 m and weight from 0.397 to 0.430 kg. Experimental Procedure The laboratory set-up and acclimation procedure are as described in Chapter 2. Both C and S-type fast-starts are filmed at 200-250 Hz for each ,fish. Individuals were induced to C-start by the rapid introduction of a meter stick within 30 cm of the fish's head and were induced to S-start by introducing goldfish prey after 72 hours of, no food. The lights and camera were turned on 1 to 2 seconds before the fast-start event to allow time for lighting conditions and the film rate to stabilize. The film records were analysed on an electronic digitiser. Ten positions along the dorsal mid-line of the fish's body at similar intervals were recorded for each frame of a fast-start event (see Chapter 2). Analysis The hydrodynamic efficiency (E) is defined as the ratio of useful power (i.e. P , power required to accelerate the fish's mass in the direction of motion) to total power (i.e. PT, the power required to accelerate the water and the fish's mass), E = PJPj- The calculation of useful power (Py = F r^j) requires knowledge of Fy, the propulsive force in the useful direction (i.e. direction of motion), and D, the displacement of the fish's center of mass. The Weihs (1973) model is used to calculate 59 propulsive forces directly (equation 2). An alternative approach is to determine the required forces (F ) given that the propulsive '' "' K. forces experienced by a fish should equal the resistive forces. For fast-starts, resistive forces are dominated by the acceleration reaction (Webb, 1982a; see equation 1). The Weihs model for is based on the same theory (Lighthill's elongate body theory) used to calculate the other terms in the efficiency equation (equation 8 is the denominator of the ratio, Py/Pj)- But, equation 1 involves fewer parameters and therefore less error accumulation. In addition, equation 1 is analytically simpler requiring determination of only one point per . if • . i • • frame; the fish's center of mass. An experimental comparison of estimates derived from these two equations are shown to be within 22% (Chapter 2). Weihs (1973) proposed that total power for fish fast-starts could be described by Lighthill's large amplitude theory (Lighthill, 1975), given by P„, = P + i/2, m w2 Ul + d/dt f1/2 m w2o7 (8) T U a 1a=0 I a 0 where U is the forward velocity of the fish. The other parameters are as described for equation 2. The first term on the r.h.s. of equation 8 describes the power required to accelerate the fish (i.e. useful power), the second term describes the kinetic energy lost in the wake arid the third term describes the power required to accelerate the added mass of water by all propulsive sections (equation 3). Equation 8 accounts for the energy required to accelerate the fish in the direction of motion (described by the 60 displacement vector of the fish's center of mass) but does not account for the power ' required to accelerate the fish body sections laterally. The latter is defined by The last two terms on the r.h.s. of equation 10 are the power required to accelerate the added mass and body mass of propulsive sections laterally. When these terms are positive, the values reflect positive work done by the fish. Negative power refers to the loss of kinetic energy (i.e. lateral deceleration of body and added mass), but may not reflect negative work done by the fish. Negative work or energy gain occurs when energy is stored elastically. Experiments on fish bone and connective tissues and on muscle show these tissues store little energy (Hebrank, 1982; Tidball and Daniel, 1986). To realize lateral deceleration of body sections requires either positive work by the fish or no work. The latter is true if we assume lateral deceleration occurs due to passive resistance by the surrounding water and resistive forces within the fish. Both active and passive deceleration are considered here, where active deceleration is calculated by taking the absolute value of the second and third term of equation 10 and (9) This term is added to equation 8 and (10) 61 passive deceleration by summing only the positive values for these terms. 62 RESULTS Three C-starts and three S-starts were chosen for analysis in which no interference occured with tank walls (i.e. fish was greater than 1 BL away from tank walls). Pike consistantly responded to a startle stimulus with a C-start whereas S-starts were used for prey attacks (Fig. 11). A typical C-start involves the formation of a C body shape from a stretched straight position in stage 1 (preparatory stage), followed by a rapid tail flip to form a reverse C at the end of stage 2 (propulsive stage). A third stage generally involves braking or coasting. In contrast, S-starts involve the formation of an S-shape at the end of stage 1 (preparatory stage) and a reverse S by the end of stage 2 (propulsive stage). Swimming continues until prey capture and involves 1 to 4 additional tail flips. Fast-starts have previously been described in three stages where the third stage involves coasting or continued swimming (Weihs, 1973; Webb and Skadsen, 1980). For most S-starts, pike continue to accelerate beyond stage 2 and thus each subsequent tail flip (1/2 a tail beat cycle) is also considered a stage. Pike never continued swimming beyond the initial position of the prey which required 1.5 to 3 tail beats (3 to 6 tail flips) for the three S-starts analyzed here. Maximum velocities (2.3 to 2.8 m/s) and durations (0.08 to 0.13s) are similar for all three C-starts (Fig- 12). By comparison, S- start performance is more variable where maximum velocities range from 1.7. to 3.4 m/s and durations from 0.075 to 0.19s. C-starts show a more rapid initial acceleration rate than S-starts but, unlike S-starts, do not continue to accelerate after the end of stage 2. Therefore, greater maximum velocities are 63 Figure 11: Kinematics of an S-start. Each line defines the backbone of the fish on which the head ( • ) and center of mass of the stretched-straight fish ( # ) are marked. The numbers identify the position of the fish at 0.015s intervals. 64 3 0 c m 65 Figure 12: Velocity profiles of pike for three C-starts and three S-starts. Error bars show measurement error range. 66 4.0 CO 2.0+ O LU • C—START #1 .. O C-START#2 A C-START #3 • — i 1 — — i — 0.000 0.050 0.100 0.150 0.200 TIME (s) ^ 4 . 0 CO \ 3 . 0 ^2.0-F o bJ 0.0 • S-START #1 O S-START #2 A S-START #3 -1.0 A A A A A A A A A - « A A A A ^ A A * A A , I 0.000 0.050 0.100 0.150 0.200 TIME (s) 67 realized by some S-starts over C-starts, despite a lower acceleration rate. Maximum lateral and perpendicular velocities of the caudal fin are greater on average for C-starts than S-starts (74 and 77% respectively; Table 4). Both C and S-starts show a consistant increase in lateral and perpendicular velocities from stages 1 to 2 with the exception of lateral velocities for S-start #2. The maximum angle of attack (the angle of a fish section relative to the velocity vector of the fish's center of mass) for the caudal fin was 126% greater for C-starts than S-starts. The largest maximum angles occur in stage 2 for C-starts and stage 3 for S-starts (Table 4). Maximum forces in the direction of motion are .1 2.8 to 8.7 times greater in stage 2 than stage 1, averaging 17.6N in stage 1 and 71.5N in stage 2. A comparison of forces by stage between C and S-starts shows maximum forces in the direction of motion are not significantly different in stage 1 (averaging 16. IN for S-starts versus 17.6N for C-starts), but are significantly lower for S-starts in stage 2 (averaging 45.8N compared to 71.5N for C-starts; p<0.01, t-test). However, the greatest maximum force for an S-start (stage 3 of S-start #3) exceeds that for a C-start by 27%. A comparison of two useful power (i.e. power used to accelerate the fish) estimates where useful force is derived from equations 1 or equation 2 (Table 5) are found to not show a consistant, directional difference. However, differences between i these two useful power estimates range from 14 to 31% for the six fast-starts analyzed here. Power output values, assuming deceleration of propulsors 68 Table 4: Maximum v e l o c i t i e s , angles and forces f o r the dominant propulsive element, the caudal f i n . The l a t e r a l v e l o c i t y , dy/dt, refers to v e l o c i t y of the caudal f i n l a t e r a l to the f i s h ' s d i r e c t i o n of motion and perpendicular v e l o c i t y , w, refers to the v e l o c i t y of the caudal f i n perpendicular to the f i n ' s long axis. MAXIMUM VELOCITY MAXIMUM MAXIMUM (m/s) ANGLE FORCE {degrees) (N) (dY/dT) (w) C-START #1 1 3.44 1.77 116.3 18 .7 2 .3.89 2.87 142.8 59.7 C-START #2 1 .3.84 2.38 116.1 24.0 2 5.92 4.66 166.7 66.2 C-START #3 1 3.38 1.24 117 . 9 10.2 2 6.25 4.41 .165.8 88.6 S-START #1 1 1.15 0.75 24.6 2.9 2 3.56 1.60 37.1 49.5 3 2.73 2.12 52.6 44.0 S-START #2 1 1.48 1.00 22.4 31.1 2 1.37 1.47 34.5 29.1 3 1.77 1.19 83.9 53.8 4 1.36 1.07 40.4 22.9 5 1.76 1.00 59.2 21.1 S-START #3 1 2.14 1.86 36.9 14.3 2 2.76 3.17 32.0 58.9 3 3.38' 2.59 73.7 112.8 4 3.14 2.26 36.6 39.9 5 3.89 2.49 43.2 56.5 6 2.73 1.69 30.5 27.2 69 Table 5: A comparison of useful power estimates for C and S a b sta r t s . Propulsive power > ^ x O. Required power = F R x U. Fish ranged i n weight from 0.397 to 0.430 kg. Propulsive Required % Propulsive Required % a b Power Power Difference Power Power Difference (Watts) (Watts) (Watts) (Watts) CI 16.9 20.1 17 SI 2.0 2.3 14 C2 17.9 13.4' 28 S2 5.6 4.1 31 C3 32.0 40.1 23 S3 24.8 20.5 19 70 requires positive work by the fish, are 12 to 37% (X = 30%) greater than values where the process is assumed passive and requires no work (Table 6). This increase in total power decreases hydrodynamic efficiency by 29 to 39% (X = 33%). Because the amount of positive work required for deceleration is unknown, the more conservative power and efficiency estimates based on the assumption that deceleration is passive are used for comparison. Total power output ranges from 12.6 to 92.3 W and total hydrodynamic efficiency varies from 16 to 39%. (Table 7). A comparison of C and S-starts shows no consistant difference for total power or efficiency. But, total hydrodynamic efficiency and total power output of C-starts are less variable than S-starts; total hydrodynamic efficiency ranges from 0.34 to 0.39 for C-starts versus 0.16 to 0.37 for S-starts and total power output ranges from 45.6 to 81.2W for C-starts versus 12.6 to 92.3W for S-starts (Table 7). Therefore, S-start efficiency and total power output can be much : lower than for C-starts. There is also a tendency for power output to increase from stage 1 to 2 for all but one fast-start (Table 7). For S-starts with greater than two stages, power output in general remains the same for stages 2 to 6. The greater variation in hydromechanical efficiency found for S-starts over C-starts is related to the number of tail beats. Figure 13 shows that efficiency increases with the number of tail beats. S-starts have lower efficiencies (0.02 to 0.19) than C-starts (0.24 to 0.44) during stages 1 and 2 (Table 7). Efficiencies for S-starts in stages 3 to 6 range from 0.24 to 0.66 i and are greater than in the first two stages. Even within stages 71 T a b l e 6: A c o m p a r i s o n o f t o t a l p o w e r o u t p u t e s t i m a t e s b a s e d o n p o s i t i v e p o w e r o n l y o r t h e a b s o l u t e v a l u e o f p o w e r . P o s i t i v e p o w e r r e f e r s t o t h e s u m m a t i o n o f t o t a l p o w e r w h e r e o n l y p o s i t i v e v a l u e s a r e i n c l u d e d f o r t h e t w o i n t e g r a l t e r m s i n e q u a t i o n 5. A b s o l u t e p o w e r r e f e r s t o t h e s u m m a t i o n o f t o t a l p o w e r w h e r e t h e a b s o l u t e v a l u e o f t h e t w o i n t e g r a l t e r m s i n e q u a t i o n 5 a r e t a k e n . F i s h r a n g e d i n w e i g h t f r o m 0.397 t o 0.430 k g . P o s i t i v e A b s o l u t e % P o s i t i v e A b s o l u t e % P o w e r P o w e r D i f f e r e n c e P o w e r P o w e r D i f f e r e n c e ( W a t t s ) ( W a t t s ) ( W a t t s ) ( W a t t s ) CI 45.6 66.5 37 SI 12.6 16.8 29 C2 52.4 74.1 34 S2 28.5 32.1 12 C3 81.2 114.9 34 S3 92.3 127.1 32 72 Table 7: Total power and hydromechanical e f f i c i e n c y values i n each stage and for the e n t i r e f a s t - s t a r t f o r C and S-starts. EFFICIENCY POWER (PU/PT) (W) C-START #1 1 0.24 32.0 2 0.44 60.1 TOTAL 0.37 45.6 C-START #2 1 0.32 62.3 2 0.36 84.5 TOTAL 0.34 73.1 C-START #3 1 0.25 39.8 2 0.44 118.0 • TOTAL 0.39 81.2 S-START #1 1 0.09 3.9 2 0.19 11.0 3 0.26 21.1 TOTAL 0.16 12.6 S-START #2 1 0.10 13.1 2 0.02 12.9 3 0.58 13.5 4 0.48 11.8 ' 5 0.66 14.1 TOTAL 0.37 15.2 S-START #3 1 0.06 36.6 2 0.12 112.0 3 0.36 97.7 4 0.24 106.7 ; 5 0.28 95.2 6 0.41 74.4 TOTAL 0.27 92.3 73 ! .1 Figure 13: The relationship between hydromechanical efficiency and fast-start kinematics for pike C and S-starts. The stage numbers refer to the end of each tail flip. Error bar shows average measurement error range. 74 7 5 differences occur. For example, hydromechanical efficiencies for S-start #3 in stages 3 to 6 are consistantly lower and average 56% less than values for S-start #2. Total power can be broken down into its component parts as described in equation 10 (Fig. 14). The power required to accelerate the fish averaged over all fast-starts is 30% of total power which is similar to the 39% required to accelerate the added mass of the propulsors (Fig. 14). Acceleration of body mass contributes a smaller but consistant amount to total power (16%) where as the loss of kinetic energy in the wake is more variable (15% ranaging from 2 to 39%). Greater variability in the percentage contribution of power terms occurs between S-starts than between C-starts. The greatest difference is the 39% loss of kinetic energy found in S-start #1 versus a 2% loss in S-start #2. 76 Figure 14: A comparison of power output for C and S-starts. The subdivisions represent the four r.h.s. terms in equation 10. Pm = P„ + 1/2 m w2 Ul + dldt r 1/2 m w2 dl T U a 'a=0 J a + dldt f 1/2 iri dyldt2 dl (10) Jo b Error bar shows average measurement error for total power. 77 DISCUSSION Sources of Error A comparison of useful power estimates in this study, where the forces for acceleration were determined from the Weihs model or the forces required to accelerate the fish's virtual mass, found no consistant difference and estimates were within 14 to 31% for both C and S starts. In chapter 2, a comparison of work estimates for an accelerating pike where the forces involved were calculated from the same two models shows a 12 to 30% difference. Similar differences were found for average and maximum acceleration rates for a trout fast-start (Weihs, 1973). Though differences between the two methods are high, the lack of a consistant difference implies that the Weihs (1973) model is representative of actual forces encountered by a fish during a fast-start. In addition, despite the 14 to 31% difference, no rationale exists to choose one method over another, and the estimate based on required forces is equally representative of the mechanical power required to propel a fish. The 14 to 31% error may in part be explained by unrealistic assumptions of the model. For example, the propulsive elements are assumed to be rigid during a fast-start when in fact they flex (Weihs, 1973). This is particularly true of the median and caudal fins which are the major contributors to total thrust in pike (Chapter 2). Errors in film analysis are also important. Harper and Blake (1989a,ft) emphasize film speed and magnification as important contributors to analytical error. According to their results, the conditions in my experimental system at 200 to 250 Hz would result 79 in a 30% underestimation of maximum acceleration rates. I argue in Chapter 2 that analytical 'errors influence propulsive and required forces differently and thus contribute to discrepancies in estimates of force, work and power output. As efficiency estimates are based on a ratio where the numerator and denominator are , !,. f. " . I ' derived from the same theory, errors would cancel for terms common to both and the resultant estimates would be less affected by analytical error. Total power estimates, however, are directly affected by analytical error and would therefore be underestimated. ! The power required to accelerate body mass of fish sections laterally during pike fast-starts averages 16% of total power. Exclusion of this component would result in the overestimation of hydrodynamic efficiency by 4%. The magnitude of the acceleration of body mass depends on the lateral acceleration rate of body and fin sections and their mass (see equation 2). Power loss occurs when kinetic energy is lost due to the deceleration of propulsive elements. The energy cost to the fish depends on whether deceleration is an active process and requires energy expenditure or passive requiring no energy cost. Including the power loss term as a positive cost or no cost results in total power output values that differs by 13 to 36% and hydrodynamic efficiency values that differ by 29 to 39%. Unfortunately, insufficient information exists to quantify the relative importance of active forces (i.e. muscle contraction) to deceleration of lateral body movements. There is some evidence to suggest both passive and active forces contribute. The fish's backbone passively resists bending and requires no energy 80 expenditure (Hebrank, 1982). Other internal structures like jr.- connective tissue and skin are expected to resist bending similarly. In contrast, j the stretching of active muscles provides resistance and requires energy expenditure (Goldspink, 1977). Hydrodynamic Efficiency Hydrodynamic efficiencies for fast-starts by pike are lower (0.16 to 0.37) on average than values for other swimming modes involving body and caudal fin undulations. The highest efficiencies reported are for continous swimming at 4 to 8 BL/s Si'-' : !< (where BL/s is the velocity of the fish normalized to the fish's length, U/L) ranging from 0.7 to 0.9 (e.g. Webb, 1975ft; 1988; Videler and Hess, 1984). McCutcheon (1977) found hydromechanical efficiency for push and coast swimming to be intermediate ranging from 0.18 to 0.7. There is, however, significant overlap in efficiencies between swimming modes (Fig. 15). Efficiency of continous swimming at low speeds (lBL/s) are 0.3 for pike and 0.46 for trout (Webb, 1988) and increase with speed. A similar positive relationship occurs for push and coast swimming. Hydromechanical efficiency for fast-starts show a similar trend. The lowest efficiencies occur in stages 1 and 2 of S-starts where the velocities attained are less than 2 BL/s. Though velocity is a variable for all swimming modes shown, the decrease in efficiency from continuous to fast-start swimming is consistant at all velocities. These results show that the more unsteady the propulsive mechanism, the lower the efficiency. 81 Figure 15: The relationship between hydromechanical efficiency and relative speed (BL/s). Data for continous swimming in pike ( A ) and trout ( A ) are from Webb (1988). Push and coast swimming data ( O ) ^ fr°m McCutcheon (1977). The fast-start data from this study are shown averaged over stages 1 and 2 (• ) for S-starts and averaged over the entire fast-start ( • ) for both C and S-starts. 82 BURST AND COAST O COWTWOUS SWIMMING 1.0 2.0 3.0 4.0 5.0 6.0 VELOCITY (BL/s) 7.0 83 Why, then, are fast-starts so expensive? The energy required to accelerate added mass is a major component of total power contributing 39% on average. For continous swimming, the time average of this component is zero where deceleration of added mass is assumed to represent an energy gain by the fish (Lighthill, 1975). The alternative; approach taken here, where deceleration of added mass is assumed to incur zero cost or a positive cost, has not been used for energetic analyses of fish continous swimming using body undulations for propulsion. However, this approach has been used in the analysis of other swimming modes (Blake, 1979; 1986). The resultant cost is positive but due to lower tail beat amplitudes and frequencies and therefore lower acceleration rates (Webb, 1988), the cost is probably lower for continous swimming than for fast-starts. The mass of water influenced by propulsive sections is a determinant of hydrodynamic efficiency (Alexander, 1983). McCutcheon (1977) concluded energy loss by the zebra danio was not due to pushing on too little water. The average water mass in the trailing edge vortex of the zebra danio was 2.64 times the body mass for stage 1 and 4.38 for stage 2. However, the added mass influenced by pike during fast-starts (where added mass is from equation 3) is only 1.2 times the body mass. This suggests the i i power lost due to pushing on a small volume of water is greater in pike. ) Energy can also be lost by accelerating water in the wrong direction. McCutcheon (1977) found this to be a major cause of the low hydromechanical efficiency of zebra danio swimming in the push-and-coast mode. For pike during C-starts, the large angles 84 maintained by the caudal region favor high thrust efficiencies (Chapter 2). The lower caudal fin angles for S-starts suggests the lower efficiencies in this swimming mode are in part due to pushing water laterally and not in the useful direction. The increase in efficiency with each stage number of a fast start parallels a declining acceleration rate. The preparatory stage involves very low efficiencies in part due to pushing in the wrong direction. As stage number increases, the angle of attack and the lateral velocities increase and result in higher efficiencies. The majority of prey captures by pike, however, occur within two to three stages (Rand and Lauder, 1981; Harper and Blake, 19906; personal observation). Lower hydromechanical efficiencies are implied, averaging 0.3 for the first three stages of all three S-starts, and .0.14 for the first 2 stages. A comparison of S and C-starts by stages shows that C-starts are more efficient on average than S-starts by 225% in stage 1 and 272% in stage 2. However, tail beat frequency for S-starts is approximately twice that for C-starts and based on time (end of stage 2 for C-starts occurs at the same time as the end of stage 4 for S-starts; i.e. 0.13s) C-starts are only 50% more efficient than S-starts. Maximum Performance Maximum power , output for northern pike, expressed per kilogram of muscle, ranges from 228 to 406 W/kg for escape behaviour and 63 to 462 W/kg for prey capture. Values are only slightly higher when expressed per kilogram of muscle fiber (69.2 to 507.7 W/kg) due to the high concentration (91%) of muscle .'! '!: ' 85 fibers in fish white niuscle (Johnston, 1983). The largest maximum power output values for a C-start and an S-start are 446.2 and 507.7 W/kg muscle ; fiber respectively. The maximum predicted for vertebrate anaerobic muscle is very similar at 500 W/kg (Weis-Fogh and Alexander, 1977). This suggests fast-start performance is constrained by muscle power output where C-starts perform closer to the theoretical maximum on average (366.1 W/kg) than S-starts (219.9 W/kg). Maximum power output reported for isolated fish white muscle fibers is 313 W/kg or 63% of the maximum theoretical value ( Johnston and ; Wokoma, 1986). Lower values for muscle performance from isolated muscle preparations than predicted may i reflect adverse affects of the laboratory procedures (Johnston and Salamonski, 1984). Maximum isometric stress of muscles may also constrain animal locomotory performance QDaniel and Webb, 1987; Daniel and Myerhofer, 1989). The maximum reported force per unit area for fish white muscle is 315 kN/m2 at 8°C (Langfeld, Altringham and Johnston, 1989). Alexander (1969) reported muscle fibers to run at 30 to 35° to the longitudinal axis in fish. This implies the cross-sectional area of a fish's body is a conservative estimate of muscle fiber cross sectional area. The maximum force produced by, pike divided by cross-sectional area at the dorsal-anal fin gives values of 32.1 to 73.2 kN/m2. Maximum muscle stress for isolated muscle fibers (145 to 315 kN/m2) are at least twice these values (Johnston and Salamonski, 1984; Johnston and Wokoma, 1986; Altringham and Johnston, 1988; Curtin and Woledge, 1988; Langfield, Altringham and Johnston, 1989). But, during cyclic contractions, maximum power output occurs at 0.3 maximum isometric 86 stress. The appropriate range based on literature values is therefore 43.5 to 94.5 kN/m and overlaps the measured range for pike. This implies that muscle forces are operating near an optimum for maximum power output and are not limited by maximum muscle stress. 87 C H A P T E R 4 M E T A B O L I C COST OF FAST-STARTS INTRODUCTION Here, the metabolic cost of fast-starts for prey capture and escape are estimated using excess post-exercise oxygen consumption (EPOC) measurements. A non-destructive method was selected to avoid errors due to handling and tissue sampling required in destructive methods. Also, the ability to make repeated measurements using a single specimen minimizes the number of fish required for study. Though die function of EPOC during recovery from anaerobically ;j fuelled activity is not fully understood (Gaesser and Brooks, 1984), estimates of energy expenditure can still be determined. A fast and slow phase are observed where the fast phase is assumed to be responsible for repletion of ATP and CrP reserves, and the slow phase represents lactate removal either by oxidation or glycogenolysis (Scarabello, 1989). Mechanical costs of fast-starts are determined simultaneously with oxygen consumption measurements. Due to the large number of fast-starts required for •'• this study, high speed film analysis was not feasible. The alternative was to use video tape analysis at low film speed (30 Hz) which requires less time but incurs greater analytical error (Harper and Blake, 1989ft). However, differences between mechanical cost estimates at 30 and 200 Hz are consistant and a correction factor can be applied. Given an estimate of the metabolic cost of a fast-start, limitations to fast-start performance by energy reserves are discussed. There is extensive literature on the biochemical energy ;j -;' * • 88 reserves and their rate of mobilization during exercise in fish (Hochachka and Somero, 1984; Wieser et al, 1985; Dobson and Hochachka, 1987; Scarabello, 1989). The energy available for anaerobic metabolism and its rate of supply can be estimated and compared with the metabolic cost of a fast-start. In this way, a determination of whether fast-start performance is limited by the amount of energy available from biochemical reserves or by their rate of supply is possible. The purpose of this study is to (1) determine the metabolic cost of fast-starts in prey capture and escape (2) compare metabolic cost with total mechanical cost and estimate metabolic efficiency from the slope of this relationship (3) assess whether metabolic energy sources constrain fast-start behaviour (4) evaluate sampling rate error and the value of video taping for estimating mechanical costs of fast-starts. 89 METHODS AND MATERIALS Fish were placed in a 90.1 1 plexiglass tank (.99m x .65m x .14m) 12 hours prior to experimentation and allowed to adjust to the laboratory conditions. The tank was supplied with aerated, dechlorinated fresh water at 2-41/min and was immersed in a larger flow-through water bath for temperature regulation. Over the duration of experiments the water temperature ranged from 11.1 to 15.8°C but varied by no more than 2°C for any one fish. To measure oxygen consumption in the experimental tank, the system was closed and recirculated with a litde giant submersible pump. A YSI probe attached to a series 5510 meter was placed in series with the water pump for continous monitoring of oxygen concentrations. The meter automatically corrected for changes in temperature and was accurate to within 0.03 mg OJl. Resting oxygen consumption rates were measureable to within 0.005 mg OJl and represent a sensitivity ratio of 1:30 over a ten minute interval. The tank volume was turned over every 11 minutes and die tests showed that water in the closed chamber mixed within 3 minutes. The probe was calibrated to Winkler titration measurements. When fish were removed, no measureable change in oxygen concentration occured. Pike activity during exercise and in recovery was recorded on a low light sensitivity video camera at 30 Hz. A mirrow angled at 45° provided an overhead view of the fish, and a 2 cm gride placed under the tank served as a scale reference on all tapes. Lighting was supplied by 2 100 W fluorescent aquarium lights located 1 m above the water surface. The tank was completely enclosed by opaque plastic sheeting to minimize visual disturbance of 90 experimental animals. Activity was observed through the video monitor. At the begining of an experiment, a plexiglass sheet was placed on the tank; top sealing the experimental system. An over head view for the video monitor was allowed through an overhead mirror angled at 45°. Oxygen consumption was monitored continously and concentrations recorded every ten minutes. Once the metabolic rate had stabilized, such that the change in oxygen concentration over three successive ten minute intervals were - within 0.01 mg O^, the fish was stimulated to fast-start. Escape responses were induced by a mild electrical shock to the tail region. The lid was temporarily removed and two electrodes attached to a pole were placed within 10 cm of the fish's tail. Fish were stimulated to fast-start from 0 to 20 times within 4 minutes. The lid was immediately replaced. The removal of the lid and disturbance of the water associated with stimulating the fish caused at most a 0.02 mg 02/l change in the oxygen concentration. To stimulate prey capture behaviour, 4 to 8 goldfish (2.90 to '8.09 gms) were placed in the tank, briefly lifting the lid. Oxygen consumption of 8 goldfish is not measurable and all prey were capture within 10 minutes. After exercise, the change in oxygen concentration was monitored for two hours. The oxygen concentration was always greater than 72% saturation. Fish were allowed to recover for 72 hours before the next experiment. Prey capture experiments were repeated 4 to 6 times and escape responses 7 to 9 times for each fish. After a series of experiments, fish were measured and weighed. A total of 5 fish were tested ranging in weight from 0.345 to 0.560 kg. 91 Video tape records were used to estimate the mechanical cost of each fast-start. .Tracings of the fish at 0.033s intervals were taken, the center of mass of the stretched-straight fish marked on each tracing and the displacement of this point measured between frames to the nearest mm. The center of mass was assumed to be 0.41BL (Webb, 1982) from the tip of the head and midway between the lines marking the sides of the fish. Knowing the displacement of the center of mass (d), the mass of the fish (m) and assuming b a longitudinal added mass of 0.2 x body mass (Webb, 1982a), the mechanical cost can be determined. This is given by * n | r W =T 1.2 mL a.d. (11) Lt b i i i=l where in is the mass of the fish, a is the acceleration of the b fish's center of mass and d the displacement during that time interval (determined by the time between : frames). Estimates of work done between frames is summed over all frames for a fast-start as indicated by the summation sign. Frame rates of 30 Hz at a XI magnification are known to result in >100% underestimates of maximum acceleration rates (Harper and Blake, 1989ft). However, the significance of this error to mechanical cost estimates is unclear. To determine a correction factor for this error, five prey capture and five escape responses previously filmed at 250 Hz were analyzed every 1, 2, 4, 8 and 25 frames simulating sampling rates of 10, 31.25, 62.5, 125 and 250 Hz. The mechanical cost was calculated for each sampling rate of 6 sequences. The oxygen debt from exercise was calculated by subtracting 92 the amount of oxygen consumed at rest from the amount consumed in the first hour of recovery. Oxygen consumption rates in the 30 minutes prior to stimulation are used to determine resting rates. The rate of consumption." stabilised close to resting rates within the first hour of recovery. Oxygen debt measurements were converted to units of energy where 1 mg 0 2 yields 14.7 J (Goolish, 1989). 93 R E S U L T S Undisturbed pike sat motionless and only occasionally swam at very low speed by paddling paired fins or by body and median fin oscillations. Experimental • set-up induced some activity ranging from slow swimming to fast-starts, but undisturbed behaviour was resumed within ten minutes. Fish reached resting oxygen consumption rates within 30 minutes of experimental set-up (Fig. 16). Pre-exercise resting rates were 75.6 ± 1.7 mg 0 2 k g V 1 (X ± 1SE; Table 8). By comparison, Diana (1982) measured resting oxygen consumption rates at 14°C to be 121.8 mg 0„ kg"1 hr"1 for a 400 gm Northern pike collected from the same drainage basin as the fish used in this study. Oxygen consumption rates were largest immediately following exercise and most declined to resting levels within 20 to 30 minutes (Fig. 17). The highest oxygen consumption rates were 226.6 ± 3.1 mg 0 2 kg"1 hr'1, and very similar to; maximum rates for a pike exercised to exhaustion at 251.8 mg 0 2 kg"1 hr"1 (Table 9). Oxygen debt in the first hour post-exercise ranged from 2.6 to 76.5 mg 0 2 kg"1 hr"1. During the 2nd hour post-exercise, rates were not significantly different from pre-exercise for escape . . . . t-behaviour (paired t-test, a = 0.05) but were significantly higher for prey capture (paired t-test, p < 0.05). Mean oxygen consumption rate for prey capture behaviour in the second hour post-exercise is 39.2 mg 0 2 hr"1 compared to 29.2 mg 0 2 hr"1 for escape behaviour. This difference is also significant (paired t-test, p < 0.05). Figure 18 shows , total work estimates for fast-starts at four sampling rates as a percentage of total work derived from 200 Hz 94 Table 8: Weight of experimental f i s h and r e s t i n g metabolic rates (mg 0 2kg *hr 1) p r i o r to exercise and i n the second hour of recovery f o r f i s h i n escape and prey capture. BEHAVIOUR WEIGHT FISH PRE-EXERCISE 2ND HOUR POST-EXERCISE (kg) ; mg 0 2 kg 1 hr 1 mg 0 2 kg 1 hr 1 ESCAPE 0.385 1 81.2 67.3 ESCAPE 0.364 2 80.0 70.6 ESCAPE 0.345 3 96.8 93.4 ESCAPE 0 .535 4 58.9 49.6 ESCAPE 0.560 5 63.1 63.2 PREY CAPTURE 0.385 1 78.9 98.6 PREY CAPTURE 0.345 3 97.3 104.0 PREY CAPTURE 0.535 4 57.6 78.1 PREY CAPTURE 0 .560 5 59.3 73.7 95 Table 9: A comparison of maximum measured oxygen consumption rates between f i s h and between time i n t e r v a l s immediately following up to 20 f a s t - s t a r t s ( f i s h number 1 to 5) or 100 f a s t - s t a r t s ( f i s h number 6). POST-EXERCISE (mg 0 kg hr ) FISH WEIGHT 2 (kg) 10 MINUTES3 20 MINUTES3 30 MINUTES3 l b 0.385 208 .9 (2) 181.2 (3) 171, .4 (4) 2 b 0.364 265.2 (5) 191.1 (4) 167 .0 (3) 3 b 0.345 279.5 (6) 225.0 (5) 207 .1 (5) 4 b 0.535 159.8 (1) 155.4 (1) 143 .7 (1.5) 5 b 0.560 219.6 (4) 176.8 (2) 143 .7 (1.5) 6 C 0.341 251.8 (4) 227.7 (6) 219 .6 (6) note: rank of oxygen consumption rate within row shown i n brackets. a , , , , Time i n t e r v a l s r e f e r to immediately following exercise bout. b Less than or equal to 20 f a s t - s t a r t s . c 100 f a s t - s t a r t s and approaching exhaustion. 96 Figure 16: Histogram of oxygen consumed by a single fish over ten minute intervals with time over the duration of an experiment. The fish activity chamber was sealed at time zero on completion of experimental set-up and 25 fast-starts induced at 70 minutes. Oxygen is monitored for 120 minutes following activity. The error bar shows measurement error range. 97 5» 0.20 o 0.15 0.10 ° 0.05 z o o U J P 0.00 o 0 30 60 90 120 150 180 TIME (min) 98 Figure 17: Histogram of recovery times after 0 to 20 fast-starts (5 fish). Recovery time refers to the time required for oxygen consumption rates to return to resting levels following exercise. 99 0.5-1 CY 0.4-z LU 0.3-o UJ 0.2-Cd b_ 0.1-0.0- 20 40 60 TIME (min) 80 100 Figure 18: Effect of sampling rate (film speed) on mechanical work estimates. Work is expressed as a percentage of estimates derived from 200 Hz film. 101 s N 1.25 X g 1.00j CM ^  O . 0.50 LiJ 0.25 J O ry Lj 0.00 D_ I O 1 T O 1 T O 1 T O 1 25 50 75 100 FILM SPEED (Hz) 125 film. The mean of 10 estimates are shown. Five prey capture sequences and five escape sequences at 200 Hz were analysed and estimates of total work at each sampling rate determined. A comparison of fast-start behaviours finds no significant difference and therefore data from both behaviours were combined in figure 18. At 30 Hz, total work estimates are at least 50% of values determined at 200 Hz. Figures 19 and 20 show that metabolic cost (Cyiebt) is positively related to the number of fast-starts and their mechanical cost. The best fit linear model for escape behaviour gives MC = 51.1 + 38.1 F , r2 = 0.54 (12) EF j E MC J = 165.4 + 10.6 M , r2 = 0.58 (13) EM E where MC is the metabolic cost, F (or F) the number of fast-starts and M (or M) the mechanical work done. The subscript E refers to escape behaviour. The number of fast-starts and the mechanical cost of fast-starts explain a similar amount of variation in metabolic cost (i.e. r2 is similar for equations 12 and 13). Slopes are not forced through zero because estimates of the Y-intercepts may represent a real elevation in metabolic rate due to a factor other than mechanical work done (e.g. excitement). Similar positive relationships exist for prey capture behaviour where MC p p = 258.6 + 54.8 F p , r2 = 0.22 (14) MC = 212.7 + 21.2 M . r2 = 0.59 (15) P M P 103 Figure 19: Relationship between oxygen debt or metabolic cost and the number of fast-starts for escape and prey capture behaviour. Error bar shows average range of measurement error. 104 NUMBER OF FAST-STARTS Figure 20: Relationship between oxygen debt or metabolic cost and useful mechanical work done during escape or prey capture behaviour. Error bars show average ranges of measurement error. 106 USEFUL MECHANICAL WORK DONE (J/kg) R-squared for equation 15 is similar to that for equations 12 and 13 but greater than for equation 14. A comparison of equations 13 and 15 shows similar Y-intercepts but slope for prey capture is 100% greater than for escape behaviour. Data from five fish are combined to form equations 12, 13, 14 and 15. The slope and Y-intercepts for individual fish are assumed to be the same. To test these assumptions an analysis of covariance was conducted for each behaviour and for metabolic costs versus the number of fast-starts or mechanical costs. No significant differences were found for slope or intercepts (a = 0.05). An individual pike was induced to fast-start by electrical stimulation 25, 50, 75, 100, 125 and 170 times with a 72 hour rest between experiments. Oxygen debt measurements were found to increase up to 100 fast-starts but did not increase further at 125 and 170 fast-starts (Table 10). After 170 fast-starts, no further fast-starts could be induced and the fish was assumed exhausted. 108 Table 10: Oxygen Debt f o r an Individual F i s h Exercised to Exhaustion NUMBER OF FAST-STARTS OXYGEN DEBT (mg 0 2 kg 1 hr 1) MECHANICAL COST (J/kg) 25 55.4 804.6 50 75. 9 1102.3 75 99.1 1439.2 100 135.7 1970.8 125 109.8 1594.6 170 125.9 1828.4 109 DISCUSSION Film Rate Error A film rate of 25 Hz gives estimates of total work done during a fast-start that are 47% less than values from 200 Hz film. At 50 Hz, total work underestimates are only 25% less and increasing sampling rates further only slighty improve estimates. This indicates estimates of total work at 200 Hz are not very different from actual values. Underestimates of maximum acceleration rates are much higher ranging from 35 to 100% for 50 to 250Hz film (Harper and Blake, 1989ft). Though work estimates are calculated using acceleration rates, the error associated with instantaneous maximum values are less than for lower acceleration rates and error for total work depends on average acceleration errors. Though the cause of error is the same for all variables derived from film displacement measurements, the magnitude of error for quantities calculated from an equation and dependant on a number of variables will be contingent on the form of the equation used. For example, differentiating displacement to determine velocity and acceleration rates increases error and the product or addition of two film derived variables results in the product or addition of errors. Therefore, film rate error is best evaluated independantly for each quantity calculated. Oxygen Debt Measurements The oxygen debt , is assumed to represent the cost of recovery from exercise. Common criticisms of this approach are that stimulating fish to exercise will increase excitement and contribute to post-exercise oxygen consumption, and that the role 110 of oxygen consumption in recovery from anaerobically fuelled exercise is unclear. The contribution of excitement to oxygen consumption at rest or during exercise, is probably low in pike. Attempts to consistantly stimulate activity with visual or auditory stimuli were unsuccessful and no change in oxygen consumption resulted. Pike tended to remain stationary in pre and post-exercise periods and showed low variability in resting oxygen consumption rates. Also, the metabolic cost of a fast-start is estimated from the slope of the relationship between energy expenditure and work done (Fig. 19 and 20) and any consistant increase in energy expenditure due to excitement is not included. The y-intercept represents any increase in oxygen consumption independant of activity and possibly due to excitement. Therefore, the metabolic cost estimate of a fast-start is not confounded by excitement. The oxygen debt hypothesis associates excess oxygen consumption after an exercise bout with lactate removal (Gaesser and Brooks, 1984). More recent evidence shows resting levels of oxygen consumption are resumed long before lactate concentrations in muscle tissues reach concentrations typical of a resting animal (see review by Gaesser and Brooks, 1984). Pike are no exception where resting levels of oxygen consumption after exhaustive exercise are achieved: after only 2 hours of recovery compared to 96 hours for replenishment of glycogen stores and lactate removal after exhaustion (Schwalme and Mackay, 1985). Gaesser and Brooks (1984) suggest oxygen debt can be divided into an initial fast phase followed by a slow phase. Their review suggests the fast-phase may function to restore adenylates and CrP. This is a 111 more acceptable hypothesis given the synchrony observed between fast phase oxygen debt''measurements and CrP and ATP replenishment in fish (Wieser et al, 1985; Scarabello, 1989). Here, pike show no slow phase of oxygen recovery and the fast phase observed is similar in duration to the fast phase for trout (Scarabello, 1989). This suggests ATP and CrP pools were depleted during repeated fast-starts but anaerobic glycolysis and lactate accumulation did not occur. This could be due to the high power requirements of fast-starts implying that only sufficient power can be supplied by CrP and ATP hydrolysis and not anaerobic glycolysis. , Energy Sources and Pool Sizes Oxygen debt may therefore be a useful measure of anaerobic energy expenditure where CrP is not fully depleted and glycolysis has not yet contributed to ATP supply. Though the assumption that anaerobic glycolysis is not turned on until CrP is fully depleted may not hold for humans (Bonen et al., 1989), evidence for a sequential mechanism in fish is clear (Driedzic et al., 1981). Concentrations of CrP and ATP in fish white muscle are very consistant averaging 17.38±1.78 and 7.62±1.88 u,moles/gm tissue respectively (Dobson and Hochachka, 1987; Driedzic et al., 1981; Guppy et al., 1979; 1 Mallet, 1985). However, Dobson and Hochachka (1987) show that 45% of the creatine pool is dephosphorylated at rest and CrP measurements are gross underestimates of actual resting concentrations. A more recent study by Schulte (1990) shows that death by injection of curare minimises stress and results in much higher estimates of resting CrP concentrations for 112 trout. These latter two studies show CrP concentrations at rest are at a maximum 45 |imoles/gm tissue. With the addition of ATP, 50(imoles ATP/gm tissue is a reasonable estimate for available energy supplied by CrP and ATP during the initial stages of anaerobic exercise. For pike, CrP and ATP pools of this size would provide 2130 J/kg fish for muscle work. This compares very well with the maximum oxygen debt observed after 100 to 170 fast-starts which was 135.7 mg O^g or 1970.8 J/kg fish. In addition, for the maximum of 20 fast-starts shown in figures 19 and 20, CrP and ATP pools can easily supply sufficient energy. Muscle Efficiency If oxygen debt is a realistic estimate of energy supplied by anaerobic metabolism for swimming activity then the slope of the linear regression between metabolic energy supplied for swimming and total mechanical cost should estimate muscle efficiency. Figure 20 shows the relationship between metabolic energy supply and useful work done. The differences in slope between escape and prey capture behaviour reflect the differences in hydrodynamic efficiency where the average value for prey capture is 0.19 and for escape is 0.37 (Chapter 3). When metabolic energy supply is expressed relative to total mechanical cost (Fig. 21), slopes are similar for both behaviours. Slope for escape behaviour is 3.92 and for prey capture is 4.02. This implies a muscle efficiency of approximately 25% which is in the middle of the range for vertebrate red muscle (i.e 20-30%, see review by Goldspink, 1977). 113 Figure 21: Relationship between oxygen debt or metabolic cost and total mechanical work done during escape or prey capture behaviour. Error bars show average measurement error ranges. 114 SIl METABOLIC COST (J/kg) o 5> m o o > o 7s o o z n OXYGEN DEBT (mg02/kg) Power Required Each fast-start is estimated to cost approximately 40-50J/kg fish and lasts for 0.12s to 0.14s. A power supply of 286-417 W is required. Only CrP and ATP hydrolysis can supply energy at an equivalent rate. By comparison, glycogen fermentation is an order of magnitude slower (Hochachka and Somero, 1984). This suggests the duration of fast-starts is limited by ATP and CrP concentrations. However, ATP and CrP pools supply sufficient energy for 40 to 50 fast-starts. This implies that the duration of a fast-start for prey capture or escape is not determined by energy stores and must be behaviourally constrained. Specific Dynamic Action (SDA) The observed increase in metabolic rate above pre-exercise levels in the second hour of recovery for pike after prey capture and not escape is potentially explained by the metabolic requirements of peristalsis and digestive processes (i.e SDA). The increase observed for pike was 23% above resting which is less than the 100% average increase in maximum post-prandial oxygen consumption previously reported for fish (see review by Jobling, 1981). However, fish require 12 hours on average to achieve maximum metabolic rates after ingestion (Jobling, 1981) and therefore the lower rates reported for pike after only two hours are reasonable. An increase in metabolic rate of 23% above resting within 2 hours of feeding may seem higher than the average for fish but given that temperature, ration size, proportion of digestible protein in diet and activity level can influence this value (Jobling, 1981; Moyle and Cech, 1982), variation around the 116 average for any given increase in metabolic for pike ranged from 1982). condition is probably rate above resting 33% in summer to high. For example, the after food consumption 126% in winter (Diana, 117 C H A P T E R 5 M E C H A N I C A L COST OF FAST-STARTS INTRODUCTION Fast-starts are described by three stages; a preparatory stage (stage 1), a propulsive stage (stage 2) and a variable third stage. This latter stage involves coasting, turning or continued swimming and is typically not included for analyses of fast-start kinematics or performance (Weihs, 1973; Webb, 1975a; 1977; 1978a,ft; 1982a; Harper and Blake, 1989a,ft; Domenici and Blake, in press). Whilst consistancy of kinematics found in stage 1 and 2 may be important for; comparison with previous studies, additional tail beats in stage 3 contribute to total performance, energetic cost of the event and possibly success in escape from predation or capturing a prey. Here, the range and frequency of fast-start performance and energetics during escape and prey capture behaviour are assessed. Distance-time plots are used to compare fast-start performance between C and S-starts. Rand and Lauder (1981) and Webb and Skadsen (1980) show a similar analysis for pike S-starts only. A performance study of C and S-starts in pike by Harper and Blake (1990ft) does not include a comparison of distance time plots. Here, differences in performance between C and S-starts are discussed with respect to kinematics and die ecological functional of each behaviour. In previous chapters, the cost and power output of fast-starts are determined for the first time. However, illustration of the distribution of fast-start costs and power 118 output requires a larger sample size. A comparison of how cost and power output vary with distance and time would demonstrate the consistancy of fast-start performance in response to a feeding or predatory stimuli and show whether fast-start responses are at a physiological maximum or, under behavioural control. From the cost estimates in this chapter and previous estimates for metabolic and propulsive efficiency in earlier chapters, total metabolic cost and its variation can be assessed. These costs are compared to literature values for the daily energy budget of pike or the energy content of prey and the ecological significance of the cost of fast-starts is evaluated. 119 METHODS AND MATERIALS Twelve northern pike were individually brought into the laboratory and induced to fast-start. Escape responses were stimulated by the rapid introduction of a meter stick and prey capture attempts were induced by the introduction of goldfish prey (3-5 gms). Experimental and filming procedures are as described in Chapter 2 using film rates of 100 or 200 Hz. A total of 29 fast-starts are chosen for analysis, 14 C-starts and 15 S-starts. For each sequence, the center of mass is digitized. The displacement of this point between frames is used to determine distance travelled and calculate total work done until the end of the fast-start. Due to variability in the number of tail beats for each fast-start, the end of the event is defined by the end of the last positive acceleration. Total distance travelled is defined by the distance between the position of the fish's center of mass at frame zero and the last frame. Total mechanical work (W ) is given by TO. W = I 1.2 m a.d/ E . ' (15) m . i i i = i where m is body mass, a is acceleration of the center of mass, d is displacement of the center of mass, E the hydromechanical efficiency and i the< frame number. Acceleration is determined by double differentiation of displacement values. First of all, the change in X and Y values for the center of mass are determined between frames. To realize a smooth AX and AY relationship with time, 2 point smoothing , is required for 100 Hz and 2 point followed by 3 point smoothing for 200 Hz. From these smoothed 120 values for AX and AY,' displacement is determined. Velocity is calculated by the division of displacement by time and acceleration derived from the change in velocity with time. A further 3 point average, is applied after the determination of velocity and acceleration values for both film speeds. 121 R E S U L T S Northern pike respond to a startle stimulus with a C-start. All of these events involve a preparatory stage (stage 1), a propulsive stage (stage 2) and a variable third stage. The latter involves a coast, brake or turn in 9 of 14 C-starts. The remaining 5 events show continued acceleration after stage 2 with one or two more tail beats. All 15 prey capture events show at least one tail beat after the end of stage 2 with 5 sequences showing 2 to 3 additional tail beats. Upon introduction of goldfish, pike orient towards or stalk prey. The latter involves slow movement towards prey using median fins only for propulsion. Once within strike distance, an S-start is employed. For 12 of the 15 fast-starts analysed, a strike occurs within one body length of the predator. Mean duration of C-starts and S-starts is 0.20±0.02s. The mean total distance travelled during a C-start is 0.25±0.08m, and not significantly different from that for S-starts at 0.23±0.04m (t-test, p=0.4). Mean total work done, however, is greater for S-starts at 26.5±2.7J/kg than C-starts at 18.6±2.8J/kg (t-test, p<0.002). A log-log plot of distance against time for C-starts and S-starts shows a significant positive relationship for both (Fig. 22a,b). The regression relationships for total distance are given by TD c = 1.080 T 0 ' 8 7 6 r2=0.67 (16) and TD = 2.519 T 1 ' 5 3 9 r2=0.75 (17) s 122 Figure 22: Log-log plot of total displacement versus time at the end of the fast-start event for A) C-starts and B) S-starts. 123 '0.50 Ld 0 0.20] 0.10 0.05 0.10 0.20 TIME (s) E 0.50 O 0.05 0.10 0.20 TIME (s) 0.50 0.50 124 The slopes are significantly different (t-test, p<0.01). C-starts have a larger intercept but a smaller slope than S-starts. The regression lines explain 67 to 75% of the variability in log distance for both behaviours. Also, 22 of the 29 fast-starts perform in the lower portion of the regression relationship in the time range of 0.1 to 0.25s and in the distance range of 0.09 to 0.40m (Fig. 22a,b\ The mechanical work done increases linearly with distance and time (Figs 23a,b and 24a,b). The regression relationships for work with distance are W = -18.0±10.1 + 274.4±29.2 D r2=0.88 (18) c c W = 23.2±10.1 + 100.5±17.7 D r2=0.71 (19) S / i s The slopes are significantly different (t-test, p<0.02). Intercept for C-starts is lower than for S-starts but slope is more than twice as high. These regression relationships explain more of the variability in mechanical work done for C-starts at 88% than for S-starts at 71%. Regression relationships for mechanical work done against time are given by W = -7.6±14.8 + 289.1±49.4 T r2=0.74 (20) c c N W = 8.6+12.9 + 189.8±49.9 T r2=0.53 (21) s s Time explains less of the variation in mechanical work done in fast-starts than distance. But, time explains more of the variation during C-starts at 74% than for S-starts at 53%. Slopes 125 Figure 23: Plot of total mechanical work done during fast-starts against distance at the end of the fast-start event for A) C-starts and B) S-starts. Error bar shows average measurement error range. 126 i (J/kg) o 100-^  < o o LU 75-50 25 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 DISTANCE (m) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 DISTANCE (m) 127 Figure 24: Plot of total mechancial work done during fast-starts against time at the end of the fast-start event for A) C-starts and B) S-starts. Error bar shows average measurement error range. 128 ( J / k g ) 0.2 0.3 0.4 0.5 TIME (s) O 25*. LU 0.0 0.1 0.2 0.3 0.4 0.5 TIME (s) 129 are found not to be significantly different between C and S-starts (t-test, p>0.25) but intercepts are different (t-test, p<0.002). The relationship between power output and time are shown in Fig. 25. Power output is relatively constant for both C and S-starts averaging 406 and 412W/kg muscle respectively. 130 Figure 25: Plot of power output per gram of muscle against time at the end of the fast-start event for A) C-starts and B) S-starts. Error bar shows average measurement error range. 131 o cn TOTAL POWER DISCUSSION Fast-start Performance Successful predator avoidance and prey capture depend on maximising the distance travelled in a given time (Webb, 1986; Harper and Blake, 1988). For fast-starts, maximum power output results in high acceleration rates from a resting position and a log log relationship is expected between distance and time. Figure 22 shows this model explains 67 and 75% of the variation in log distance for C-starts and S-starts respectively. Fish may not always respond maximally in escape or prey capture behaviour which would explain the observed variation. The variation in power output shown in Fig. 25 illustrates this point. Pike initially achieve greater distances per unit time in escape behaviour than in prey capture. The higher hydrodynamic efficiencies of C-starts over S-starts during stages 1 and 2 are a probable explanation (Chapter 3). C-start performance persists for 0.12 to 0.3s which Webb (1986) shows to be sufficient time for predator escape. The superior performance of S-starts after this time is due to higher, hydrodynamic efficiencies after stage 2 (see Chapter 3) and a linear swimming path. A tendancy for power output to decrease with time for C-starts may also contribute to lower performance. Webb and Skadsen (1980) report a similar log log relationship of distance versus time for Esox S-starts (D = 85.8 T - ) but also report data for C-starts from Webb (1978a) where the slope is greater than for S-starts (D = 151 T1'43). A probable explanation for this difference is that performance in Webb (1978a) is monitored only to the end of stage 2 and accumulative distance is reported for the curved path of C-starts rather than 133 total displacement. The majority of C-starts observed for pike were terminated at the end of stage 2 where the mean distance travelled was 0.14±0.01m or 0.33 ; BL. This duration and performance is typical for pike attacked by a predator for which a high escape success is realized (Webb, 1986). The majority of prey attacks by pike were within 0.1 to 0.3 meters or 0.23 to 0.69 BL. This short reaction distance is typical of Esox species preying on a number of fish species (Webb and Skadsen, 1980; Rand and Lauder, 1981) and is shorter than reaction distances for largemouth bass (Savino and Stein, 1989). These studies show that pike have higher prey capture success than bass but a lower rate of capture at the same prey densities. Pike are . capable of accelerating over greater distances and yet choose to minimise reaction distances before attacking. Minimising the cost of attack is a possible explanation. Energetic Cost of Fast-starts The mechanical cost of fast-starts ranges from 18 to 105 J/kg. The cost per unit distance is initially greater for S-starts than C-starts but at distances over 0.24m the cost of C-starts is greater. Again, the explanation is probably the differences in efficiencies and the linear path of swimming for S-starts. For the same amount of work over 50 J/kg, S-starts realize greater distances than C-starts. Reducing cost of capture may be important if energy reserves are low or the potential gain from a prey is low. The relationship between total mechanical work done and time 134 are not significantly different for C and S-starts. This is predicted if power output is assumed maximal during all fast-starts. Though there is some variation in the power output observed, average values are similar and change little with time i r for C and S-starts (Fig. 25). Combining both data sets, Work = -1.04 + 246.8 T, r2=64%. The metabolic cost of a fast-start is estimated by dividing the total mechanical cost by metabolic efficiency (0.25 see Chapter 4). The resultant costs range from 72 to 420 J/kg where the median value is 179 J/kg. These metabolic costs are higher than measurements in Chapter 4. A possible explanation is that the small chamber required for oxygen consumption measurements limited performance. A similar cost of 84 J/kg is reported for prey capture events by juvenile coho salmon involving burst swimming (Puckett and Dill, 1984). Much lower costs are reported for larval Sacramento perch capturing evasive and non-evasive planktonic prey ranging from 1.5 to 6.3 x 10~2J/kg (Vinyard, 1982). Given a greater range of cost, CrP and ATP reserves provide sufficient energy for 4 to 24 fast-starts (see discussion in Chapter 4). Glycogen reserves at 40 mmole/kg tissue (Scwalme and Mackay, 1985) provides energy for 8 to 46 additional fast-starts. The performance during a fast-start is therefore not limited by energy reserves assuming complete recovery from any prior anaerobic activity. Ecological Significance of the Cost of Fast-starts Repeated escape or prey capture behaviour could affect daily 135 energy expenditure. Resting metabolic rates of 75.6 mg 0 2 kg^ hr"1 (Chapter 4) are equivalent to 2.66 x 104 J kg"1 day"1 and are similar to other estimates for pike from Alberta lakes (Diana, 1982). To increase daily energy budget by 10% would require 2660 J/kg or 6 to 37 fast-starts. Though the number of fast-starts conducted by pike per day is unknown, greater than five is reasonable (see below), i ; The number of fast-starts (X) used in prey capture can be estimated from feeding frequency (F), stomach content (N=number of prey) and capture success (S) where X = ^ (22) Diana (1979) monitored the feeding habits of Northern pike in Lac St Anne and found that pike fed once every 2.66 days and captured 2.32 fish per feed averaged over the summer months (May to October). Prey capture ; success by Northern pike varies with prey species from 0.1 for bluegill to 0.78 for gizzard shad (Wahl and Stein, 1988). The incorporation of these values into the equation gives X values ranging from 1.1 to 8.8 attacks (fast-starts) per day. Using the median of 179 J/kg for metabolic cost of a fast-start, this is equivalent to 0.7 to 5.9% of daily maintenance costs. Larger numbers of attacks per day are possible where prey size is small and larger numbers of prey are required to fill the stomach. Diana (1979) found that <10% of pike with full stomachs contained 6 to 42 prey items which would require 2.9 to 20.5 fast-starts per day assuming S = 0.78. This is equivalent to 2.0 to 13.8% of daily maintenance costs. Therefore the number of fast-starts required to capture prey in the field overlaps the 136 range required to increase daily maintenance costs by 10% but rarely exceeds it. The ; choice of strike distances of less than one body length by pike may 'be a strategy to reduce the energetic cost of capture. Other factors may also favor a short attack distance by pike. Prey capture success is known to decline with distance for many predators, including sit-and-wait predators. Presumably this is due to an increase in closing time (the time required to reach the prey in an attack) with distance between predator and prey. Dill (1974) developed a model for closing time which predicts that closing time is constant beyond a distance of 0.4 meters for a pike accelerating maximally at 5 20 m/s and length of 0.4m (Fig. 26). This suggests prey capture success is constant beyond 0.4m or 1 BL attack distance. The benefit of a short reaction distance is again to minimize cost of capture. The importance of the cost of capture depends on the energy gained from a prey. The average daily ration for pike in the summer at Lac Ste. Anne is 47.8 kJ/kg day"1 for males and 72.9 kJ/kg day"1 for females (Diana, 1979). Given the 1.45 to 8.7 fast-starts per day required to attain this intake (see earlier i . discussion), the cost of prey capture (fast-starts) ranges from 0.14% to 7.6% of daily ration. Diana (1979) estimates that 27.7% of injested energy is used for somatic or gonad growth. That is, the cost of prey capture represents 0.52 to 27.4% of energy available for growth. Therefore, the cost of prey capture activity involving high powered anaerobic activity of short duration can be significant (i.e. represent greater than 10% of energy available for growth) when expressed relative to the energy content of prey. 137 Previous studies have used time to estimate cost of capture for pike assuming , activity i costs are constant (Hart and Connellan, 1984). In this study, the cost of fast-starts is shown to contribute significantly to activity costs potentially increasing the daily energy budget and reducing net energy gain from prey. Without knowledge ' of the mechanical or metabolic costs of activity, the cost of searching and capture of prey is seriously underestimated. 138 Figure 26: The relationship between reaction time of the prey and attack distance of the predator based on a constant acceleration rate (calculated from Dill, 1974). 139 1 4 0 C H A P T E R 6 S U M M A R Y A) Parameter estimation from the Weihs model A comparison of propulsive force estimates using the Weihs model with required forces shows maximum forces differ by 14 to 22% for three C-starts. The average difference is 17% which is similar to the 12 to 30% found by Weihs (1973). Total displacement, mean and final velocity, and mean and maximum acceleration rate derived from propulsive and required force estimates are within 4 to 19% for C-starts. Estimates of total work done using required and propulsive forces are within 9 to 31% for three C-starts and estimates of power output are within 14 to 31% for three C-starts and three S-starts. The use of higher film rates in this study than in the Weihs (1973) study (i.e. 250 Hz vs 65 Hz) does not decrease discrepancies between propulsive and required force estimates on average and discrepancies are shown to vary by only 8%. Variability in the difference between propulsive and required force estimates for replicate fast-starts, and differences between estimates for performance parameters derived from these forces are shown here for the first time. B) Estimates of hydromechanical efficiency, metabolic efficiency and the energetic cost of fast-starts. Hydromechanical efficiency averaged 0.37 for C-starts and 0.27 for S-starts. The range of efficiencies was greater for S-starts (0.16 to 0.37) than for C-starts (0.34 to 0.39). Values increased with each tail beat and speed showing a maximum 141 hydromechanical efficiency of 0.66 in stage 5 of one S-start. Hydromechanical efficiency increases with speed for other body-caudal fin swimming modes (push-and-coast and continous swimming) where values for fast-starts are lower at all swimming speeds. These are the first estimates of hydrodynamic efficiency for fish fast-starts. Estimates of metabolic efficiency are 0.094 for C-starts and 0.047 for S-starts. Estimates of white muscle efficiency, assuming metabolic efficiency is the product of hydromechanical and muscle efficiency, are similar for S and C-starts and averages 0.252. This is very similar to estimates of muscle efficiency for red muscle at 0.20 to 0.30 (Goldspink, 1977; Hill, 1950). The mean energetic cost of fast-starts is 201.2±30.0 J/kg for C-starts and 186.0±18.7 J/kg for S-starts. Power output is similar for C and S-starts ranging from 406 to 412 W/kg. These costs are higher than previously reported for fast-start like activity bursts in fish. C) Morphological and Kinematic Constraints Lift and acceleration forces are both positive and similar in magnitude during acceleration of the dominant propulsive sections. During deceleration, acceleration forces are negative whilst lift forces remain positive. The optimal conditions of a sharp angle of attack and high lateral velocities predicted by Weihs (1973) only apply during acceleration and not deceleration. Because fish must reverse the direction of motion and angle of attack of propulsive sections, deceleration is essential and optimal 142 conditions can not be maintained. The C body form of escape behaviour produces larger angles of attack than S-starts which results in higher efficiencies. The S body form allows maintainance of direction but sacrifices hydromechanical efficiency. The result is that velocities are higher in the first 0.3s for C-starts than for S-starts. The caudal fin and body section with the dorsal and anal fins contribute > 90% of total thrust. The anal and dorsal fins contribute 28% which provides quantitative support to the prediction that the posterior location of median fins increases thrust in pike. C) Physiological Constraint Maximum acceleration ability of pike in C-starts and S-starts is limited by maximum power output of muscles. The maximum power output for C-starts and S-starts are 446.2 and 507.7 W/kg muscle fiber and very similar/ to the 500 W/kg maximum predicted for muscle fibers (Weis-Fogh and Alexander, 1977). Also, estimates of muscle stress at maximum force are 32.1 to 73.2 kN/m2 which are less than 50% of literature values for maximum stress of isolated fish white muscle fibers. The observed stress for white muscle in pike are close to the optimal, for maximum power output at 0.3 maximum stress (Hill, 1950). Power output is not always maximal for C-starts and S-starts where 60% of C-starts and 65% of S-starts are in the 400 to 600 W/kg range. This suggests that both S and C-starts are at times under behavioural control. 143 Power demand during fast-starts ranges from 286 to 417 W. Only hydrolysis of ATP and CrP can supply energy at this rate. But, energy pool sizes of ATP and CrP are not limiting. More than 150 fast-starts can be repeated in rapid succession. Literature values for CrP and ATP concentrations in white fish muscle are sufficient to support 4 to 24 of the more expensive fast-starts reported in chapter 5. Given that energy reserves are much greater than demand for a single fast-start, and that pike are observed to fast-start repeatedly, the duration of fast-starts does not appear to be limited by biochemical energy reserves. The duration of fast-starts appears to be under behavioural control whilst the intensity of fast-starts is near the physiologically maximum. E) Ecological Considerations The cost of a fast-start represents 0.3 to 1.97% of the daily energy budget and 0.52 to 27.4% of the energy available from diet. Therefore, 5 to 30 fast-starts would be necessary to increase metabolic rate by 10%. Based. on the capture success of prey by pike, and concentrations of prey in stomachs of pike from field studies indicating feeding frequency, the number of fast-starts required for prey capture ranges from 1.45 to 26.3. It is concluded that the,; cost of fast-starts could contribute significantly to daily maintenance costs, reduce energy available for growth or reproduction and thus influence the evolutionary fitness of pike. 144 REFERENCES Alexander, R. McN. 1969. The orientation of muscle fibers in the myomeres of fishes. J. Mar. Biol. Assoc. U. K., 49: 263-290. Alexander, R. McN. 1983. Animal Mechanics, 2nd ed. Blackwell, Oxford. < Alexander, R. McN. 1989. Optimization of gaits in the locomotion of vertebrates. Physio. Rev. 69(4): 1199-1227. 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