Pectoral Fin Locomotion in the Striped Surfperch: II. Scaling Swimming Kinematics and Performance at a Gait Transition

During the past 30 years, the influence of body size on the kinematics of locomotion in vertebrates has been the subject of extensive study. Comparative physiologists have been particularly successful in relating the body mass of terrestrial tetrapods spanning a broad range of adult sizes to the temporal and spatial patterns of limb movement during running (e.g. Heglund et al. 1974; Pennycuick, 1975; Huey, 1982; Alexander and Maloiy, 1984; Heglund and Taylor, 1988; Marsh, 1988; Bennett et al. 1989; Strang and Steudel, 1990; White and Anderson, 1994; Zani and Claussen, 1994). One of the challenges for workers studying the scaling of locomotor mechanics is to select a speed at which meaningful comparisons among differently sized animals can be made. The concept of physiologically equivalent speed was developed by Heglund et al. (1974) and Heglund and Taylor (1988) specifically to allow comparisons of gait parameters among mammals of different sizes and geometric proportions. At equivalent speeds, differently sized mammals consume the same amount of metabolic energy per unit body mass during a stride (Taylor et al. 1982; Taylor, 1985; Heglund and Taylor, 1988) or incur a minimal energetic cost of locomotion (Pennycuick, 1975; Hoyt and Taylor, 1981) and experience similar levels of peak musculoskeletal stress in their limbs (Taylor, 1985; Biewener and Taylor, 1986; Perry et al. 1988). The similar stresses and power requirements for differently sized animals have been cited to justify kinematic comparisons at these speeds. An equivalent speed commonly used in studies of the scaling of running mechanics is the speed at the transition between two gaits (e.g. trot–gallop transition). Kinematic variables such as stride frequency and stride length change in a regular and predictable way with body mass at gait transitions (Heglund et al. 1974; Heglund and Taylor, 1988).

Studies of the scaling of oscillatory locomotor movements in aquatic vertebrates have placed less emphasis on comparisons of differently sized animals at gait transition speeds. Among bony and cartilaginous fishes, speeds selected for kinematic comparison across size include maximum sprint speed (Bainbridge, 1958; Wardle, 1975; Webb, 1977) and minimum stalling speed (Hunter and Zweifel, 1971), which can be difficult to induce and measure reliably, and similar body length-specific speed (Webb and Keyes, 1982; Williams and Brett, 1987; Graham et al. 1990), which is unlikely to elicit comparable levels of activity. Webb et al. (1984) compared tail-beat kinematics of large and small trout at the critical swimming speed (U_crit), the speed at which fish are thought to make their maximum sustained (aerobic) effort. Although U_crit is intended to represent a physiologically equivalent speed for differently sized fish by reflecting the transition from aerobic to anaerobic metabolism (Webb et al. 1984), there is a debate as to whether it estimates this transition accurately (Wilson and Egginton, 1994).

To date, there has been very little work on the scaling of locomotor movements in fishes that use modes of swimming other than axial undulatory propulsion (but see Archer and Johnston, 1989). Despite this relative lack of study, swimming with the pectoral fins (labriform locomotion: Breder, 1926) is employed by a diversity of bony fishes (Lindsey, 1978; Blake, 1983b). Many species have been reported to swim at low speeds by oscillation of the pectoral fins and to switch at higher speeds to axial undulation (pectoral–caudal transition: reviewed by Webb, 1994b; see also Whoriskey and Wootton, 1987; Parsons and Sylvester, 1992; Gibb et al. 1994; Stobutzki and Bellwood, 1994; Drucker and Jensen, 1996). We view this change in swimming mode as a gait transition (sensuAlexander, 1989; Webb, 1994a) and argue that the speed at which it occurs (U_p−c) is physiologically equivalent for labriform swimmers of different size.

The surfperches (family Embiotocidae) are unusual among bony fishes in their sole reliance on the pectoral fins for propulsion over a wide range of swimming speeds. In this paper, we describe the relationship between body size and (1) pectoral fin dimensions, (2) gait transition speed and (3) the kinematics of labriform locomotion in an ontogenetic series of striped surfperch Embiotoca lateralis. Focusing on patterns of pectoral fin excursion at U_p−c, we develop the first allometric equations for labriform swimmers relating the kinematic variables affecting swimming speed to body mass. Analysis of the allometry of U_p−c allows testing of the hypothesis (Drucker and Jensen, 1996) that length-specific labriform swimming speeds do not elicit comparable levels of exercise in fish of different sizes.

Surfperch (Embiotoca lateralis Agassiz) were collected by beach seine at Argyle Bay, San Juan Island, Washington, USA, and maintained in large flow-through seawater aquaria at 12 °C at the University of Washington’s Friday Harbor Laboratories. Seventeen male fish comprising six discrete yearly size classes (5.4–25.6 cm standard length, SL; 6.8–32.6 cm total length, TL; 4.0–557.5 g body mass, M_b) were selected for experimentation (Table 1). The flow tank used in this study and details of the experimental protocol have been described previously (Drucker and Jensen, 1996). Briefly, each fish underwent an exercise trial at increasing velocity designed to induce the transition from labriform to combined pectoral and caudal fin locomotion. Swimming speed was increased in 0.2 SL s⁻¹ increments at 3 min intervals until the fish reached its maximum speed and quickly became exhausted. The dorsal and lateral aspects of each subject were video-taped simultaneously at 60 fields s⁻¹. Field-by-field viewing of video tapes allowed measurement of kinematic gait parameters at U_p−c.

Following its swimming trial, each member of the study group was anesthetized in a dilute solution of tricaine methanesulfonate in order to allow measurement of pectoral fin dimensions. The length of the pectoral fin (L_p), taken as the distance (in cm) from the tip to the midpoint of the base, fin area (S, in cm2) and fin aspect ratio (AR), defined as L_p2/S, were measured using the program Image, version 1.51 (National Institutes of Health, USA) running on an Apple Macintosh computer.

The pectoral fin-beat period (T) was partitioned into two distinct phases: a propulsive period (T_pr) extending from the onset of abduction to the end of adduction, and a pause or ‘refractory’ period, beginning at the end of adduction, during which the fin remains fully furled against the body in preparation for the following abduction (see Fig. 1 in Drucker and Jensen, 1996). The proportion of the fin stroke cycle occupied by propulsive fin movements was defined as T_pr/T. Fin-beat frequency (s⁻) was measured as described in Drucker and Jensen (1996). Both uncorrected frequency (f_p) taken as T⁻¹ and corrected, or propulsive, frequency (f_p′) defined as T_pr⁻¹ were determined at U_p−c. Fin-beat amplitude (ϕ) was measured as the angle (rad) subtended by the fin tip during abduction in the plane perpendicular to the incident water current.

Stride length (λ_s) is the distance (in m) traveled by the fish during one complete pectoral fin-beat cycle (cf. Wardle, 1975) and was calculated at U_p−c using the equation:

where U is the swimming speed (in m s⁻¹) and f_p is in s⁻¹.

Geometrically similar animals have linear dimensions that scale with M_b^1/3 and measures of body area proportional to M_b^2/3. Dimensionless parameters calculated from morphological measurements are expected to be size-independent. In Embiotoca lateralis, all body proportions measured deviated significantly from the expectations of geometric similarity. The deviation was relatively slight for standard body length (Table 2: b=0.32), but larger fish had substantially shorter pectoral fins (b=0.29), smaller fin areas (b=0.63) and lower fin aspect ratios (b=−0.069) than predicted by geometric similarity.

Several gait parameters measured at the pectoral–caudal gait transition speed exhibit a clear size-dependency. Small fish switch gaits at higher pectoral fin-beat frequencies and with shorter stride lengths than large fish (Fig. 1A,B). Corrected and uncorrected fin-beat frequency scale similarly: f_p and f_p′ at U_p−c∝M_b^−0.12 to M_b^−0.14 (Table 2). Unlike frequency, U_p−c is not a simple function of M_b. Absolute U_p−c (m s⁻¹) generally increases with size, but the largest fish switch gaits at disproportionately low speeds (Fig. 1C). Length-specific U_p−c (SL s⁻¹) declines curvilinearly with M_b when plotted on logarithmic coordinates (Fig. 1D). U_p−c expressed as total body lengths per second (TL s⁻¹) does, however, decline linearly with body length (Table 2). At a given total length, surfperches achieve higher relative pectoral–caudal gait transition speeds than other labriform swimmers studied within a 5–10 °C temperature range (Fig. 2).

Four other important kinematic variables measured at U_p−c are independent of body size in Embiotoca lateralis. Despite moderate to weak degrees of correlation between these gait parameters and M_b (Table 2), the absolute variation in each dependent variable is low. At U_p−c, the proportion of the fin-beat period occupied by propulsive fin movements (T_pr/T) does not vary significantly with body mass (Fig. 3A; mean ± S.D. 0.54±0.06), a result that follows from the constancy of f_p/f_p′ at U_p−c (Fig. 1A). Similarly, the slope of the relationship between length-specific stride length at U_p−c and body mass is not significantly different from zero at α=0.05 (Fig. 3B; 4.84±0.47). Angular fin-beat amplitude (2.31±0.14 rad) and pectoral fin advance ratio (1.06±0.11) also show no significant dependence on M_b at the gait transition (Fig. 3C,D; Table 2).

Below, we argue that U_p−c is physiologically equivalent for labriform swimmers of different size. As originally defined, an equivalent speed is one at which the metabolic cost of locomotion incurred per gram per stride and the peak musculoskeletal stresses experienced are scale-independent (Taylor et al. 1982; Perry et al. 1988). Although the energetics and mechanics of labriform locomotion are not investigated here, the size-independence of key gait parameters at the pectoral–caudal gait transition speed provides evidence that surfperch of different sizes are at comparable levels of exercise at U_p−c.

An expectation for differently sized animals moving in a kinematically similar fashion is that the fraction of the stride period in which forward thrust is generated should be constant. For terrestrial tetrapods, this fraction is the duty factor, D, defined as the relative period of contact of a given limb with the ground (McGhee, 1968). As predicted by theory, D is size-independent at gait transition speeds (McMahon, 1977; Alexander and Jayes, 1983; Biewener, 1983). The quantity T_pr/T for labriform swimmers, which is comparable to the duty factor of running animals, shows a similar independence of body mass at U_p−c (Fig. 3A).

It is also predicted that animals at equivalent speeds should exhibit constant length-specific stride lengths. Expressed as a multiple of hip height, λ_s varies little at the trot–gallop transition in quadrupedal mammals spanning five orders of magnitude in M_b (Alexander and Jayes, 1983: Froude numbers of 2–3). Similarly, surfperch at the pectoral–caudal gait transition use a size-independent relative stride length, λ_s/L_p (Fig. 3B). This result, together with the scale-independence of T_pr/T and angular fin-beat amplitude (Fig. 3A,C), supports the hypothesis that pectoral fins of different size have ‘dynamically similar’ motions at U_p−c (cf. Alexander and Jayes, 1983).

In the absence of direct measurement of muscle power, propulsive efficiency of paired, oscillating appendages may alternatively be related to their advance ratio (von Mises, 1945; Vogel, 1981). This parameter has been determined for the wings of flying animals (e.g. Vogel, 1966; Ellington, 1984; Pennycuick, 1990) and here is calculated for the pectoral fins of the surfperch (equation 2). As noted by Webb (1975), J is a quantity comparable to ‘slip’, the ratio of U, the forward swimming speed of a fish relative to the current, and c, the backward speed of the propulsive wave generated relative to the fish’s body. U/c has been used in studies of axial undulation to reflect the propulsive efficiency of the caudal propeller (Lighthill, 1960; Webb, 1971b; Videler and Wardle, 1978). Since c is unknown for the pectoral fins of Embiotoca lateralis, J is taken in this study as an indicator of mechanical efficiency. For the size range of surfperch examined in this study, the advance ratio at the gait transition speed does not vary significantly with body mass (Fig. 3D; Table 2). Thus, until direct measurement of P_D/P_m is made (equation 3), we estimate that at U_p−c the efficiency of converting muscle power to thrust power is size-independent, and valid comparisons of kinematics and performance may be made across size.

In studies of the energetics of fish locomotion, it is commonly reported that the aerobic muscle power available for steady swimming (P_aerob) increases with swimming speed at a slower rate than the power required to overcome drag (P_D). Thus, (P_aerob−P_D) decreases with U (Webb, 1975). When P_D exceeds P_aerob, a change in gait involving recruitment of more powerful, anaerobic muscle fibers is expected. Since the mass-specific energetic demand (P_D/M_b) of a swimming fish increases with body size, but the mass-specific aerobic capacity of the locomotor muscle (P_aerob/M_b) decreases with body size, maximum aerobic swimming performance tends to exhibit pronounced negative allometry (Goolish, 1991). Such a pattern is observed not only in fish employing axial undulation (Webb et al. 1984) but also in the labriform swimmer Embiotoca lateralis. The pectoral–caudal gait transition speed (body lengths s⁻¹), above which anaerobic myotomal muscle is recruited, declines regularly with body size (Figs 1D, 2).

The absolute gait transition speed generally increases with body mass, but the fastest speeds are not exhibited by the largest animals (Fig. 1C). Fish in the largest two size classes (23–26 cm SL) exhibit lower average absolute U_p−c values than does the 21 cm size class. A similar pattern of declining performance at the largest sizes is observed in aquatic and terrestrial vertebrates at maximum anaerobic speed and may stem from energetic or structural limitations imposed on large animals (reviewed by Goolish, 1991). In addition, the relationship between swimming speed and body size may be influenced by the allometry of propulsor dimensions. In Embiotoca lateralis, pectoral fin area, S, increases through ontogeny at a significantly slower rate than expected by models of geometrically similar growth (Table 2). Since the thrust power generated by a pectoral fin during drag-based propulsion is directly related to S (Blake, 1979), disproportionately smaller fins may limit the maximum labriform swimming speed achieved by larger fish. Since E. lateralis probably also derives thrust from the production of pectoral lift forces, as proposed for the shiner surfperch Cymatogaster aggregata (Webb, 1973), it is expected that absolute U_p−c would decline in the largest fish as a result of their relatively low pectoral fin aspect ratios (Table 2) and hence coefficients of lift (Blake, 1983a).

An area of interest for future investigation is the mechanism by which surfperches attain consistently higher U_p−c values than similarly sized labriform swimmers from other families (Fig. 2). Embiotoca lateralis has a relatively narrow range of high speeds over which it can swim by axial undulation before rapidly fatiguing (Drucker and Jensen, 1996), a limitation that may be attributed to a reduced capacity for anaerobic power production of the myotomal muscle (Davison, 1988). The pectoral musculature of surfperch may thus be specialized for increased aerobic performance. At U_p−c, embiotocids and other pectoral fin swimmers of a given size use the same fin-beat frequency (Fig. 1A). Surfperches may generate more mechanical power per fin stroke at a given f_p by virtue of a greater pectoral muscle volume. In such a case, higher swimming speeds may be attained before recruitment of myotomal muscle and a change in gait are required. The scaling of pectoral muscle volume and its influence on the allometry of swimming performance remain to be investigated in the Embiotocidae.

Negative scaling of stride frequency at equivalent speeds of locomotion has been predicted by biomechanical theory (Hill, 1950; McMahon, 1975; Goldspink, 1977) and demonstrated empirically for a diversity of vertebrates (e.g. Bainbridge, 1958; Greenewalt, 1962; Heglund and Taylor, 1988; Marsh, 1988; Clark and Fish, 1994). In striped surfperch, pectoral fin-beat frequency at the pectoral–caudal gait transition speed also declines with body size (f_p∝M_b^−0.12; Table 2). Fin-beat frequencies observed at U_p−c in the shiner surfperch (mean M_b 36 g) and two species of centrarchids (91–101 g) appear to follow the same scaling relationship (Fig. 1A). Archer and Johnston (1989) report pectoral fin-beat frequencies at the transition from labriform swimming to axial undulation in juvenile and adult notothenioid fish. With the assumption that length scales as M_b^1/3, we calculate for this species a scaling relationship very similar to that determined for striped surfperch: f_p at U_p−c∝M_b^−0.13.

The size-dependence of stride frequency for labriform swimmers is consistent with that observed for fishes swimming by axial undulation. Although f_p′ (1/propulsive period) is more directly comparable to tail-beat frequency than is f_p (1/pectoral fin-beat period) at a given speed (Drucker and Jensen, 1996), f_p is proportional to propulsive frequency at U_p−c (Fig. 1A). Caudal fin-beat frequency (f_c) at estimated maximum aerobic and anaerobic swimming speeds for a range of species scales approximately with M_b^−0.1 to M_b^−0.2 (excluding Carassius auratus, Table 3). The variability in the mass exponent for f_c may reflect recognized uncertainty in eliciting top speed in the laboratory (Bainbridge, 1958). The general agreement of scaling exponents between the labriform and undulatory swimmers (Table 3) is suggestive of a common physiological mechanism, but must be interpreted with caution (Marsh, 1988). We suggest the following testable explanation for the observed similarity in the allometry of stride frequency.

Although the pectoral–caudal gait transition speed of labriform swimmers and the maximum speed of axial swimmers represent dramatically different levels of exercise, the mechanical properties of the muscle driving locomotion in both cases may be similar. An important determinant of muscle performance (i.e. force and power output) is the value of V for active fibers expressed as a fraction of their maximal shortening velocity, V_max (reviewed by Rome, 1994). In axial swimmers, both red and white myotomal fibers operate within a narrow range of velocities (V/V_max is approximately 0.2–0.4) over which the mechanical power produced is maximal. We expect that the pectoral musculature of labriform swimmers works at a similar V/V_max at the gait transition speed. The similarity in the scaling of stride frequency in the two types of swimmers then may reflect a common size-dependence of V_opt, the shortening velocity yielding peak power (equation 4). The shortening velocity for maximal power output of myotomal fiber bundles undergoing oscillatory contractions in vitro scales in proportion to M_b to the −0.17 power (Anderson and Johnston, 1992), a mass exponent within the range of those observed for tail-beat frequency at maximum swimming speed (Table 3). The power–velocity relationship of surfperch pectoral fin muscle is presently unknown, but it is predicted that V_opt has a similar size-dependence.

The allometry of stride frequency for fishes is strikingly similar to that observed for terrestrial vertebrates during steady locomotion. For many bipedal and quadrupedal runners, f measured at the trot–gallop gait transition and maximum running speed scales with M_b^−0.14 to M_b^−0.24 (Table 3; but see Huey, 1982; Bennett et al. 1989). Unlike swimmers, however, animals running at a constant speed propel themselves by muscle contractions that are likely to be nearly isometric (Taylor, 1994). Rather than optimize mechanical power (V/V_max=0.2–0.4), runners are thought to maximize the force developed by locomotor muscle (V/V_max≈0) (Roberts, 1995; cf. James et al. 1995). Regardless of the relative velocity of muscle shortening, however, at an equivalent speed of locomotion, animals of different sizes are expected to have a constant V/V_max for a fixed level of muscle performance. Accordingly, stride frequency at an equivalent speed should be proportional to V_max as well as to V (equation 4). Thus, the general similarity in the scaling of f in vertebrates utilizing fundamentally different locomotor modes and, as is likely, distinct muscle fiber types may stem from an underlying constancy in the allometry of V_max. The maximum shortening velocity of muscle fibers from the limbs of runners varying widely in body mass shows a size-dependence similar to that of stride frequency: V_max∝M_b^−0.13 (McMahon, 1975; Seow and Ford, 1991; cf. Marsh, 1988; Bennett et al. 1989). Although V_max of myotomal fibers was found to be independent of body size in the dogfish Scyliorhinus canicula (Curtin and Woledge, 1988), the scaling of this property is yet to be measured from the locomotor muscle of other axial swimmers or from the pectoral muscle of any labriform swimmer.

The comparison of kinematic allometries between ontogenetic series of fish and taxonomically diverse ranges of other animals requires validation. Development causes increases in body size as well as changes in the twitch kinetics of single fiber types (Marsh, 1988), the proportion of different fibers within a muscle (Kugelberg, 1976) and whole-muscle mechanical advantage (Dodson, 1975; Carrier, 1983). There is presently no information about the ontogenesis of contractile properties and fiber type composition of pectoral fin musculature or the allometry of relevant muscle lever arms, and thus the effects of neuromuscular and skeletal maturation and of body size cannot be separated in this study. Additional study of the pectoral fin musculoskeletal system is required to address the potential complications in comparing intra-and interspecific scaling of gait parameters.

Swimming performance is commonly expressed as speed in body lengths traveled per second after Bainbridge (1958) in order to allow comparisons among fishes of different size. In the absence of detailed data on the effects of body size on swimming performance, workers have compared gait parameters such as stride frequency among fishes of different size at similar length-specific swimming speeds (e.g. Webb and Keyes, 1982; Williams and Brett, 1987; Graham et al. 1990). This study demonstrates that normalization of speed to body length may not be a sufficient correction for comparisons of kinematics across size. In Embiotoca lateralis, U_p−c, the maximum speed sustainable by pectoral fin oscillation, when expressed in body lengths s⁻¹ declines sharply with body size (Figs 1D, 2). Thus, for larger fish, a given length-specific speed represents a greater percentage of U_p−c and requires a relatively higher level of activity than for smaller fish. For example, 2.0 TL s⁻¹ represents approximately 80 % U_p−c for a 15 cm striped surfperch, but is 100 % U_p−c for a fish only 7 cm longer (Fig. 2). Kinematic comparisons at such a speed may not be appropriate.

For studies investigating the effects of body size on swimming kinematics, we advocate the comparison of fishes of different size at a physiologically equivalent speed at which locomotor movements are dynamically similar and have the same propulsive efficiency. Kinematic patterns at intermediate levels of activity may be compared at swimming speeds expressed not as a certain number of body lengths per second but as a percentage of the equivalent speed (cf. Drucker and Jensen, 1996). For labriform swimmers, an equivalent speed for comparison across size is the pectoral–caudal gait transition speed.

Traditionally, patterns of swimming movements in axial undulators of different size have been compared at the critical swimming speed (U_crit), at which fish are thought to make their maximum aerobic effort (Webb, 1971a; Webb et al. 1984). Wilson and Egginton (1994) recently noted that U_crit does not precisely estimate the transition from aerobic to anaerobic metabolism in trout and that rapidly fatiguable glycolytic myotomal fibers are probably recruited at sub-critical speeds. Electromyography was used to determine the swimming speed at which anaerobic white muscle activity was initiated during swimming trials at increasing velocity. This threshold velocity for white muscle recruitment (U_WMcrit), like U_p−c for labriform swimmers, represents a gait transition speed. The onset of white myotomal electrical activity corresponds to the switch from steady axial undulation to intermittent ‘burst-and-coast’ swimming behavior (Rome et al. 1990a; Wilson and Egginton, 1994). Whether defined electromyographically or kinematically, this transition speed should be useful as an equivalent speed for comparison of axial swimmers of different sizes. The extensive past use of U_crit as an equivalent speed may not be discounted, since the Froude efficiency of the caudal propeller is largely size-independent at this speed (Webb et al. 1984). However, gait transition speeds marking the switch from aerobic to anaerobic power output may elicit more physiologically relevant equivalent levels of activity for comparisons of swimming fish of different sizes.

We are indebted to F. A. Jenkins, Jr, J. H. Jones, K. F. Liem, R. L. Marsh, T. J. Roberts and an anonymous referee for their critical comments. Special thanks to Dick Taylor and Tom McMahon for helpful discussions on biomechanical scaling. Access to the flume and other facilities at the Friday Harbor Laboratories was generously granted by P. Jumars, L. Self and D. Willows. This work was supported by grants from the Lerner-Gray Fund for Marine Research, the Putnam Fund of Harvard University and NSF BSR-8818014 to K. F. Liem.