Effects of Partial Caudal-Fin Amputation on the Kinematics and Metabolic Rate of Underyearling Sockeye Salmon (Oncorhynchus Nerka) At Steady Swimming Speeds

Breder (1926) and Gray (1968) have noted that caudal-fin amputation in fish swimming in the carangiform mode does not markedly impair steady, or sustained swimming performance. The effects of amputation are explained in terms of re-distribution of thrust-related hydrodynamic loading over the remaining portion of the tail and the body. This would change the loading on the muscle system, which is expected to affect the efficiency of muscular activity (Hill, 1950). A change in muscle efficiency implies an alteration in the amount of metabolically available energy transmitted to the mechanical caudal-propeller system, and consequently a change in metabolic energy expenditure or thrust/drag relations.

Recently, interest in fish propulsive mechanics has again increased with revision or new models of the locomotor system being formulated (Lighthill, 1969, 1970, 1971; Wu, 1971a, b,c, Weihs, 1972, 1973). Of particular interest is the hydromechanical model proposed in Lighthill (1969), a simplified form of that developed in detail by Lighthill (1960, 1970, 1971), but which can be expressed in a form of immediate predictive value to a wide range of biological situations.

However, this model implies that amputation of the caudal fin would greatly reduce thrust generated, and consequently decreased swimming speed would be expected at all levels of activity.

A boundary-layer thinning hypothesis has been advanced by Dr Q. Bone (in Lighthill, 1971) which considers the effect of locomotory movements on drag, particularly at the caudal fin where lateral movements are greatest (Bainbridge, 1963). This hypothesis could explain the apparent discrepancy of reduced thrust without reduced steady speeds by reduced drag following caudal-fin amputation.

This paper therefore seeks to use caudal-fin amputation as a tool to examine drag and thrust energetic relations for a swimming fish. Lighthill ‘s (1969) model is used to analyse thrust mechanics. Conventional equations are used to describe drag. These are developed for a simplified drag distribution between the body and caudal fin as suggested by the boundary-layer thinning hypothesis.

Forty yearling cultured sockeye salmon (Oncorhynchus nerka) were selected for uniform size from a stock acclimated to 15 °C. The fish were assigned to one of four groups by means of a random number process. Each fish was lightly anaesthetised with MS 222 and various portions of the caudal-fin lobes were amputated (Fig. 1):

Group 1 : control, pelvic fins amputated, caudal fin intact.

Group 2 : epaxial caudal-fin lobe amputated.

Group 3 : hypaxial caudal-fin lobe amputated.

Group 4: epaxial and hypaxial caudal-fin lobes amputated.

Pelvic fins were intact in groups 2 to 4. Epaxial or hypaxial caudal-fin lobes were amputated in groups 2 and 3 in case there was a mechanical difference in subsequent swimming patterns. Amputation of fin lobes was not complete, only fin rays being removed. In group 4 a flexible but short section of the caudal-fin was retained contiguous with the caudal peduncle. In this way it was hoped to avoid the effects of complete amputation on kinematics demonstrated by Gray (1933 c) for the whiting.

Following the operation, each group of fish was held in separate 197-l tanks for 2 weeks. Tanks were flushed continuously at 60 1/hr. Temperature was controlled at 15·0 ± 0·5 °C, and dissolved oxygen levels were maintained close to air saturation. Fish were fed to excess once a day on Abernathy pellets.

Water was circulated in the tank at a mean velocity of approximately 20 cm/sec. Fish swam continuously against this current.

Individual fish were starved for 2 days, lightly anaesthetised, and introduced to the fish chamber of a water-tunnel respirometer (Brett, 1964). The water velocity was set at 15 cm/sec, and fish were trained to swim steadily by means of an electrified grid downstream of the fish chamber. The respirometer was continuously flushed with air-saturated water, maintaining dissolved oxygen levels close to air saturation (10 mg O₂/l). Temperature was controlled at 15·0 ± 0·2 °C at all times.

The following day, and never less than 16 h after placing the fish in the respirometer, swimming performance and oxygen consumption were measured in an increasing-velocity test (Brett, 1964), with speed increments of 7·5 cm/sec every 45 min. The time to exhaustion after the last velocity increment was recorded in order to calculate the 45 min critical swimming speed, 45 min U_crit (Brett, 1964). No speed corrections for blocking of the chamber profile were applied, as the fish never occupied more than 7 % of the cross-sectional area.

At each swimming speed, tail beat frequency, trailing-edge amplitude and propulsive wavelength were measured. Frequency was measured by timing 50 tail-beat cycles every 5 min, with the fish swimming steadily near the chamber centre. Amplitude was measured photographically during the same or similar swimming periods, lateral and dorsal views being recorded with the aid of a 45° mirror above the fish chamber. In most cases time exposures of 0·25–0·5 sec were used in still photographs. The resulting photographs showed the limits of lateral body movements for several tail-beat cycles. These limits were clearly defined because the velocity of lateral movements is momentarily zero at positions of maximum amplitude (Gray, 1933a, b, c). These photographs were supplemented by cine-film records, recorded at 54 frames/sec.

Wavelength was measured from photographs taken at 1/30 or 1/60 sec, and from cine-film records.

Records were obtained for fish swimming in a cylindrical chamber. Corrections were applied for spherical abberation. These were minimal because fish tend to swim near the chamber centre.

Data obtained from the two photographic methods gave the same results. Consequently, pooled data were used in analysis.

Oxygen consumption was calculated from the decrease in dissolved oxygen tension after cutting off the water flow through the respirometer. Oxygen tensions were measured by a Mackereth macro-electrode (Mackereth, 1964), and continuously recorded on a pen recorder. Measurements were commenced at the 15th min following a velocity increment, ensuring that fish had settled down at each swimming speed (Webb, 1971b). When the dissolved oxygen tension fell to 85 % air saturation, water was again flushed through the respirometer, rapidly returning oxygen levels close to 100 % air saturation. Metabolic rates were computed in mg O₂/kg h.

Experiments were performed in the spring.

At the end of an experiment, fish were blotted on a moist cloth to remove excess water, and weighed to the nearest 0·01 g. Total length was recorded, both at the end of an experiment and at the time of operation. Caudal-fin trailing-edge depth was measured. The outline of the caudal-fin, including the expanding portion of the caudal peduncle, was drawn on paper, and the area was measured by means of a planimeter. These measurements are included in Table 1, together with values for some derived parameters discussed below.

A caudal-fin trailing-edge amplitude, cm

C total drag coefficient

C_B body drag coefficient

C_T caudal-fin drag coefficient

d_T caudal-fin trailing-edge depth

E total power generated by locomotory movements, ergs/sec

E_D power required to overcome total drag, ergs/sec

E_DB power required to overcome body drag, ergs/sec

E_DT power required to overcome caudal-fin drag, ergs/sec

E_K power lost as kinetic energy, ergs/sec

E_T thrust power, ergs/sec

f caudal-fin beat frequency, sec

L total length of fish, cm

m_T trailing-edge virtual mass, g/cm

R_L Reynolds number, based on L

S total wetted surface area, cm²

S_B wetted surface area of body, cm²

S_T wetted surface area of caudal-fin, cm²

U swimming speed, cm/sec

U_crit 45 min critical swimming speed, cm/sec

V backward velocity of propulsive wave, cm/sec

w W(V − U)/V, cm/sec

W lateral velocity of trailing edge, cm/sec

W_R resultant velocity of trailing edge, cm/sec

k, m, n, p, q constant

β shape factor for m_T

θ rotational component for caudal-fin motions. Note cos θ is equal to Lighthill ‘s (1971) ∂a/ ∂x

λ_B length of propulsive wave, cm

ν kinematic viscosity of water, stokes

π 3.14

ρ density of water, g/cm³

The swimming movements of fish in groups 1 to 3 were typical of fish swimming in the sub-carangiform mode (Breder, 1926; Bainbridge, 1963; Gray, 1933c; Webb, 1971a). Amplitude increased over the posterior half of the body to reach maximum values over the posterior third of the caudal fin. Group 4 was intermediate between this type of motion and that described by Gray (1933c) for the whiting following complete caudal-fin amputation. Thus amplitude tended to continue increasing posteriorly to some extent, with the tail somewhat splayed outwards. Therefore, the portion of flexible caudal fin left intact was not sufficient to permit completely normal locomotory movements. λ_B was similar in all groups. Expressed as specific wavelengths, λ_B/L, values were 1·02, 1·00, 0·95 and 1·03 for groups 1–4 respectively.

Partial caudal-fin lobe amputation had a relatively small effect on critical swimming speed, supporting observations by Breder (1926) and Gray (1933c). Values were 61·6 ± 2·7, 59·5 ± 3·9, 57·4 ± 6·0 and 51·8 ±7·3 (cm/sec, mean ± 2 S.E.) for groups 1-4 respectively. (7_crtt was just significantly lower for group 4 compared with the control group 1 (Student ‘s ‘t’ test, P > 0·05). Values for U_crit were lower than those reported elsewhere for this species (Brett & Glass, 1973), but reflect normal seasonal variance.

Webb (1971a) has demonstrated the utility of expressing kinematics and performance levels in relation to mechanical scope in order to compare kinematic changes following experimental manipulation of the locomotor system. Mechanical scope was defined as the difference between the product f × A at zero speed and at (U_crit, providing λ_B was unchanged. More simply, levels of mechanical scope could be expressed as a percentage of U_crit, as % U_crit. Analytical use of such mechanical scope makes the assumption that fish are exercised to a physiological limit at U_crit, as demonstrated by fatigue of the fish and failure to swim. This transformation of activity levels to % U_crit will be used here to facilitate discussion. Original data are given in Table 2.

The relationship between/and % U_crit was the same for each group of fish (Fig. 2).

It was curved slightly at lower % U_crit (and hence low U) as demonstrated for several other species swimming in the sub-carangiform mode (Bainbridge, 1958; Webb, 1971a). This curvature was associated with compensatory changes in A, such that A increased with speed to reach maximum values as U_crit approached. This trend is shown for the present fish in Fig. 2.

Where both f and A vary with swimming speed their product f × A appears to be linearly related with U or % U_crit (Webb, 1971a). This was confirmed for the sockeye salmon used in the present experiments (Fig. 2).

The data for oxygen consumption at various swimming speeds were best expressed as least-squares linear regression equations relating the logarithm of oxygen consumption to U (Brett, 1964; Brett & Glass, 1973). Only the equations are presented here (Table 3). Standard and active metabolic rates were calculated as described by Brett (1964).

There was no significant difference in standard or active metabolic rates within the four groups of fish tested (Students ‘t’), although the active rate was somewhat higher for group 4 fish (Table 3). Both active and standard rates were typical for the species for equivalent activity levels (Brett & Glass, 1973).

Data for oxygen consumption shows that caudal-fin amputation affected neither standard nor active metabolic rates, and metabolic scope was comparable for four groups.

Metabolic rates and metabolic scope were not affected by amputation. Consequently, the metabolic power made available to the muscular system will be the same in each of the four groups of fish at a given level of activity, expressed as % U_crit. The contribution made by anaerobic metabolism is neglected. However, as discussed by Webb (1971 b) this contribution is expected to be small in comparison with that from aerobic metabolism. Furthermore, there is no reason to expect different anaerobic contributions to the energy budget of fish in the different groups, because all fish were equally exhausted at the end of an experiment.

It should be noted that there is no intention to consider the level of activity at U_crit as the maximum physiologically permissible level. It is a level designated as the maximum level of activity which fish would be able to maintain for a period of 45 min. Clearly other and higher maxima would be permissible at higher speeds and vice versa (Bainbridge, 1958).

Consideration of the kinematic data shows that at a given level of mechanical scope f, A and λ_B are the same for each group. Webb (1971 b) has pointed out that these parameters not only describe caudal-propeller mechanics, but also propulsive-muscle mechanics because the two parts of the system are morphologically equivalent for fish swimming in sub-carangiform modes. When f, A and λ_B are the same, then so are muscle shortening speed and muscle power output (Hill, 1950). Therefore, at a given % U_crit, not only is the metabolic power input to the muscles the same for each group, but so is the muscle power input to the caudal propeller ; that is, amputation of various caudal-fin lobes did not affect the power input to the caudal propeller at similar activity levels.

Subsequent discussion of the effects of partial and complete caudal-fin-lobe amputation can therefore be restricted to the mechanics of the caudal propeller system.

The mechanics of sub-carangiform locomotion observed in the present fish are best described by the hydromechanical model proposed by Lighthill (1960, 1969, 1970, 1971). This model considers realistic fish-type body motions, and realistic fish-type body shapes and cross-sections. By comparison of the model ‘s predictions for E_T and E with general equations for drag and metabolic power expenditure, insight can be gained into the drag distribution for swimming fish and biological use of the model.

As with all hydromechanical models, inertial forces associated with body movements are emphasised and thrust forces of viscous origin neglected.

Taking into account boundary-layer thinning and increased W_R for the caudal fin implies a substantial drag cost associated with swimming movements. This drag would be reduced by removal of parts of the caudal fin. E_T will also be reduced because of the reduction in d_T following amputation. If the reduction in E_T through reduced d_T were of the same order as the reduction E_D, through reduced S_T then the situation can easily be visualized where caudal-fin-lobe amputation results in small changes in U_crit.

In order to test the hypothesis that the reduction in drag power required is of the same order as the decrease in thrust predicted by the model, equation 4 must be rewritten to include the special case of drag arising on the caudal fin.

The more appropriate form of the drag equation thus validates the form of Light-hill ‘s simplified bulk-momentum model in predicting E_T, and also supports the hypothesis that the laterally moving portions of the body experience an augmented drag (Bone, in Lighthill, 1971).

Breder (1926) and Gray (1933c) have suggested an alternative explanation for the small reductions in steady or sustained swimming performance following caudal-fin surgery. This considers that thrust generation is transferred from the caudal fin to the body. This explanation would require compensatory changes in the kinematics, and this is not supported by the present data. Even the differences observed in group 4, where most of both caudal-fin lobes were amputated, are small compared with other groups.

Although the data support the predictions of E_T for the simplified form of Light-hill ‘s model, they do not support the predictions of E. The power input to the caudal propeller is the same at equivalent levels of activity, and therefore so should the total mechanical power output of the mechanical system. However, it can be seen from equation 1, that E as well as E_T will vary mainly with m_T, and consequently be reduced with d_T following caudal-fin surgery.

The explanation for this discrepancy follows mainly from the form of the model discussed here, that is, the model of greatest predictive potential to biologists studying intact fish. In treating mean bulk-momentum changes in the trailing-edge region, it neglects the distribution of momentum changes along the length of the body which are discussed by Lighthill ‘s (1970, 1971) detailed treatment of locomotion and also by Wu (1971c).

One of the factors discussed in detail was the interaction of different parts of the body having different sectional designs as in the sockeye salmon. Such interactions occur between the leading edge of the caudal fin and trailing edges of the anal fin, and probably the posteriorly-thinning dorsal aspect of the body. Interactions result in energy economies without detriment to thrust. Clearly these advantages are lost by caudal-fin surgery of the form used here, and are not taken into account by the bulk-momentum form of the model. Lighthill (1970) also showed that tapering body sections tended to waste more energy than sections of deep caudal-fin type. Amputation tends to result in tapering body shapes, and energy lost because of this has not been accounted for.

In addition, the relations that apply to thrust and propeller-disc area (von Mises, 1945) will apply equally to the caudal fin. A large propeller generates thrust over a relatively large area, while the circumference available for energy loss through cross-flows is relatively small. Generation of an equivalent thrust/unit propeller-disc area for a smaller propeller would require a greater energy input, because proportionally more energy is lost in cross-flows around the relatively larger circumference. These losses are also neglected by the model.

In summary, kinematic data suggests that E_T is well predicted by the simpler model, but that E is not. The physiological data suggests that E will be the same for groups at similar activity levels, but is not well predicted by the model in the form considered most applicable in practical situations. Reasons are advanced suggesting that this is because energy losses exceed those predicted.

Much of this wasted energy is associated with forces of viscous origin, which are not included in the model. However, for normal fish swimming at typically high R_L, Lighthill (1960, 1970) has indicated that such forces will be negligible compared with inertial forces. Lighthill (1969, 1970) and originators of other models (see Webb, 1971a for references) have repeatedly indicated the desirability of a composite model treating inertial and viscous forces, but as they have observed, the current problems in formulating such a model are immense.

On the basis of the foregoing discussion, it might be thought that the simpler form of Lighthill ‘s model is not appropriate for applied use with fish. Certainly the detailed form is more desirable. However, it requires an arduous analysis of the type that Taylor (1952) does not recommend, high-quality film records, and is virtually confined to the laboratory.

In contrast, it must be noted that the discussion of fish propulsion mechanics given here is for a highly abnormal situation, specifically designed to obtain insight into both practical models and drag mechanisms. Such extreme caudal-fin modification is not usually found in normal fish populations where observed caudal-fin damage does not usually destroy its composite functional integrity. Thus, normal populations of fish would not require the detailed model. In fact, it has been shown that Lighthill ‘s simpler model gives a good description of propulsive energetics for trout, especially in its prediction of E_T (Webb, 1971a, b). Thus, it is considered that this model is applicable to normal fish, and as such its potential for the evaluation of locomotory activities in both laboratory and wild fish populations cannot be under-estimated.

So far, the various equations describing thrust and drag have been treated generally, with no attempt at their numerical solution. Using control group 1 data, a value for E_T of 2·97 × 10⁵ ergs/sec is obtained at U_crit.Brett (1963) and Webb (1971b) have shown that overall efficiency of conversion of metabolic power to mechanical thrust is greatest at this level of activity. The mean metabolic scope for activity (the oxygen available for locomotion at U_crit) has a mean value 514mg O₂/kgh for the four groups. The c.g.s. energy equivalent for oxygen can be taken as 1·47 × 10⁸ ergs/ mg O₂/sec (Alexander, 1967; Webb, 1971b). Then, at U_crit, the overall efficiency as described by Webb (1971a) is 22%. This value is of the same order commonly found for other vertebrates working at similar levels of activity (see Webb, 1971b).

Estimates for C_T are shown in Fig. 5 as a function of the mean W_R. The lower line was computed for data from group 1 and groups 2 and 3, and the upper line for data from groups 1 and 4. Fig. 5 indicates that the caudal-fin drag coefficient will be highest at low W_R, and hence usually at low U. At such swimming speeds V is relatively greater than U, in comparison with higher swimming speeds (Webb, 1971a, b). Therefore, the angles subtended by the body to the flow will tend to be high, and drag will, tend to be elevated in a similar fashion to that on a hydrofoil (von Mises, 1945). However, C_T decreases as W_R (and usually U) increase, so that at higher speeds it approaches minimal values. This would make for good energetic economy as energy available for locomotion becomes limiting at higher speeds. At U_crit, C_T is approximately one order of magnitude higher than expected in the absence of lateral movements of the caudal fin.

It should be noted that values for C_T given are approximations and will err on the high side. This is because W_R is calculated for trailing-edge motions, and consequently does not apply to the whole caudal fin. The mean value for W_R over the whole fin would be lower, and hence C_T higher. Consequently the form of Fig. 5 is more important than the absolute values estimated.

The general observation of the small effect of caudal-fin amputation on steady and sustained swimming performance of fish swimming in the sub-carangiform mode raises the question of the utility of that structure. The ability of the caudal fin to suffer extensive damage without reducing sustained performance is of obvious selective value. But this does not explain the evolutionary pressures that would give rise to a large, not particularly strong structure of no selective value for sustained activity.

Recent studies by Weihs (1972) on turning manoeuvres in Carassius auratus and Cyrpinus erythrophthalmus, and on acceleration in Salmo trutta and Esox esox (Weihs, 1973) indicates that a well developed caudal-fin of large depth is necessary for these activities. It is therefore suggested that the deep caudal fin shapes characteristic of a majority of fish have evolved in response to requirements of high acceleration, fast turning and high speed manoeuverability.

This work was completed during the tenure of a National Research Council of Canada postdoctorate fellowship. Facilities were provided by the Fisheries Research Board of Canada, Pacific Biological Station at Nanaimo and the courtesy of Dr J. R. Brett. I wish to record my thanks for their generous support. I am indebted to Dr J. R. Brett for his continued encouragement and invaluable discussions and comments.