The Effect of Size on the Fast-Start Performance of Rainbow Trout Salmo Gairdneri, and A Consideration of Piscivorous Predator-Prey Interactions

The performance of fish at high levels of unsteady (acceleration) activity is virtually unknown. During fast-start activity, fish accelerate at high rates (Gero, 1952; Gray, 1953; Hertel, 1966; Fierstine & Walters, 1968; Weihs, 1973; Webb, 1975 a) to achieve very high velocities (Fierstine & Walters, 1968; Webb, 1975 a). Only small distances are travelled during acceleration (Weihs, 1973; Webb, 1975 a) so this activity - is of secondary importance in such activities as avoiding nets, or negotiating fish ladders. The large distances covered at high steady speeds following the initial acceleration are important in these cases.

Acceleration fast-starts are of primary importance in such activities as jumping water falls, when high momentum must be acquired in a short time (Stuart, 1962), and in piscivorous predator-prey interactions between solitary predators and single or grouped prey. Such predator-prey interactions typically involve an acceleration lunge by the predator and acceleration manoeuvre by the prey in attempting to escape (Hoogland, Morris & Tinbergen, 1956; Mauck & Coble, 1971; Nursall, 1973). No studies have been performed to elucidate the mechanics of such interactions and there are few pertinent behavioural studies (Baerends, 1971).

The effect of size on fast-start performance is expected to be of significance in predator-prey situations. Acceleration rates should theoretically be relatively independent of size since body mass and added water mass inertia constitute the major resistance to acceleration (Webb, 1975b), whereas muscle mass is a relatively constant percentage of body mass or increases slightly with size. This is supported by observations on maximum acceleration rates of crudely geometrically similar fish, perch, pike, trout, and tuna, which have peak rates of 40 to 50 m/s² (Gero, 1952; Gray, 1953; Hertel, 1966; Fierstine & Walters, 1968; Weihs, 1973;Webb, 1975a). The maximum acceleration rate of the geometrically dissimilar green sunfish is substantially lower (Webb, 1975 a). No other details of acceleration performance in fast-starts are known in relation to size.

In contrast, high acceleration rates of large fish might be disadvantageous for predators, given currently observed fast-start kinematic patterns. Descriptions of single fast-starts in trout from 14 to 33 cm in length have shown that the anterior of the body recoils so that the path of the fish subtends some angle to its original axis (Hertel, 1966; Weihs, 1973; Webb, 1975 a). The angle subtended is proportional to acceleration rate (Hertel, 1966; Weihs, 1973). As a result, fast-start movements apparently involve a turn, the magnitude of which depends on acceleration rate. This would be disadvantageous for a predator accelerating towards a specific objective. Conversely, such recoil yawing turns might assist the prey in avoiding a predator. It would be expected that a predator would need to minimize the recoil yawing angle, which for the type of kinematics previously described would require reduced acceleration rates.

Manoeuvre is also an important locomotory component of predator-prey interactions. For example, a prey can escape from a faster predator if it can turn in a smaller circle to enter the space delineated by the smallest turning circle of the predator (Howland, 1973). The predator is then unable to intercept the prey without first stopping and then reorientating its axis of motion, or by executing an extended turn initially away from the prey. The turning ability of fish in fast-start activity is not known.

This paper describes the effect of size of rainbow trout on fast-start performance. The results are used to discuss the importance of various performance parameters for piscivorous predator-prey interactions following approach behaviour of the predator to within striking distance. An attempt is made to predict the catch and scape strategies for the predator and single prey as well as the required initial starting distances separating the fish. Salmonids were used because they are, essentially, morphologically unspecialized for locomotion (Webb, 1976), and fish comprise a substantial portion of the food consumed by larger individuals (Scott & Crossman, 1973).

It should be noted that the predictions are based on performance data alone and not on observed predator-prey interactions. Technical factors and inherent problems in the fish behavioural responses prevent detailed analysis of both mechanics and behaviour simultaneously. For example, closed-circuit T.V. cannot provide the magnification required for the analysis of mechanics, and problems of timing and duration of an interaction make high speed cine-photography undesirable for recording behaviour. Experiments to test the hypotheses generated in this paper are being initiated.

Experiments were performed on seven groups of rainbow trout, Salmo gairdneri (Richardson), ranging in mean total length from 9·6 to 38·7 cm. Fish were obtained from a local trout farm and held in 1000 1 tanks. Water was recirculated through a filter and gravel beds, and the volume was replaced every four days. Dissolved oxygen was maintained close to air saturation by means of airstones. Fish were acclimated to 15 ± 0·2°C by increasing the temperature from 4°C at the rate of 1 °C per day and thereafter holding fish at the acclimation temperature for two weeks. Fish were fed to excess once a day with Purina Trout Chow, but were starved for 48 h prior to an experiment.

The apparatus and methods used have been described in detail by Webb (1975 a). Single fish from the various size groups were selected at random and acclimated overnight (at least 16 h) to an enclosed fish chamber 90 cm square and 10 cm deep. A slow continuous flow of 150 ml/h was maintained through the chamber controlling temperature at 15 ±0·2°C and dissolved oxygen close to air saturation.

Following acclimation, fish were subjected to a single d.c. electric shock stimulus every hour. Stimuli of 0·22, 0·44, 0·67, 0·89, and 1·11 V/cm were given in a random sequence. Stimuli were applied by means of two aluminium grids at opposite ends of the fish chamber. Fish responses were recorded on 16 mm film at 64 f.p.s. The film record included a time clock and stimulus marker.

At the end of an experiment, fish were weighed and total length was measured. The centre of mass for the stretched-straight body was determined using plumblines (Webb, 1975a). Total wetted surface area and axial muscle mass were measured as described elsewhere (Webb, 1971, 1973). These morphometric data are summarized in Table 1 for the seven groups of fish.

Film records were analysed frame by frame. Tracings were made of successive positions of the body centre-line. These were superimposed to observe kinematics and movements of the stretched-straight centre of mass about which propulsive forces act.

Statistical comparisons were made between groups using Duncan’s new multiple range test. Differences in fast-start performance parameters for two types of kinematic modes described below were compared using the Student t test (Steel & Torrie, 1960).

Fast-start activity was divisible into the usual three kinematic stages originally described by Weihs (1973). There was typically a preparatory stroke, kinematic stage 1, followed by the main propulsive stroke, kinematic stage 2. There was a variable kinematic stage 3, where behaviour ranged from continued acceleration, through adoption of steady swimming, to an unpowered glide (Webb, 1975 a). Continued acceleration or steady swimming, frequently with high speed manoeuvre (Weihs, 1972), were the most common stage 3 behaviour patterns.

Analysis was concentrated on the first two kinematic stages. These two stages together constitute a behavioural phase 1. This is the important part of a fast-start during which high momentum is rapidly acquired (Webb, 1975 a). The variable stage 3 constitutes a phase 2 when large distances are covered at the velocities acquired in phase 1, and fish can also freely manoeuvre.

In contrast to earlier observations, two major phase 1 fast-start kinematic patterns were found. These will be referred to as ‘L-starts’ and ‘S-starts’. The former pattern has been described by Hertel (1966), Weihs (1973) and Webb (1975 a).

In an L-start the body was bent into an L- or U-shape during kinematic stages 1 and 2 (Fig. 1 A) as the tail and anterior of the body rotated in opposite directions about the centre of mass of the stretched-straight body. The centre of mass recoiled laterally and forward while accelerating in stage 1, and was further accelerated forward during stage 2 as the tail moved laterally in the opposite direction to that in stage 1. The path of the centre of mass approached a variety of centrifugal spirals in most cases. The initial radius of the path was small early in stage 1, but was large by the end of stage 2. The path of the centre of mass commonly approached a straight line by the end of stage 2 when stage 3 was continued powered propulsion (Fig. 1 A) or a glide. The path continued in a small radius circle when a sharp turn was combined with acceleration (Fig. 1C). A turning component was always included in an L-start, this being frequently amplified into an acceleration turn as shown in Fig. 1C.

S-starts were characterized by the body being bent into a double flexure during stages 1 and 2, the body adopting an S-shape (Fig. 1B). The body shape was analogous to the normal propulsive wave of a steadily swimming fish, but the amplitude was larger and more uniform along the body length. The waves of curvature travelled backwards along the body as in an L-start (Webb, 1975 a) and steady swimming. The initial S-shape of the body of pike before a lunge was noted by Hoogland et al. (1956).

An important consequence of the double body flexure was that net acceleration of the centre of mass could be more or less in line with the original body axis because recoil forces were balanced along the body length. Therefore, in comparison with an L-start, a turning component was not a necessary concomitant to acceleration.

Fast-starts and high speed turns were commonly combined during stages 1 and 2 into acceleration turns as previously described for trout and green sunfish (Webb, 1975 a). In an L-start, acceleration turns were usually observed during stage 2 and were typically in the same direction as the stage 1 recoil yawing movements (Fig. 1C). In four cases, a turn in stage 2 was in the opposite direction to the initial yawing of the anterior of the body (Fig. 1D). In Fig. 1D, the fish first yawed to the left while the centre of mass began to describe an anticlockwise centrifugal spiral. Stage 1 was completed by frame 4. In stage 2, starting with frame 5, the head began to move to the right, while the centre of mass continued to describe its original path. Kinematically, this represented the beginning of the new turn initiated by the anterior of the body in stage 2 while tail movements sustained the original movement of the centre of mass. In frame 6, the turn to the left was continued by the anterior of the body, but the movement of the centre of mass was interrupted, the positions for frames 5 and 6 overlapping. Subsequently, in frames 6 to 9, the centre of mass again accelerated but in a clockwise arc. The important point to note is that a turn which corrected for recoil yawing movements before the completion of stage 2, interrupted the fast-start sequence and resulted in loss of the momentum that had already been acquired.

Acceleration turns were also a common component of S-starts. These occurred as part of either stages 1 or 2 and were in the same direction as the curvature of the anterior body flexure during each stage. In S-starts, fish initiated turns to either left or right before the completion of stage 2, but without interrupting the motion of the body or losing momentum.

High speed manoeuvre and turns were common characteristics of stage 3. Following the completion of stages 1 and 2, fish often turned to either the left or right without interruption of forward progression. These movements are described by Weihs (1972).

It should be noted that L- and S-starts were modes in a continuous spectrum of fast-start kinematic variation. The majority of observations were clearly one type or the other, but 10 –15% of observations could not be classified with confidence into either of the modal fast-start patterns (see Fig. 3).

The cumulative distance covered by the stretched-straight body centre of mass about which propulsive forces act was continuous during stages 1 and 2 for normal L-starts (Fig. 2 A) and L-starts acceleration turns (Fig. 2C) as previously described (Weihs, 1973; Webb 1975b). The same continuity was found for S-starts (Fig. 2B). The distance/time curve was discontinuous for L-starts when stage 2 included a turn in the opposite direction to stage 1 recoil yawing of the anterior of the body (Fig. 1D). For the sequence shown in Fig. 1D, the fish began to accelerate as usual but then rapidly decelerated and almost came to a halt with the initiation of the new turn.

Distance-time curves extended into stage 3 were also continuous when a fish continued to accelerate. Acceleration rate reduced to zero or became negative with the adoption of steady swimming or an unpowered glide, respectively.

S-starts were not observed in earlier experiments on the same species (Weihs, 1973; Webb, 1975 a). This kinematic pattern was immediately noticed when tracings were made of fast-start kinematics of larger fish. It therefore appeared likely that S-starts were more common among larger fish. During analysis, each fast-start pattern was recorded as an L-, S-, or ambiguous start, and percentages of each were determined for the seven groups of fish (Fig. 3). The percentage of L-starts decreased, while that of S-starts increased as length increased. For the smallest group (mean length 9 ·6 cm) no S-starts were identified with certainty. For the largest fish (mean lengths 34 ·6 cm and 38-7 cm) S-starts comprised approximately 60 –65 % of total observations.

No significant differences in duration of stages 1 and 2 were found, as previously observed (Weihs, 1973; Webb, 1975 a). Therefore, results are only given for performance up to the end of stage 2. In general, no significant differences (5 % probability level) were found in performance of L- and S-starts within any of the seven groups of fish. As an example, data are presented for the duration of fast starts to the end of stage 2 for L and S patterns for each group (Table 2). Differences in duration were not significant for the two acceleration patterns within groups except for the largest fish (mean length 38 ·7 cm). This result was not considered typical but reflected the activity of an unusually athletic fish. If the data for this fish are excluded, no significant differences would be found in the duration of L- and S-starts for any group of fish.

Acceleration rates for the group of largest fish were also higher than other groups, and differences were just significant (5% probability level). Distance covered and velocity attained did not differ between L- and S-starts for this group because higher acceleration rates were offset by the lower acceleration times to the end of stage 2. The differences between L- and S-starts for the group of largest fish are again attributable to the high performance of one fish. Acceleration rates, distance covered and velocity attained at the end of stage 1 were not significantly different between L- and S-starts for any other group of fish.

Exponents for the power equation (1) relating distance covered with time were not significantly different between L- and S-starts, nor among groups of fish. The overall mean value was 1 ·71 somewhat higher than that of 1 ·60 determined earlier by Webb (1975 a) for trout (mean length 14 ·3 cm) but the same as that for green sunfish (mean length 8 ·0 cm). Since the exponent was less than 2, acceleration rates were not uniform but decreased with time from an early acquired maximum as discussed by Webb (1975 a). Similarly, velocity did not increase uniformly, but increased rapidly early in stage 1, often tending to approach a maximum by stage 3.

Fast-start performance did not generally differ between the two fast-start kinematic patterns. Therefore, data for L- and S-starts were combined to evaluate size effects (Table 3).

The duration of fast-start movements to the end of stage 2 increased with size. The differences were significant at the 5% level for length differences of 10 –15 cm. The increase in time required to complete the stage 1 and 2 acceleration movements for larger fish is consistent with observations of tailbeat frequency and size at given steady performance levels. At a given speed, tailbeat frequency decreases with size (Hunter & Zweifel, 1971) so that the time to complete a given cycle increases with size (Wardle, 1975) and the time required to complete a given propulsive stage increased in the same way. The duration of both stage 1 and stage 2 was approximately 1 ·5 times the values obtained by Wardle at 14 °C. Wardle (1975) considers that maximum swimming speeds are limited by the rate of contraction of the white muscles. Since the duration of stages 1 and 2 in acceleration were substantially greater than the minimum contraction times, acceleration performance is probably limited by other, presently uncertain, factors. The difference in muscle contraction times measured by Wardle (1975) and the times implied here may result from higher instantaneous muscle loads in acceleration reducing muscle shortening speeds (see Gray, 1968).

Acceleration rates were found to be essentially independent of size (Table 3). The performance of the group of largest fish was somewhat superior to that of other groups but was not considered representative, as discussed above.

Distance covered and velocity attained at the end of stage 2 increased with size. This follows because acceleration rates were independent of size, whereas the duration of acceleration movements increased with size.

Since acceleration rate was independent of size whereas the duration of fast-starts increased with size, comparison of performance between groups should be made for a given time (Table 4) for fish accelerating from rest. The extrapolation of performance data in Table 4 to 0·1 s for all fish assumes that acceleration continues in stage 3 for smaller fish with acceleration times of less than 0·1 s to the end of stage 2. This assumption would be reasonable for a fish responding to a relatively sustained stimulus, for example a predator. Both distance covered and velocity attained after 0·1 s were found to be independent of size (5 % probability level). Therefore, acceleration performance was independent of size for a given acceleration time period.

The turning radius of the body was measured for acceleration turns such as those illustrated in Fig. 1C. During such manoeuvres, the fish turned tightly to move in the opposite direction to the initial body axis by the end of stage 2. Such turns represented 20% of all observed fast-starts and were assumed to be the smallest turning radii possible for an acceleration turn. This method of measuring minimum turning radii is clearly subject to some error and smaller turning radii might be possible. In practice, the very sharp turns were never ambiguous and varied relatively little.

The smallest turning radius increased with size (Table 3). However, the radius was a constant fraction of the total body length, L, with an overall mean of 0·17 L. Howland (1973) predicted on theoretical grounds that the minimum turning radius for fish should be independent of velocity, but proportional to length. The present results are consistent with this hypothesis.

The present observations show that size has little effect on acceleration performance including velocities attained and distances covered in a given time interval for fish starting from rest. This conclusion is of particular interest with respect to piscivorous predator-prey interactions because it would appear that a predator would be unable to catch a geometrically similar prey during an acceleration lunge. Furthermore, this conclusion might be more generally applicable as the restraint of geometrical similarity may not be too rigorous. Thus the maximum acceleration rates of trout, perch, pike, and tuna are all of the same order of magnitude (Gero, 1952; Gray, 1953; Hertel, 1966; Fierstine & Walters, 1968; Weihs, 1973; Webb, 1975 a). Performance differences do occur for radically different body forms, as for example between trout and green sunfish (Webb, 1975a).

Larger fish of a given species can reach higher steady speeds than smaller individuals (see review by Beamish, 1976) so that a predator could theoretically intercept a prey fish after a prolonged chase. However, fish predator-prey interactions are not usually prolonged, except in such cases as pack hunting and mobbing prey (Nursall, 1973). Instead, single predators attack solitary or schooling prey and typically use ambushing or stalking behaviour to approach within a few centimetres of the prey. The predator then lunges in an acceleration fast-start to intercept the prey. These activities have been described for pike and perch (Hoogland et al. 1956; Mauck & Coble, 1971; Nursall, 1973). These two species differ in terms of morphological specialization for locomotion but show similar predatory lunging attacks. Thus the pike is specialized for lunging, while fish such as perch are relatively unspecialized in terms of locomotion (Webb, 1976). It should also be noted that specialized predators have almost exclusively white myotomal muscle (Boddeke, Slijper & van der Stellt, 1959) that rapidly fatigues. This would make extended chases by such fish unlikely.

The above considerations indicate that normal piscivorous solitary predator and prey interactions involve high speed acceleration fast-starts rather than prolonged chase activity. This well known observation is assumed here to be the normal situation and the present results will be interpreted in this context. In addition, since predators regularly catch their prey, differences in performance between predator and prey must occur. The factors affecting predator-prey interception must therefore be considered in more detail.

Howland (1973) has formulated a model to describe locomotory interactions between predators and prey in constant velocity chase situations. The same general principles apply to acceleration motion in the present situation.

Equations (6)-(9) and (11) will not apply directly to unsteady activity since U is time-dependent. However, fish performance can be described in terms of distance travelled, S₁ for the predator, and S₂ for the prey. Then S₁ and S₂ replace U₁T and U₂T respectively in equations (6)-(9) and (11) as appropriate.

In the nose-to-tail case, S₁ must exceed S₂ for the predator to be able to intercept the prey. Such a difference will occur because the prey will not instantaneously respond to an attack initiated by the predator. For the same reason, will also exceed S₂ in the nose-to-nose case. In both cases, when interception occurs at time, T, the predator will accelerate for a time, T, and the prey for a time, T−ΔT₂ where ΔT₂ is the prey reaction time to the stimulus given by the predator’s attack.

Reaction times for the predator, ΔT₁, will also affect the outcome of a predator-prey interaction. However, this will only be of significance when the predator is forced to turn to intercept the prey. Tracking turns by the predator will be minimized when the predator accelerates to intercept the prey as soon as possible because then the prey has least time to move away from the initial predator-prey axis. This suggests that the predator should minimize interception time to try to catch the prey before it can manoeuvre. Alternatively, the prey could obtain an advantage from predator reaction time by moving normal to this original axis, maximizing the required turn of the predator.

Reaction times for predator and prey responses are not known with certainty. Diamond (1971) describes reaction times of tens of milliseconds for tail-flip responses following Mauthner cell stimulation in goldfish. According to Russell (1974) this response lasts 50– 100 ms (of the same duration as stages 1 and 2 observed here), starting 14 ms after stimulation of the Mauthner neurone. The present experiments indicate reaction times of the order of 20 ms. Unfortunately, the film framing rate was not high enough to determine reaction times with accuracy.

From equation (12), it follows that when T is large for a given ΔT₂, the swimming speeds of the predator and prey will tend to approach each other. Within the context of Howland’s (1973) model, it would then be advantageous for prey to manoeuvre to enter the circle delineated by the predator’s smallest turning radius. However, since R is so small this strategy is not realistic for fish. Therefore, prey escape is expected to be critically dependent on predator reaction time and possible error together with the normal situation that a chase is not prolonged.

In addition, it cannot be assumed that fish will turn in their minimum radii. For example, consider a 50 cm predator attacking a prey fish with a length of 25 % the predator’s length (Popova, 1967) in the nose-to-tail case. The minimum turning radius of the prey would be 2· 1 cm, and the fish would turn through 180° to swim towards the predator after travelling 6· 7 cm in 0·07 s. The predator would need to be within approximately 5 cm of the prey to intercept in that time. For any larger turning radius of the prey, the predator would have to approach more closely. It would therefore be advantageous for the prey to make large radius turns in the nose-to-tail case. The turning radius of the prey will also dictate the turning radius of the predator, if the latter is to intercept. Consequently, prey turning radius will be a key parameter in determining the outcome of predator-prey interactions. The prey turning radius theoretically varies from the smallest turning radius to infinity, but the latter limit could only occur with S-start kinematics. Therefore, no particular relationship between U₂/U₁ and R₂/R₁ (equation 10) can be expected.

It should be noted that equation (10) will not apply to the present time-dependent motion in any case. No simple relation will hold between U₂ /U₁ and R₂/R₁ where T differs for the two fish as a result of prey reaction time.

The initial starting distance (X₀) separating predator and prey will be particularly important in determining the success of a predator attack. X_o must be less than some given distance depending on the duration of an interaction, prey reaction time and turning radius. Initial starting distances are apparently fairly small. Hoogland et al. (1956) state that pike usually approach to within about 5 cm of their prey, whereas Nursall (1973) states that initial distances are typically less than 15 cm for the same species. This range of 5– 15 cm will be assumed to represent typical values for X₀.

Before considering solutions to the various equations, the parameters identified above should be collated. These are still restricted to cases of geometric similarity.

First, the predator has the opportunity to catch its prey because of the latter’s reaction time, ΔT₂. Secondly, the path of the predator must depend on the initial distance separating the predator and the prey, X_o, and the turning radius of the prey, R₂. These two factors alone dictate the feasibility of a predator intercepting its prey in any given time.

When X₀ and initial R₂ favour prey capture, the prey has the opportunity to escape by manoeuvring. Then the predator must also manoeuvre when its ΔT₁ with attendant error possibility will provide the prey with a chance to escape.

It is apparent that relative predator-prey performance can indicate the likelihood of predator success (Howland, 1973) but cannot predict the outcome.

Interrelations between X_o and R₂ are illustrated in Fig. 4 when the predator just intercepts the prey after given times, T, for the fish accelerating from rest (Fig. 4A), and for various prey ΔT₂ (Fig. 4B). As expected, the greater T and ΔT₂, the greater the permissible range of X₀ for the predator.

The prey can minimize the range of X₀ for the predator (to the prey’s advantage) by making R₂ large relative to the minimum turning radius. However, when R₂ is large, the prey’s displacement relative to the original predator-prey axis will be small. This in turn will minimize predator correction, minimizing the importance of predator ΔT₁ Required predator corrections will be maximized when the prey turns in the smallest

R₂ to accelerate at 90 ° to its original axis. Turning angles of this magnitude were typical of L-starts in the present experiments. Turning through a larger angle would result in the prey moving closer to the predator.

A turn through 90 ° occurs when ⁠. Fig. 4A indicates that R₂ is not likely to be limited by the minimum acceleration turning radius unless the prey is very large or T is very small.

The magnitude of R₂ may be limited in practice within a fairly narrow range. The lower limit of R₂ should not exceed that given when ⁠. The maximum will be given by the recoil path of the centre of mass during L-starts of smaller fish. since X_o is maximized when R₂ is large, values of R₂ would be expected to approach the upper limit in order to increase the prey’s chance of escape. Furthermore, the prey presumably accelerate at the maximum rate. Since the recoil of the centre of mass is proportional to acceleration rate (Hertel, 1966; Weihs, 1973) and maximum acceleration rates were found to be independent of size, R₂ should tend to be independent of prey size.

The smallest value of R₂ may not depend primarily on size but on the acceleration time to the end of stage 2. This occurs because smaller fish (with a greater probability of L-starts) would not be free to make correction manoeuvres before the end of stage 2 and it is disadvantageous to turn through an arc greater than to move towards the predator. Therefore, the minimum radius to turn through 90 ° is given when R₂= 2.S₂/π.

Assuming the above reasoning is applicable to real predator-prey interactions, the prey’s response to a predator attack would be reasonably predictable. Under these circumstances, an experienced predator would learn to execute the best interception tactics with erosion of the advantages accruing to the prey from predator ΔT_2.

The outcome of a predator-prey interaction will still depend on prey manoeuvre, providing this is unpredictable. This argument emphasizes that the prey must be able to manoeuvre freely, independent of acceleration. For L-starts, such free manoeuvre is restricted to stage 3. The unpredictability of avoidance behaviour following initial acceleration of Notropis hudsonius is graphically described by Nursall (1973).

An estimate of the optimum (maximum) duration of a predator-prey interaction can be made for the predator to catch the prey, assuming that the ability of the prey to escape is dependent on the prey’s ability to manoeuvre freely. For a smaller prey fish, with likely L-starts, manoeuvre is not free until the end of stage 2, which will be of the order of 0 ·08 s from the start of the prey’s response to attack (Table 3). The prey’s ΔT₂ is expected to be of the order of 0 ·02 s. Therefore, the prey can freely manoeuvre after approximately 0 ·1 s following attack, and the predator should strike within that time. It should be noted that according to the above reasoning, the decrease in acceleration time to the end of stage 2 with decreasing size is advantageous to the prey because the prey would be able to manoeuvre freely earlier than a larger fish. Conversely, the predator should attack the largest possible prey. This advantage might be offset by the increasing number of S-starts in larger fish with a consequently less predictable range of initial acceleration patterns of the prey.

Fig. 4 shows that the predator would be unable to intercept the prey in 0 ·1 s for the nose-to-tail case unless X_o was less than 5 cm or ΔT₂ was greater than about 0 ·025 s. These values are the thresholds for the ranges expected, but indicate that there would be very little latitude for predator error.

The various strategies for a predator and prey in the nose-to-tail case are summarized in Table 5 essentially as predictions that can be tested for predator-prey interactions. In general, the predator should approach the prey as closely as possible under any circumstances, a not unexpected conclusion. The prey should prolong an interaction until it can manoeuvre freely. ΔT₂ should be as small as possible but this is not under the fish’s control. When ΔT₂ is small, and presumably similar for both predator and prey, then for the prey to have the best chance of escape, R₂ should be as large as possible. This will minimize the range of permissible X_o for a given T before which free manoeuvre is possible. When ΔT₁ is large, the prey would have the best chance of escape when R₂ is small enough that the prey moves normal to its original path, forcing the predator to manoeuvre. In the nose-to-nose case, timing and predator accuracy are expected to be crucial in determining the outcome of an interaction.

Examples of relations between X_o and R₂ for the nose-to-nose case are illustrated for various T(Fig. 5 A) and various ΔT₂ at T = 0 ·1 s (Fig. 5B). As expected, the range of permissible X₀ is very much larger in the case where two fish initially move towards each other. Applying the principles discussed for the nose-to-tail case, X_o will be within the range observed for pike (Hoogland et al. 1956; Nursall, 1973) for T up to 0 ·1 s. Therefore, the predator will have a wider range of possible X_o in situations approaching the nose-to-nose case.

In contrast to the nose-to-tail case, the permissible range of X_o will be minimized when the prey turns in the smallest possible R₂. Then the prey would quickly complete a full turn to move away from the predator. Such a turn is easily executed and completed during the first two stages of a fast start (Fig. 1C). A turn of this nature would again initiate a chase situation, and subsequent prey escape would depend on its free manoeuvre following the completion of stage 2.

The radius of the smallest possible turn is given when S₂/R₂ = w. Any smaller R₂ would result in a full turn completed before the end of stage 2 and correction would then be problematic. Any larger R₂ would result in the prey moving towards the predator for a longer period of time. Then the range of X_o for the predator rapidly increases. For example, the range of permissible X₀ would be 10 ·4 cm when T = 0 ·1s, ΔT₂ = 0 ·02 s, S₂/R₂= π. X_o increases by a factor of 1 ·5 when ⁠. In this respect, the apparent decrease in X_o with increasing ΔT₂ in Fig. 5 A is not realistic for a prolonged interaction between a predator and prey. It merely reflects the delay in the prey’s response, but in practice the prey would continue to move towards the predator with reduced chance of escape.

Interactions are summarized in Table 6 for the nose-to-nose case. In general, it is apparent that the predator should have a better chance of catching the prey when the initial predator-prey orientation approaches the nose-to-nose case. This conclusion is supported by observations by Hoogland et al. (1956) and Nursall (1973) that perch prefer to take prey by the head. Hoogland et al. (1956) found that perch attempted to manoeuvre into a nose-to-nose situation before striking their prey.

The frequency of L- and S-starts varies with size so that larger predators are likely to show S-starts. The significance of this size effect lies in the difference in freedom to manoeuvre during stages 1 and 2 of the two fast-start patterns. This freedom is high in S-starts but low in L-starts when a recoil yawing turn is a consequence of acceleration.

S-start patterns are advantageous to a predator since it must accelerate towards a specific objective. Even when X_o is small, the predator must also turn to some extent depending on the direction of prey response. S-starts permit acceleration in a straight line as well as turns to either side during stages 1 and 2.

However, it would be expected that S-starts would also be advantageous for the prey. Such acceleration patterns would permit the prey to accelerate in a straight line (R₂= infinity) in the nose-to-tail case, while still permitting tight turns in the nose-to-nose case. Instead, an L-start will result in a larger R₂ than is considered advantageous in the nose-to-nose case. The only advantage that is likely to accrue from L-starts by the prey will be in forcing the predator to manoeuvre. According to the present interpretation, this would imply that ΔT₁ is intermediate in value, probably of the order of 0 ·025 s.

The outcome of a predator-prey interaction between geometrically similar fish apparently depends more on reaction times and accurate timing than on performance differences. If the predator and prey are geometrically dissimilar, performance differences may become important. For example, reduced prey performance for geometrically dissimilar prey increases the probability of prey capture in the same basic way as does increasing ΔT₂. Thus, for the predator to catch its prey, X₀ should be small, and when the range of permissible X_o is large, predator success is favoured. Increasing ΔT₂ increases the range of X_o (Figs. 4B, 5 B). Reduced prey performance will similarly increase the permissible range of X₀. In contrast to increased ΔT₂, body form differences will not effect the timing when the prey is first able to manoeuvre freely.

Acceleration rate, and hence the values for S at T, depend on the percentage of the body represented by myotomal muscle (Webb, 1975a). A body with a circular crosssection maximizes the percentage of myotomal muscle and also minimizes the body surface area per unit mass and, therefore, frictional drag. Any body sectional shape deviating from a circular section will result in a reduced percentage of myotomal muscle and reduced acceleration rate (Webb, 1975a; 1976).

The magnitude of possible effects of body shape on X_o can be illustrated from data in Webb (1975 a). Observations of acceleration performance were made on the green sunfish, which has a compressed truncate body. The compression of the body is not as great as for some other fish, particularly reef inhabitants. The sunfish had a mean length of 8 ·0 cm and the myotomal muscle was 34% of the body mass. The fish travelled 2 ·85 cm in 0 ·08 s, the time to completion of stage 2. According to the present data, an 8 ·0 cm trout, with 46% of the body represented by myotomal muscle, would travel 8 ·0 cm in the same time and also complete acceleration stage 2. Webb (1975 a) obtained a lower value for S of 5 ·4 cm, travelled in 0 ·08 s to the end of stage 2 for trout with a mean length of 14 ·3 cm and 49% body mass as myotomal muscle. The differences in performance may result from effects of stock and/or season. The results show that X_o could be increased by 2 ·5 to 5 cm because of the difference in body morphology. These distances are large in relation to the range predicted as optimal (Tables 5 and 6) and also to that observed for pike (Hoogland et al. 1956; Nursall, 1973) and would clearly favour the predator. It should be noted that many fish with a body form unfavourable for acceleration, e.g. Ictalurids and some Centrachids, often have other passive defences in the form of spines or hard rays.

The various cases of predator-prey interactions discussed above assume the predator and prey are stationary before the predator attacks. If the fish were in fact moving, the range of X_o could be decreased in approaching the nose-to-tail case and increased in approaching the nose-to-nose case. Descriptions of predator and prey behaviour suggest that initial swimming speeds of both are likely to be small and often negligible (Hoogland et al. 1956; Nursall, 1973).

This work was supported by the National Science Foundation Grant no. BMS75- 18423.