Rainbow trout provide the first experimental evidence for adherence to a distinct Strouhal number during animal oscillatory propulsion

Reproductive success for many salmonid species depends on completion of a return migration to natal riverine spawning grounds (Farrell et al., 2008; Finstad et al., 2005). During these migrations, fish cope with changes in salinity, water temperature (T_water) and water speed (Hodgson and Quinn, 2002; Klemetsen et al., 2003). Elevated T_water linked to climate change, however, is thought to be having a negative impact on migration success in some river systems (Karppinen et al., 2002; Laine et al., 2002; Thorstad et al., 2008). Reports show that salmon temporarily cease migration in water over 21°C (Farrell et al., 2008), and there is no evidence of successful migrations being established by a population at a temperature in excess of 19°C (Hodgson and Quinn, 2002). Fish are ectotherms, so increased T_water elevates metabolic rate, resulting in a reduced aerobic capacity (the difference between maximum and minimum metabolic rate) (Farrell, 2009; Wang and Overgaard, 2007). Because locomotion is energetically costly, the reduced aerobic scope at warm temperatures, coupled with a decreased oxygen carrying capacity of water, may have implications for the biomechanical efficiency of swimming.

Rainbow trout, Oncorhynchus mykiss (Walbaum 1792), are sub-carangiform swimmers relying on oscillations of their tail (caudal fin) driven by muscle to produce thrust for forward propulsion. It is well established that vertebrate skeletal muscle function is affected by temperature, with Q₁₀ reported to range from 1.5 to 3.0 (Bennett, 1984; James, 2013), and, as fish are ectotherms, changes to T_water will directly affect muscle temperature (Johnston and Temple, 2002;

Rome et al., 1984). Previous studies have shown tail beat kinematics to be affected by T_water changes (Stevens, 1979). Consequently, T_water manipulations may provide a potential mechanism for experimentally testing the importance of adherence to a given optimum St, as well as being of importance in identifying the effects of temperature upon migratory swimming ability.

In the present study, (rate of oxygen consumption) and tail beat kinematics were quantified in rainbow trout swimming at two temperatures over a range of increasing U. Using the same individuals of a single species in both temperature treatments obviates the aforementioned variation in St that is due to body size, species and U. The hypotheses tested were that the St used at a given U would not be affected by temperature, as the fish would strive to maintain optimum swimming kinematics. St may vary across U, however, and of course, whether this hypothesis is truly tested was also dependent upon an observable change in kinematics. The second hypothesis was that the metabolic stress caused by the increased T_water would lead to an increase in , which would be more marked at higher, more physiologically demanding speeds.

St increased with U, but did not differ between temperature treatments across all speeds (Fig. 1, Table 1). The increase in St with U based upon the lines of best fit from the GLM (Fig. 1A) was slight, however, being 0.19 for both treatments at 0.68 m s⁻¹, and 0.22 and 0.23 at 1.11 m s⁻¹ for control and warm treatments, respectively (Fig. 1A).

A increased concomitantly with, and at the same incremental rate as, U in both treatments (Fig. 1B). A, however, was higher (by 4 mm) in the control group at all speeds. A did not differ between individual fish (Table 1). In contrast, f_tail was not affected by U, but was higher in the warm temperature treatment (4.70±0.08 Hz) than in the control treatment (4.17±0.09 Hz) (Table 1). f_tail also varied among individual fish. The increased St with U is therefore modulated through an increase in A. The warm temperature induced a change in fish kinematics whereby St was maintained at control temperature levels through a trade-off between f_tail, which was increased, and A, which was decreased.

increased with increasing U at the same incremental rate in both treatments (Table 1). , however, was higher at all speeds in the warm temperature treatment than at the control temperature (Fig. 2). The same absolute increase across all speeds at the warm temperature suggests that the increased metabolic cost is focused on basal processes and not necessarily swimming locomotion per se. differed between individual fish (Table 1).

Fore–aft positional change (accelerations) within the working section was small for both T_water treatments (means were 0.005±0.001 and 0.003±0.001 m s⁻² for control and warm temperatures, respectively). Furthermore, there was no interaction effect between T_water and U (F_1,65=0.80, η_p²<0.01, P=0.375) on the accelerations during the recorded swimming bouts, and they did not differ between fish, T_water treatment or with U (fish, F_7,66=1.44, η_p²=0.13, P=0.204: T_water, F_1,66=0.909, η_p²=0.01, P=0.344: U, F_1,66=3.34, η_p²=0.05, P=0.072). Hence, fore–aft positional change was both minimal and consistent throughout all of the experimental trials. This, coupled with the fact that data were only collected when the fish remained in the centre of the working section, means that the fish were swimming at a steady and near-constant U.

As hypothesised, when the locomotor system of the trout was disturbed, they adhered to the same St at any given U (Fig. 1A). Which variable the temperature directly affected (Fig. 1B,C) is not evident, but St was maintained through a trade-off between an increase in f_tail and decrease in A. Nonetheless, this is the first experimental (involving a manipulation) evidence for an apparent adherence to a preferred (perhaps optimum) St for an animal using oscillatory propulsion. At both temperatures, a slight increase in St with U was driven by increases in A, whilst f_tail was constant across all velocities. Invariant f_tail suggests that muscle contraction frequency may be optimised within very narrow bounds (James, 2013), with the centre of these bounds increasing with temperature (Fig. 1C). The contractile properties of vertebrate muscle function are widely agreed to show high temperature dependence (Bennett, 1984; James, 2013), and muscle contraction kinetics are slowed and maximum power output of red muscle decreased at lower temperatures in a number of bony fish and shark species (Altringham and Block, 1997; Bernal et al., 2005; Bernal and Sepulveda, 2005; Bernal et al., 2009; Donley et al., 2012; Donley et al., 2007; Shadwick et al., 2004).

An invariant f_tail and increasing A with increasing U is contrary to previous findings. Earlier work in fish suggests that f_tail is modulated (increased) whilst A remains constant with increasing U (Bainbridge, 1958; Hunter and Zweifel, 1971; Rome et al., 1990; Rome et al., 1984; Stevens, 1979; Tytell, 2004; Webb, 1971), although at very low speeds A may also be modulated (Bainbridge, 1958; Webb, 1971). A similar increasing f_tail and invariant A with U was also found across seven species of cetaceans (Rohr and Fish, 2004). In birds, f_wing also appears to increase with U, but A decreases with U [e.g. see table 2 in Tobalske et al. (Tobalske et al., 1999)]. There are, however, many differences between the present study and those previously conducted: the specification and design of the flume, the method for persuading the fish to swim (light versus electric grid), the camera resolution and the species studied. For example, the cetaceans were swimming freely around a large elliptical pool, in a broad range of temperatures from 12 to 20°C and were cajoled into swimming at maximum U, which may not be their preferred cruising speed (Rohr and Fish, 2004). Also, it is intuitive to expect differences in tail beat kinematics across species, relating to habitat (i.e. still water versus flowing water species) and swimming form (i.e. carangiform, sub-carangiform, anguilliform or thunniform). Therefore, without a multi-species study under standardised conditions, which remains a priority for future work, it is perhaps premature to speculate at length about the incongruence in speed effects on tail-beat kinematics.

The majority of calculated St for the rainbow trout were between 0.20 and 0.40, within the hypothesized optimum range for high propulsive efficiency (Triantafyllou et al., 1993). Nevertheless, several values fell below the optimum range (Fig. 1). Thrust, however, is still produced outside of the optimum range, albeit with a much reduced propulsive efficiency (Anderson et al., 1998; Barrett et al., 1999; Read et al., 2003; Triantafyllou et al., 1991). Perhaps the low St recorded here were due to unpreferred kinematics resulting from stress effects. St was previously shown to decrease with U, ranging from 0.45 to 0.30 in rainbow trout (Webb, 1971) and ~0.41 to 0.30 in jack mackerel (Hunter and Zweifel, 1971), and was found to be independent of U in seven species of cetacean (Rohr and Fish, 2004), which is contrary to the findings of the present study. Previous studies on temperature change and fish tail kinematics are limited and the effects are not consistent, which again may be species dependent. For example, increased T_water increased f_tail in bass (Stevens, 1979), decreased f_tail in rainbow trout (Stevens, 1979) and had no effect on f_tail in carp, Cyprinus carpio (Rome et al., 1990). T_water also did not affect A in carp (Rome et al., 1990). Therefore, although the previous data for rainbow trout (Webb, 1971) are contrary to the findings of the present study, those for bass are congruent (Stevens, 1979). Again, these differences are likely to be species specific, as a result of different data analysis approaches or differences in methodology. Indeed, A is generally chosen as a proxy for wake width. Although this is a reasonable assumption, it is likely that tail shape and other kinematic parameters (for example, the phase angle between tail heave and pitch) will subtly affect the relationship between A and wake width, which in turn would lead to differences in St calculations between species. If hydrodynamics dominate, however, then for an individual fish, St should not vary as significantly as other parameters, as shown in this present study.

increased with U and was higher at the higher T_water treatment (Fig. 2). The incremental change in with U was similar at both T_water values and, therefore, the hypothesised greater increase in at higher T_water was not observed. The increased metabolic costs at increased T_water appear to be a consequence of an increase in basal/routine processes. An increase in with increasing U until U_crit – defined as the maximum aerobic swimming speed of the fish (Jain et al., 1997) – is in agreement with previous studies (Brodeur et al., 2001; Gamperl et al., 2002; Steinhausen et al., 2008). Furthermore, acute temperature changes (increasing T_water by a rate of 2°C h⁻¹) leading to increased is well documented (Altimiras et al., 2002). Here, continued to rise towards U_crit, instead of levelling off at high U (Gamperl et al., 2002; Thorstad et al., 2008). This result may be explained if the fish were not fully reaching U_crit. Indeed, fish refusing to swim at U_crit is frequently reported in swim flumes that do not employ electric grids (Rodnick et al., 2004).

Swimming performance also appeared to be influenced by T_water, with faster top speeds being measured at higher T_water in five out of eight fish (Fig. 2), which is in agreement with previous work (Farrell, 2002; Rome et al., 1990; Rome et al., 1984; Taylor et al., 1997). This finding suggests that warmer T_water may aid swimming performance, at least within the thermal tolerance zone of the fish.

In conclusion, rainbow trout at any given U adhered to the same St, even though their tail beat kinematics were disrupted by a T_water change. This is the first experimental evidence for the potential importance of maintaining kinematics at a single optimum (or preferred) St. An increase in T_water did increase basal metabolic costs, but contrary to hypothesised, it did not affect the incremental cost (changes in with U) of swimming. It would appear that rainbow trout, and perhaps other fish species, possess the plasticity to maintain their movement patterns at a biomechanical optimum when faced with thermal adjustments to muscle function and increases in basal energy expenditure. In fact, marginal increases in T_water may actually improve swimming performance in terms of the top speed attainable, which may be advantageous for migration, foraging or predator avoidance. Furthermore, future predictions of changes to T_water of lakes and rivers are only 5–10°C over the next 100 years (Sharma et al., 2007), and it appears that rainbow trout, at least, can cope with this easily in terms of swimming biomechanics.

All experimental procedures were covered by a UK Home Office project licence (40/3584) held by H.A.S. and were under the ethical approval of the University of Manchester.

Eight sexually immature female rainbow trout (mean length=0.29±0.003 m, mean body mass=262.20±0.03 g) (Chirk Trout Farm, Wrexham, UK) were housed on a 12 h:12 h dark:light cycle in aerated 500 l re-circulated freshwater tanks at 11±1°C. Temperature, pH, ammonia and nitrate levels were closely monitored and 30% water changes were conducted every 3 days. Fish were fed to satiation on commercial trout pellets three times a week, but were fasted for 24 h prior to experimentation. All husbandry and housing conditions were in accordance with the local handling protocols and adhere to UK Home Office legislation.

Tail beat kinematics were captured using an HDR-SR8E (Sony, Japan) video camera filming at 100 frames s⁻¹ positioned on a tripod above the working section so that the sensor plane was parallel to the water surface. The working section was briefly illuminated by a single halogen lamp during filming. To determine A, the position of the tail tip was digitized and tracked using Tracker 4^© video analysis software (Open Source Physics, Java framework). Data were only collected from fish that were swimming in the centre of the working section. U was adjusted to account for fore–aft positional variations within the working section between the beginning and end of the video clip. No corrections to U were made to account for either fish buoyancy or blockage effects. Of course, these were the same in both treatments so do not compromise the validity of the comparison between the two temperature treatments.

Experiments were conducted on individual fish over the course of 3 weeks. Experiments were run on all fish at 11±1°C, which was also the acclimation (control) temperature and then at 20±1°C. This temperature was chosen because 20°C is below the critical thermal maximum for rainbow trout, but above optimum temperature (T_opt) and thus should cause a reduction in their aerobic capacity (Farrell, 2009) and affect swimming kinematics. All aspects of the respirometry and kinematic evaluation were kept constant between the two temperatures.

Fish were netted from the holding tank and transferred into the swim flume respirometer. Fish length was measured so that speed increments relative to each individual's body length (l_body; m) could be calculated as l_body/U. l_body increments were used to keep individual fish effort constant, but actual U (0.28 m s⁻¹ to 1.11 m s⁻¹) was used in the data analyses. Note that slight changes in water viscosity between the two temperatures (~1.2 and 1.0 mPa s at 11 and 20°C, respectively) were unlikely to have any effects on the fish (Danos and Lauder, 2012).

Fish were then held in the respirometer for 12 h prior to the start of the swimming speed trial. During this period, U was maintained at 0.28 m s⁻¹ (~1l_body s⁻¹) to provide a current for the fish to orientate towards whilst remaining quiescent and to ensure continuous mixing within the respirometer. For experiments at 20°C, the fish was placed in the swim flume at 11±1°C and the water was gradually heated to 20±1°C over the 12 h period prior to the start of the swimming trial. Water oxygen saturation in the swim tunnel was always maintained at >90% by air stones positioned in the reservoir.

For the swimming trial, the fish was subjected to a ramp increase in U, where U was increased from 1l_body s⁻¹ (resting) in increments of 0.0033l_body s⁻¹ until the fish was swimming at a rate of 2.5l_body s⁻¹, which is approximately 70–75% of U_crit. Studies have shown that fish swimming at 70–75% of U_crit have a near-maximal aerobic capacity (Lee et al., 2003; Steinhausen et al., 2008). U was then increased at a rate of 0.2l_body s⁻¹ every 30 min until exhaustion (indicative of U_crit). Kinematics and were recorded at each U. Exhaustion was defined as the point at which the fish stopped swimming, and did not respond to a bright light stimulus by recommencing swimming. At the point of exhaustion, U was decreased to 1l_body s⁻¹ and after an hour of recovery the fish was removed from the respirometer and weighed to determine M_b.

The data distribution of each of the kinematics variables did not differ from normality (Shapiro–Wilk test): St (W=0.985, n=76, P=0.535), A (W=0.978, n=76, P=0.214), f_tail (W=0.984, n=76, P=0.431) and (W=0.972, n=59, P=0.185).

Possible effects of the two temperature (T_water) treatments (warm and control) upon the kinematics variables (and fore–aft positional change within the working section) were investigated using general linear models (GLMs). T_water was included as a factor, individual fish as a random factor and U as a covariate. Individual was included in the GLM because of the repeated measures taken for each fish. Although all the fish swam at a range of U values in both temperature treatments, the number of increments varied, rendering the data unsuitable for a repeated-measures model. The interaction term T_water × U was included to test for differences in the slope of the relationship between the kinematics variable and U. If not statistically significant, the interaction term (T_water × U) was removed from the final GLM.

All statistical analyses were performed using IBM® SPSS® Statistics v.20 and means are displayed ±s.e.m. In some cases within the GLMs unequal group variances were encountered. In these cases, SPSS implements a Satterthwaite's correction of the denominator degrees of freedom and it is this value that is noted in the statistical outputs in the subsequent text (Table 1).

The authors would like to thank Prof. Pat Butler, University of Birmingham, for the generous donation of the swim-flume respirometer. We would also like to thank two anonymous reviewers for their helpful comments on an earlier version of the manuscript.