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Swimming speeds are the most important index for the evaluation of the fish swimming performance. The terminologies and classifications of the fish swimming performance were summarized in this paper. Taking into consideration of the widely used evaluation approaches of the fish swimming performance by different researchers, a recommended classification methodology of the fish swimming performance was proposed by the authors. And a new concept of the swimming speed, the Maximum Domed Swimming Speed (DSS), was introduced into this new classification framework together with a discussion on its calculation method and the practical significance. According to the classification system, the fish swimming speeds are classified into five categories: Optimum Swimming Speed, Maximum Sustained Swimming Speed, Critical Swimming Speed, Maximum Domed Swimming Speed, and Burst Swimming Speed. Other concepts of swimming speeds are generally merged into the above five categories, respectively. Furthermore, possible relevancies among the Maximum Sustained Swimming Speed (MSS), the Critical Swimming Speed (CSS), and the Maximum Domed Swimming Speed (DSS) were discussed. It was concluded that these three swimming speeds, in a sense, can be regarded as the equivalent indices for the evaluation of fish swimming performance.

Swimming performance is considered as a critical character determining the survival of many fishes in the natural circumstance [

However, while doing so, only a few authors adhere to the experimental protocols originally suggested. Instead, they applied a great variety of durations for testing the swimming speeds of fishes. Take the sustained swimming speed as an example, the swimming time durations of 4 h [

The main purpose of this paper is to propose a new classification of the swimming speeds according to the swimming status of fishes without strict limitation to their swimming time durations. And a new concept of swimming speed, the Maximum Domed Swimming Speed, was introduced into this new classification framework together with a discussion on its calculation and the practical significance.

Briefly, we classified the swimming status into continuous swimming and transient swimming, as shown in

In steady swimming status, fishes are exposed to a certain velocity which is not altered during the test. Generally, it is also called cruising swimming or sustained swimming [

According to the discussion above, we classified the following two concepts: the Optimum Cruising Swimming Speed and the Maximum Cruising (or Sustained) Swimming Speed into the steady swimming performance. A research purpose such as foraging, growth rate, migrating distance, and so on, must be determined when the former concept is used, and the period of swimming time is needed for the latter. For example, Ware [

Hammer’s [

The Maximum Cruising (or Sustained) Swimming Speed refers to the maximal steady speed that a fish can withstand for a certain length of swimming time and the fish will end in fatigue. Customarily, the concept, Maximum Sustained Swimming Speed (MSS) was used more often by many authors than the Maximum Cruising Swimming Speed because the word “cruising” is normally regarded as the sign of swimming status of a fish without fatigue. Apparently, the MSS depends solely on the swimming time with other conditions unchanged. A period of swimming time less than 20 s is regarded as the range of transient swimming status, and thus 20 s is normally accepted as the lower limit for a fish to maintain sustained swimming status [7,9]. Theoretically, there is no limitation to the maximum swimming time. But the longer the swimming time is given, the lower the MSS will be. It is difficult, if not impossible, to measure the MSS directly. However, it is rather easy to record the swimming times of the fishes at different steady speeds in laboratory experiments. Therefore, it is definitely possible to set up a regression relationship between the swimming speed and the swimming time, and the MSS can be obtained by interpolating in the regression curve according to the designated swimming time that a fish will be forced to swim [

Fish is exposed to varying speeds in unsteady swimming status which includes incremental swimming and decremental swimming. To date, almost all the tests of unsteady swimming performance were carried out in the incremental swimming status. The spontaneous swimming is, needless to say, a status of unsteady swimming but not an index for evaluating a fish’s swimming performance. A fish exposed to waves may also be regarded as a case being in unsteady swimming status. However, this is a very complicated topic and to date there is no relative result been published. Considering about its specialty, we suggest carrying out the research works in this field separately and it will not be discussed in this paper.

To date, the Critical Swimming Speed (CSS) is the most important index to evaluate the unsteady swimming performance [23-27]. It is measured using incremental swimming approach. The current velocities are not increased gradually, but rather in steps, each speed being maintained for a certain period of time until exhaustion occurs [

The CSS has been favored largely because it takes a shorter time to conduct and uses smaller batches of fish for a statically meaningful value [5,27,32]. However, the CSS protocol is sometimes still time consuming and is not without limitations. A long period of testing time is required when large time intervals and small velocity increments are used in the tests. Therefore, some other approaches were proposed to cut down the time durations in the tests. Jain et al. [

It is generally assumed that the CSS is the speed at which the maximum oxygen uptake occurs [

The maximal tidal current velocity is the key factor determining the final condition of a fish exposed to tidal current. If a fish can finish the whole process of a half tidal period (approximate 6 h 12 min for semi-diurnal tide) and happens to be fatigued in the end, the maximal tidal current velocity is called the Maximum Domed Swimming Speed (DSS). The DSS is very difficult, if not impossible, to measure either in the laboratory or in the natural environment. The authors proposed a semi-empirical & theoretical method for calculating the DSS, which is based on the tidal current theory and the empirical relationship between the maximum sustained swimming speed and the maximum sustained swimming time. This will be discussed more in the following.

In many fishes, the Burst Swimming Speed (BSS), anaerobic speed, is more useful to avoid predator attack, gain food, escape from trawls than sustained swimming speed [4,34], and is critical to their survival. It is generally accepted that burst swimming is performed anaerobically and it can only be maintained for a very short periods of less than 15 - 20 s [7,9]. According to Webb [

The Maximum Domed Swimming Speed (DSS) refers to the maximal tidal current velocity that a fish can finish the time duration of a half tidal period and happens to be fatigued in the end. During this process, the fish will be exposed to the currents which will increase from zero to the DSS and drop down to zero again according to the tidal principle. The DSS has practical meanings as it can be used for selection of suitable fish farming sites.

As mentioned above, the DSS is difficult to be obtained through directly laboratory measurements. A mediate method is needed. Again, we take the ideal semidiurnal tidal current as an example. The values and directions of tidal current will vary with time, which are controlled by the half-day period and the half-month period, and can be calculated using the following formula [

where, is the tidal current velocity at time. The first term in the right part is the velocity variation in the half-day period and is followed by that in the half-month period. is the average velocity amplitude which is written as:

where, and refer to the maximum tidal current velocities in spring tide and neap tide, respectively. is the coefficient of velocity fluctuation and is calculated by:

in Formula (1) is the half-day period, which equals to 12.4 h; is the half-month period, which equals to 14.75 d. For evaluation the swimming performance of a fish, the half-day period () is long enough. Thus, only the first term in the right part of Formula (1) is used and the average velocity amplitude is substituted by the maximal tidal current velocity, i.e.

Within the half-day period, the current velocity will reach the same maximum values twice, but run in opposite directions. Fortunately, the current direction has no influence to the fish swimming performance. Therefore, it is can be discussed within, namely, in which the velocity will increase from zero to its maximal value and drop down to zero again. Here, is the very speed of the DSS.

In order to obtain, the DSS, we have to correlate Formula (4) to fish swimming performance. According to some authors [11,12], there is a kind of exponential relationship between the maximum sustained swimming time and the MSS, which is written as:

where, means the maximum sustained swimming time when a fish is forced to swim at velocity (the MSS); and are the coefficients which can be obtained through experimental measurements and statistical analysis. By substituting (4) into (5), we have:

where, means the maximum sustained swimming time of a fish exposed to the tidal current velocity at time. The Critical Swimming Speed () is calculated using the following formula as originally given by Brett [

where, is the penultimate velocity at which the fish swam before fatigue; is the velocity increment (cm/s); is the elapsed time in the last velocity stage; is the time interval (normally form 20 min to 60 min [

The, i.e. the DSS, can be calculated by Formula (8) through numerical integrating. However, the DSS depends on the coefficients and which are obtained through experimental tests. This means that the DSS is relevant to the MSS. They may, in a sense, be regarded as the equivalent index for evaluating the swimming performance of fishes.

Swimming speeds including Sustained Swimming Speed, Critical Swimming Speed and Burst Swimming Speed are the most commonly used indices for evaluating fish swimming performance in the past several decades. Researching works on swimming speeds including their definitions, measuring approaches, affecting factors and the interrelationships have been carried out extensively. Hammer [

Taking into consideration of the widely used evaluation approaches of fish swimming performance by different researchers, a new classification methodology was proposed by the authors of this paper. And a new concept of swimming speed, the DSS, was introduced into this new classification framework together with a discussion on its calculation method and practical significance. According to the new classification system, fish swimming speeds are classified into five major categories: Optimum Cruising Swimming Speed (OSS), Maximum Sustained Swimming Speed (MSS), Critical Swimming Speed (CSS), Maximum Domed Swimming Speed (DSS), and Burst Swimming Speed (BSS), as shown in

It has always been a question about the influence of testing protocols on fish swimming performance. With regarding to the CSS, the influence of time intervals and velocity increments on its result has caught many attentions [22,27]. However, it still cannot draw a general conclusion on how the testing protocols will affect the final values of the CSS. Hammer [

Despite the defectives of the CSS, it has been used extensively as an important index of fish swimming performance because of the smaller batches and less experimental time to run the tests [5,27]. By contrast, more batches and longer time are needed to run the MSS tests, and the numerical regression and interpolation processes are needed to obtain the final values of the MSS. However, the MSS within any time durations and the maximum sustained swimming time at any speeds can be figured out once the regression relationship between them has been set up. In addition, it is a good way for investigating the biochemical changes, such as fat, glycogen and lactate, in muscles and livers of fishes [

Before carrying out the tests of the MSS, the fishes should be introduced into a flume tank and be acclimatized to the temperature, light, original current, and so on. After a period of acclimation, the current is increased steadily [

Both the DSS and the CSS belong to the unsteady swimming speeds. The DSS is tested according to the tidal current variation law, while the CSS testing uses an artful protocol in a rather random way. However, they are similar in the process as one DSS test covers double CSS tests without considering about the influence of the change of velocity orientations (increase or decrease) on the results. Therefore, a kind of relationship may be found through substantial tests on both speeds. Once the relationship between them has been set up, the swimming speeds can be converted each other. The most important is the CSS will possess a practical meaning. But before doing so, the influences of the velocity orientation, velocity increment, time duration, time interval, and so on, on the final values of swimming speeds, should be investigated in advance.

In the other hand, the DSS can be figured out using Formula (8) which is derived based on the mathematical regression model of the MSS as Formula (5). This means a certain relationship between the DSS and the MSS definitely exists. However, an assumption was introduced from the CSS Formula (7) into DSS Formula (8): the stamina of a fish is distributed uniformly during the whole period of steady swimming. This assumption is never proposed but has been used naturally in the CSS calculation. Anyway, more verification on its validity is needed. The authors of this paper made some preliminary tests on the DSS of six Sciaenops ocellatus (caught from a fishing cage with average body length of 36.3 cm). During the tests, the DSS was 76 cm/s calculated by formula (8). The velocity increased from zero to 76 cm/s and then decreased to zero again according to the semidiurnal law. Although all the six fishes passed the maximum velocity, they stopped swimming at different time on the decreasing stage. The results are rather discrete. A possible reason is that the fishes had been cultured in a laboratory tank for 11 days and had been used for several other experimental tests. More tests and new scenarios are probably needed for further verifications.

As discussed above, we may draw a general conclusion that these three swimming speeds are, to some extent, the same indices for evaluating fish swimming performance. Amongst these three speeds, the DSS has a very clear practical meaning. It should be chosen as an important index for the selection of fish farming sites. Furthermore, it is recommended to use the MSS for evaluating the swimming performance of freshwater fishes, while the CSS and DSS may have little meaning because the river currents are generally steady.

This work was financially supported by the National Science and Technology Support Program No.51109187, the Zhejiang Provincial Climbing Program No. pd2013217, and the project form Zhoushan Science and Technology Bureau, No.2013C41002.