Optimal swim speeds for traversing velocity barriers: an analysis of volitional high-speed swimming behavior of migratory fishes
S.O. Conte Anadromous Fish Research Center, USGS-Leetown Science Center, PO Box 796, One Migratory Way, Turners Falls, MA 01376, USA
e-mail: tcastro-santos{at}usgs.gov
Accepted 9 November 2004
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Summary |
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Key words: burst swimming, anadromy, sprinting, migration, fishway, fish passage
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Introduction |
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Because of the fitness consequences of swimming performance, locomotor
behavior is a good candidate for optimization. There is disagreement, however,
on what constitutes optimal behavior. Most work in this area has applied
hydraulic equations to generate predictions of optimizing behaviors (Weihs,
1973,
1977
;
Webb, 1993
;
Videler, 1993
). These authors
used equations based on the combined energetic costs of basal metabolic rate
and drag on swimming fish, predicted from hydraulic principles, to create
cost-of-transport models that yield predictions of optimal swim speed; Weihs
(1974
) and Videler and Weihs
(1982
) further described how
burst-and-coast swimming can afford energetic advantages. Trump and Leggett
(1980
) used a different
approach, calculating the metabolic cost of transport directly from empirical
equations derived from respirometry data. Both models generated similar
predictions, namely that fish could maximize energetic efficiency by swimming
at speeds corresponding to about one body length per second (BL
s-1). Data supporting these predictions are sparse, due to the
difficulties of monitoring swimming fish in their native habitat, and a review
of the literature by Bernatchez and Dodson
(1987
) found that such
optimizing behavior is rare, characterizing only certain populations with long
migrations.
Both the hydrodynamic and metabolic cost-of-transport models require the
assumption of ready availability of energy. While this may be reasonable for
aquatic animals swimming at sustained speeds, it does not hold at faster
speeds. At these speeds, contributions of anaerobic metabolism to power
production create limits to endurance, with energy supplied increasingly from
stores contained within muscle fibers, and insufficient time and circulation
to remove metabolic waste products (Brett,
1964).
Because of this, high-speed swimming is not associated with continuous
behaviors like filter feeding or migration through lentic environments (e.g.
Ware, 1975); instead it is
associated with short-term, fitness-critical behaviors, such as capture of
mobile prey, predator avoidance, and traversing velocity barriers during
migrations. For these behaviors, the trade-off between swim speed and fatigue
time may define performance. This relationship has been well studied at
prolonged speeds (Beamish,
1978
; Videler,
1993
; Webb, 1994
),
and is generally thought to follow a log-linear model:
![]() | (1) |
The maximum distance a fish can swim (Ds) can be
described as Us x T, or, from
Equation 1:
![]() | (2) |
|
This relationship is more complex for diadromous migrants confronted with
velocity barriers, such as might be found at rapids, culverts or other
constrictions in a river. Because distance through a velocity barrier is often
unknown, and because of the sometimes dire fitness consequences of failing to
traverse the barrier, fish traversing such barriers should pursue a
distance-maximizing strategy. Moreover, the distance that needs to be
maximized is not the distance swum, or through-water distance, but rather the
distance over ground, as this is what defines the boundaries of the velocity
barrier. In the presence of flow, the ground distance (Dg)
attained at fatigue time becomes:
![]() | (3) |
![]() | (4) |
![]() | (5) |
![]() | (6) |
This relationship, however, is not constant across modes. Brett
(1964) first observed, and
numerous subsequent studies have confirmed (see tables and figures in
Beamish, 1978
;
Videler, 1993
), the existence
of two distinct unsustainable modes of steady swimming: prolonged mode, which
can be maintained for durations of 20 s to 200 min, and sprint mode, which
results in fatigue in less than 20 s. Although a biological explanation for
the existence of these two modes has never been definitively established, the
change is generally thought to be the result of a shift from mixed
contributions of aerobic and anaerobic metabolism and muscle groups in
prolonged mode to almost pure anaerobic metabolism and muscle groups in sprint
mode (Brett, 1964
;
Webb, 1975
). Regardless of the
underlying cause, the slopes of the swim speedfatigue time
relationships of these two modes vary in ways that are consistent across taxa,
namely b is steeper (larger negative magnitude) in prolonged mode
than in sprinting, and the transition between modes is discrete. This means
that the distance-maximizing swim speed, while still a constant groundspeed
within a particular mode, will show a discrete shift to a higher value as fish
shift from prolonged to sprint mode.
Because of the parameters describing the swim speedfatigue time
relationship, maximum distance in prolonged mode (DmaxP)
greatly exceeds that in sprint mode (DmaxS) at low
Uf. However, as Uf increases, this
difference declines, and eventually DmaxS exceeds
DmaxP (Fig.
2A). This suggests that there exists a critical speed of flow
Ufcrit, at which a mode shift should occur
(Fig. 2B). At
Uf values less than this, fish should swim at the optimum
prolonged speed; at greater values, they should swim at the optimum sprint
speed. This critical flow speed can be calculated as the point where the
predicted distance maxima are equal, i.e. from Equations
1,
4 and
6, where
![]() | (7) |
![]() | (8) |
|
The above leads to the following hypotheses: (1) when confronted with velocity challenges, fish should swim at a constant groundspeed of 1/b BL s-1; (2) selected groundspeed will vary with mode, being lower at prolonged than at burst speeds; (3) The velocity of flow at which the shift to the sprint optimum will occur is described by Equation 8; and (4) to the extent that fish fail to approximate Ugopt, the deviation will reduce maximum distance of ascent. This paper describes tests of these hypotheses with data from six species, volitionally swimming up a large scale, open-channel flume.
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Materials and methods |
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Water levels were monitored and recorded every 60 s in the headpond, at
three locations within the flume, and in the staging area. Settings for the
headgate and tailwater weir were likewise monitored. Instantaneous velocity
estimates were generated for each point of a 10 cm grid over the full
cross-section of the flume using a combination of physical modeling and
hydraulic equations, confirmed with direct measurements in the flume
(Fig. 3;
Castro-Santos, 2002;
Haro et al., 2004
). Mean
cross-sectional velocities were then controlled to within ±5% of their
average values within each nominal velocity, corresponding to 1.5, 2.5, 3.5
and 4.5 m s-1, the variability arising from fluctuating water
levels, both in the power canal and within the facility
(Table 1).
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Data collection
To avoid using coercive measures to motivate fish to swim, we relied
instead on the innate rheotactic behaviors of six fish species that migrate
annually through rivers of Northeast USA. Collections and testing were
performed between the months of April and July, 19971999, on dates
corresponding with periods of upstream migration for each species. Test fish
were captured from traps at nearby fishways (American shad Alosa
sapidissima Wilson 1811, striped bass Morone saxatilis Walbaum
1792, and white suckers Catostomus commersonii Lacepède 1803),
coastal streams (alewife A. pseudoharengus Wilson 1811) from the
Herring River, Bourne MA, and blueback herring A. aestivalis Mitchill
1814 from the Charles River, Watertown, MA), or electrofished [blueback
herring, striped bass, walleye Sander vitreus Mitchill 1818 (formerly
Stizostedion vitreum Mitchill 1818) and white sucker] from the
Connecticut River.
Fish were transported to the flume facility in one of two truck-mounted
tanks containing either 1000 or 4000 liters. There they were measured (fork
length, FL), sexed, and each was fitted with an externally attached
passive integrated transponder (PIT) tag. This consisted of a
glass-encapsulated, cylindrical tag measuring 32 mm x 3 mm, length
x diameter, fastened to a fishhook, which was inserted through the
cartilage at the base of the dorsal fin (second dorsal, in the case of the
percomorphs; see Castro-Santos et al.,
1996, for a complete description of the PIT tag system). Tagged
fish were released into open, flow-through holding ponds
(Burrows and Chenoweth, 1970
),
connected hydraulically to the fish passage complex and held for 24 h before
testing. The linkage between the holding ponds and the flume facility
precluded the need to handle fish the day they were tested. Instead, groups of
2030 fish were crowded from the holding ponds into the facility at the
start of each trial, and the tailwater weir was raised to confine the fish to
the staging area. Once the velocity of flow was brought to the desired level,
the exclusion screen was opened, and fish were allowed to ascend the flume of
their own volition. Duration of trials ranged from 1 to 6 h.
Progress of individual fish up the flume was monitored both electronically
and visually. The flume was electronically graduated with PIT detection
antennas wired around the outside every 2.5 m, beginning at 0.5 m from the
entrance. Antennas were driven by controllers that charged and read tags as
they moved through, and sent the identifying codes back to a central computer
at a rate of 14 Hz. The computer logged these codes, recording position to
within ± 50 cm and time to the nearest 0.01 s
(Castro-Santos et al., 1996;
Castro-Santos, 2002
).
The flume was also graduated visually, in part to verify the accuracy of the PIT tag data. Four video cameras (NTSC i.e. a standard video format) were positioned 5 m above the flume; high-speed video (250500 frames s-1) provided additional detailed information on swimming mechanics during 16 trials. The floor and one wall of the flume were covered with a retroreflective surface (Scotchlite 6780, 3-M Corp., St Paul, MN, USA) that was graduated into 50 cm intervals with black crosshatch marks. The other wall of the flume was made of clear acrylic, 2.5 cm thick. Mirrors, the full height of the flume and situated at a 45° angle to it, allowed each camera to monitor dorsal and lateral views of the swimming fish simultaneously, thus positioning the fish in three dimensions.
The speed at which fish moved up the flume (groundspeed, Ug) was measured by calculating the difference in mean times between pairs of antennas. Maximum distance of ascent (Dmax) corresponded to the highest recorded reader. Mean groundspeed was the time between detections at the first antenna and the Dmax antenna, divided by Dmax. Swim speed (Us) was measured by adding the measured water velocity (Uf) to Ug.
Video was also used to determine if fish were actively seeking out low velocity zones. At least 10 individuals were tracked swimming up the flume from each species-nominal velocity combination. The proportion of time (to the nearest 5%) that each fish spent in each of 15 cross-sectional quadrants was measured using the dual perspectives provided by the camera arrangement. A correction factor (CF) was calculated for each fish by summing the proportion of time spent in each quadrant multiplied by the ratio of the water velocity in that quadrant to the mean cross-sectional velocity (Fig. 3). The resulting values were used to calculate an overall correction factor by which to multiply the mean cross-sectional flume velocity for each species-velocity combination.
Analysis
The above data were used to calculate swim speedfatigue time
relationships for each species and mode, as described below. The associated
equations were then used to evaluate whether the models described in Equations
1,
2,
3,
4,
5,
6,
7,
8 can be used to predict
distance-maximizing behavior, whether these species exhibited such behaviors,
and if not, how that affected distance of ascent.
The swim speedfatigue time relationship was calculated by regressing
speed at which the fish swam against the natural log of the time it took for
fish to reach their maximum distance of ascent. Data for this relationship
were pooled across velocities. Often, fish ascended the full length of the
flume; in this case the observation is not of fatigue, but of the failure of
the fish to fatigue. This constitutes censored data, some of the implications
of which are discussed elsewhere (Hosmer
and Lemeshow, 1999;
Castro-Santos and Haro, 2003
;
Castro-Santos, 2004
): using
methods of survival analysis, the observed data are included, coded for
censoring, and the likelihood of the regression model is maximized with
respect to the probability density function f(T) for
complete observations, and to the survivorship function S(T)
for censored observations. This method generates sufficient and consistent
least-biased estimates of the swim speedfatigue time relationship
(Neter et al., 1985
;
Hosmer and Lemeshow,
1999
).
The model was then modified to test for evidence of a mode shift between
prolonged and sprint modes (maximum prolonged speed: Ump).
A dummy variable and an interaction term were included:
![]() | (9) |
Evidence for optimizing behavior was assessed by comparing observed
groundspeed with predicted values; Ufcrit was calculated
from Equation 8 and the
regression models described above. If the optimization model is correct, then
there should be costs associated with deviating from Uopt;
specifically, fish that swim faster or slower than Ugopt
should swim less far. Alternatively, if fish select swim speeds that differ
from the predicted optimum, but that in fact represent true
distance-maximizing optima that this model fails to predict, then deviation
from the mean (`true optimum') will likewise yield reduced distance of ascent.
I tested for each of these conflicting hypotheses by regressing the expected
cost of deviating from the optimum groundspeed, measured as the difference in
distance of ascent predicted at the optimum minus the observed groundspeed
(values are always positive), against Dmax, censoring
where fish arrived at the uppermost reader. These residuals are denoted
RP and RS for prolonged and sprint
predictions, respectively. To test for optimizing behavior not predicted from
the model, I regressed the absolute value of the residual groundspeed,
, against
Dmax, censoring as above. Significant positive slopes
indicate greater distances achieved by deviating from
Ugopt and
;
significant negative slopes indicate costs of deviation. Either significant
positive slopes or non-significance support the null hypothesis against the
model; only a significant negative slope supports the alternative hypothesis
suggested by the model, and significance tests are correspondingly
one-tailed.
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Results |
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Flume tolerances and behavior
Water velocities (Uf) deviated from the target
velocities both in time and over the cross-section of the flume. These
deviations are described elsewhere
(Castro-Santos, 2002;
Haro et al., 2004
), and are
summarized in Fig. 3 and
Table 1. Although flow was
turbulent at all velocities (Reynold's number >300,000) the turbulence was
disorganized, consisting of random fluctuations and microeddies with no
evident periodicity (Haro et al.,
2004
). This means that, with the exception of slightly lower
velocities in the corners (Fig.
3), opportunities for fish to take advantage of hydraulic
structure were minimal. Preferred zones of ascent within the flume varied
among individuals and species, with the following general trends: (1) most
fish tended to swim within 20 cm of the bottom, this effect being least at the
1.5 and 4.5 m s-1 conditions; (2) most fish avoided the walls,
generally swimming more than 20 cm from either wall; and (3) white sucker
consistently swam in the corners at 1.5 and 2.5 m s-1, presumably
taking advantage of the lower velocities there, but at higher velocities they
swam closer to the middle of the flume. Correction factors and adjusted mean
velocities are presented in Table
1.
The PIT detection antenna array provided a nearly continuous record of the position of fish within the flume. Read range of the antennas extended 50 cm up- and downstream of each antenna. By taking the mean value of time for each antenna, fish were located in time and space with an accuracy of ±18 cm, i.e. 95% of fish were within 18 cm of the antenna at the time their presence was logged, with no apparent bias in the error.
Once within the flume, fish tended to move steadily up the channel until
they reached Dmax. Swimming behavior was mostly steady,
with burstcoast behavior observed only rarely, and then among large
individuals swimming against the lower velocity flows. Subsequent behavior
also varied with speed of flow. At the fastest flows, fish tended to fall back
passively, oriented either up- or downstream or even lateral to the flow,
maintaining at most enough velocity relative to flow to maintain equilibrium.
At intermediate water velocities, they tended to maintain greater velocity
relative to the flow (again, oriented either up- or downstream), but usually
returning rapidly to the staging area. At the slowest flows, some fish
proceeded to exit the top of the flume, or lingered near the upstream end (see
Fig. 2.5 in Castro-Santos,
2002). Some individuals made multiple ascents; in this case I used
the first ascent where a fish attained its Dmax value in
my analyses. This usually occurred on the first attempt (6595% of
individuals, by species).
Swim speedfatigue time curves
The relationship between swim speed and fatigue time is presented in
Fig. 4 and
Table 2. Whenever fish ascended
to 18 m or above, observations were included as censored, i.e. the fish did
not fatigue as of the last observation. This means that the ability to measure
fatigue was limited by the constraints of the apparatus. The regression
techniques used here, however, account for censored data and generate
sufficient and consistent least-biased estimates of the swim
speedfatigue time relationship; uncertainty arising from all sources,
including censoring, is reflected in the standard error of the estimates.
Since censoring constitutes incomplete observation, and was more prevalent
among lower swim speeds (Fig.
4), variance of the estimates are correspondingly greater at
prolonged than at burst speeds. The presence of censored data also explains
why regression lines in Fig. 4
do not fall in the middle of the data; they are instead adjusted upward to
account for those fish that did not fatigue
(Allison, 1995;
Hosmer and Lemeshow, 1999
;
Castro-Santos and Haro,
2003
).
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Discrete prolonged and sprint modes were found with corresponding slopes and intercepts for American shad, striped bass, walleye and white sucker, but not for alewife or blueback herring. The locations of these mode shifts represent the models with the best fit. A 95% confidence interval (based on the likelihood statistic) around the models with the selected breakpoints indicates that actual values may fall within about ±1 BL s-1 of the best model. Over this range of potential models, parameter estimates varied little: standard deviations (S.D.) of model bP values ranged from 0.010.05, except for American shad, for which the S.D.=0.23; values of model bS standard deviations were even more stable, ranging from <0.01 to 0.04 BL s-1 for all species. Note that the variance in bP S.D. values among models matches the proportionately larger standard error value for this estimate in the best models (Fig. 4).
Among blueback herring, a small sample size resulted in poor power to detect a mode shift that was probably present (P=0.08). A further mode shift may have been present for striped bass: when data greater than the observed breakpoint of 10.4 BL s-1 were excluded, an additional shift was detected at 5.7 BL s-1. To avoid potential bias introduced by including an additional mode, data less than 5.7 BL s-1 were excluded from the regression analyses. Interestingly, when swim speeds below Ump were excluded from the American shad analysis, an additional mode shift became apparent here also at 10.2 BL S-1.
Slopes and intercepts for each species are presented in Table 2, along with the predicted groundspeed optima (Ugopt) within each mode and the estimated maximum prolonged speed (Ump). Where no mode shift was observed, these parameters are assumed to correspond to their values for sprinting otherwise they are subscripted with P or S to refer to prolonged and sprint modes, respectively. A separate regression for striped bass swimming at speeds <5.7 BL s-1 resulted in coefficients of a=6.6 and b=0.98.
The groundspeed at which the various species of fish actually swam is shown for each nominal velocity in Fig. 5, with the predicted optima overlaid for reference. Variance in estimates of slope lead directly to variance in predicted optimal swim speeds. Since |bP| was always of greater magnitude than |bS|, the inverse predicts a lower optimal swim speed at prolonged than at sprinting modes. However, the inverse of the variance also increases proportionally, thus two estimates with similar variance, such as in striped bass, yield predictions with ranges of substantially different magnitude.
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Where data from two modes were available, values of Ufcrit ranged from 4.28 to 5.92 BL s-1, or between the relative speeds for the 1.5 and 2.5 m s-1 nominal velocities (from Tables 1, 2; Equation 8). Thus, of all species that exhibited a mode shift, most individuals should select the optimal groundspeed for the prolonged mode at the 1.5 m s-1 condition and that for the sprint mode at the higher velocities. American shad did precisely this, and the other clupeids also appeared to follow a distance-maximizing strategy (Fig. 5). Although most alewife swam at groundspeeds slightly slower than the predicted optima, this is because several outliers fish that had unusually short fatigue time at low swim speeds (Fig. 4) acted to reduce the slope of the swim speedfatigue time curve. When these observations are removed, the mean groundspeeds coincide with the predicted optima. Among the nonclupeids, the actual behavior was quite different. Instead, these three species selected a constant groundspeed that corresponded with the optimum for the prolonged mode, regardless of Uf (with the possible exception of striped bass at 1.5 m s-1), even though most of these fish were swimming at speeds corresponding with the sprinting mode. This consistency was remarkable: among white suckers, for example, a 7.1 BL s-1 range of Uf produced a Ug range of only 0.88 BL s-1.
Among species that exhibited mode shifts, >90% of all individuals swam
at speeds corresponding with the prolonged mode when swimming against 1.5 m
s-1. Although 100% of clupeids swam at sprint modes at nominal
velocities 2.5 m s-1, behavior of non-clupeids was more
variable. Here, 1069% swam within prolonged mode at each of the higher
velocities, except for white sucker, where all fish swimming against the 4.5 m
s-1 condition swam in sprint mode
(Table 3).
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I used the same distinction described above to test for the costs of deviating from predicted optima: tests include data from only those velocities where >10% of individuals swam within the designated mode. The results of these tests, as well as tests of the cost of deviating from the observed mean swim speed within each velocity, are presented in Table 3. These tests indicate that the distance-maximization models are correct in sprint mode, but results for prolonged mode were equivocal. Significant reductions in Dmax were associated with deviation from UgoptS among all species, but there was no correlation between Dmax and deviation from UgoptP, except among white sucker, where deviation was associated with greater distances of ascent. This is not surprising, because most of these individuals should, under the model, have made the switch to the sprint optimum. Similarly, there was no significant effect of deviating from the mean groundspeed, except for striped bass and white sucker, where greater deviation was associated with greater distance of ascent.
In addition, I separately tested for the possibility that
UgoptP was the optimizing speed at the 1.5 m
s-1 condition as well as at the faster nominal velocities. Only
walleye showed a significant cost of deviation under the 1.5 m s-1
condition (negative correlation; P=0.004). Heavy censoring under the
1.5 m s-1 condition resulted in poor power to detect a cost here:
only among walleye did fewer than 50% of individuals successfully reach the
upper end of the flume under this condition
(Haro et al., 2004). Thus,
failure to identify a cost of deviating from the predicted optimum probably
reflects the constraints of the experimental apparatus, rather than any flaw
in the model. At the higher velocities, where all species should have been
swimming at the sprint optimum, only white sucker showed any effect, with
greater distance of ascent associated with deviation from
UgoptP. This concurs with the model hypotheses, and
indicates that fish swimming at UgoptP were not selecting
a distance-maximizing strategy at these speeds.
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Discussion |
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Assumptions and parameters
The approach to quantifying the swim speedfatigue time relationship
presented here differs substantially from the standardized approach developed
by Brett (1964). Where others
have produced fatigue using coercive methods such as electrified screens,
prodding, or impingement avoidance to induce fish to swim against sequentially
increased water velocities, we have presented fish that are innately motivated
to swim upstream with an opportunity to do so volitionally, measuring fatigue
as a behavioral choice to abandon the effort.
This approach is not without assumptions, however, and the following are implicit in this analyses: (1) a linear relationship adequately describes the effect of swim speed on the log of fatigue time; (2) the methods and data presented here were sufficient to identify any mode shifts; (3) the apparatus provided a realistic estimate of the slope(s) of this relationship; and (4) fish are either unaware of the length of the velocity barrier, or such knowledge does not affect their behavior.
Substantial empirical evidence exists to support the first assumption, both
in this study and elsewhere (numerous references in
Beamish, 1978;
Videler, 1993
). The second
assumption is more suspect, however. Although clear mode shifts were
identified for American shad, white sucker and walleye, the phenomenon was
less clear for the other species. Because of their smaller size, alewife and
blueback herring swam at faster relative speeds against a given flow than did
the larger fish, and the absence of slow swimming speed data precluded
identification of mode shifts for both species. Conversely, the large size of
some striped bass allowed them to swim at a slower mode against the 1.5 m
s-1 flow condition. In both cases, these limitations may have
precluded accurate prediction of Ugopt, particularly
against low velocity flow.
The third assumption is also suspect: because fish were able to abandon their effort at will, estimates of fatigue time at a given speed will inevitably be low. This is true for two reasons: (1) fish probably do not voluntarily swim to exhaustion; and (2) some individuals may exert less effort than others, i.e. abandon their effort at a reduced level of fatigue. Both behavioral characteristics can be expected to reduce the intercept value of the swim speedfatigue time relationship. The slope, in contrast, may have remained unaffected if fish abandoned their ascent at a similar level of fatigue. However, at faster flows (Uf) and swim speeds (Us), the range of times at which fish could abandon their effort was reduced, i.e. skewness was constrained at zero time. Greater skewness at smaller values of Us led to reduced magnitude of the slope, as well as greater variance of the estimate. For these reasons, estimates of both slope and intercept values are conservative, and one can expect estimates of Ugopt to be correspondingly high. The presence of outliers had this effect on the alewife models; among other species, the magnitude of this error appears to be relatively small.
A further limitation of this approach that calls into question the validity
of assumptions 2 and 3 is the absence of the cross-sectional uniformity of
flow and consistency of velocity that characterizes most controlled laboratory
studies. Future modifications to the flume apparatus may address this
limitation; however, such nonuniformity of flow is a feature of natural
rivers, culverts and fishways, and may provide a realistic context for fish
behavior (Haro et al., 2004).
In any case, the disorganized, microturbulent character of the flow in this
flume can be expected to have acted to decrease performance
(Enders et al., 2003
);
opportunities for fish to take advantage of eddies (e.g.
Hinch and Rand, 2000
;
Liao et al., 2003
) were
minimal or nonexistent here. By continuously monitoring hydraulic parameters,
changes in water velocity were accounted for; combining this with the
correction factors (Table 1) removed any bias from values of water velocity assigned to each ascending
fish. In this way, performance measures described here can be considered
accurate, but conservative relative to actual performance in a natural
setting.
The adequacy of the methods for identifying mode shifts and slopes was also
limited by the finite length of the flume and the resulting censored
observations, particularly at low water velocities. The statistical methods
applied here, though novel in this application, are well-known to be robust in
the presence of censoring. Any uncertainty arising from the censored data is
adequately accounted for by and included in the standard error estimates; the
large sample sizes presented here should be more than sufficient to eliminate
any systematic bias introduced using these methods
(Allison, 1995;
Hosmer and Lemeshow, 1999
).
Heavy censoring at the lowest water velocities did limit the power of these
estimates, however, especially among American shad swimming in prolonged
mode.
The fourth assumption is more reasonable. Since all fish were naïve,
they clearly had no previous knowledge of the length of the barrier. They
were, however, able to stage multiple attempts, and it is possible that some
knowledge was acquired in this way
(Castro-Santos, 2004). With
knowledge of the length of the barrier, fish could select either a
time-minimizing (i.e. speed-maximizing) strategy (swim faster than
Ugopt, and thus minimize, for example, exposure to
predators), or a time-maximizing strategy (swim slower than
Ugopt, and thus reduce instantaneous energetic costs). By
matching fatigue time and swim speed to barrier length (Figs
1,
2A), fish could potentially
reduce energetic costs or other risks associated with the distance-maximizing
swim speeds. While these strategies may make sense in some circumstances, they
are unlikely in this context. Moreover, because most individuals achieved the
greatest distance on the first attempt, there is no reason to expect the fish
to adopt any strategy other than distance-maximization, i.e. by swimming at
the appropriate Ugopt.
Although this approach will probably tend to underestimate the
physiological limits to performance, it may provide a more realistic measure
of the behaviors that fish actually exhibit in the wild, and may therefore be
more meaningful from ecological and evolutionary perspectives. Moreover,
because of the limitations of the coercive approach, along with those of the
machines within which fish are usually swum, few studies exist that describe
swimming performance at such high speeds. Indeed, many of the observed swim
speeds far exceeded predicted maxima for fish of this size and morphology
(Videler and Wardle,
1991).
Swim speed optimization
Of the six species tested, only the anadromous clupeids fully adopted the
predicted distance-maximizing behavior. This was most evident with American
shad, which switched from UgoptP to
UgoptS at the predicted flow velocities, and maintained a
relatively constant groundspeed in sprint mode against a
Uf range >4 BL S-1.
The nonclupeids also adopted constant groundspeeds, but these were appropriate only for prolonged mode (UgoptP), and no apparent benefit accrued to any species for swimming at UgoptP at Uf>Ufcrit. This is evident from the general absence of significant negative correlations with the RU and RP residuals, and is consistent with the hypothesis that this was not a distance-maximizing strategy. On the contrary, positive coefficient values for white sucker and striped bass suggest that there was a cost associated with the observed speed, and fish that deviated from the mean swam greater distances. Conversely, fish did maximize distance by swimming at UgoptS at flows >Ufcrit, as indicated by the strongly significant negative values of coefficients of the RS statistic.
These results, while supporting the hypotheses indicated by the model, may
instead be an artifact of varying condition of individual fish: fish in better
condition may swim faster and farther than the others
(Brett et al., 1958;
Hochachka, 1961
). Furthermore,
inaccuracies arising from the scaling of swim and flow speeds to body lengths
may cause spurious results (Drucker,
1996
; see also Packard and
Boardman, 1999
for a more mathematical treatment of this issue).
This is a concern primarily for the striped bass models, owing to the large
size range; scaling errors should be minimal among the other species
(Table 1). Nevertheless, these
data do support the idea that an optimum groundspeed exists for each mode, and
that failure to swim at the correct speed results in reduced distance of
ascent.
The same logic used above can be applied to mode shifts in the absence of
flow. The distance-maximizing critical swim speed at which fish should switch
from prolonged to sprint modes (Uscrit) occurs when
![]() | (10) |
Trump and Leggett (1980)
explored the effect of currents on optimal swim speeds, and produced
predictions that are superficially similar to those presented here. Where a
velocity challenge is encountered that is constant in time but finite in
space, their model predicts an optimal groundspeed of m-1,
where m is the exponent of the energy equation
Es=aemUs [J kg-1
s-1] (Brett, 1965
;
Webb, 1975
), much like the
model presented here. However, because the slope of the metabolismswim
speed relationship should increase as fish recruit anaerobic processes, the
optimal groundspeed should decrease as fish switch from prolonged to burst
modes exactly the opposite of what my model predicts, and what these
data suggest.
Likewise, the predictions of models generated by Weihs
(1973) and Videler
(1993
) are not supported by
these data. When Weihs' equations
7 and
8
(Weihs, 1973
), and Videler's
equations 9.1 and 9.2 (Videler,
1993
) are adjusted for flow (similar to Equations
2,
3,
4 here), both sets of models
predict distance-maximizing groundspeeds that accelerate with increasing flow.
Again, this is not in accordance with the observed behaviors. None of these
other models was developed for fish swimming in nonsustainable modes, however,
and recruitment of anaerobic metabolism, alternative gaits, etc., may alter
the relationship between cost of transport and swim speed on which they are
based.
Other strategies may optimize for conditions unlike those present in this
study. For example, fish may approach velocity barriers by swimming at maximum
possible speed. This could be appropriate for leaping species like salmon that
may want to maximize the likelihood of traversing a falls of unknown height.
None of the species tested here employs leaping behavior in migration, so it
is not surprising that maximum speed was not employed. Another strategy might
be to employ alternate gait patterns, thereby improving energetic efficiency
(Weihs, 1974;
Videler and Weihs, 1982
), or
to capitalize on low-velocity zones, as white sucker did against the lower
velocities here. Any such kinematic or behavioral strategy will still have an
associated swim speedfatigue time relationship, however, and so will be
intrinsically included in the models presented here. As such, these models may
be considered robust in the presence of behavioral, kinematic, and
physiological diversity.
One optimizing strategy that these models may not adequately account for is
the staging of repeated attempts. By increasing the rate at which they stage
successive attempts fish can increase the likelihood of passage (Castro-Santos
2002,
2004
). Fish may reduce
recovery time by swimming at slower speeds, thereby increasing attempt rate
and possibly offsetting the costs incurred by deviating from
Ugopt. This strategy still does not account for the
consistency in groundspeed observed here, particularly among the non-clupeids,
nor for the fact that most individuals reached their maximum distance of
ascent on the first attempt. It seems likely that some other factor is at
work.
The apparent presence of distance-maximizing behavior among the anadromous
clupeids, and its partial absence among the potomodromous non-clupeids,
suggests the presence of underlying selective processes. Webb
(1994) points out that the
range of gaits available to fishes can have profound evolutionary
consequences; perhaps the relationship between swim speed and fatigue time is
shaped in part by the hydraulic conditions fish need to traverse in order to
maximize fitness. Anadromous clupeids need to ascend rivers during spring
freshets to spawn, when high flows and cold temperatures place strong demands
on swimming capacity. Thus sprinting among these fish constitutes a
fitness-critical migratory mode. Potomodromous species, in contrast, have
greater choice in where they spawn, and the striped bass used here are
amphidromous, entering the river to feed. The fastest modes for these species
may therefore not be associated with migration, but rather with other
fitness-crucial behaviors, like predation and predator avoidance. By selecting
the appropriate groundspeed for the prolonged mode, these species may be
optimizing for different habitats, a behavior that could help explain observed
limits to their distributions.
In addition to their ecological context, these results also have important implications with respect to the design of fish passage structures. To maintain such consistent groundspeeds, fish must use some means of detecting their progress relative to the ground (presumably vision). This may help explain why anadromous fish often follow structure when migrating up rivers, and also points to the potential harmful effect of entrained bubbles and turbulence on passage success, and even on willingness to attempt to traverse zones of difficult passage.
Bainbridge (1960) observed
that maximum distance of ascent through fishways is governed by the swim
speedfatigue time relationship, and such data have been used
extensively to determine the location and size of resting pools within
fishways (Beamish, 1978
). The
distance of ascent predicted from this relationship, however, assumes that
fish swim at their optimum speed which, as in this study, may often not be the
case. Any recommendations for fishway designs based on the swim
speedfatigue time relationship should therefore take into account the
expected variability around the optimum, and the costs of such variability in
terms of distance of ascent when predicting passage success.
List of symbols
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Acknowledgments |
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References |
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