1l.4 Swimming Strategy
373
During time t, the fish travels distance I, i. e.:
(1l.49)
This means that for some optimal swimming velocity, Uopt , the distance, I,
becomes maximum when
dl
-
= 0 at U = Uopt .
dU
After differentiating we obtain:
(1l.50)
(11.51)
Equation (11.47) shows that the maximum range (for a given energy store) of:
(1l.52)
is reached when the swimming power and basal metabolic power are equal.
Using the ratio ~ = U /Uopt , a corresponding ratio of swimming range can be
expressed as follows:
(1l.53)
The ratio I/Imax as a function of U /Uopt is shown in Fig. 11.3. There is a rather
wide range of velocities at which the swimming range is reasonable large. For
example, for swimming velocities varying from half of the optimum velocity to
twice of that velocity, the swimming range is larger than 80% of the maximum
range, Imax.
Experiments with migrating sockeye salmon, Oncorhynchus nerka, in the
ocean between Vancouver Island and mainland Canada, showed that fish of an
average length, L, of 66.3 cm had an average velocity, U, of 66.7 cm/s, which
gives U / L ~1 S-l (Quinn, 1988). Two bluefin tuna with estimated weights
of 225 kg and 170 kg, tagged in the Gulf of Mexico were recaught 118 and
119 days later off Norway. They swam the distance of 7778 km at a velocity
of 0.76 mis, or U / L = 0.3 s-l (Mather, 1962). It is probably not realistic to
assume that the fish swam all 118 (or 119) days with the same velocity. It is
more likely that the swimming velocity varied.