13.4 Larval Settlement and External Fertilization
415
in which ay, a z and (3 are empirical coefficients chosen to best match these
relationships. Using the fact that x = Ot, the relationships (13.39) can be
rewritten in terms of time. For short distances, the coefficient (3 ~ l.
Denny and Shibata (1989) argued that the rate at which ova are fertilized is
given by:
dCE
- = -<.pCS(t)CE(t),
dt
(13.40)
where cs(t) and CE(t) are instaneous concentrations of sperm and eggs, respectively, and <. p is the proportionality coefficient. They used sea urchins
as an example to provide some values for the biological parameters of the
model. In particular, they assumed that the rate of sperm and egg release was
Q s = 1 - 3 X 10 6 / sand Q e = 10 4 / s, respectively. Both have been released at
5 cm above substratum and the distance, l, separating male and female was
equal to 0.1 m. Mean and friction velocities, 0 and u., were assumed as l.1
m/s and 0.11 m/s, respectively. The results of the model showed that the fraction of eggs fertilized is low, less than 1 % for the parameters used. Even when
the distance, I, is as small as 1 cm, the fraction of eggs fertilized is only 3.9%
and decreases with increasing values of mean velocity, O. The model results
compare favourably with experimental data of Pennington (1985).
As was shown in the previous section, turbulent mixing provides an effective
mechanism for rapid transport of larvae to the substratum, even in the absence
of sinking velocities. However, in the case of external fertilization, the rapid
dilution of gametes by turbulent mixing may drastically reduce the efficiency of
external fertilization with some negative consequences for animal reproduction.
13.4.3 Dispersion of Coral Eggs Following Mass Coral Spawning
The distribution and dispersion of planktonic larvae released by benthic organisms are of fundamental importance to the ecology of aquatic benthic communities. On the Great Barrier Reef, corals engage in mass spawning during a
brief period each year. Clear patterns in the timing of mass spawning have
been identified and this provides a basis for the annual larval influx prediction
(Oliver and Willis, 1987; Willis and Oliver, 1990).
During the spawning periods, enormous quantities of eggs and larvae are
injected into the reef system. The eggs and larvae of most coral species are
highly buoyant and they accumulate at the surface. Under the assumption
that currents are steady in time and spatial current gradients are negligible,
the concentration of coral eggs and larvae can be predicted from the advectiondiffusion equation (8.30) as:
(13.41 )
415
in which ay, a z and (3 are empirical coefficients chosen to best match these
relationships. Using the fact that x = Ot, the relationships (13.39) can be
rewritten in terms of time. For short distances, the coefficient (3 ~ l.
Denny and Shibata (1989) argued that the rate at which ova are fertilized is
given by:
dCE
- = -<.pCS(t)CE(t),
dt
(13.40)
where cs(t) and CE(t) are instaneous concentrations of sperm and eggs, respectively, and <. p is the proportionality coefficient. They used sea urchins
as an example to provide some values for the biological parameters of the
model. In particular, they assumed that the rate of sperm and egg release was
Q s = 1 - 3 X 10 6 / sand Q e = 10 4 / s, respectively. Both have been released at
5 cm above substratum and the distance, l, separating male and female was
equal to 0.1 m. Mean and friction velocities, 0 and u., were assumed as l.1
m/s and 0.11 m/s, respectively. The results of the model showed that the fraction of eggs fertilized is low, less than 1 % for the parameters used. Even when
the distance, I, is as small as 1 cm, the fraction of eggs fertilized is only 3.9%
and decreases with increasing values of mean velocity, O. The model results
compare favourably with experimental data of Pennington (1985).
As was shown in the previous section, turbulent mixing provides an effective
mechanism for rapid transport of larvae to the substratum, even in the absence
of sinking velocities. However, in the case of external fertilization, the rapid
dilution of gametes by turbulent mixing may drastically reduce the efficiency of
external fertilization with some negative consequences for animal reproduction.
13.4.3 Dispersion of Coral Eggs Following Mass Coral Spawning
The distribution and dispersion of planktonic larvae released by benthic organisms are of fundamental importance to the ecology of aquatic benthic communities. On the Great Barrier Reef, corals engage in mass spawning during a
brief period each year. Clear patterns in the timing of mass spawning have
been identified and this provides a basis for the annual larval influx prediction
(Oliver and Willis, 1987; Willis and Oliver, 1990).
During the spawning periods, enormous quantities of eggs and larvae are
injected into the reef system. The eggs and larvae of most coral species are
highly buoyant and they accumulate at the surface. Under the assumption
that currents are steady in time and spatial current gradients are negligible,
the concentration of coral eggs and larvae can be predicted from the advectiondiffusion equation (8.30) as:
(13.41 )