164
W.M. Hamner and J.L. Largier
where C(x,t) is concentration of particles at given place and time; u is the mean
“advection” velocity in the x-direction, K x is the “eddy diffusivity” describing the
level of mixing or “diffusion” due to fl ow variability in the x-direction. Ideally a
three-dimensional equation is needed to fully describe dispersion, but for shallow
water with a well-mixed water column, typical of most fi sh aggregation sites, one
only need track concentration (per surface area) in the two horizontal dimensions –
usually expressed as alongshore and cross-shore in coastal environments.
In the context of aggregation spawning, three phases of dispersion are of interest:
the fi rst is the dispersion of gametes immediately after fertilization (tens of seconds
to a few minutes), the second is the initial dispersion of fertilized eggs/larvae when
concentrations are greater than they would be in the absence of aggregated spawning
(days), and the third, the later dispersion of early phase planktotrophic larvae over
subsequent days and weeks that must result in delivery to suitable recruitment
habitat for successful completion of dispersal. It is believed that eggs and yolk-sac
larvae behave as passive drifters for the fi rst two phases (Leis 2006 ) , while in the
later stages of the third phase transport is signifi cantly affected by larval behaviour
(and thus not addressed by this simple model).
6.2.2 Formation of the Initial Cloud of Gametes
At spawning the need to bring about contact between eggs and sperm is crucial so
that fertilization can occur. The high rates of egg fertilization that are observed
(Kifl awi et al. 1998 ; Colin unpublished data) suggest that contact rates are typically
high enough to ensure near total fertilization in aggregation spawning, presumably
due to the close proximity of so many gametes and/or due to the signifi cant smallscale turbulence produced by the rapid swimming action of spawning fi sh (Fig. 6.2 ,
Bell and Colin 1986 ) . Whether aggregation spawning fertilization rates differ from
non-aggregation spawning rates has not been accurately assessed, and, given the
numbers of species involved and diversity of spawning behaviour, is not really a
useful comparison. For most aggregation spawning fertilization rates are 90% or
higher . The dimensions and concentration of this initial cloud of gametes depend on
the number of spawning adults, their fecundity and the nature of currents during spawning, factors which often cannot be determined. We can assume that the initial shape
and size of the cloud are determined by the distribution of spawning adults and their
numbers and sizes, and then altered by the effect of currents.
While vigorous large-scale mixing due to energetic fl ow structures is undesirable
at this time, as it will tear the gamete clouds apart too quickly, small-scale turbulent
mixing may assist in a high rate of contact between these “particles” (Petersen et al.
1992 ; Kifl awi et al. 1998 ) . If aggregations spawn in locations or times of weak fl ow
(see Chap. 5 ), large-scale mixing can be precluded or minimized and the gamete
clouds may persist in high concentrations for several minutes, often with subsequent
spawning releases occurring within the same water volume as earlier ones, perhaps
increasing already high fertilization rates (Kifl awi et al. 1998 ) .
W.M. Hamner and J.L. Largier
where C(x,t) is concentration of particles at given place and time; u is the mean
“advection” velocity in the x-direction, K x is the “eddy diffusivity” describing the
level of mixing or “diffusion” due to fl ow variability in the x-direction. Ideally a
three-dimensional equation is needed to fully describe dispersion, but for shallow
water with a well-mixed water column, typical of most fi sh aggregation sites, one
only need track concentration (per surface area) in the two horizontal dimensions –
usually expressed as alongshore and cross-shore in coastal environments.
In the context of aggregation spawning, three phases of dispersion are of interest:
the fi rst is the dispersion of gametes immediately after fertilization (tens of seconds
to a few minutes), the second is the initial dispersion of fertilized eggs/larvae when
concentrations are greater than they would be in the absence of aggregated spawning
(days), and the third, the later dispersion of early phase planktotrophic larvae over
subsequent days and weeks that must result in delivery to suitable recruitment
habitat for successful completion of dispersal. It is believed that eggs and yolk-sac
larvae behave as passive drifters for the fi rst two phases (Leis 2006 ) , while in the
later stages of the third phase transport is signifi cantly affected by larval behaviour
(and thus not addressed by this simple model).
6.2.2 Formation of the Initial Cloud of Gametes
At spawning the need to bring about contact between eggs and sperm is crucial so
that fertilization can occur. The high rates of egg fertilization that are observed
(Kifl awi et al. 1998 ; Colin unpublished data) suggest that contact rates are typically
high enough to ensure near total fertilization in aggregation spawning, presumably
due to the close proximity of so many gametes and/or due to the signifi cant smallscale turbulence produced by the rapid swimming action of spawning fi sh (Fig. 6.2 ,
Bell and Colin 1986 ) . Whether aggregation spawning fertilization rates differ from
non-aggregation spawning rates has not been accurately assessed, and, given the
numbers of species involved and diversity of spawning behaviour, is not really a
useful comparison. For most aggregation spawning fertilization rates are 90% or
higher . The dimensions and concentration of this initial cloud of gametes depend on
the number of spawning adults, their fecundity and the nature of currents during spawning, factors which often cannot be determined. We can assume that the initial shape
and size of the cloud are determined by the distribution of spawning adults and their
numbers and sizes, and then altered by the effect of currents.
While vigorous large-scale mixing due to energetic fl ow structures is undesirable
at this time, as it will tear the gamete clouds apart too quickly, small-scale turbulent
mixing may assist in a high rate of contact between these “particles” (Petersen et al.
1992 ; Kifl awi et al. 1998 ) . If aggregations spawn in locations or times of weak fl ow
(see Chap. 5 ), large-scale mixing can be precluded or minimized and the gamete
clouds may persist in high concentrations for several minutes, often with subsequent
spawning releases occurring within the same water volume as earlier ones, perhaps
increasing already high fertilization rates (Kifl awi et al. 1998 ) .