168
W.M. Hamner and J.L. Largier
60 m in 3.7 h and corresponds to fourfold dilution of egg/larval concentration; in
turn, the 60 m cloud (K ~ 0.025 m
2
/s) mixes to 120 m in 6 h and dilution is now
16-fold; and so on – 120–240 m in 9.5 h; 240–480 m in 15 h; and 480–960 m in 24 h –
yielding a total dilution of 1,024 and patch size of order 1 km in 58 h (2.4 days).
Thus, if adult spawners move from within a 1 km long reef to a point when they
aggregate to spawn a cloud 30 m in diameter, rather than spawning as a distributed
population creating a 1 km cloud of eggs/larvae, then it will take a few days for the
aggregation spawned cloud to approach the size and concentration of the nonaggregated cloud (which would have grown somewhat over the same period to about
3 km in size). A key factor here is the spatial scale from which spawners aggregate;
it will take signifi cantly more time for larval densities to approach those of nonaggregation-spawned larvae if spawners come together from distances of 10 or
100 km or more. The densities of larvae produced from an average 100 km distance
migration (probably typical of Nassau grouper) would still be more concentrated by
the time of fi rst feeding than if those same larvae were spawned over the entire
100 km distance. The additional larvae of many other fi shes present in the water
invariably greatly outnumber Nassau (and other) grouper larvae. Serranid larvae
are always very low in relative numbers compared to other reef fi shes in plankton
tows, light trap and crest net catches (Leis 1991 ; Dufour and Glazin 1993 ; Sponaugle
et al. 2005 ) , so that instead of competing among themselves, the grouper larvae are
in reality competing more with larvae of other species, i.e. the costs of aggregating
in terms of higher grouper larval concentrations are moot.
Typically, mixing in the direction of advection is dominated by shear dispersion
effects (e.g. Clarke et al. 2007 ) , including the role of wakes and eddies associated
with small-scale topography (cf., Largier 2004 for discussion of along-stream
dispersion at larger scales). As suggested by data in Heyman et al. ( 2005 ) and
dispersion studies in other environments (e.g. Stacey et al. 2000 ; Clarke et al. 2007 ) ,
observed nearshore dispersion rates are better represented by K ~ 1–10 m
2
/s, even at
smaller cloud sizes. During advective transport, if along-stream mixing can be represented by K ~ 1 m
2
/s, then the 30 m cloud would mix to 1 km and 1,000-fold dilution
in about ½ day (or faster for larger K). This is consistent with the few observations
collected by Appeldoorn et al. ( 1994 ) at spawning sites of bluehead wrasse on
inshore reefs off Puerto Rico. They found that water parcels tracked from different
sites tended to merge during the 24 h period of observations, i.e. the clouds from
different aggregation sites had merged within a day of release, yielding a larger,
more dilute, cloud that can be expected to be similar to one which would have
resulted from spawning without aggregation. However, in the case of cubera
snapper, where spawning may yield 10
10 eggs in a cloud of order 30 m, a 1,000-fold
dilution still corresponds to high plankton concentrations of order 10,000 eggs/m
2 –
corresponding to 1,000 eggs/m
3 over a 10 m near-surface layer. Clearly, subsequent
mixing is probably required to preclude competition among young larvae for food.
The second 1,000-fold dilution, which would reduce concentrations to order 1 larva/
m
3
, can be expected to take a bit longer than a few days – although non-zero larval
mortality may decrease larval concentrations more quickly.
W.M. Hamner and J.L. Largier
60 m in 3.7 h and corresponds to fourfold dilution of egg/larval concentration; in
turn, the 60 m cloud (K ~ 0.025 m
2
/s) mixes to 120 m in 6 h and dilution is now
16-fold; and so on – 120–240 m in 9.5 h; 240–480 m in 15 h; and 480–960 m in 24 h –
yielding a total dilution of 1,024 and patch size of order 1 km in 58 h (2.4 days).
Thus, if adult spawners move from within a 1 km long reef to a point when they
aggregate to spawn a cloud 30 m in diameter, rather than spawning as a distributed
population creating a 1 km cloud of eggs/larvae, then it will take a few days for the
aggregation spawned cloud to approach the size and concentration of the nonaggregated cloud (which would have grown somewhat over the same period to about
3 km in size). A key factor here is the spatial scale from which spawners aggregate;
it will take signifi cantly more time for larval densities to approach those of nonaggregation-spawned larvae if spawners come together from distances of 10 or
100 km or more. The densities of larvae produced from an average 100 km distance
migration (probably typical of Nassau grouper) would still be more concentrated by
the time of fi rst feeding than if those same larvae were spawned over the entire
100 km distance. The additional larvae of many other fi shes present in the water
invariably greatly outnumber Nassau (and other) grouper larvae. Serranid larvae
are always very low in relative numbers compared to other reef fi shes in plankton
tows, light trap and crest net catches (Leis 1991 ; Dufour and Glazin 1993 ; Sponaugle
et al. 2005 ) , so that instead of competing among themselves, the grouper larvae are
in reality competing more with larvae of other species, i.e. the costs of aggregating
in terms of higher grouper larval concentrations are moot.
Typically, mixing in the direction of advection is dominated by shear dispersion
effects (e.g. Clarke et al. 2007 ) , including the role of wakes and eddies associated
with small-scale topography (cf., Largier 2004 for discussion of along-stream
dispersion at larger scales). As suggested by data in Heyman et al. ( 2005 ) and
dispersion studies in other environments (e.g. Stacey et al. 2000 ; Clarke et al. 2007 ) ,
observed nearshore dispersion rates are better represented by K ~ 1–10 m
2
/s, even at
smaller cloud sizes. During advective transport, if along-stream mixing can be represented by K ~ 1 m
2
/s, then the 30 m cloud would mix to 1 km and 1,000-fold dilution
in about ½ day (or faster for larger K). This is consistent with the few observations
collected by Appeldoorn et al. ( 1994 ) at spawning sites of bluehead wrasse on
inshore reefs off Puerto Rico. They found that water parcels tracked from different
sites tended to merge during the 24 h period of observations, i.e. the clouds from
different aggregation sites had merged within a day of release, yielding a larger,
more dilute, cloud that can be expected to be similar to one which would have
resulted from spawning without aggregation. However, in the case of cubera
snapper, where spawning may yield 10
10 eggs in a cloud of order 30 m, a 1,000-fold
dilution still corresponds to high plankton concentrations of order 10,000 eggs/m
2 –
corresponding to 1,000 eggs/m
3 over a 10 m near-surface layer. Clearly, subsequent
mixing is probably required to preclude competition among young larvae for food.
The second 1,000-fold dilution, which would reduce concentrations to order 1 larva/
m
3
, can be expected to take a bit longer than a few days – although non-zero larval
mortality may decrease larval concentrations more quickly.