Lw. Botsford et al., BIMODALITY IN SIZE DISTRIBUTIONS - THE RED-SEA URCHIN STRONGYLOCENTROTUS-FRANCISCANUS AS AN EXAMPLE, Ecological applications, 4(1), 1994, pp. 42-50
We use a model based on the size-structured von Foerster equation to d
escribe how size-dependent growth and mortality rates, pulsed recruitm
ent, and variability in growth affect the shape of a size distribution
. The deterministic, equilibrium size distribution with constant recru
itment increases with size when the difference between mortality rate
and the rate at which growth rate decreases with size is positive (gro
wth dominated), and decreases when it is negative (mortality dominated
). Pulsed recruitment causes modes whose relative amplitudes are indic
ated by the corresponding constant recruitment case. For typical anima
l growth patterns, the distance between pulses decreases with age. Pul
ses merge and can be selectively obscured by variability in growth so
that their relative amplitudes no longer correspond to the constant re
cruitment case. We use this information to evaluate why bimodality occ
urs in size distributions of the red sea urchin, Strongylocentrotus fr
anciscanus, in some habitats, but not others. The mode at larger sizes
, which occurs in all habitats, arises because the distribution is mor
tality dominated and the final sizes of individuals vary. The upper ha
lf of a second mode at smaller sizes is caused by higher mortality rat
es at sizes greater than the peak of that mode. The lower half may be
due either to a refuge from predation under the spine canopy of adults
or to sampling selectivity.