Bimodality in Size Distributions: The Red Sea Urchin Strongylocentrotus Franciscanus as an Example

Abstract

We use a model based on the size—structured von Foerster equation to describe how size—dependent growth and mortality rates, pulsed recruitment, and variability in growth affect the shape of a size distribution. The deterministic, equilibrium size distribution with constant recruitment increases with size when the difference between mortality rate and the rate at which growth rate decreases with size is positive (growth dominated), and decreases when it is negative (mortality dominated). Pulsed recruitment causes modes whose relative amplitudes are indicated by the corresponding constant recruitment case. For typical animal growth patterns, the distance between pulses decreases with age. Pulses merge and can be selectively obscured by variability in growth so that their relative amplitudes no longer correspond to the constant recruitment case. We use this information to evaluate why bimodality occurs in size distributions of the red sea urchin, Strongylocentrotus franciscanus, in some habitats, but not others. The mode at larger sizes, which occurs in all habitats, arises because the distribution is mortality dominated and the final sizes of individuals vary. The upper half of a second mode at smaller sizes is caused by higher mortality rates 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.