Size distribution dynamics for a marine sessile organism with space-limitation in growth and recruitment: Application to a coral population

1. Corals are clonal organisms and show a plastic growth. We study a partial differential equation model for the dynamics of size distribution of corals and predict the trajectory of recovery after a catastrophic disturbance, such as the recent bleaching that killed most corals in southern Japan. 2. We assume that the mean growth rate of colony size, measured in projected area, is a linear function of colony size, and that the variance in growth rate is proportional to the size, which is consistent with the growth data of a coral Acropora hyacinthus Dana 1846. 3. The model incorporates the space-limitation in colony growth and recruitment. The growth rate and recruitment rate are proportional to the fraction of free space within the local habitat. 4. In many corals, including A. hyacinthus, recruitment occurs in a short period once a year. However, our model illustrates that the colony size distribution does not show distinguishable cohorts since the observed variance in growth rate is large. The model with discrete settlement and a large variance in growth rate results in size distributions that are very well approximated by an explicitly soluble model with constant recruitment and no growth variance. 5. When mortality is low, the dynamics of size distribution show two different phases in the recovery process. In the first phase, size distribution is determined by recruitment and growth, and can be predicted well by the case without mortality. After free space is depleted, recruitment and growth slow down and become balanced with mortality. The equilibrium size distribution is controlled by all the three processes. Both for the transient and the equilibrium size distribution, the average colony size increases with growth rate but decreases with recruitment rate. 6. Strongly skewed colony-size distributions in which small size classes have the largest numbers are generated for a wide range of parameters by the space-limitation in growth, even without partial death of colonies.