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

Abstract

Summary 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.

Dynamics of Marine Sessile Organisms with Space-limited Growth and Recruitment: Application to Corals

“…We assume that the growth rate of a colony is proportional to its size. According to the observed data of a coral Acropora hyacinthus in Okinawa, Japan, the annual increment of the projected area of colonies is a linear function of the size ( Muko et al, 2001). Under this assumption, the increase in the total area occupied by type i is simply proportional to the coverage X G .…”

“…We consider an open system, in which recruits are supplied from a pelagic pool of larvae produced by adults in distant habitats. In a twin paper (Muko et al, 2001), we study the di!usion models for the dynamics of colony-size distribution in a coral population, in which growth rate depends on the amount of free space in the local site as well as recruitment. The series of models with space-limited growth and recruitment is an extension of Roughgarden et al (1985).…”

Effect of colony size and age on resource allocation between growth and reproduction in the corals Goniastrea aspera and Favites chinensis

“…Therefore, partial mortality of a colony occurs in colonial corals and distorts the positive relationship between colony size and colony age, the latter being measured as time since the establishment of the first polyp of a colony (Hughes & Jackson 1980, 1985. As a result, estimating colony age from colony size is difficult in colonial animals (Babcock 1991, Muko et al 2001, Bone & Keough 2005). In contrast to studies on solitary animals, therefore, aspects of age dependence in population dynamics and life histories have been less studied in colonial animals.…”

Effects of tissue loss, age and size on fecundity in the octocoral Pseudopterogorgia elisabethae

“…Their clonal nature allows them to grow indeterminately (Hughes, 1984), survive partial mortality (Hughes and Jackson, 1980), propagate through fragmentation (Jackson and Coates, 1986;Kai and Sakai, 2008;Lasker, 1984), and grow at varying rates in response to environmental conditions (Hughes and Connell, 1987;Muko et al, 2001aMuko et al, , 2001b. These processes have the net effect of decoupling size and age (Hughes, 1984;Hughes and Jackson, 1980).…”