Models of coral growth: spontaneous branching, compactification and the Laplacian growth assumption

In stony corals it is often observed that specimens collected from a sheltered growth site have more open and more thinly branched growth forms than specimens of the same species from more exposed growth sites, where stronger water currents are found. This observation was explained using an abiotic computational model inspired by coral growth, in which the growth velocity depended locally on the absorption of a resource dispersed by advection and diffusion (Kaandorp and Sloot, J. Theor. Biol 209 (2001) 257). In that model a morphological range was found; as the Péclet-number (indicating the relative importance of advective and diffusive nutrient transport) was increased, more compact and spherical growth forms were found. Two unsatisfactory items have remained in this model, which we address in the present paper. First, an explicit curvature rule was responsible for branching. In this work we show that the curvature rule is not needed: the model exhibits spontaneous branching, provided that the resource field is computed with enough precision. Second, previously no explanation was given for the morphological range found in the simulations. Here we show that such an explanation is given by the conditions under which spontaneous branching occurs in our model, in which the compactness of the growth forms depends on the ratio of the rates of growth and nutrient transport. We did not find an effect of flow. This suggests that the computational evidence that hydrodynamics influences the compactness of corals in laminar flows may not be conclusive. The applicability of the Laplacian growth paradigm to understand coral growth is discussed.