Simple models of density band formation in massive corals

Abstract

Three growth processes in massive colonies of Porites are incorporated into simple, mathematical models of skeletal density band formation. The growth processes are (i) extension of the colonial skeleton at its outer surface, (ii) thickening of skeleton through the depth of skeleton occupied by tissue and (iii) periodic, essentially monthly, uplift of the lower margin of the tissue layer. As far as possible the models are constructed using realistic values for parameters associated with growth. The growth processes are driven or modulated by a single, sine wave, forcing function which could correspond to annual changes in environmental parameters such as light and temperature. Extension and thickening are allowed to vary with the forcing function or are held constant. This generates four models. All models display a pattern of fine, monthly density bands associated with periodic uplift of the lower margin of the tissue layer. The models with variable thickening show that density bands can appear to be formed several months out of phase with the forcing function. Both appearance and apparent timing of density bands vary in models with variable extension and variable thickening. These are also affected by the ratio of the depth of skeleton occupied by tissue to annual extension and by intra-annual (seasonal) change in extension. These simple, realistic models may reconcile many of the apparent contradictions which surround coral density banding.