Module population as generations and connections: models and conjectures on the architecture and colonial development of hard and soft corals.

Juan A. Sanchez


Modular organisms have a very different population biology when compared with unitary organisms, and neither shape nor growth in these organisms has been easy to characterize. Modular organisms such as coral colonies, both hard and soft, have a diverse array of architectural themes varying between massive-, string-, bushy-, pinnate- or fan-like structures, which have evolved through convergent/parallel evolution. These contrasting forms create a challenging problem in developing a general model of the architecture and growth of corals. Techniques such as L-systems can be used to reconstruct the architecture of coral colonies, but the models require a different set of rules for each coral architecture. I propose a stage-structured model of colony development that predicts the population of modules (number and age) in a colony in terms of just module generations and connections. This model can also incorporate the effects of partial mortality of colonies due to environmental influences (i.e. competition and grazing) and the growth variation at each species. Different architectures of both hard and soft coral colonies are constructed by module replications, which is ordered by generations. Generations are connected hierarchically as a product of iterative growth. The model can be formalized as a semi-Markov (or uncompleted) chain, where a single module initiates colony development and following a period of growth the whole colony dies at certain size (or time). The model summarized all the possible pathways that a colony may develop. Presented as a transition diagram, module replication runs in one direction, generation replication in a perpendicular one, and shape appears closing the triangle as a hypotenuse. The first generation of modules is the one with more integrated modules of the same kind (or generation) while the next generations, even though may have more modules, have less integrated modules. Theoretically all the generations at marginal (or apical) parts may produce modules at the same time. The size of secondary generations, as well as the whole colony, is limited by the growth of the first generation. Differences in architectures are expressed in the model in terms of different number of generation and/or modules at each. The proposed model may be unified method to study a diverse array of modular organisms predicting somehow number and aging of modules through time. =20

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