Morphospace of foraminiferal shells: results from the moving reference model

The moving reference model of foraminiferal tests (shells) is based on principal morphogenetic rules revealed from real foraminifera. The model has introduced apertures as moving reference points based on minimization of the distance between them. These modifications greatly enhanced variability of simulated shells closely resembling actual complexity of small polythalamous foraminifers. The resulted theoretical morphospace of all simulated forms is far more extensive than any produced before. The fragments of the multidimensional theoretical morphospace are presented in two forms, i.e. a (classical) box model and a morphotree. The theoretical morphospace of foraminifera reveals regions of the morphospace that include similar forms. These specific fields in the morphospace, called morphophases, are separated from each other by either sharp or gradual morphophase transitions, which involve sharp or gradual changes in morphology controlled by changes of the model parameters. Optimized emplacement of foraminiferal apertures is responsible for these morphophase transitions. The overall morphospace splits into the 'possible range' and the 'forbidden range'. The 'possible range' includes existent and nonexistent foraminiferal forms, which are further separated into 'vacant', 'dysfunctional', and 'deficient' ranges. All the ranges provide additional knowledge on theoretical foraminiferal morphology. The 'vacant range' of possible, although nonexistent, morphologies is limited and that may suggest that the real evolution of foraminifera has discovered most of the morphologic possibilities. It is suggested that the 'forbidden' and 'deficient' ranges present model constraints useful for understanding morphogenesis, which may be tested by further modifications of the model. The analysed theoretical morphospace verifies the moving reference model, indicating the fundamental role of apertures in the morphogenesis of foraminifera.